The best news yet!?

All;

I am very happy and excited to make this post. I believe
I've identified a practical digital microtonal keyboard.

Since 1996 when I came to the field, the story has been the
same: if you're a guitarist, for around the same price as a
standard axe you can have a guitar with any number of
frets/octave you're crazy enough to attempt to play. But
no such keyboard option has existed.

Instruments like the Starr Labs Microzone and Cortex Designs
Terpstra Keyboard look excellent, but the prices hover in
the $8K range. Still less than an acoustic piano, but much
more than digital keyboards.

Then H-Pi announced their Tonal Plexus. It brought the
price down to $3,000 (TPX6 + shipping case). But its
keyswitches frankly leave much to be desired (in my opinion)
and its key layout is a bit unorthodox.

A product that actually beat the Plexus to the market is
the C-Thru Music AXiS. It was discussed here in 2005
already. But it wasn't designed for microtonal music, and
it wasn't clear how well it would work.

Well I'm happy to report that it should work (thanks to
their very responsive and knowledgeable staff). For $2100,
including shipping and flight case, you too can have a
192-note MIDI controller with velocity-sensing keys (unlike
the Tonal Plexus)! That's over 6 octaves of 31-tone equal
temperament, and almost 5 octaves of 41-ET. Not ideal but
let's remember Western music was built out by guys like
Byrd who played a lot of 3-octave virginals.

The AXiS has 192 isomorphically-arranged velocity-sensing
keyswitches that can be split into 3 zones of 64 MIDI notes
each. This means all you need is to run three instances of
a synth like Pianoteq (which is just blowing my mind... I
could live the rest of my life and never want another
synth... by the way re. an earlier thread it works great
with > 12 notes per octave). The only hitch is, you will
need three .scl files for each tuning (one for each keyboard
zone, unless your tuning happens to be periodic every 64
notes). This is a bit of a pain but nothing out of the line
of duty for the average MIDI musician.

If your pocketbook is a bit deeper, you can get an Opal
Keyboard. One of the creators of the AXiS broke away from
C-Thru Music and created this company. They're using the
same size and shape of keys and layout as the AXiS, but use
nice woods to build their enclosures and... CLAIM TO HAVE
WEIGHTED KEYS. The price is approximately $1500 more than
the AXiS.

On either instrument the keys are arranged in 21 columns.
This means it's going to give you < 2 octaves with the usual
12-row Bosanquet mapping. However, it's perfectly possible
to do Bosanquet-like mappings with 7 columns (3 octaves on
the AXiS) or 5 columns (4 octaves). However the most
natural way to map to the AXiS will probably be with
something that is closer to the "harmonic table" layout it
was designed for. Bill Wesley's "array" music proves such
layouts are cool.

I was going to wait to post this until I had a chance to
play the AXiS and/or Opal, but I couldn't wait. That means
it's perfectly possible that the actions suck. Both
companies claim they'll refund your money if you don't like
their product. And Jordan Rudess like it:
http://www.c-thru-music.com/cgi/?page=info_axis_vid_manual

Some URLs relevant to this post:
http://www.c-thru-music.com
http://www.theshapeofmusic.com
http://www.starrlabs.com
http://www.cortex-design.com/body-project-terpstra-1.htm
http://www.pianoteq.com

-Carl

Thank you, Carl, for posting that. I'm going to check into it.

Robin

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> All;
>
> I am very happy and excited to make this post. I believe
> I've identified a practical digital microtonal keyboard.
>
> Since 1996 when I came to the field, the story has been the
> same: if you're a guitarist, for around the same price as a
> standard axe you can have a guitar with any number of
> frets/octave you're crazy enough to attempt to play. But
> no such keyboard option has existed.
>
> Instruments like the Starr Labs Microzone and Cortex Designs
> Terpstra Keyboard look excellent, but the prices hover in
> the $8K range. Still less than an acoustic piano, but much
> more than digital keyboards.
>
> Then H-Pi announced their Tonal Plexus. It brought the
> price down to $3,000 (TPX6 + shipping case). But its
> keyswitches frankly leave much to be desired (in my opinion)
> and its key layout is a bit unorthodox.
>
> A product that actually beat the Plexus to the market is
> the C-Thru Music AXiS. It was discussed here in 2005
> already. But it wasn't designed for microtonal music, and
> it wasn't clear how well it would work.
>
> Well I'm happy to report that it should work (thanks to
> their very responsive and knowledgeable staff). For $2100,
> including shipping and flight case, you too can have a
> 192-note MIDI controller with velocity-sensing keys (unlike
> the Tonal Plexus)! That's over 6 octaves of 31-tone equal
> temperament, and almost 5 octaves of 41-ET. Not ideal but
> let's remember Western music was built out by guys like
> Byrd who played a lot of 3-octave virginals.
>
> The AXiS has 192 isomorphically-arranged velocity-sensing
> keyswitches that can be split into 3 zones of 64 MIDI notes
> each. This means all you need is to run three instances of
> a synth like Pianoteq (which is just blowing my mind... I
> could live the rest of my life and never want another
> synth... by the way re. an earlier thread it works great
> with > 12 notes per octave). The only hitch is, you will
> need three .scl files for each tuning (one for each keyboard
> zone, unless your tuning happens to be periodic every 64
> notes). This is a bit of a pain but nothing out of the line
> of duty for the average MIDI musician.
>
> If your pocketbook is a bit deeper, you can get an Opal
> Keyboard. One of the creators of the AXiS broke away from
> C-Thru Music and created this company. They're using the
> same size and shape of keys and layout as the AXiS, but use
> nice woods to build their enclosures and... CLAIM TO HAVE
> WEIGHTED KEYS. The price is approximately $1500 more than
> the AXiS.
>
> On either instrument the keys are arranged in 21 columns.
> This means it's going to give you < 2 octaves with the usual
> 12-row Bosanquet mapping. However, it's perfectly possible
> to do Bosanquet-like mappings with 7 columns (3 octaves on
> the AXiS) or 5 columns (4 octaves). However the most
> natural way to map to the AXiS will probably be with
> something that is closer to the "harmonic table" layout it
> was designed for. Bill Wesley's "array" music proves such
> layouts are cool.
>
> I was going to wait to post this until I had a chance to
> play the AXiS and/or Opal, but I couldn't wait. That means
> it's perfectly possible that the actions suck. Both
> companies claim they'll refund your money if you don't like
> their product. And Jordan Rudess like it:
> http://www.c-thru-music.com/cgi/?page=info_axis_vid_manual
>
>
> Some URLs relevant to this post:
> http://www.c-thru-music.com
> http://www.theshapeofmusic.com
> http://www.starrlabs.com
> http://www.cortex-design.com/body-project-terpstra-1.htm
> http://www.pianoteq.com
>
>
> -Carl
>

Here's another idea:
Sys-ex tuning commands.
I mean suppose there were a place to find Sys-ex scripts to "safely" tune MIDI instruments to support arbitrary TET tunings (perhaps there already is but I just don't know about it?!).

Most mid-to-high level digital synthesizers actually support 22 (indian) and 24-TET, including my "pre-historic" Yamaha CS6X (which now goes for around $300 street price).
Also many keyboards have a "transpose" button or can designate a button as one (again "even" a cs6x can do this). So for sake of practicality you could choose a 7 to 12 note subset of, say, 31-TET that you want to use and then use the transpose key to transpose it...rather then implementing some ridiculous number of keys on the keyboard.

I also use a program called OPEN-MPT which is free AND supports scala files. I can hook up my cs6x as an input device for this and have OPEN-MPT map whatever I play on the keyboard into arbitrary scales. Seriously, I think there are many ways to skin the cat far as making a practical micro-tonal keyboard.

Carl Lumma <carl@...> wrote: All;

I am very happy and excited to make this post. I believe
I've identified a practical digital microtonal keyboard.

Since 1996 when I came to the field, the story has been the
same: if you're a guitarist, for around the same price as a
standard axe you can have a guitar with any number of
frets/octave you're crazy enough to attempt to play. But
no such keyboard option has existed.

Instruments like the Starr Labs Microzone and Cortex Designs
Terpstra Keyboard look excellent, but the prices hover in
the $8K range. Still less than an acoustic piano, but much
more than digital keyboards.

Then H-Pi announced their Tonal Plexus. It brought the
price down to $3,000 (TPX6 + shipping case). But its
keyswitches frankly leave much to be desired (in my opinion)
and its key layout is a bit unorthodox.

A product that actually beat the Plexus to the market is
the C-Thru Music AXiS. It was discussed here in 2005
already. But it wasn't designed for microtonal music, and
it wasn't clear how well it would work.

Well I'm happy to report that it should work (thanks to
their very responsive and knowledgeable staff). For $2100,
including shipping and flight case, you too can have a
192-note MIDI controller with velocity-sensing keys (unlike
the Tonal Plexus)! That's over 6 octaves of 31-tone equal
temperament, and almost 5 octaves of 41-ET. Not ideal but
let's remember Western music was built out by guys like
Byrd who played a lot of 3-octave virginals.

The AXiS has 192 isomorphically-arranged velocity-sensing
keyswitches that can be split into 3 zones of 64 MIDI notes
each. This means all you need is to run three instances of
a synth like Pianoteq (which is just blowing my mind... I
could live the rest of my life and never want another
synth... by the way re. an earlier thread it works great
with > 12 notes per octave). The only hitch is, you will
need three .scl files for each tuning (one for each keyboard
zone, unless your tuning happens to be periodic every 64
notes). This is a bit of a pain but nothing out of the line
of duty for the average MIDI musician.

If your pocketbook is a bit deeper, you can get an Opal
Keyboard. One of the creators of the AXiS broke away from
C-Thru Music and created this company. They're using the
same size and shape of keys and layout as the AXiS, but use
nice woods to build their enclosures and... CLAIM TO HAVE
WEIGHTED KEYS. The price is approximately $1500 more than
the AXiS.

On either instrument the keys are arranged in 21 columns.
This means it's going to give you < 2 octaves with the usual
12-row Bosanquet mapping. However, it's perfectly possible
to do Bosanquet-like mappings with 7 columns (3 octaves on
the AXiS) or 5 columns (4 octaves). However the most
natural way to map to the AXiS will probably be with
something that is closer to the "harmonic table" layout it
was designed for. Bill Wesley's "array" music proves such
layouts are cool.

I was going to wait to post this until I had a chance to
play the AXiS and/or Opal, but I couldn't wait. That means
it's perfectly possible that the actions suck. Both
companies claim they'll refund your money if you don't like
their product. And Jordan Rudess like it:
http://www.c-thru-music.com/cgi/?page=info_axis_vid_manual

Some URLs relevant to this post:
http://www.c-thru-music.com
http://www.theshapeofmusic.com
http://www.starrlabs.com
http://www.cortex-design.com/body-project-terpstra-1.htm
http://www.pianoteq.com

-Carl

Hi Michael,

> Here's another idea:
> Sys-ex tuning commands.
> I mean suppose there were a place to find Sys-ex scripts to
> "safely" tune MIDI instruments to support arbitrary TET tunings
> (perhaps there already is but I just don't know about it?!).

That's been around for a long time. My message was about
keyboard controllers. Retuning synths is a comparative piece
of cake to obtaining a generalized keyboard. Scala has
good MTS support. But it's kindof obsolete in the face of
all the softsynths that now support scale files directly.

> Most mid-to-high level digital synthesizers actually
> support 22 (indian) and 24-TET, including my "pre-historic"
> Yamaha CS6X (which now goes for around $300 street price).
> Also many keyboards have a "transpose" button or can designate
> a button as one (again "even" a cs6x can do this). So for sake
> of practicality you could choose a 7 to 12 note subset of, say,
> 31-TET that you want to use and then use the transpose key to
> transpose it...rather then implementing some ridiculous number
> of keys on the keyboard.

I don't think 192 is ridiculous. In fact, they're suggesting
that many keys for 12-ET.

The subsetting thing is interesting and lots of synths
do it (Kurzweil K2xxx series and Peter Fazer's Midicodeg to
name just two). The devil is in the details. Kurt Bigler
and I also developed and implemented an algorithm for his
organ. It's cool but it'll never replace a fully-capable
keyboard.

>Seriously, I think there are many ways to skin the cat far
>as making a practical micro-tonal keyboard.

Lots of good music has been made on remapped halberstadt
keyboards, but as a serious approach to microtonal keyboards
it can't be taken seriously.

-Carl

Dear Carl,

thanks for sharing your information and enthusiasm. Just to better understand you message I try to summarise. C-Thru Music AXiS can be freely tuned, because you can split the 192 into 3 MIDI channels (a 64 keys): you would simply tune three MIDI sound generators according needs. Great!

Now, the biggest question for me remains: what are suitable key mappings? You mention a Bosanquet mapping and a "harmonic table" layout. Could you be more specific about the latter?

Thank you!

Best
Torsten

On May 24, 2008, at 7:37 PM, Carl Lumma wrote:

> All;
>
> I am very happy and excited to make this post. I believe
> I've identified a practical digital microtonal keyboard.
>
> Since 1996 when I came to the field, the story has been the
> same: if you're a guitarist, for around the same price as a
> standard axe you can have a guitar with any number of
> frets/octave you're crazy enough to attempt to play. But
> no such keyboard option has existed.
>
> Instruments like the Starr Labs Microzone and Cortex Designs
> Terpstra Keyboard look excellent, but the prices hover in
> the $8K range. Still less than an acoustic piano, but much
> more than digital keyboards.
>
> Then H-Pi announced their Tonal Plexus. It brought the
> price down to $3,000 (TPX6 + shipping case). But its
> keyswitches frankly leave much to be desired (in my opinion)
> and its key layout is a bit unorthodox.
>
> A product that actually beat the Plexus to the market is
> the C-Thru Music AXiS. It was discussed here in 2005
> already. But it wasn't designed for microtonal music, and
> it wasn't clear how well it would work.
>
> Well I'm happy to report that it should work (thanks to
> their very responsive and knowledgeable staff). For $2100,
> including shipping and flight case, you too can have a
> 192-note MIDI controller with velocity-sensing keys (unlike
> the Tonal Plexus)! That's over 6 octaves of 31-tone equal
> temperament, and almost 5 octaves of 41-ET. Not ideal but
> let's remember Western music was built out by guys like
> Byrd who played a lot of 3-octave virginals.
>
> The AXiS has 192 isomorphically-arranged velocity-sensing
> keyswitches that can be split into 3 zones of 64 MIDI notes
> each. This means all you need is to run three instances of
> a synth like Pianoteq (which is just blowing my mind... I
> could live the rest of my life and never want another
> synth... by the way re. an earlier thread it works great
> with > 12 notes per octave). The only hitch is, you will
> need three .scl files for each tuning (one for each keyboard
> zone, unless your tuning happens to be periodic every 64
> notes). This is a bit of a pain but nothing out of the line
> of duty for the average MIDI musician.
>
> If your pocketbook is a bit deeper, you can get an Opal
> Keyboard. One of the creators of the AXiS broke away from
> C-Thru Music and created this company. They're using the
> same size and shape of keys and layout as the AXiS, but use
> nice woods to build their enclosures and... CLAIM TO HAVE
> WEIGHTED KEYS. The price is approximately $1500 more than
> the AXiS.
>
> On either instrument the keys are arranged in 21 columns.
> This means it's going to give you < 2 octaves with the usual
> 12-row Bosanquet mapping. However, it's perfectly possible
> to do Bosanquet-like mappings with 7 columns (3 octaves on
> the AXiS) or 5 columns (4 octaves). However the most
> natural way to map to the AXiS will probably be with
> something that is closer to the "harmonic table" layout it
> was designed for. Bill Wesley's "array" music proves such
> layouts are cool.
>
> I was going to wait to post this until I had a chance to
> play the AXiS and/or Opal, but I couldn't wait. That means
> it's perfectly possible that the actions suck. Both
> companies claim they'll refund your money if you don't like
> their product. And Jordan Rudess like it:
> http://www.c-thru-music.com/cgi/?page=info_axis_vid_manual
>
> Some URLs relevant to this post:
> http://www.c-thru-music.com
> http://www.theshapeofmusic.com
> http://www.starrlabs.com
> http://www.cortex-design.com/body-project-terpstra-1.htm
> http://www.pianoteq.com
>
> -Carl
>
>
>
--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586227
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

A diagram of the Bosanquet keyboard can be found here:

http://www.lucytune.com/midi_and_keyboard/hexboard.html

On 24 May 2008, at 23:00, Torsten Anders wrote:

> Dear Carl,
>
> thanks for sharing your information and enthusiasm. Just to better
> understand you message I try to summarise. C-Thru Music AXiS can be
> freely tuned, because you can split the 192 into 3 MIDI channels (a
> 64 keys): you would simply tune three MIDI sound generators according
> needs. Great!
>
> Now, the biggest question for me remains: what are suitable key
> mappings? You mention a Bosanquet mapping and a "harmonic table"
> layout. Could you be more specific about the latter?
>
> Thank you!
>
> Best
> Torsten
>
> On May 24, 2008, at 7:37 PM, Carl Lumma wrote:
>
> > All;
> >
> > I am very happy and excited to make this post. I believe
> > I've identified a practical digital microtonal keyboard.
> >
> > Since 1996 when I came to the field, the story has been the
> > same: if you're a guitarist, for around the same price as a
> > standard axe you can have a guitar with any number of
> > frets/octave you're crazy enough to attempt to play. But
> > no such keyboard option has existed.
> >
> > Instruments like the Starr Labs Microzone and Cortex Designs
> > Terpstra Keyboard look excellent, but the prices hover in
> > the $8K range. Still less than an acoustic piano, but much
> > more than digital keyboards.
> >
> > Then H-Pi announced their Tonal Plexus. It brought the
> > price down to $3,000 (TPX6 + shipping case). But its
> > keyswitches frankly leave much to be desired (in my opinion)
> > and its key layout is a bit unorthodox.
> >
> > A product that actually beat the Plexus to the market is
> > the C-Thru Music AXiS. It was discussed here in 2005
> > already. But it wasn't designed for microtonal music, and
> > it wasn't clear how well it would work.
> >
> > Well I'm happy to report that it should work (thanks to
> > their very responsive and knowledgeable staff). For $2100,
> > including shipping and flight case, you too can have a
> > 192-note MIDI controller with velocity-sensing keys (unlike
> > the Tonal Plexus)! That's over 6 octaves of 31-tone equal
> > temperament, and almost 5 octaves of 41-ET. Not ideal but
> > let's remember Western music was built out by guys like
> > Byrd who played a lot of 3-octave virginals.
> >
> > The AXiS has 192 isomorphically-arranged velocity-sensing
> > keyswitches that can be split into 3 zones of 64 MIDI notes
> > each. This means all you need is to run three instances of
> > a synth like Pianoteq (which is just blowing my mind... I
> > could live the rest of my life and never want another
> > synth... by the way re. an earlier thread it works great
> > with > 12 notes per octave). The only hitch is, you will
> > need three .scl files for each tuning (one for each keyboard
> > zone, unless your tuning happens to be periodic every 64
> > notes). This is a bit of a pain but nothing out of the line
> > of duty for the average MIDI musician.
> >
> > If your pocketbook is a bit deeper, you can get an Opal
> > Keyboard. One of the creators of the AXiS broke away from
> > C-Thru Music and created this company. They're using the
> > same size and shape of keys and layout as the AXiS, but use
> > nice woods to build their enclosures and... CLAIM TO HAVE
> > WEIGHTED KEYS. The price is approximately $1500 more than
> > the AXiS.
> >
> > On either instrument the keys are arranged in 21 columns.
> > This means it's going to give you < 2 octaves with the usual
> > 12-row Bosanquet mapping. However, it's perfectly possible
> > to do Bosanquet-like mappings with 7 columns (3 octaves on
> > the AXiS) or 5 columns (4 octaves). However the most
> > natural way to map to the AXiS will probably be with
> > something that is closer to the "harmonic table" layout it
> > was designed for. Bill Wesley's "array" music proves such
> > layouts are cool.
> >
> > I was going to wait to post this until I had a chance to
> > play the AXiS and/or Opal, but I couldn't wait. That means
> > it's perfectly possible that the actions suck. Both
> > companies claim they'll refund your money if you don't like
> > their product. And Jordan Rudess like it:
> > http://www.c-thru-music.com/cgi/?page=info_axis_vid_manual
> >
> > Some URLs relevant to this post:
> > http://www.c-thru-music.com
> > http://www.theshapeofmusic.com
> > http://www.starrlabs.com
> > http://www.cortex-design.com/body-project-terpstra-1.htm
> > http://www.pianoteq.com
> >
> > -Carl
> >
> >
> >
>
> --
> Torsten Anders
> Interdisciplinary Centre for Computer Music Research
> University of Plymouth
> Office: +44-1752-586227
> Private: +44-1752-558917
> http://strasheela.sourceforge.net
> http://www.torsten-anders.de
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

While everything that Carl says here is pretty reasonable, I think
he's way too quick to dismiss H-Ph and the Tonal Plexus.

I just got my TPX6s last week, and it is really something!
It took me about 2 hours before I started accepting the strange
different feel of three different key shapes. Then they started to
make sense and it's really pretty nice. I can play the thing
actually, and it's just great. I don't understand Carl's dismissal of
the layout as "unconventional" - that's a pretty strange criticism
coming from a microtonalist looking for new alternative controllers.
I think the Hunt layout is as good, no actually better, than any
"conventional" layout I'm otherwise aware of.

As far as the keyswitches "leaving much to be desired" - I think
that's a reasonable description of almost anything that isn't the
fantasy ideal. The hex keyboards ARE great, I really don't doubt it,
and yet they also leave much to be desired. For instance, I desire a
logical way to consistently access 7 and 11 limit notes while
modulating around various keys - and there's a limit to that
possibility with the hex keyboards without other compromises. Does
that mean they should be dismissed? No way, but my point is nothing
is truly perfect.

Anyway, I would never have chosen the hex instruments instead of the
Tonal Plexus. I wouldn't turn down the chance to have an accessory
hex keyboard for the heck of it, but it's not the same thing at all.

The Tonal Plexus has allowed me to easily explain to some friends and
students and such all sorts of musical ideas that the hex keyboards
could not have done the same way. The hex keyboards would allow for
other explanations that are nice too though.

Fact is, having 1200 (!) keys ready to play is not something you could
EVER compare 192 to. No way. They aren't comparable. I do miss
velocity sensitivity, but not *that* much. H-Pi did make the keyboard
have a humanizing random-velocity-within-a-range function and overall
velocity range is controllable with a fader or footpedal.
In addition to all that, I really can just PLAY without a whole host
of long set-up of tuning tables and compromises.

The quality of H-Pi's design is really very good, and service is
excellent. And I do want to be clear (as compared to Carl's mention)
that the H-Pi product options range (with case) from around $1400 - $4000.

To see the options and some aspects of comparison to the other
instruments mentioned, check out:
http://www.h-pi.com/TPX28compare.html

Sure, I might seem like I'm a salesman for H-Pi by now, but what can I
say? I'm totally thrilled with my new keyboard and wouldn't wish for
one of the hex things instead. I really want H-Pi to be successful
because I want my other fantasy requests for the next generation
models to get implemented. But I'm really very happy with what I've got.

I've got all sorts of things I'd like to mention and share... For
instance, I discovered a way to control the sending of various tuned
notes through specific channels, then have them drone on while playing
on other channels with independent timbres and controls and everything!
But anyway, I'm dedicating most of my discussion about the Tonal
Plexus to what I hope will become a community of users over at the
h-pi.com forum. But I'll pop in here with any substantial news or
work or anything.

A concluding thought: some people I know said that 20 years ago it
looked like microtonal stuff would become widely available and develop
new music and they thought the push happened and failed and it wasn't
going to happen again. But now things are really taking shape. It is
a good time to be a microtonalist.

In Harmony,
Aaron Wolf

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> All;
>
> I am very happy and excited to make this post. I believe
> I've identified a practical digital microtonal keyboard.
>
> Since 1996 when I came to the field, the story has been the
> same: if you're a guitarist, for around the same price as a
> standard axe you can have a guitar with any number of
> frets/octave you're crazy enough to attempt to play. But
> no such keyboard option has existed.
>
> Instruments like the Starr Labs Microzone and Cortex Designs
> Terpstra Keyboard look excellent, but the prices hover in
> the $8K range. Still less than an acoustic piano, but much
> more than digital keyboards.
>
> Then H-Pi announced their Tonal Plexus. It brought the
> price down to $3,000 (TPX6 + shipping case). But its
> keyswitches frankly leave much to be desired (in my opinion)
> and its key layout is a bit unorthodox.
>
> A product that actually beat the Plexus to the market is
> the C-Thru Music AXiS. It was discussed here in 2005
> already. But it wasn't designed for microtonal music, and
> it wasn't clear how well it would work.
>
> Well I'm happy to report that it should work (thanks to
> their very responsive and knowledgeable staff). For $2100,
> including shipping and flight case, you too can have a
> 192-note MIDI controller with velocity-sensing keys (unlike
> the Tonal Plexus)! That's over 6 octaves of 31-tone equal
> temperament, and almost 5 octaves of 41-ET. Not ideal but
> let's remember Western music was built out by guys like
> Byrd who played a lot of 3-octave virginals.
>
> The AXiS has 192 isomorphically-arranged velocity-sensing
> keyswitches that can be split into 3 zones of 64 MIDI notes
> each. This means all you need is to run three instances of
> a synth like Pianoteq (which is just blowing my mind... I
> could live the rest of my life and never want another
> synth... by the way re. an earlier thread it works great
> with > 12 notes per octave). The only hitch is, you will
> need three .scl files for each tuning (one for each keyboard
> zone, unless your tuning happens to be periodic every 64
> notes). This is a bit of a pain but nothing out of the line
> of duty for the average MIDI musician.
>
> If your pocketbook is a bit deeper, you can get an Opal
> Keyboard. One of the creators of the AXiS broke away from
> C-Thru Music and created this company. They're using the
> same size and shape of keys and layout as the AXiS, but use
> nice woods to build their enclosures and... CLAIM TO HAVE
> WEIGHTED KEYS. The price is approximately $1500 more than
> the AXiS.
>
> On either instrument the keys are arranged in 21 columns.
> This means it's going to give you < 2 octaves with the usual
> 12-row Bosanquet mapping. However, it's perfectly possible
> to do Bosanquet-like mappings with 7 columns (3 octaves on
> the AXiS) or 5 columns (4 octaves). However the most
> natural way to map to the AXiS will probably be with
> something that is closer to the "harmonic table" layout it
> was designed for. Bill Wesley's "array" music proves such
> layouts are cool.
>
> I was going to wait to post this until I had a chance to
> play the AXiS and/or Opal, but I couldn't wait. That means
> it's perfectly possible that the actions suck. Both
> companies claim they'll refund your money if you don't like
> their product. And Jordan Rudess like it:
> http://www.c-thru-music.com/cgi/?page=info_axis_vid_manual
>
>
> Some URLs relevant to this post:
> http://www.c-thru-music.com
> http://www.theshapeofmusic.com
> http://www.starrlabs.com
> http://www.cortex-design.com/body-project-terpstra-1.htm
> http://www.pianoteq.com
>
>
> -Carl
>

Typo in first sentence, it's h-pi not h-ph, sorry.

--- In tuning@yahoogroups.com, "Aaron Wolf" <backfromthesilo@...> wrote:
>
> While everything that Carl says here is pretty reasonable, I think
> he's way too quick to dismiss H-Ph and the Tonal Plexus.
>
> I just got my TPX6s last week, and it is really something!
> It took me about 2 hours before I started accepting the strange
> different feel of three different key shapes. Then they started to
> make sense and it's really pretty nice. I can play the thing
> actually, and it's just great. I don't understand Carl's dismissal of
> the layout as "unconventional" - that's a pretty strange criticism
> coming from a microtonalist looking for new alternative controllers.
> I think the Hunt layout is as good, no actually better, than any
> "conventional" layout I'm otherwise aware of.
>
> As far as the keyswitches "leaving much to be desired" - I think
> that's a reasonable description of almost anything that isn't the
> fantasy ideal. The hex keyboards ARE great, I really don't doubt it,
> and yet they also leave much to be desired. For instance, I desire a
> logical way to consistently access 7 and 11 limit notes while
> modulating around various keys - and there's a limit to that
> possibility with the hex keyboards without other compromises. Does
> that mean they should be dismissed? No way, but my point is nothing
> is truly perfect.
>
> Anyway, I would never have chosen the hex instruments instead of the
> Tonal Plexus. I wouldn't turn down the chance to have an accessory
> hex keyboard for the heck of it, but it's not the same thing at all.
>
> The Tonal Plexus has allowed me to easily explain to some friends and
> students and such all sorts of musical ideas that the hex keyboards
> could not have done the same way. The hex keyboards would allow for
> other explanations that are nice too though.
>
> Fact is, having 1200 (!) keys ready to play is not something you could
> EVER compare 192 to. No way. They aren't comparable. I do miss
> velocity sensitivity, but not *that* much. H-Pi did make the keyboard
> have a humanizing random-velocity-within-a-range function and overall
> velocity range is controllable with a fader or footpedal.
> In addition to all that, I really can just PLAY without a whole host
> of long set-up of tuning tables and compromises.
>
> The quality of H-Pi's design is really very good, and service is
> excellent. And I do want to be clear (as compared to Carl's mention)
> that the H-Pi product options range (with case) from around $1400 -
$4000.
>
> To see the options and some aspects of comparison to the other
> instruments mentioned, check out:
> http://www.h-pi.com/TPX28compare.html
>
> Sure, I might seem like I'm a salesman for H-Pi by now, but what can I
> say? I'm totally thrilled with my new keyboard and wouldn't wish for
> one of the hex things instead. I really want H-Pi to be successful
> because I want my other fantasy requests for the next generation
> models to get implemented. But I'm really very happy with what I've
got.
>
> I've got all sorts of things I'd like to mention and share... For
> instance, I discovered a way to control the sending of various tuned
> notes through specific channels, then have them drone on while playing
> on other channels with independent timbres and controls and everything!
> But anyway, I'm dedicating most of my discussion about the Tonal
> Plexus to what I hope will become a community of users over at the
> h-pi.com forum. But I'll pop in here with any substantial news or
> work or anything.
>
> A concluding thought: some people I know said that 20 years ago it
> looked like microtonal stuff would become widely available and develop
> new music and they thought the push happened and failed and it wasn't
> going to happen again. But now things are really taking shape. It is
> a good time to be a microtonalist.
>
> In Harmony,
> Aaron Wolf
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > All;
> >
> > I am very happy and excited to make this post. I believe
> > I've identified a practical digital microtonal keyboard.
> >
> > Since 1996 when I came to the field, the story has been the
> > same: if you're a guitarist, for around the same price as a
> > standard axe you can have a guitar with any number of
> > frets/octave you're crazy enough to attempt to play. But
> > no such keyboard option has existed.
> >
> > Instruments like the Starr Labs Microzone and Cortex Designs
> > Terpstra Keyboard look excellent, but the prices hover in
> > the $8K range. Still less than an acoustic piano, but much
> > more than digital keyboards.
> >
> > Then H-Pi announced their Tonal Plexus. It brought the
> > price down to $3,000 (TPX6 + shipping case). But its
> > keyswitches frankly leave much to be desired (in my opinion)
> > and its key layout is a bit unorthodox.
> >
> > A product that actually beat the Plexus to the market is
> > the C-Thru Music AXiS. It was discussed here in 2005
> > already. But it wasn't designed for microtonal music, and
> > it wasn't clear how well it would work.
> >
> > Well I'm happy to report that it should work (thanks to
> > their very responsive and knowledgeable staff). For $2100,
> > including shipping and flight case, you too can have a
> > 192-note MIDI controller with velocity-sensing keys (unlike
> > the Tonal Plexus)! That's over 6 octaves of 31-tone equal
> > temperament, and almost 5 octaves of 41-ET. Not ideal but
> > let's remember Western music was built out by guys like
> > Byrd who played a lot of 3-octave virginals.
> >
> > The AXiS has 192 isomorphically-arranged velocity-sensing
> > keyswitches that can be split into 3 zones of 64 MIDI notes
> > each. This means all you need is to run three instances of
> > a synth like Pianoteq (which is just blowing my mind... I
> > could live the rest of my life and never want another
> > synth... by the way re. an earlier thread it works great
> > with > 12 notes per octave). The only hitch is, you will
> > need three .scl files for each tuning (one for each keyboard
> > zone, unless your tuning happens to be periodic every 64
> > notes). This is a bit of a pain but nothing out of the line
> > of duty for the average MIDI musician.
> >
> > If your pocketbook is a bit deeper, you can get an Opal
> > Keyboard. One of the creators of the AXiS broke away from
> > C-Thru Music and created this company. They're using the
> > same size and shape of keys and layout as the AXiS, but use
> > nice woods to build their enclosures and... CLAIM TO HAVE
> > WEIGHTED KEYS. The price is approximately $1500 more than
> > the AXiS.
> >
> > On either instrument the keys are arranged in 21 columns.
> > This means it's going to give you < 2 octaves with the usual
> > 12-row Bosanquet mapping. However, it's perfectly possible
> > to do Bosanquet-like mappings with 7 columns (3 octaves on
> > the AXiS) or 5 columns (4 octaves). However the most
> > natural way to map to the AXiS will probably be with
> > something that is closer to the "harmonic table" layout it
> > was designed for. Bill Wesley's "array" music proves such
> > layouts are cool.
> >
> > I was going to wait to post this until I had a chance to
> > play the AXiS and/or Opal, but I couldn't wait. That means
> > it's perfectly possible that the actions suck. Both
> > companies claim they'll refund your money if you don't like
> > their product. And Jordan Rudess like it:
> > http://www.c-thru-music.com/cgi/?page=info_axis_vid_manual
> >
> >
> > Some URLs relevant to this post:
> > http://www.c-thru-music.com
> > http://www.theshapeofmusic.com
> > http://www.starrlabs.com
> > http://www.cortex-design.com/body-project-terpstra-1.htm
> > http://www.pianoteq.com
> >
> >
> > -Carl
> >
>

i have never had a problem mapping 7 or 11 to a hexagonal layout 7 especially as they can be only two ranks up. the 11 you can map either above or below.
I think Xenharmonikon 3 covers all types of such animals mapped pretty easily. IMHO
The advantage to a bar though is that is does give you more surface area to find a place for your finger to land. One could go with Bonsanquet original then. Which i would like to try.

I am glad the price is coming down, but still i can build some nice instruments for that price

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Aaron Wolf wrote:
>
>
>
> As far as the keyswitches "leaving much to be desired" - I think
> that's a reasonable description of almost anything that isn't the
> fantasy ideal. The hex keyboards ARE great, I really don't doubt it,
> and yet they also leave much to be desired. For instance, I desire a
> logical way to consistently access 7 and 11 limit notes while
> modulating around various keys - and there's a limit to that
> possibility with the hex keyboards without other compromises. Does
> that mean they should be dismissed? No way, but my point is nothing
> is truly perfect.
>
> >
> > -Carl
> >
>
>

At this point, it seems everyone is a microtonalist

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Aaron Wolf wrote:
>
>
>
> A concluding thought: some people I know said that 20 years ago it
> looked like microtonal stuff would become widely available and develop
> new music and they thought the push happened and failed and it wasn't
> going to happen again. But now things are really taking shape. It is
> a good time to be a microtonalist.
>
> In Harmony,
> Aaron Wolf
>
> w
> >
>
>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> At this point, it seems everyone is a microtonalist
>

It does? What a strange community of folks you must live with and
hang out with... Maybe you were just joking, but it's hard to tell in
print.

I recently met a doctoral student in music theory at the local
university who, when I mentioned my anticipated Tonal Plexus, said
essentially, "oh, intonation other than 12-tempered? You must be into
renaissance music. I don't know any other reason to do anything
besides normal temperament..."

Yeah, but you can't map 7 and 11 to a hex layout without losing the
5-limit aspect of the layout as it is normally marketed. That's my
reference to "other compromises". There is no way that a hex layout
could achieve what the Hunt layout does (granted in a tempered way).
With the Hunt layout, I can consistently access all harmonies
instantaneously. With hex, you must choose which ones to use before
hand, or limit yourself to complex illogical layout and/or limited
frequency range.

I want to play all the way to 19 at least, ideally to 31, and not be
missing ANY of the options. The Tonal Plexus allows that, although
tempered. But I can set up a tuning table for it that makes it all
pure JI for a very extended JI with a set tonal center. And this
compromise may be eliminated if H-Pi implements my request that they
agreed is worthwhile: an adaptive algorithm unlike typical ones, just
adaptive to eliminate the up-to-3-cent error of the 205ET temperament.
With that adaption added, the TPX will be nearly ideal in my mind, as
far as layout at least.

-Aaron Wolf

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> i have never had a problem mapping 7 or 11 to a hexagonal layout 7
> especially as they can be only two ranks up. the 11 you can map either
> above or below.
> I think Xenharmonikon 3 covers all types of such animals mapped pretty
> easily. IMHO
> The advantage to a bar though is that is does give you more surface
> area to find a place for your finger to land. One could go with
> Bonsanquet original then. Which i would like to try.
>
> I am glad the price is coming down, but still i can build some nice
> instruments for that price
>
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>
>
>
> Aaron Wolf wrote:
> >
> >
> >
> > As far as the keyswitches "leaving much to be desired" - I think
> > that's a reasonable description of almost anything that isn't the
> > fantasy ideal. The hex keyboards ARE great, I really don't doubt it,
> > and yet they also leave much to be desired. For instance, I desire a
> > logical way to consistently access 7 and 11 limit notes while
> > modulating around various keys - and there's a limit to that
> > possibility with the hex keyboards without other compromises. Does
> > that mean they should be dismissed? No way, but my point is nothing
> > is truly perfect.
> >
> > >
> > > -Carl
> > >
> >
> >
>

in LA before i left everyone was doing microtonal music now. or called it such.

i don't know which scenario is preferable either

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Aaron Wolf wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > At this point, it seems everyone is a microtonalist
> >
>
> It does? What a strange community of folks you must live with and
> hang out with... Maybe you were just joking, but it's hard to tell in
> print.
>
> I recently met a doctoral student in music theory at the local
> university who, when I mentioned my anticipated Tonal Plexus, said
> essentially, "oh, intonation other than 12-tempered? You must be into
> renaissance music. I don't know any other reason to do anything
> besides normal temperament..."
>
>

you can use a hex layout with any tempered scale including Hunts, can't you?
You can use a different part of the hex keyboard to control the whole tuning of the board.
for instance you can modulate diamonds around the eikosany if you want. This is even what the last scale a tron could do

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Aaron Wolf wrote:
>
> Yeah, but you can't map 7 and 11 to a hex layout without losing the
> 5-limit aspect of the layout as it is normally marketed. That's my
> reference to "other compromises". There is no way that a hex layout
> could achieve what the Hunt layout does (granted in a tempered way).
> With the Hunt layout, I can consistently access all harmonies
> instantaneously. With hex, you must choose which ones to use before
> hand, or limit yourself to complex illogical layout and/or limited
> frequency range.
>
> I want to play all the way to 19 at least, ideally to 31, and not be
> missing ANY of the options. The Tonal Plexus allows that, although
> tempered. But I can set up a tuning table for it that makes it all
> pure JI for a very extended JI with a set tonal center. And this
> compromise may be eliminated if H-Pi implements my request that they
> agreed is worthwhile: an adaptive algorithm unlike typical ones, just
> adaptive to eliminate the up-to-3-cent error of the 205ET temperament.
> With that adaption added, the TPX will be nearly ideal in my mind, as
> far as layout at least.
>
> -Aaron Wolf
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > i have never had a problem mapping 7 or 11 to a hexagonal layout 7
> > especially as they can be only two ranks up. the 11 you can map either
> > above or below.
> > I think Xenharmonikon 3 covers all types of such animals mapped pretty
> > easily. IMHO
> > The advantage to a bar though is that is does give you more surface
> > area to find a place for your finger to land. One could go with
> > Bonsanquet original then. Which i would like to try.
> >
> > I am glad the price is coming down, but still i can build some nice
> > instruments for that price
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> >
> >
> >
> > Aaron Wolf wrote:
> > >
> > >
> > >
> > > As far as the keyswitches "leaving much to be desired" - I think
> > > that's a reasonable description of almost anything that isn't the
> > > fantasy ideal. The hex keyboards ARE great, I really don't doubt it,
> > > and yet they also leave much to be desired. For instance, I desire a
> > > logical way to consistently access 7 and 11 limit notes while
> > > modulating around various keys - and there's a limit to that
> > > possibility with the hex keyboards without other compromises. Does
> > > that mean they should be dismissed? No way, but my point is nothing
> > > is truly perfect.
> > >
> > > >
> > > > -Carl
> > > >
> > >
> > >
> >
>
>

Hi Torsten,

> Dear Carl,
>
> thanks for sharing your information and enthusiasm. Just to better
> understand you message I try to summarise. C-Thru Music AXiS can be
> freely tuned, because you can split the 192 into 3 MIDI channels (a
> 64 keys): you would simply tune three MIDI sound generators
> according needs. Great!

Yup.

> Now, the biggest question for me remains: what are suitable key
> mappings?

Sky's the limit! Well that, and the 21-column limit. :)

> You mention a Bosanquet mapping and a "harmonic table"
> layout. Could you be more specific about the latter?

See their website for info on the harmonic table. The idea
is to make consonances short on the keyboard and give up
a left-right ascending pitch axis. Some concertinas work
like this. You could argue there are too many runs in Byrd.

-Carl

Kraig,

Of course you can set up any scale at all in a hex keyboard, but that
doesn't mean it will make logical sense or be reasonable to remember
what is where. But in this case, no, you simply can't take a 192 note
hex keyboard and make it play 205ET.

Anyway, my point wasn't that hex was actually incapable of anything in
terms of notes- just that it is incapable of being something other
than hex. And in that regard, it is incapable of achieving the
beneficial aspects that are particular to the Hunt layout. And those
I'm not going to go into here, they are apparent with any objective
study of the Hunt layout. I readily agree that hex also has its own
particular benefits as well, but if I have only one, I prefer the Hunt
layout at this point.

-Aaron Wolf

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> you can use a hex layout with any tempered scale including Hunts,
can't you?
> You can use a different part of the hex keyboard to control the whole
> tuning of the board.
> for instance you can modulate diamonds around the eikosany if you
want.
> This is even what the last scale a tron could do
>
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>
>
>
> Aaron Wolf wrote:
> >
> > Yeah, but you can't map 7 and 11 to a hex layout without losing the
> > 5-limit aspect of the layout as it is normally marketed. That's my
> > reference to "other compromises". There is no way that a hex layout
> > could achieve what the Hunt layout does (granted in a tempered way).
> > With the Hunt layout, I can consistently access all harmonies
> > instantaneously. With hex, you must choose which ones to use before
> > hand, or limit yourself to complex illogical layout and/or limited
> > frequency range.
> >
> > I want to play all the way to 19 at least, ideally to 31, and not be
> > missing ANY of the options. The Tonal Plexus allows that, although
> > tempered. But I can set up a tuning table for it that makes it all
> > pure JI for a very extended JI with a set tonal center. And this
> > compromise may be eliminated if H-Pi implements my request that they
> > agreed is worthwhile: an adaptive algorithm unlike typical ones, just
> > adaptive to eliminate the up-to-3-cent error of the 205ET temperament.
> > With that adaption added, the TPX will be nearly ideal in my mind, as
> > far as layout at least.
> >
> > -Aaron Wolf
> >
> > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>,
Kraig
> > Grady <kraiggrady@> wrote:
> > >
> > > i have never had a problem mapping 7 or 11 to a hexagonal layout 7
> > > especially as they can be only two ranks up. the 11 you can map
either
> > > above or below.
> > > I think Xenharmonikon 3 covers all types of such animals mapped
pretty
> > > easily. IMHO
> > > The advantage to a bar though is that is does give you more surface
> > > area to find a place for your finger to land. One could go with
> > > Bonsanquet original then. Which i would like to try.
> > >
> > > I am glad the price is coming down, but still i can build some nice
> > > instruments for that price
> > >
> > >
> > > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > > _'''''''_ ^North/Western Hemisphere:
> > > North American Embassy of Anaphoria Island <http://anaphoria.com/
> > <http://anaphoria.com/>>
> > >
> > > _'''''''_ ^South/Eastern Hemisphere:
> > > Austronesian Outpost of Anaphoria
> > <http://anaphoriasouth.blogspot.com/
> > <http://anaphoriasouth.blogspot.com/>>
> > >
> > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > >
> > >
> > >
> > >
> > > Aaron Wolf wrote:
> > > >
> > > >
> > > >
> > > > As far as the keyswitches "leaving much to be desired" - I think
> > > > that's a reasonable description of almost anything that isn't the
> > > > fantasy ideal. The hex keyboards ARE great, I really don't
doubt it,
> > > > and yet they also leave much to be desired. For instance, I
desire a
> > > > logical way to consistently access 7 and 11 limit notes while
> > > > modulating around various keys - and there's a limit to that
> > > > possibility with the hex keyboards without other compromises. Does
> > > > that mean they should be dismissed? No way, but my point is
nothing
> > > > is truly perfect.
> > > >
> > > > >
> > > > > -Carl
> > > > >
> > > >
> > > >
> > >
> >
> >
>

Hi Aaron (W.),

> I don't understand Carl's dismissal of
> the layout as "unconventional" - that's a pretty strange
> criticism coming from a microtonalist looking for new
> alternative controllers.

I was trying to be nice, in hopes of avoiding another off-list
verbally-abusive tirade from its creator.

> As far as the keyswitches "leaving much to be desired" - I think
> that's a reasonable description of almost anything that isn't the
> fantasy ideal.

I'm fully capable of coming up with ideals beyond what the
AXiS or Opal keyboards offer, don't worry.

> The hex keyboards ARE great, I really don't doubt
> it, and yet they also leave much to be desired. For instance,
> I desire a logical way to consistently access 7 and 11 limit
> notes while modulating around various keys - and there's a
> limit to that possibility with the hex keyboards without other
> compromises.

Oh? What are those?

> Fact is, having 1200 (!) keys ready to play is not something
> you could EVER compare 192 to. No way.

It is comparable and it's worse unless you really need the
pitch resolution. And regular paradigmers don't.

> A concluding thought: some people I know said that 20 years ago
> it looked like microtonal stuff would become widely available
> and develop new music and they thought the push happened and
> failed and it wasn't going to happen again. But now things are
> really taking shape. It is a good time to be a microtonalist.

That's true.

-Carl

In my view, the "harmonic table" is great, for 5-limit harmonies. I
wish there were a way to have the same simple conceptually idea that
worked for higher limits, but obviously even 7-limit would need a
3-dimensional system or something...

Actually, something like it might be worth trying with the Tonal
Plexus. I could have a decent size harmonic series going up from the
bottom of each column... or maybe a center pitch and a harmonic series
up and subharmonics down. And then just try different relations of
how each column relates.

Honestly, I can relate to the enthusiasm about the AXiS. I'd probably
be seriously considering one if H-Pi didn't exist and it were the only
serious and affordable option. And I certainly understand how some
people have certain artistic goals that would lead them to possibly
prefer it. I do wish I had velocity sensitivity, but for my purposes
the AXiS is too limiting - in that it couldn't access all the various
pitches that I'd want ever all at once. My fantasy dream instrument
is something like a Tonal Plexus with velocity and aftertouch sensitivity.

Anyway, the main thing I wanted to say is that despite my promotion of
the TPX, I have to admit I agree with the general idea that in some
ways it would be good at times to be freed from strict connection to
left-right run-style ascending pitch.

-A Wolf

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Torsten,
>
> > Dear Carl,
> >
> > thanks for sharing your information and enthusiasm. Just to better
> > understand you message I try to summarise. C-Thru Music AXiS can be
> > freely tuned, because you can split the 192 into 3 MIDI channels (a
> > 64 keys): you would simply tune three MIDI sound generators
> > according needs. Great!
>
> Yup.
>
> > Now, the biggest question for me remains: what are suitable key
> > mappings?
>
> Sky's the limit! Well that, and the 21-column limit. :)
>
> > You mention a Bosanquet mapping and a "harmonic table"
> > layout. Could you be more specific about the latter?
>
> See their website for info on the harmonic table. The idea
> is to make consonances short on the keyboard and give up
> a left-right ascending pitch axis. Some concertinas work
> like this. You could argue there are too many runs in Byrd.
>
> -Carl
>

--- In tuning@yahoogroups.com, "Aaron Wolf" <wolftune@...> wrote:
>
> Yeah, but you can't map 7 and 11 to a hex layout without losing the
> 5-limit aspect of the layout as it is normally marketed.

??

> There is no way that a hex layout
> could achieve what the Hunt layout does (granted in a tempered way).
> With the Hunt layout, I can consistently access all harmonies
> instantaneously. With hex, you must choose which ones to use before
> hand, or limit yourself to complex illogical layout and/or limited
> frequency range.

Can you give an example?

-Carl

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> you can use a hex layout with any tempered scale including Hunts,
> can't you?

Yes.

There are ultimately only two kinds of isomorphic keyboard
layout:
http://en.wikipedia.org/wiki/Regular_tiling#Regular_tilings

1. rectangular (which is its own dual)
and
2. hex or triangular (which are equivalent as they are duals)

There's not terribly much difference between them, at least
not at this stage of the game (though I've argued that hex
layouts should be flat, whereas rectangular layouts could
be stepped or flat).

I believe the Plexus uses a rectangular layout.

-Carl

Aaron Wolf wrote...

> I readily agree that hex also has its own
> particular benefits as well, but if I have only one, I
> prefer the Hunt layout at this point.

How many hex keyboards have you played?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hi Aaron (W.),
>
> > I don't understand Carl's dismissal of
> > the layout as "unconventional" - that's a pretty strange
> > criticism coming from a microtonalist looking for new
> > alternative controllers.
>
> I was trying to be nice, in hopes of avoiding another off-list
> verbally-abusive tirade from its creator.
>

That sounds like saying that actually you hold a grudge about
something and you would have liked to really bash the thing because
you hate it. I don't want to put words in your mouth. I'm just
pointing out that saying that claiming "unconventional" is the nice
way to put it sounds like a claim that it really is a crappy layout in
your view. You're welcome to think what you want, but calling it
crappy or unconventional is in neither case useful criticism.

For anyone interested in the options, it would be more reasonable to
explain in normal terms why you or anyone else would choose not to
prefer it. Perhaps a reasonable statement would be that it is not
truly "generalized" and therefore not for anyone who wanted a truly
generalized keyboard.

>
> > The hex keyboards ARE great, I really don't doubt
> > it, and yet they also leave much to be desired. For instance,
> > I desire a logical way to consistently access 7 and 11 limit
> > notes while modulating around various keys - and there's a
> > limit to that possibility with the hex keyboards without other
> > compromises.
>
> Oh? What are those?
>

I guess I mean hard to get many different primes within something
similar to the harmonic table layout. Sure, you could get a decent
number of primes set up in rows or something above fundamental, just
like I could on the Tonal Plexus, and in that case, the AXiS would be
a better tool in some regards. But with only 192 keys, I couldn't go
so far as 19 full harmonics over a single octave of 12-chromatic notes.

> > Fact is, having 1200 (!) keys ready to play is not something
> > you could EVER compare 192 to. No way.
>
> It is comparable and it's worse unless you really need the
> pitch resolution. And regular paradigmers don't.
>

Paradigmers? What is that? And you miss the basic idea... if you
stick with a small number of keys, you have to determine and set a
tuning before you go and play. Only with decent resolution and lots
of range all accessible at once is one free to truly experiment
without planning in advance. The whole reason I was drawn to the TPX
is because I have done all the research and I know there are reasons
to choose all sorts of different notes. I didn't want to be debating
whether I wanted 25/16 or 14/9 or a tempered compromise. With the TPX
I can just have both. And maybe I can play with it for a couple
years, and then decide that I really never care about one of those, or
that a tempered compromise would be fine. And then I could get an
AXiS and know what options I want. But I very well might want to
actually have both those pitches independently, and in that case the
Tonal Plexus is the only real option.

I really don't think you can make such judgments about all musicians
who may be interested in exploring beyond 12-ET, that they they
wouldn't care about these things or that they'd think more keys is
worse. It's fine if you yourself feel that way.

-AW

> There are ultimately only two kinds of isomorphic keyboard
> layout:
> http://en.wikipedia.org/wiki/Regular_tiling#Regular_tilings
>
> 1. rectangular (which is its own dual)
> and
> 2. hex or triangular (which are equivalent as they are duals)
>
> There's not terribly much difference between them, at least
> not at this stage of the game (though I've argued that hex
> layouts should be flat, whereas rectangular layouts could
> be stepped or flat).
>
> I believe the Plexus uses a rectangular layout.
>
> -Carl
>

Not exactly, the Plexus uses an offset rectangular layout. In each
column, the keys are straight above each other, but there is an offset
from column to column, and the different key shape and markings make
it additionally more complex than a general rectangular layout. Fact
is, as I said in other posts, it is not a generalized keyboard. That
is good for what it is, but bad for anyone wanting a generalized one.
The standard piano is not generalized either, and I have to say that
you'd be pretty rash to say that there is no place for the standard
piano and that nobody in history ever had any reason to prefer it over
a generalized keyboard.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Aaron Wolf wrote...
>
> > I readily agree that hex also has its own
> > particular benefits as well, but if I have only one, I
> > prefer the Hunt layout at this point.
>
> How many hex keyboards have you played?
>
> -Carl
>

I haven't had one for extended time, but I played on the AXiS at the
NAMM show last year.

a hex keyboard can be any size up to 205, (ovals are nice too!)
i can't imagine using all those at once anyways
as time goes on i find my self using less notes not more. which is why i prefer scales with unequal size steps.
but obvious it works for your uses.

As for timbres in JI. I found early on that what ever the timbre i had at hand, JI worked quite well even with complex sounds cause one could still hear simple relationships.
Partch's instruments and anything but sine waves. And the tuning is quite compelling.
Sure one can obscure the harmonics but then you weaken the feeling of pitch altogether. I have tried reading the pitches of some unusually shaped instruments and found a tuner will read correctly for a small band around that pitch. So depending on context the pitch can be heard correctly. This would be advantageous of temperaments. but one want a whole slew of timbres to use, in fact timbre is often more important than pitch in say pop music.
do i want a tuning where my flute sounds sound wrong and my gongs correct, at this point i don't think i would be concerning my self much with pitch, cause the stronger it was the worse it would sound.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Aaron Wolf wrote:
>
> Kraig,
>
> Of course you can set up any scale at all in a hex keyboard, but that
> doesn't mean it will make logical sense or be reasonable to remember
> what is where. But in this case, no, you simply can't take a 192 note
> hex keyboard and make it play 205ET.
>
> Anyway, my point wasn't that hex was actually incapable of anything in
> terms of notes- just that it is incapable of being something other
> than hex. And in that regard, it is incapable of achieving the
> beneficial aspects that are particular to the Hunt layout. And those
> I'm not going to go into here, they are apparent with any objective
> study of the Hunt layout. I readily agree that hex also has its own
> particular benefits as well, but if I have only one, I prefer the Hunt
> layout at this point.
>
> -Aaron Wolf
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > you can use a hex layout with any tempered scale including Hunts,
> can't you?
> > You can use a different part of the hex keyboard to control the whole
> > tuning of the board.
> > for instance you can modulate diamonds around the eikosany if you
> want.
> > This is even what the last scale a tron could do
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> >
> >
> >
> > Aaron Wolf wrote:
> > >
> > > Yeah, but you can't map 7 and 11 to a hex layout without losing the
> > > 5-limit aspect of the layout as it is normally marketed. That's my
> > > reference to "other compromises". There is no way that a hex layout
> > > could achieve what the Hunt layout does (granted in a tempered way).
> > > With the Hunt layout, I can consistently access all harmonies
> > > instantaneously. With hex, you must choose which ones to use before
> > > hand, or limit yourself to complex illogical layout and/or limited
> > > frequency range.
> > >
> > > I want to play all the way to 19 at least, ideally to 31, and not be
> > > missing ANY of the options. The Tonal Plexus allows that, although
> > > tempered. But I can set up a tuning table for it that makes it all
> > > pure JI for a very extended JI with a set tonal center. And this
> > > compromise may be eliminated if H-Pi implements my request that they
> > > agreed is worthwhile: an adaptive algorithm unlike typical ones, just
> > > adaptive to eliminate the up-to-3-cent error of the 205ET temperament.
> > > With that adaption added, the TPX will be nearly ideal in my mind, as
> > > far as layout at least.
> > >
> > > -Aaron Wolf
> > >
> > > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> > <mailto:tuning%40yahoogroups.com>,
> Kraig
> > > Grady <kraiggrady@> wrote:
> > > >
> > > > i have never had a problem mapping 7 or 11 to a hexagonal layout 7
> > > > especially as they can be only two ranks up. the 11 you can map
> either
> > > > above or below.
> > > > I think Xenharmonikon 3 covers all types of such animals mapped
> pretty
> > > > easily. IMHO
> > > > The advantage to a bar though is that is does give you more surface
> > > > area to find a place for your finger to land. One could go with
> > > > Bonsanquet original then. Which i would like to try.
> > > >
> > > > I am glad the price is coming down, but still i can build some nice
> > > > instruments for that price
> > > >
> > > >
> > > > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > > > _'''''''_ ^North/Western Hemisphere:
> > > > North American Embassy of Anaphoria Island > <http://anaphoria.com/ <http://anaphoria.com/>
> > > <http://anaphoria.com/ <http://anaphoria.com/>>>
> > > >
> > > > _'''''''_ ^South/Eastern Hemisphere:
> > > > Austronesian Outpost of Anaphoria
> > > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>
> > > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>>
> > > >
> > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > >
> > > >
> > > >
> > > >
> > > > Aaron Wolf wrote:
> > > > >
> > > > >
> > > > >
> > > > > As far as the keyswitches "leaving much to be desired" - I think
> > > > > that's a reasonable description of almost anything that isn't the
> > > > > fantasy ideal. The hex keyboards ARE great, I really don't
> doubt it,
> > > > > and yet they also leave much to be desired. For instance, I
> desire a
> > > > > logical way to consistently access 7 and 11 limit notes while
> > > > > modulating around various keys - and there's a limit to that
> > > > > possibility with the hex keyboards without other compromises. Does
> > > > > that mean they should be dismissed? No way, but my point is
> nothing
> > > > > is truly perfect.
> > > > >
> > > > > >
> > > > > > -Carl
> > > > > >
> > > > >
> > > > >
> > > >
> > >
> > >
> >
>
>

--- In tuning@yahoogroups.com, "Aaron Wolf" <wolftune@...> wrote:
>
> In my view, the "harmonic table" is great, for 5-limit harmonies. I
> wish there were a way to have the same simple conceptually idea that
> worked for higher limits, but obviously even 7-limit would need a
> 3-dimensional system or something...

It's not obvious to me.

> I do wish I had velocity sensitivity, but for my purposes
> the AXiS is too limiting - in that it couldn't access all the
> various pitches that I'd want ever all at once.

That's valid. Are you finding the high-resolution of
205-ET useful?

From my point of view, 205 has less 11-limit error than 41,
but more 11-limit error than 72...

(best-val 72 '(2 3 5 7 11) max-damage)
(72 (72 114 167 202 249) 2.9803805315009413)

(best-val 205 '(2 3 5 7 11) max-damage)
(205 (205 325 476 575 709) 3.456271457396042)

Even though any dyad in 205 has a max error of 2.9 cents,
you can't necessarily get that for all the dyads in a chord
at once. As you can see above, you'll experience a 3.5-cent
error in one of the dyads in an 11-limit otonality, even
if you use the best approximation available in 205. And
because 205 isn't 11-limit consistent (unlike 41 and 72),
the best approximation to a chord can be different than what
you get if you just tune the chord straight up like you'd
expect (which in this case would be 205 325 476 576 709).

All of that said, the Tonal Plexus certainly is an exciting
instrument with eons of musical potential and you're a very
talented musician, so that's a good fit.

-Carl

I understand Zawinul would switch his keyboard the other way around at times:) high to low

Personally prefer the left/right thing. melody over harmony
It is something i miss in allot of Partch's design where he leaned toward 'harmonic" solutions to his layouts. The organs are as close that was available to him. When i had a chance to play upon them knowing how close they were to a 41 tone pattern made it quite easy for me to begin jumping in in a way different than the others.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Aaron Wolf wrote:
>
>
>
> Anyway, the main thing I wanted to say is that despite my promotion of
> the TPX, I have to admit I agree with the general idea that in some
> ways it would be good at times to be freed from strict connection to
> left-right run-style ascending pitch.
>
> -A Wolf
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, "Carl > Lumma" <carl@...> wrote:
> >
> > Hi Torsten,
> >
> > > Dear Carl,
> > >
> > > thanks for sharing your information and enthusiasm. Just to better
> > > understand you message I try to summarise. C-Thru Music AXiS can be
> > > freely tuned, because you can split the 192 into 3 MIDI channels (a
> > > 64 keys): you would simply tune three MIDI sound generators
> > > according needs. Great!
> >
> > Yup.
> >
> > > Now, the biggest question for me remains: what are suitable key
> > > mappings?
> >
> > Sky's the limit! Well that, and the 21-column limit. :)
> >
> > > You mention a Bosanquet mapping and a "harmonic table"
> > > layout. Could you be more specific about the latter?
> >
> > See their website for info on the harmonic table. The idea
> > is to make consonances short on the keyboard and give up
> > a left-right ascending pitch axis. Some concertinas work
> > like this. You could argue there are too many runs in Byrd.
> >
> > -Carl
> >
>
>

> > > I don't understand Carl's dismissal of
> > > the layout as "unconventional" - that's a pretty strange
> > > criticism coming from a microtonalist looking for new
> > > alternative controllers.
> >
> > I was trying to be nice, in hopes of avoiding another off-list
> > verbally-abusive tirade from its creator.
>
> That sounds like saying that actually you hold a grudge about
> something and you would have liked to really bash the thing
> because you hate it.

Hardly. You asked why I used strange language, and I told
the truth.

> You're welcome to think what you want, but calling it
> crappy or unconventional is in neither case useful criticism.

I could go on at length why the layout isn't the greatest
for me (and probably not for you either), but it really
depends on what you want to do and your musical ideals.

If you don't want to put words in my mouth, you can start
by not putting the word "crappy" in my mouth.

> > > The hex keyboards ARE great, I really don't doubt
> > > it, and yet they also leave much to be desired. For instance,
> > > I desire a logical way to consistently access 7 and 11 limit
> > > notes while modulating around various keys - and there's a
> > > limit to that possibility with the hex keyboards without
> > > other compromises.
> >
> > Oh? What are those?
>
> I guess I mean hard to get many different primes within something
> similar to the harmonic table layout.

You may be confusing the harmonic table with hex keyboards
in general. Nevertheless, any isomorphic keyboard is completely
defined by two intervals, including the Tonal Plexus. Thanks
to the magic of temperament, one can in fact get intervals other
than those two to appear quickly in the mapping.

> I really don't think you can make such judgments about all
> musicians who may be interested in exploring beyond 12-ET, that
> they they wouldn't care about these things or that they'd think
> more keys is worse. It's fine if you yourself feel that way.

I didn't do that. "Paradigmers" is a term I made up which I
should probably never use. Anyway, a central idea behind
tuning theory is that you should strive to get as many
consonances per note as possible. There's an underlying
notion that more notes = more cognitive load. That's all I
was trying to say. Now you may say that the organization
of the Plexus makes those extra notes easy as can be. If you
stare at the halberstadt layout painted on the thing, that
may be partially true. But if you're interested in other
kinds of scales that don't fit in the halberstadt framework,
I don't think it is.

-Carl

Wouldn't be fun to play with a penrose tiling in much the same way you did with those other shapes a while back.
Often the limitation of a tuning or in this case mapping becomes part of its character. this is what always work for me with the eikosany.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > you can use a hex layout with any tempered scale including Hunts,
> > can't you?
>
> Yes.
>
> There are ultimately only two kinds of isomorphic keyboard
> layout:
> http://en.wikipedia.org/wiki/Regular_tiling#Regular_tilings > <http://en.wikipedia.org/wiki/Regular_tiling#Regular_tilings>
>
> 1. rectangular (which is its own dual)
> and
> 2. hex or triangular (which are equivalent as they are duals)
>
> There's not terribly much difference between them, at least
> not at this stage of the game (though I've argued that hex
> layouts should be flat, whereas rectangular layouts could
> be stepped or flat).
>
> I believe the Plexus uses a rectangular layout.
>
> -Carl
>
>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> Wouldn't be fun to play with a penrose tiling in much the same
> way you did with those other shapes a while back.

I think Erv beat me to it. :)

-Carl

--- In tuning@yahoogroups.com, "Aaron Wolf" <wolftune@...> wrote:
> > > I readily agree that hex also has its own
> > > particular benefits as well, but if I have only one, I
> > > prefer the Hunt layout at this point.
> >
> > How many hex keyboards have you played?
>
> I haven't had one for extended time, but I played on the AXiS at the
> NAMM show last year.

What did you think of the build quality, and velocity sensing?

-Carl

He used lines for the directions, you used the relations of one space to another which might come out a bit differently. The latter might be way more complex since the two shapes come in 5 different angles ( or does the smaller occur more).
The hexagonal layout can do the rectangular thing if you omit the diagonals skipping to the next on on the horizontal plane plus set of the vertical.
This is useful if you want to map say two series that are separated by another interval. two Pythagoras. series say a 7/6 apart like Margo Schulter. Likewise you can put the diamond right on the layout, or the co prime grid as Stephen Taylor demonstrates on the UTube excerpt

Ideally as long as we can still dream, i would like to have something that just came on a computer like screen where you can change the shape and size of the keyboard at will.
putting up lattices if you will even. go from one to another by some common tone transform where what you were holding was reconfigured to fit and then maybe morphs into the new one.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > Wouldn't be fun to play with a penrose tiling in much the same
> > way you did with those other shapes a while back.
>
> I think Erv beat me to it. :)
>
> -Carl
>
>

I've got nothing against hex keyboards, I just also like the Tonal
Plexus. They both have a place.

As for timbres, I do agree, and I understand the simple relationships
and also the issues of difference tones etc. And generally I agree
with everything you wrote here. The Partch example is a good one. My
point is just that it is relevant. For instance, the exact precision
or acceptability of any particular temperament is affected by timbre
noticeable.

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> a hex keyboard can be any size up to 205, (ovals are nice too!)
> i can't imagine using all those at once anyways
> as time goes on i find my self using less notes not more. which is why
> i prefer scales with unequal size steps.
> but obvious it works for your uses.
>
> As for timbres in JI. I found early on that what ever the timbre i had
> at hand, JI worked quite well even with complex sounds cause one could
> still hear simple relationships.
> Partch's instruments and anything but sine waves. And the tuning is
> quite compelling.
> Sure one can obscure the harmonics but then you weaken the feeling of
> pitch altogether. I have tried reading the pitches of some unusually
> shaped instruments and found a tuner will read correctly for a small
> band around that pitch. So depending on context the pitch can be heard
> correctly. This would be advantageous of temperaments. but one want a
> whole slew of timbres to use, in fact timbre is often more important
> than pitch in say pop music.
> do i want a tuning where my flute sounds sound wrong and my gongs
> correct, at this point i don't think i would be concerning my self much
> with pitch, cause the stronger it was the worse it would sound.
>
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>
>
>
> Aaron Wolf wrote:
> >
> > Kraig,
> >
> > Of course you can set up any scale at all in a hex keyboard, but that
> > doesn't mean it will make logical sense or be reasonable to remember
> > what is where. But in this case, no, you simply can't take a 192 note
> > hex keyboard and make it play 205ET.
> >
> > Anyway, my point wasn't that hex was actually incapable of anything in
> > terms of notes- just that it is incapable of being something other
> > than hex. And in that regard, it is incapable of achieving the
> > beneficial aspects that are particular to the Hunt layout. And those
> > I'm not going to go into here, they are apparent with any objective
> > study of the Hunt layout. I readily agree that hex also has its own
> > particular benefits as well, but if I have only one, I prefer the Hunt
> > layout at this point.
> >
> > -Aaron Wolf
> >
> > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>,
Kraig
> > Grady <kraiggrady@> wrote:
> > >
> > > you can use a hex layout with any tempered scale including Hunts,
> > can't you?
> > > You can use a different part of the hex keyboard to control the
whole
> > > tuning of the board.
> > > for instance you can modulate diamonds around the eikosany if you
> > want.
> > > This is even what the last scale a tron could do
> > >
> > >
> > > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > > _'''''''_ ^North/Western Hemisphere:
> > > North American Embassy of Anaphoria Island <http://anaphoria.com/
> > <http://anaphoria.com/>>
> > >
> > > _'''''''_ ^South/Eastern Hemisphere:
> > > Austronesian Outpost of Anaphoria
> > <http://anaphoriasouth.blogspot.com/
> > <http://anaphoriasouth.blogspot.com/>>
> > >
> > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > >
> > >
> > >
> > >
> > > Aaron Wolf wrote:
> > > >
> > > > Yeah, but you can't map 7 and 11 to a hex layout without
losing the
> > > > 5-limit aspect of the layout as it is normally marketed. That's my
> > > > reference to "other compromises". There is no way that a hex
layout
> > > > could achieve what the Hunt layout does (granted in a tempered
way).
> > > > With the Hunt layout, I can consistently access all harmonies
> > > > instantaneously. With hex, you must choose which ones to use
before
> > > > hand, or limit yourself to complex illogical layout and/or limited
> > > > frequency range.
> > > >
> > > > I want to play all the way to 19 at least, ideally to 31, and
not be
> > > > missing ANY of the options. The Tonal Plexus allows that, although
> > > > tempered. But I can set up a tuning table for it that makes it all
> > > > pure JI for a very extended JI with a set tonal center. And this
> > > > compromise may be eliminated if H-Pi implements my request
that they
> > > > agreed is worthwhile: an adaptive algorithm unlike typical
ones, just
> > > > adaptive to eliminate the up-to-3-cent error of the 205ET
temperament.
> > > > With that adaption added, the TPX will be nearly ideal in my
mind, as
> > > > far as layout at least.
> > > >
> > > > -Aaron Wolf
> > > >
> > > > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>
> > <mailto:tuning%40yahoogroups.com>,
> > Kraig
> > > > Grady <kraiggrady@> wrote:
> > > > >
> > > > > i have never had a problem mapping 7 or 11 to a hexagonal
layout 7
> > > > > especially as they can be only two ranks up. the 11 you can map
> > either
> > > > > above or below.
> > > > > I think Xenharmonikon 3 covers all types of such animals mapped
> > pretty
> > > > > easily. IMHO
> > > > > The advantage to a bar though is that is does give you more
surface
> > > > > area to find a place for your finger to land. One could go with
> > > > > Bonsanquet original then. Which i would like to try.
> > > > >
> > > > > I am glad the price is coming down, but still i can build
some nice
> > > > > instruments for that price
> > > > >
> > > > >
> > > > > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > > > > _'''''''_ ^North/Western Hemisphere:
> > > > > North American Embassy of Anaphoria Island
> > <http://anaphoria.com/ <http://anaphoria.com/>
> > > > <http://anaphoria.com/ <http://anaphoria.com/>>>
> > > > >
> > > > > _'''''''_ ^South/Eastern Hemisphere:
> > > > > Austronesian Outpost of Anaphoria
> > > > <http://anaphoriasouth.blogspot.com/
> > <http://anaphoriasouth.blogspot.com/>
> > > > <http://anaphoriasouth.blogspot.com/
> > <http://anaphoriasouth.blogspot.com/>>>
> > > > >
> > > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > > >
> > > > >
> > > > >
> > > > >
> > > > > Aaron Wolf wrote:
> > > > > >
> > > > > >
> > > > > >
> > > > > > As far as the keyswitches "leaving much to be desired" - I
think
> > > > > > that's a reasonable description of almost anything that
isn't the
> > > > > > fantasy ideal. The hex keyboards ARE great, I really don't
> > doubt it,
> > > > > > and yet they also leave much to be desired. For instance, I
> > desire a
> > > > > > logical way to consistently access 7 and 11 limit notes while
> > > > > > modulating around various keys - and there's a limit to that
> > > > > > possibility with the hex keyboards without other
compromises. Does
> > > > > > that mean they should be dismissed? No way, but my point is
> > nothing
> > > > > > is truly perfect.
> > > > > >
> > > > > > >
> > > > > > > -Carl
> > > > > > >
> > > > > >
> > > > > >
> > > > >
> > > >
> > > >
> > >
> >
> >
>

So what is it you are working with these days. The full hexad, and/or beyond some close to 12 tone matrix?
just curious

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Aaron Wolf wrote:
>
> I've got nothing against hex keyboards, I just also like the Tonal
> Plexus. They both have a place.
>
> As for timbres, I do agree, and I understand the simple relationships
> and also the issues of difference tones etc. And generally I agree
> with everything you wrote here. The Partch example is a good one. My
> point is just that it is relevant. For instance, the exact precision
> or acceptability of any particular temperament is affected by timbre
> noticeable.
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > a hex keyboard can be any size up to 205, (ovals are nice too!)
> > i can't imagine using all those at once anyways
> > as time goes on i find my self using less notes not more. which is why
> > i prefer scales with unequal size steps.
> > but obvious it works for your uses.
> >
> > As for timbres in JI. I found early on that what ever the timbre i had
> > at hand, JI worked quite well even with complex sounds cause one could
> > still hear simple relationships.
> > Partch's instruments and anything but sine waves. And the tuning is
> > quite compelling.
> > Sure one can obscure the harmonics but then you weaken the feeling of
> > pitch altogether. I have tried reading the pitches of some unusually
> > shaped instruments and found a tuner will read correctly for a small
> > band around that pitch. So depending on context the pitch can be heard
> > correctly. This would be advantageous of temperaments. but one want a
> > whole slew of timbres to use, in fact timbre is often more important
> > than pitch in say pop music.
> > do i want a tuning where my flute sounds sound wrong and my gongs
> > correct, at this point i don't think i would be concerning my self much
> > with pitch, cause the stronger it was the worse it would sound.
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria.com/ > <http://anaphoria.com/>>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> >
> >
> >
> > Aaron Wolf wrote:
> > >
> > > Kraig,
> > >
> > > Of course you can set up any scale at all in a hex keyboard, but that
> > > doesn't mean it will make logical sense or be reasonable to remember
> > > what is where. But in this case, no, you simply can't take a 192 note
> > > hex keyboard and make it play 205ET.
> > >
> > > Anyway, my point wasn't that hex was actually incapable of anything in
> > > terms of notes- just that it is incapable of being something other
> > > than hex. And in that regard, it is incapable of achieving the
> > > beneficial aspects that are particular to the Hunt layout. And those
> > > I'm not going to go into here, they are apparent with any objective
> > > study of the Hunt layout. I readily agree that hex also has its own
> > > particular benefits as well, but if I have only one, I prefer the Hunt
> > > layout at this point.
> > >
> > > -Aaron Wolf
> > >
> > > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com> > <mailto:tuning%40yahoogroups.com>,
> Kraig
> > > Grady <kraiggrady@> wrote:
> > > >
> > > > you can use a hex layout with any tempered scale including Hunts,
> > > can't you?
> > > > You can use a different part of the hex keyboard to control the
> whole
> > > > tuning of the board.
> > > > for instance you can modulate diamonds around the eikosany if you
> > > want.
> > > > This is even what the last scale a tron could do
> > > >
> > > >
> > > > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > > > _'''''''_ ^North/Western Hemisphere:
> > > > North American Embassy of Anaphoria Island > <http://anaphoria.com/ <http://anaphoria.com/>
> > > <http://anaphoria.com/ <http://anaphoria.com/>>>
> > > >
> > > > _'''''''_ ^South/Eastern Hemisphere:
> > > > Austronesian Outpost of Anaphoria
> > > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>
> > > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>>
> > > >
> > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > >
> > > >
> > > >
> > > >
> > > > Aaron Wolf wrote:
> > > > >
> > > > > Yeah, but you can't map 7 and 11 to a hex layout without
> losing the
> > > > > 5-limit aspect of the layout as it is normally marketed. That's my
> > > > > reference to "other compromises". There is no way that a hex
> layout
> > > > > could achieve what the Hunt layout does (granted in a tempered
> way).
> > > > > With the Hunt layout, I can consistently access all harmonies
> > > > > instantaneously. With hex, you must choose which ones to use
> before
> > > > > hand, or limit yourself to complex illogical layout and/or limited
> > > > > frequency range.
> > > > >
> > > > > I want to play all the way to 19 at least, ideally to 31, and
> not be
> > > > > missing ANY of the options. The Tonal Plexus allows that, although
> > > > > tempered. But I can set up a tuning table for it that makes it all
> > > > > pure JI for a very extended JI with a set tonal center. And this
> > > > > compromise may be eliminated if H-Pi implements my request
> that they
> > > > > agreed is worthwhile: an adaptive algorithm unlike typical
> ones, just
> > > > > adaptive to eliminate the up-to-3-cent error of the 205ET
> temperament.
> > > > > With that adaption added, the TPX will be nearly ideal in my
> mind, as
> > > > > far as layout at least.
> > > > >
> > > > > -Aaron Wolf
> > > > >
> > > > > --- In tuning@yahoogroups.com > <mailto:tuning%40yahoogroups.com> <mailto:tuning%40yahoogroups.com>
> > > <mailto:tuning%40yahoogroups.com>,
> > > Kraig
> > > > > Grady <kraiggrady@> wrote:
> > > > > >
> > > > > > i have never had a problem mapping 7 or 11 to a hexagonal
> layout 7
> > > > > > especially as they can be only two ranks up. the 11 you can map
> > > either
> > > > > > above or below.
> > > > > > I think Xenharmonikon 3 covers all types of such animals mapped
> > > pretty
> > > > > > easily. IMHO
> > > > > > The advantage to a bar though is that is does give you more
> surface
> > > > > > area to find a place for your finger to land. One could go with
> > > > > > Bonsanquet original then. Which i would like to try.
> > > > > >
> > > > > > I am glad the price is coming down, but still i can build
> some nice
> > > > > > instruments for that price
> > > > > >
> > > > > >
> > > > > > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > > > > > _'''''''_ ^North/Western Hemisphere:
> > > > > > North American Embassy of Anaphoria Island
> > > <http://anaphoria.com/ <http://anaphoria.com/> > <http://anaphoria.com/ <http://anaphoria.com/>>
> > > > > <http://anaphoria.com/ <http://anaphoria.com/> > <http://anaphoria.com/ <http://anaphoria.com/>>>>
> > > > > >
> > > > > > _'''''''_ ^South/Eastern Hemisphere:
> > > > > > Austronesian Outpost of Anaphoria
> > > > > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>
> > > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>
> > > > > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>
> > > <http://anaphoriasouth.blogspot.com/ > <http://anaphoriasouth.blogspot.com/>>>>
> > > > > >
> > > > > > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > > Aaron Wolf wrote:
> > > > > > >
> > > > > > >
> > > > > > >
> > > > > > > As far as the keyswitches "leaving much to be desired" - I
> think
> > > > > > > that's a reasonable description of almost anything that
> isn't the
> > > > > > > fantasy ideal. The hex keyboards ARE great, I really don't
> > > doubt it,
> > > > > > > and yet they also leave much to be desired. For instance, I
> > > desire a
> > > > > > > logical way to consistently access 7 and 11 limit notes while
> > > > > > > modulating around various keys - and there's a limit to that
> > > > > > > possibility with the hex keyboards without other
> compromises. Does
> > > > > > > that mean they should be dismissed? No way, but my point is
> > > nothing
> > > > > > > is truly perfect.
> > > > > > >
> > > > > > > >
> > > > > > > > -Carl
> > > > > > > >
> > > > > > >
> > > > > > >
> > > > > >
> > > > >
> > > > >
> > > >
> > >
> > >
> >
>
>

> > I do wish I had velocity sensitivity, but for my purposes
> > the AXiS is too limiting - in that it couldn't access all the
> > various pitches that I'd want ever all at once.
>
> That's valid. Are you finding the high-resolution of
> 205-ET useful?
>

I am certainly finding it useful in the sense that there are certain
times that I really notice the difference of one pitch or another, but
honestly I think that something slightly smaller, perhaps even 72,
would be enough for me to usually specify the pitch I want. In other
words, any temperament at all has its issues, and I'm not convinced
that 205 is in a league above any other. However, I do appreciate the
resolution in some ways.

My request for H-Pi, as mentioned in other posts is to create an
algorithm that does adaptive tuning to create pure JI intervals within
the specification of the 205ET unit. By having 205ET as the base, any
interval could be played without vagueness or multiple options. So
for instance, I could play even my example of 14/9 versus 25/16 and
have the algorithm make either interval pure, and there's no need for
the way most algorithms work which would need some way to determine
which interval I want or always choose one of the two. By specifying
which 205ET key I want, it would only have one option. Anyway, Mr.
Hunt agreed with me on the value of this suggestion and expressed
clear goals of implementing it. So if this is done, then the issues
of 205ET versus 72Et or others in terms of how close they are to JI
for particular limits would be irrelevant.

> All of that said, the Tonal Plexus certainly is an exciting
> instrument with eons of musical potential and you're a very
> talented musician, so that's a good fit.
>
> -Carl
>

Thanks for the positive note. My interest is not only in playing but
in teaching, and there exist substantial and historical aspects to how
Mr. Hunt's theory and layout can help visually explain things to
students, just like how guitarists and singers are often taught to
understand scale terminology in relation to the piano layout. In this
case, I get the piano layout, it is compatible with traditional
teaching but extended to understand the real nature of pitch.

And as for performance, I appreciate that the layout allows easy
access to an approximation of 12ET for any time I'd need to relate to
tempered musicians. As I said, the same conceptual layout might work
for me in 72ET, though I'm not sure that over all that would be any
better, just different.

Best,
Aaron

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> So what is it you are working with these days. The full hexad, and/or
> beyond some close to 12 tone matrix?
> just curious
>

Kraig, was this question directed to me? I'm not even sure what you
are asking... I am not doing anything related to 12-tone music and
never have.
-Aaron Wolf

> I didn't do that. "Paradigmers" is a term I made up which I
> should probably never use. Anyway, a central idea behind
> tuning theory is that you should strive to get as many
> consonances per note as possible. There's an underlying
> notion that more notes = more cognitive load. That's all I
> was trying to say. Now you may say that the organization
> of the Plexus makes those extra notes easy as can be. If you
> stare at the halberstadt layout painted on the thing, that
> may be partially true. But if you're interested in other
> kinds of scales that don't fit in the halberstadt framework,
> I don't think it is.
>
> -Carl
>

Instead of saying cognitive load is to be avoided though, what about
just saying it is what it is. It is of artistic use to create
cognitive load. I totally disagree with your statement about getting
as many consonances as possible. That is only one end of things. The
goal is to have as much range as possible between dissonance and
consonance, cognitively and acoustically. By having access to very
strong consonance, very strong dissonance, and everything in between,
the artist is free to manipulate tension and resolve in whatever
manners fit the desired expression.

-AW

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Aaron Wolf" <wolftune@> wrote:
> > > > I readily agree that hex also has its own
> > > > particular benefits as well, but if I have only one, I
> > > > prefer the Hunt layout at this point.
> > >
> > > How many hex keyboards have you played?
> >
> > I haven't had one for extended time, but I played on the AXiS at the
> > NAMM show last year.
>
> What did you think of the build quality, and velocity sensing?
>
> -Carl
>

First off, if you've never been to a NAMM show, let me tell you: you
can't really hear things. Sometimes a high-end booth has a soundproof
thing or is in a weird out of the way corridor. But on the main
floor, there is a noise-patrol guy who goes around attempting and
failing to keep noise levels under something like 86dB. I think the
realistic ambient noise at the NAMM show generally is over 90dB.

So, velocity sensitivity? All I could tell was that, yes it was
velocity sensitive.

Now, build quality? It wasn't a shoddy toy. But when I basically
realized that it was built for just 12ET (which again, a year ago they
didn't mention anything about microtonality at all, apparently there
have been firmware updates since then, and I didn't know about the
3-split option workaround that you are suggesting)... well, once I
realized it was just 12ET I really didn't spend as much time bothering
with it.

The hex aspect of it, in terms of playability, was fine.

Again, I saw it at the time as just the harmonic table that is the
standard tuning of it. It wasn't suggested that it could be tuned any
other way. I didn't actually spend that long with it. I felt pretty
quick that I got the gist, and I respected it but was disappointed in
it being 12ET.

-Aaron W

> > > I do wish I had velocity sensitivity, but for my purposes
> > > the AXiS is too limiting - in that it couldn't access all the
> > > various pitches that I'd want ever all at once.
> >
> > That's valid. Are you finding the high-resolution of
> > 205-ET useful?
>
> I am certainly finding it useful in the sense that there are
> certain times that I really notice the difference of one pitch
> or another, but honestly I think that something slightly
> smaller, perhaps even 72, would be enough for me to usually
> specify the pitch I want. In other words, any temperament at
> all has its issues, and I'm not convinced that 205 is in a
> league above any other. However, I do appreciate the
> resolution in some ways.

Adaptively tuning 41 or 72 would pretty much rock (because
the adjustments are so small you wouldn't notice them and
because the tunings can distinguish a lot of JI so the
algorithm doesn't have to guess so much as it does in 12-ET).
It would also rock to use timbres with partials tuned to
41 or 72. Again, the difference from harmonic partials
would be so small the timbres would sound completely
natural.

> > All of that said, the Tonal Plexus certainly is an exciting
> > instrument with eons of musical potential and you're a very
> > talented musician, so that's a good fit.
>
> Thanks for the positive note. My interest is not only in
> playing but in teaching, and there exist substantial and
> historical aspects to how Mr. Hunt's theory and layout can
> help visually explain things to students, just like how
> guitarists and singers are often taught to understand scale
> terminology in relation to the piano layout. In this case,
> I get the piano layout, it is compatible with traditional
> teaching but extended to understand the real nature of pitch.
>
> And as for performance, I appreciate that the layout allows
> easy access to an approximation of 12ET for any time I'd need
> to relate to tempered musicians.

Of course 72 contains 12, for exact correspondence with
trad. musicians.

> As I said, the same conceptual layout might work for me in
> 72ET, though I'm not sure that over all that would be any
> better, just different.

Yup.

-Carl

--- In tuning@yahoogroups.com, "Aaron Wolf" <wolftune@...> wrote:
> By having access to very
> strong consonance, very strong dissonance, and everything in between,
> the artist is free to manipulate tension and resolve in whatever
> manners fit the desired expression.

Very well put.

--- In tuning@yahoogroups.com, "Aaron Wolf" <wolftune@...> wrote:
>
> > I didn't do that. "Paradigmers" is a term I made up which I
> > should probably never use. Anyway, a central idea behind
> > tuning theory is that you should strive to get as many
> > consonances per note as possible. There's an underlying
> > notion that more notes = more cognitive load. That's all I
> > was trying to say. Now you may say that the organization
> > of the Plexus makes those extra notes easy as can be. If you
> > stare at the halberstadt layout painted on the thing, that
> > may be partially true. But if you're interested in other
> > kinds of scales that don't fit in the halberstadt framework,
> > I don't think it is.
>
> Instead of saying cognitive load is to be avoided though, what
> about just saying it is what it is. It is of artistic use to
> create cognitive load. I totally disagree with your statement
> about getting as many consonances as possible. That is only
> one end of things. The goal is to have as much range as possible
> between dissonance and consonance, cognitively and acoustically.

Not sure what that means but any of these micro tunings pretty
much let you wreak high havoc when it comes to dissonance.

> By having access to very strong consonance, very strong
> dissonance, and everything in between, the artist is free to
> manipulate tension and resolve in whatever manners fit the
> desired expression.

That sounds great but I'm not sure what it has to do with
the price of tea in china.

-Carl

--- In tuning@yahoogroups.com, "Aaron Wolf" <wolftune@...> wrote:
>
> > > I haven't had one for extended time, but I played on the
> > > AXiS at the NAMM show last year.
> >
> > What did you think of the build quality, and velocity sensing?
>
> First off, if you've never been to a NAMM show, let me tell
> you: you can't really hear things.

I was gonna say, if you could hear above the din. :)

> Now, build quality? It wasn't a shoddy toy. But when I
> basically realized that it was built for just 12ET (which again,
> a year ago they didn't mention anything about microtonality at
> all, apparently there have been firmware updates since then,
> and I didn't know about the 3-split option workaround that you
> are suggesting)... well, once I realized it was just 12ET I
> really didn't spend as much time bothering with it.
>
> The hex aspect of it, in terms of playability, was fine.
>
> Again, I saw it at the time as just the harmonic table that is
> the standard tuning of it. It wasn't suggested that it could be
> tuned any other way. I didn't actually spend that long with it.
> I felt pretty quick that I got the gist, and I respected it but
> was disappointed in it being 12ET.

I kinda wrote it off, too. Well not wrote it off, but there
was like a cloud hanging over it. Then I saw Elaine Walker's
vids on YouTube, and I started to wonder. :)

-Carl

I wasn't suggesting serialism, more the number of tonal centers. perhaps diatonic is some cyclical fashion?
i mean you are refering to some progression sounding weird to some people, are you working off of diatonicism

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Aaron Wolf wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > So what is it you are working with these days. The full hexad, and/or
> > beyond some close to 12 tone matrix?
> > just curious
> >
>
> Kraig, was this question directed to me? I'm not even sure what you
> are asking... I am not doing anything related to 12-tone music and
> never have.
> -Aaron Wolf
>
>

Ok, then:

To answer your question, I am not working within some limited
theoretical framework. What I like about the Tonal Plexus is that it
has enough keys and enough resolution that a large number of
theoretical ideas are all possible without planning any tuning or
arrangement in advance. In that regard, I can freely explore without
constant mental reference to theory. Considering the cognition of
music, I can draw upon whatever parameter I want to explore in the
moment - such as having a sharper leading tone just for the extra
"leading" quality and extra dissonance before the resolve. Or I can
stick to harmonic intervals. It's all there for me to explore.

Now, my theoretical perspective is generally toward otonal JI. In
relation to barbershop harmony, jazz harmony, even classical stuff...
I like to play harmonic chords and modulate around the notes in
various ways. I am exploring the options of sustaining or repeating
one part of a chord and then playing a new harmony that includes that
one part but makes it a new identity, and in doing that, I can easily
find myself modulating through a wide range of total notes. I also
like to explore ethnic tunings or what could be similar to ethnic
tunings, which could involve even things like stretched octaves. With
205ET I can play a noticeably stretched octave that isn't horrible,
which would be harder with less resolution. My feeling is that these
choices all have different affective impact on the listener, and I
want access to all the different expressive choices. That said, my
preference is definitely toward solid harmony, and I intend to learn
to play some extended barbershop arrangements on the keyboard. I
assume you recall hearing the Melodyne'd barbershop recordings I've
shared in the past years...

Now to specifically address the tonal center question, my feeling is
that cognitive sense of tonal sense is very flexible depending on some
specific factors. Being harmonically supported helps. Playing a
pitch in any resolution sense, such as on a strong beat, for a long
time, even while APPEARING VISUALLY to be satisfied and relaxed, or
telling people verbally that this is the destination pitch, or
repeating a lot, and once again, strong harmonic support... these
things all help listeners accept something as a tonal center. And
certainly, I have to admit and work with known stylistic expectations
as well. I'm interested in controlling and exploring all the ways to
work with these factors.

What sounds "weird" to most people is any time I allow them to expect
something, such as diatonic notes, and then play something that is not
only non-diatonic but is outside the realm of deviations that they've
stylistically learned to relate to. The more I play from the
beginning in ways that denies their previous stylistic expectations,
the more they will be ready for new things. Although I also at times
might want to make them feel "weird" too. All these things are the
purview of an expressive, creative approach.

Please feel free to ask for any specific clarification if you're
curious about my thoughts in any further detail.

Best,
AW

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> I wasn't suggesting serialism, more the number of tonal centers.
perhaps
> diatonic is some cyclical fashion?
> i mean you are refering to some progression sounding weird to some
> people, are you working off of diatonicism
>
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>
>
>
> Aaron Wolf wrote:
> >
> > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>,
Kraig
> > Grady <kraiggrady@> wrote:
> > >
> > > So what is it you are working with these days. The full hexad,
and/or
> > > beyond some close to 12 tone matrix?
> > > just curious
> > >
> >
> > Kraig, was this question directed to me? I'm not even sure what you
> > are asking... I am not doing anything related to 12-tone music and
> > never have.
> > -Aaron Wolf
> >
> >
>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:

> Ideally as long as we can still dream, i would like to have something
> that just came on a computer like screen where you can change the shape
> and size of the keyboard at will.
> putting up lattices if you will even. go from one to another by some
> common tone transform where what you were holding was reconfigured to
> fit and then maybe morphs into the new one.

I believe that eventually almost all microtonal keyboards are going to
be in the form of multitouch screens. This will be the cheapest option
and allows experimenting with all kinds of shapes for keyboards.
I saw somewhere (can't find it now) a clip where someone made a
homebrew multitouch interface from a piece of paper, cardboard box and
a webcam in ten minutes! He also downloaded some existing free
software for it. I imagine one could make it velocity sensitive too
because the harder you press a surface the larger is the area of
fingertips pressing the surface.

Kalle Aho

Carl,

You clearly understand and agree with my
adaptive-within-high-number-temperament request. And yes, it could
work with 41 or 72, and in many regards, I'd be happy with that. The
result with 205 might be slightly more complex to play, but the
musical results of any of these are essentially the same. And anyway,
the fact is there *is* something to Mr. Hunt's "average just
noticeable difference" concept. With 205, the adaptivity will be
truly melodically imperceptible. That would not be the case with 41,
though it wouldn't be too bad.

Anyway, the first keyboard that exists that can play a decent range of
72ET with JI adaptivity within that - I would want one for sure. If
it were velocity sensitive as well, that'd be totally awesomely
incredible. All that isn't to say that it would be better in *every*
regard than the Tonal Plexus, but it would be better in many ways.
But again, this fantasy keyboard doesn't exist. If you go and make
it, I'll be interested.

Best,
AW

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > > > I do wish I had velocity sensitivity, but for my purposes
> > > > the AXiS is too limiting - in that it couldn't access all the
> > > > various pitches that I'd want ever all at once.
> > >
> > > That's valid. Are you finding the high-resolution of
> > > 205-ET useful?
> >
> > I am certainly finding it useful in the sense that there are
> > certain times that I really notice the difference of one pitch
> > or another, but honestly I think that something slightly
> > smaller, perhaps even 72, would be enough for me to usually
> > specify the pitch I want. In other words, any temperament at
> > all has its issues, and I'm not convinced that 205 is in a
> > league above any other. However, I do appreciate the
> > resolution in some ways.
>
> Adaptively tuning 41 or 72 would pretty much rock (because
> the adjustments are so small you wouldn't notice them and
> because the tunings can distinguish a lot of JI so the
> algorithm doesn't have to guess so much as it does in 12-ET).
> It would also rock to use timbres with partials tuned to
> 41 or 72. Again, the difference from harmonic partials
> would be so small the timbres would sound completely
> natural.
>
> > > All of that said, the Tonal Plexus certainly is an exciting
> > > instrument with eons of musical potential and you're a very
> > > talented musician, so that's a good fit.
> >
> > Thanks for the positive note. My interest is not only in
> > playing but in teaching, and there exist substantial and
> > historical aspects to how Mr. Hunt's theory and layout can
> > help visually explain things to students, just like how
> > guitarists and singers are often taught to understand scale
> > terminology in relation to the piano layout. In this case,
> > I get the piano layout, it is compatible with traditional
> > teaching but extended to understand the real nature of pitch.
> >
> > And as for performance, I appreciate that the layout allows
> > easy access to an approximation of 12ET for any time I'd need
> > to relate to tempered musicians.
>
> Of course 72 contains 12, for exact correspondence with
> trad. musicians.
>
> > As I said, the same conceptual layout might work for me in
> > 72ET, though I'm not sure that over all that would be any
> > better, just different.
>
> Yup.
>
> -Carl
>

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@> wrote:
>
> > Ideally as long as we can still dream, i would like to have something
> > that just came on a computer like screen where you can change the
shape
> > and size of the keyboard at will.
> > putting up lattices if you will even. go from one to another by some
> > common tone transform where what you were holding was reconfigured to
> > fit and then maybe morphs into the new one.
>
> I believe that eventually almost all microtonal keyboards are going to
> be in the form of multitouch screens. This will be the cheapest option
> and allows experimenting with all kinds of shapes for keyboards.
> I saw somewhere (can't find it now) a clip where someone made a
> homebrew multitouch interface from a piece of paper, cardboard box and
> a webcam in ten minutes! He also downloaded some existing free
> software for it. I imagine one could make it velocity sensitive too
> because the harder you press a surface the larger is the area of
> fingertips pressing the surface.
>
> Kalle Aho
>

Well, despite the rapid technology improvements, I expect that
something along those lines being really functional is still a couple
decades away. There is some value (though certainly debatable to a
degree) to the Tonal Plexus' varying tactile feel of different key
shapes. Such things would not be possible with a multitouch screen
(that I can imagine at this time anyway).

It is a neat thought though, and hopefully will eventually exist.
-AW

On 25 May 2008, at 06:05, Jon Szanto wrote:

> --- In tuning@yahoogroups.com, "Aaron Wolf" <wolftune@...> wrote:
> > By having access to very
> > strong consonance, very strong dissonance, and everything in > between,
> > the artist is free to manipulate tension and resolve in whatever
> > manners fit the desired expression.
>
> Very well put.
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Sorry about the double post. Hit send instead of save, before typing my response. (Still half asleep after editing dialogue soundtracks all night)

Yes well put Aaron.

One of the reasons that I was impressed with the hex Bosanquet/Wilson layout, was that using my scalecoding principle that notes which are closer/distant on the spiral of fourths and fifths are more con/dissonant, respectively;
the con/dissonance characteristics of intervals should become intuitive when playing, as the direction and distance between keypads would be the same for all identical musical intervals.

It enables users to also matching the traditional note naming (A to G - #, x and b, bb patterns), and the geometric relationships remain constant regardless of key.

[Too many different concepts in "much-too-long" sentences;

never mind the smart readers, i.e. those who matter, will get it,

This is an "elitist list", isn't it? ;-)]

I wonder whether it is possible to physically reposition and recolour the keypads on the device which so impressed Carl. I already assume that one can reprogramme the note assignments in any way one chooses.

Back to Soundtrack Pro 2 ;-(

On 25 May 2008, at 06:05, Jon Szanto wrote:

> --- In tuning@yahoogroups.com, "Aaron Wolf" <wolftune@...> wrote:
> > By having access to very
> > strong consonance, very strong dissonance, and everything in > between,
> > the artist is free to manipulate tension and resolve in whatever
> > manners fit the desired expression.
>
> Very well put.
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Dear all,

thanks Charles and Carl for your replies concerning key-mappings for this hexagon keyboard. It seems to me that several generalised keyboards went for a similar key arrangement (e.g., the TERPSTRA and the Wilson Generalized Keyboards from Starr Labs). The Scalatron keys are round, but the arrangement is also similar.

What key-mappings are used for these keyboards? I understand that in principle you can tune them any way you like, but of course some mappings make more sense than others. In particular, I am interested in mappings which allow for 3 to 7 prime limit harmony (or even beyond). For example, Charles kindly sent a Wilson layout (see below). I understand that when tuned in 31 ET, this mapping would allow for 3 to 7 limit primes. Also the default harmonic table of the AXiS could be tuned in some non-12 ET way (e.g., in JI). However, it appears to me a harmonic table would only allow for 3 and 5-limit harmony -- or any other two prime factor limits, because the table is two-dimensional. Are there other typical/common key-mappings for such a honey-comb key arrangement? Which key-mappings are suitable for 3, 5, and 7 limit (or even beyond), for example, by something like 31 ET?

Sorry if these question is a FAQ.

Thank you!

Best
Torsten

On May 25, 2008, at 12:54 AM, Charles Lucy wrote:
> A diagram of the Bosanquet keyboard can be found here:
>
> http://www.lucytune.com/midi_and_keyboard/hexboard.html
>

On May 25, 2008, at 2:13 AM, Carl Lumma wrote:
> > Now, the biggest question for me remains: what are suitable key
> > mappings?
>
> Sky's the limit! Well that, and the 21-column limit. :)
>
> > You mention a Bosanquet mapping and a "harmonic table"
> > layout. Could you be more specific about the latter?
>
> See their website for info on the harmonic table. The idea
> is to make consonances short on the keyboard and give up
> a left-right ascending pitch axis. Some concertinas work
> like this. You could argue there are too many runs in Byrd.

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586227
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

--- In tuning@yahoogroups.com, "Aaron Wolf" <wolftune@...> wrote:
>
> Carl,
>
> You clearly understand and agree with my
> adaptive-within-high-number-temperament request. And yes, it
> could work with 41 or 72, and in many regards, I'd be happy
> with that. The result with 205 might be slightly more complex
> to play, but the musical results of any of these are essentially
> the same. And anyway, the fact is there *is* something to
> Mr. Hunt's "average just noticeable difference" concept. With
> 205, the adaptivity will be truly melodically imperceptible.
> That would not be the case with 41, though it wouldn't be
> too bad.

The size of the adaptive tuning shifts depends on the comma(s)
being tempered out by the music. Any Western music that doesn't
use 12-ET enharmonics (almost all of it written prior to the
Romantic period and much of it even today) can be adaptively
tuned with shifts no greater than 5 cents, which is already
basically melodically imperceptible. By the time you get to
the commas of 41 it's just a total wash, so there's no benefit
to going higher in that regard.

> Anyway, the first keyboard that exists that can play a decent
> range of 72ET with JI adaptivity within that - I would want
> one for sure.

The adaptivity would best reside in the synthesizer, not
the keyboard. Using Max/MSP or any one of a number of
similar packages with the AXiS (or Plexus), it should be
fairly straightforward to implement.

> If it were velocity sensitive as well, that'd be totally
> awesomely incredible.

AXiS then.

> But again, this fantasy keyboard doesn't exist. If you go and
> make it, I'll be interested.

OK, I'll think about it!

-Carl

Hi Torsten,

> In particular, I am interested
> in mappings which allow for 3 to 7 prime limit harmony (or even
> beyond). For example, Charles kindly sent a Wilson layout (see
> below). I understand that when tuned in 31 ET, this mapping would
> allow for 3 to 7 limit primes.

Please start with:

http://anaphoria.com/xen3b.PDF

> Also the default harmonic table of the
> AXiS could be tuned in some non-12 ET way (e.g., in JI).

Yes.

> However, it appears to me a harmonic table would only allow
> for 3 and 5-limit harmony -- or any other two prime factor
> limits, because the table is two-dimensional.

If I set the two directions to 6/5 and 7/6, what happens?

But that's not all. What's 4/3 + 4/3 in 22-ET?

> Are there other typical/common key-mappings for such
> a honey-comb key arrangement?

I think it'd be a stretch to say any extended keyboard
mapping was "typical". Please remember that you are currently
engaged in one of the most esoteric of all human activities. :)

> Which key-mappings are suitable for 3, 5, and 7 limit (or
> even beyond), for example, by something like 31 ET?

Your best bet is to buy a keyboard and experiment. That
said, the metric usually suggested is: given a chord like
4:9:22 or whatever you want, what is the radius of the
smallest circle that contains it on the keyboard? Given
a tuning system, you can optimize mappings this way, with
and without the condition that there be a
monotonically-ascending pitch axis. Dave Keenan even
has a spreadsheet that does stuff like this automatically
(its location left as an exercise for the reader to discover).

-Carl

If you go to
http://anaphoria.com/wilson.html
and look under
KEYBOARD DESIGNS/RELATED TO THE SCALE TREE
there are quite a few mappings there along with the templates that generate them

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Torsten Anders wrote:
>
> Dear all,
>
> thanks Charles and Carl for your replies concerning key-mappings for
> this hexagon keyboard. It seems to me that several generalised
> keyboards went for a similar key arrangement (e.g., the TERPSTRA and
> the Wilson Generalized Keyboards from Starr Labs). The Scalatron keys
> are round, but the arrangement is also similar.
>
> What key-mappings are used for these keyboards? I understand that in
> principle you can tune them any way you like, but of course some
> mappings make more sense than others. In particular, I am interested
> in mappings which allow for 3 to 7 prime limit harmony (or even
> beyond). For example, Charles kindly sent a Wilson layout (see
> below). I understand that when tuned in 31 ET, this mapping would
> allow for 3 to 7 limit primes. Also the default harmonic table of the
> AXiS could be tuned in some non-12 ET way (e.g., in JI). However, it
> appears to me a harmonic table would only allow for 3 and 5-limit
> harmony -- or any other two prime factor limits, because the table is
> two-dimensional. Are there other typical/common key-mappings for such
> a honey-comb key arrangement? Which key-mappings are suitable for 3,
> 5, and 7 limit (or even beyond), for example, by something like 31 ET?
>
> Sorry if these question is a FAQ.
>
> Thank you!
>
> Best
> Torsten
>
> On May 25, 2008, at 12:54 AM, Charles Lucy wrote:
> > A diagram of the Bosanquet keyboard can be found here:
> >
> > http://www.lucytune.com/midi_and_keyboard/hexboard.html > <http://www.lucytune.com/midi_and_keyboard/hexboard.html>
> >
>
> On May 25, 2008, at 2:13 AM, Carl Lumma wrote:
> > > Now, the biggest question for me remains: what are suitable key
> > > mappings?
> >
> > Sky's the limit! Well that, and the 21-column limit. :)
> >
> > > You mention a Bosanquet mapping and a "harmonic table"
> > > layout. Could you be more specific about the latter?
> >
> > See their website for info on the harmonic table. The idea
> > is to make consonances short on the keyboard and give up
> > a left-right ascending pitch axis. Some concertinas work
> > like this. You could argue there are too many runs in Byrd.
>
> --
> Torsten Anders
> Interdisciplinary Centre for Computer Music Research
> University of Plymouth
> Office: +44-1752-586227
> Private: +44-1752-558917
> http://strasheela.sourceforge.net <http://strasheela.sourceforge.net>
> http://www.torsten-anders.de <http://www.torsten-anders.de>
>
>

[ Attachment content not displayed ]

Hi Mike,

> Furthermore, that has always been my criticism of 72-tet as
> well -- I thought it was the greatest thing in the world until
> I realized that the saturated #15 chord (C E- G B- D F#- A C#-)
> is inconsistent in 72-tet -- rounding errors will cause the
> best approximation for the C#- to jump up one step to C#.

72 is 17-limit consistent, so I'm not sure what you're running
into. What JI tuning are you trying to hit here? Or maybe
you're running into a chord that can't be tuned in JI (which
are sometimes called "magic chords").

-Carl

On May 25, 2008, at 9:56 PM, Carl Lumma wrote:
> Please start with:
>
> http://anaphoria.com/xen3b.PDF

Great, thank you very much!

Also thanks to you Kraig for pointing me to these other papers.

Best
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586227
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

once you get to this number of tones, it is just as easy to use just and allow for the errors it creates, which gives each key or root it own flavor with more closely related ones will tend to share more in common. After a while ones just goes to the area that fits what one wants. But inconsistencies is what drove my mind bonkers with ETs. not to open that debate:) Some prefer inconsistencies and the more the merrier has been quite rigorously pursued here, as it should be.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Mike Battaglia wrote:
>
> In regards to 205-tet, it might be relatively easy to get any interval > you want, but is it relatively consistent with 5.8537 cent step sizes?
>
> Furthermore, that has always been my criticism of 72-tet as well -- I > thought it was the greatest thing in the world until I realized that > the saturated #15 chord (C E- G B- D F#- A C#-) is inconsistent in > 72-tet -- rounding errors will cause the best approximation for the > C#- to jump up one step to C#. There are a lot of other "extended" > harmonies that are prevalent in jazz and later-era classical music > that turn out to be just as inconsistent in 72-tet as well. Since > composers often didn't have microtonal resources to work with, their > solution to finding new sounds was often simply to branch out further > along the 5-limit JI lattice (in a metaphorical sort of way) to > "extend" the harmonies that they already had access to, and so these > harmonies that are inconsistent in 72-tet are unfortunately relatively > common.
>
> In fact, just to generalize, the relatively small step size of 16.667 > cents means that any error over 8.333 cents will round up or down to > an adjacent step, and since the error for 3/2 in 72-tet is around 2 > cents, 5 stacked fifths is enough to screw up the rounding in 72-tet. > The -3 cent error for 5/4 means that 3 of those stacked will be > inconsistent. The same thing applies to the 7th and 11th harmonics as > well.
>
> This in my experience makes 72-tet relatively hard to play at times. > You can either abandon the consistency principle and just accept a > small amount of error for the sake of easier conceptualization, which > I think sounds bad and much unlike the extremely fine and "pure" > character of 72-tet that makes it so attractive to begin with -- or > you come up with some rule to adjust the harmonies, like a rule of +1 > step every 5 fifths or so, which is pretty messy to think about, > especially when you get into upper structure triads and higher-limit > harmonies. Either way, the inconsistency of 72-tet is the deal-breaker > for me, especially when you compare it to lower-division temperaments > like 53-tet, or even to some degree 41-tet. But 53-tet doesn't do so > well with 7-limit harmonies, and so I hate equal temperaments. But I > love them.
>
> -Mike
>
> On Sun, May 25, 2008 at 5:08 PM, Kraig Grady <kraiggrady@... > <mailto:kraiggrady@...>> wrote:
>
> If you go to
> http://anaphoria.com/wilson.html <http://anaphoria.com/wilson.html>
> and look under
> KEYBOARD DESIGNS/RELATED TO THE SCALE TREE
> there are quite a few mappings there along with the templates that
> generate them
>
>
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/
> <http://anaphoria.com/>>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria
> <http://anaphoriasouth.blogspot.com/
> <http://anaphoriasouth.blogspot.com/>>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> Torsten Anders wrote:
> >
> > Dear all,
> >
> > thanks Charles and Carl for your replies concerning key-mappings for
> > this hexagon keyboard. It seems to me that several generalised
> > keyboards went for a similar key arrangement (e.g., the TERPSTRA and
> > the Wilson Generalized Keyboards from Starr Labs). The Scalatron
> keys
> > are round, but the arrangement is also similar.
> >
> > What key-mappings are used for these keyboards? I understand that in
> > principle you can tune them any way you like, but of course some
> > mappings make more sense than others. In particular, I am interested
> > in mappings which allow for 3 to 7 prime limit harmony (or even
> > beyond). For example, Charles kindly sent a Wilson layout (see
> > below). I understand that when tuned in 31 ET, this mapping would
> > allow for 3 to 7 limit primes. Also the default harmonic table
> of the
> > AXiS could be tuned in some non-12 ET way (e.g., in JI). However, it
> > appears to me a harmonic table would only allow for 3 and 5-limit
> > harmony -- or any other two prime factor limits, because the
> table is
> > two-dimensional. Are there other typical/common key-mappings for
> such
> > a honey-comb key arrangement? Which key-mappings are suitable for 3,
> > 5, and 7 limit (or even beyond), for example, by something like
> 31 ET?
> >
> > Sorry if these question is a FAQ.
> >
> > Thank you!
> >
> > Best
> > Torsten
> >
> > On May 25, 2008, at 12:54 AM, Charles Lucy wrote:
> > > A diagram of the Bosanquet keyboard can be found here:
> > >
> > > http://www.lucytune.com/midi_and_keyboard/hexboard.html
> <http://www.lucytune.com/midi_and_keyboard/hexboard.html>
> > <http://www.lucytune.com/midi_and_keyboard/hexboard.html
> <http://www.lucytune.com/midi_and_keyboard/hexboard.html>>
> > >
> >
> > On May 25, 2008, at 2:13 AM, Carl Lumma wrote:
> > > > Now, the biggest question for me remains: what are suitable key
> > > > mappings?
> > >
> > > Sky's the limit! Well that, and the 21-column limit. :)
> > >
> > > > You mention a Bosanquet mapping and a "harmonic table"
> > > > layout. Could you be more specific about the latter?
> > >
> > > See their website for info on the harmonic table. The idea
> > > is to make consonances short on the keyboard and give up
> > > a left-right ascending pitch axis. Some concertinas work
> > > like this. You could argue there are too many runs in Byrd.
> >
> > --
> > Torsten Anders
> > Interdisciplinary Centre for Computer Music Research
> > University of Plymouth
> > Office: +44-1752-586227
> > Private: +44-1752-558917
> > http://strasheela.sourceforge.net
> <http://strasheela.sourceforge.net>
> <http://strasheela.sourceforge.net
> <http://strasheela.sourceforge.net>>
> > http://www.torsten-anders.de <http://www.torsten-anders.de>
> <http://www.torsten-anders.de <http://www.torsten-anders.de>>
> >
> >
>
>
>

I think he is talking about accumulated errors like we saw with the midi standard- with divisions down in the one and a half cent range. Once one tuned up a Pythagorean pentatonic , one was already one unit off. The beats obscure any of the material one was hoping for. /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
>
> Hi Mike,
>
> > Furthermore, that has always been my criticism of 72-tet as
> > well -- I thought it was the greatest thing in the world until
> > I realized that the saturated #15 chord (C E- G B- D F#- A C#-)
> > is inconsistent in 72-tet -- rounding errors will cause the
> > best approximation for the C#- to jump up one step to C#.
>
> 72 is 17-limit consistent, so I'm not sure what you're running
> into. What JI tuning are you trying to hit here? Or maybe
> you're running into a chord that can't be tuned in JI (which
> are sometimes called "magic chords").
>
> -Carl
>
>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Aaron Wolf" <wolftune@> wrote:
> >
> > Carl,
> >
> > You clearly understand and agree with my
> > adaptive-within-high-number-temperament request. And yes, it
> > could work with 41 or 72, and in many regards, I'd be happy
> > with that. The result with 205 might be slightly more complex
> > to play, but the musical results of any of these are essentially
> > the same. And anyway, the fact is there *is* something to
> > Mr. Hunt's "average just noticeable difference" concept. With
> > 205, the adaptivity will be truly melodically imperceptible.
> > That would not be the case with 41, though it wouldn't be
> > too bad.
>
> The size of the adaptive tuning shifts depends on the comma(s)
> being tempered out by the music. Any Western music that doesn't
> use 12-ET enharmonics (almost all of it written prior to the
> Romantic period and much of it even today) can be adaptively
> tuned with shifts no greater than 5 cents, which is already
> basically melodically imperceptible. By the time you get to
> the commas of 41 it's just a total wash, so there's no benefit
> to going higher in that regard.
>

Overall, I agree with you, except in the level that you really dismiss
*any* value of higher temperaments in this regard. Fact is, with a
step size of nearly 30 cents, the exact issues of how to average the
harmonies... well, for instance, if I have a 3 note chord that
averages sharp of the regular 41ET notes, and then another that one
common pitch but averages flat... well, the amount of shift could be
melodically very noticeable.

To a degree the function of higher precision is more conscious control
or awareness of these things. In other words, by using 205ET and then
adapting, any larger shift would be something that would necessitate
choosing a new key. And in that regard, it allows the artist to opt
for a less harmonic note if they want to avoid the melodic shift. By
having more precision, it allows the user to still access harmonic
ratios well, but have the option of choosing melodic function over
harmonic at times. With 205ET, I can choose to raise a note
intentionally sharp of harmonic without going so far as to make it
really noticeably dissonant. That wouldn't be possible with only 41,
and not the same with 72. These issues cannot be so easily dismissed
unless you assume all pitch related choices are based on finding
consonant harmony above all else.

> > Anyway, the first keyboard that exists that can play a decent
> > range of 72ET with JI adaptivity within that - I would want
> > one for sure.
>
> The adaptivity would best reside in the synthesizer, not
> the keyboard. Using Max/MSP or any one of a number of
> similar packages with the AXiS (or Plexus), it should be
> fairly straightforward to implement.
>
> > If it were velocity sensitive as well, that'd be totally
> > awesomely incredible.
>
> AXiS then.
>
> > But again, this fantasy keyboard doesn't exist. If you go and
> > make it, I'll be interested.
>
> OK, I'll think about it!
>
> -Carl
>

I think it would be fantastic for you to make this happen. You said
yourself that you like the idea, so it seems reasonable for your own
artistic reasons to see it through. And I really would be interested
in it if it were done, but I'm currently busy learning my TPX.

Peace,
AW

Mike,

I have the same question as Carl, except that I also want to simply
add that 205ET obviously not only has more precision, but any time a
rounding needs to jump to the next key, that is much less of a jump
than 72. I've played all sorts of chords, including what is usually
in jazz called a #11-b9 which is all the harmonics up to 17, and I
think that's what you're talking about here. I've played that on my
TPX, and it is fine to me, except that it isn't totally pure JI, which
no temperament ever is.

The neat thing is that the TPX is retunable EASILY. So I could easily
tune the keys to perfectly match exactly whatever it is you are
wanting to do.

Best,
AW

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> In regards to 205-tet, it might be relatively easy to get any
interval you
> want, but is it relatively consistent with 5.8537 cent step sizes?
>
> Furthermore, that has always been my criticism of 72-tet as well -- I
> thought it was the greatest thing in the world until I realized that the
> saturated #15 chord (C E- G B- D F#- A C#-) is inconsistent in 72-tet --
> rounding errors will cause the best approximation for the C#- to
jump up one
> step to C#. There are a lot of other "extended" harmonies that are
prevalent
> in jazz and later-era classical music that turn out to be just as
> inconsistent in 72-tet as well. Since composers often didn't have
microtonal
> resources to work with, their solution to finding new sounds was often
> simply to branch out further along the 5-limit JI lattice (in a
metaphorical
> sort of way) to "extend" the harmonies that they already had access
to, and
> so these harmonies that are inconsistent in 72-tet are unfortunately
> relatively common.
>
> In fact, just to generalize, the relatively small step size of
16.667 cents
> means that any error over 8.333 cents will round up or down to an
adjacent
> step, and since the error for 3/2 in 72-tet is around 2 cents, 5 stacked
> fifths is enough to screw up the rounding in 72-tet. The -3 cent
error for
> 5/4 means that 3 of those stacked will be inconsistent. The same thing
> applies to the 7th and 11th harmonics as well.
>
> This in my experience makes 72-tet relatively hard to play at times.
You can
> either abandon the consistency principle and just accept a small
amount of
> error for the sake of easier conceptualization, which I think sounds
bad and
> much unlike the extremely fine and "pure" character of 72-tet that
makes it
> so attractive to begin with -- or you come up with some rule to
adjust the
> harmonies, like a rule of +1 step every 5 fifths or so, which is pretty
> messy to think about, especially when you get into upper structure
triads
> and higher-limit harmonies. Either way, the inconsistency of 72-tet
is the
> deal-breaker for me, especially when you compare it to lower-division
> temperaments like 53-tet, or even to some degree 41-tet. But 53-tet
doesn't
> do so well with 7-limit harmonies, and so I hate equal temperaments.
But I
> love them.
>
> -Mike
>
> On Sun, May 25, 2008 at 5:08 PM, Kraig Grady <kraiggrady@...>
> wrote:
>
> > If you go to
> > http://anaphoria.com/wilson.html
> > and look under
> > KEYBOARD DESIGNS/RELATED TO THE SCALE TREE
> > there are quite a few mappings there along with the templates that
> > generate them
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria.com/>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria
<http://anaphoriasouth.blogspot.com/>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > Torsten Anders wrote:
> > >
> > > Dear all,
> > >
> > > thanks Charles and Carl for your replies concerning key-mappings for
> > > this hexagon keyboard. It seems to me that several generalised
> > > keyboards went for a similar key arrangement (e.g., the TERPSTRA and
> > > the Wilson Generalized Keyboards from Starr Labs). The Scalatron
keys
> > > are round, but the arrangement is also similar.
> > >
> > > What key-mappings are used for these keyboards? I understand that in
> > > principle you can tune them any way you like, but of course some
> > > mappings make more sense than others. In particular, I am interested
> > > in mappings which allow for 3 to 7 prime limit harmony (or even
> > > beyond). For example, Charles kindly sent a Wilson layout (see
> > > below). I understand that when tuned in 31 ET, this mapping would
> > > allow for 3 to 7 limit primes. Also the default harmonic table
of the
> > > AXiS could be tuned in some non-12 ET way (e.g., in JI). However, it
> > > appears to me a harmonic table would only allow for 3 and 5-limit
> > > harmony -- or any other two prime factor limits, because the
table is
> > > two-dimensional. Are there other typical/common key-mappings for
such
> > > a honey-comb key arrangement? Which key-mappings are suitable for 3,
> > > 5, and 7 limit (or even beyond), for example, by something like
31 ET?
> > >
> > > Sorry if these question is a FAQ.
> > >
> > > Thank you!
> > >
> > > Best
> > > Torsten
> > >
> > > On May 25, 2008, at 12:54 AM, Charles Lucy wrote:
> > > > A diagram of the Bosanquet keyboard can be found here:
> > > >
> > > > http://www.lucytune.com/midi_and_keyboard/hexboard.html
> > > <http://www.lucytune.com/midi_and_keyboard/hexboard.html>
> > > >
> > >
> > > On May 25, 2008, at 2:13 AM, Carl Lumma wrote:
> > > > > Now, the biggest question for me remains: what are suitable key
> > > > > mappings?
> > > >
> > > > Sky's the limit! Well that, and the 21-column limit. :)
> > > >
> > > > > You mention a Bosanquet mapping and a "harmonic table"
> > > > > layout. Could you be more specific about the latter?
> > > >
> > > > See their website for info on the harmonic table. The idea
> > > > is to make consonances short on the keyboard and give up
> > > > a left-right ascending pitch axis. Some concertinas work
> > > > like this. You could argue there are too many runs in Byrd.
> > >
> > > --
> > > Torsten Anders
> > > Interdisciplinary Centre for Computer Music Research
> > > University of Plymouth
> > > Office: +44-1752-586227
> > > Private: +44-1752-558917
> > > http://strasheela.sourceforge.net
<http://strasheela.sourceforge.net>
> > > http://www.torsten-anders.de <http://www.torsten-anders.de>
> > >
> > >
> >
> >
>

Yeah, that's right. That's why I plan to develop a key-centric pure
extended JI version of the TPX tuning to sue with the 205 layout.
With the TPX, I'm certainly not limited to 205ET. I can use pure JI
and allow for errors, as you suggest, but with so many keys I can get
pretty much all the common options.

-AW

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> once you get to this number of tones, it is just as easy to use just
and
> allow for the errors it creates, which gives each key or root it own
> flavor with more closely related ones will tend to share more in
common.
> After a while ones just goes to the area that fits what one wants. But
> inconsistencies is what drove my mind bonkers with ETs. not to open
that
> debate:) Some prefer inconsistencies and the more the merrier has been
> quite rigorously pursued here, as it should be.
>
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>
>
>
> Mike Battaglia wrote:
> >
> > In regards to 205-tet, it might be relatively easy to get any
interval
> > you want, but is it relatively consistent with 5.8537 cent step sizes?
> >
> > Furthermore, that has always been my criticism of 72-tet as well -- I
> > thought it was the greatest thing in the world until I realized that
> > the saturated #15 chord (C E- G B- D F#- A C#-) is inconsistent in
> > 72-tet -- rounding errors will cause the best approximation for the
> > C#- to jump up one step to C#. There are a lot of other "extended"
> > harmonies that are prevalent in jazz and later-era classical music
> > that turn out to be just as inconsistent in 72-tet as well. Since
> > composers often didn't have microtonal resources to work with, their
> > solution to finding new sounds was often simply to branch out further
> > along the 5-limit JI lattice (in a metaphorical sort of way) to
> > "extend" the harmonies that they already had access to, and so these
> > harmonies that are inconsistent in 72-tet are unfortunately
relatively
> > common.
> >
> > In fact, just to generalize, the relatively small step size of 16.667
> > cents means that any error over 8.333 cents will round up or down to
> > an adjacent step, and since the error for 3/2 in 72-tet is around 2
> > cents, 5 stacked fifths is enough to screw up the rounding in 72-tet.
> > The -3 cent error for 5/4 means that 3 of those stacked will be
> > inconsistent. The same thing applies to the 7th and 11th harmonics as
> > well.
> >
> > This in my experience makes 72-tet relatively hard to play at times.
> > You can either abandon the consistency principle and just accept a
> > small amount of error for the sake of easier conceptualization, which
> > I think sounds bad and much unlike the extremely fine and "pure"
> > character of 72-tet that makes it so attractive to begin with -- or
> > you come up with some rule to adjust the harmonies, like a rule of +1
> > step every 5 fifths or so, which is pretty messy to think about,
> > especially when you get into upper structure triads and higher-limit
> > harmonies. Either way, the inconsistency of 72-tet is the
deal-breaker
> > for me, especially when you compare it to lower-division temperaments
> > like 53-tet, or even to some degree 41-tet. But 53-tet doesn't do so
> > well with 7-limit harmonies, and so I hate equal temperaments. But I
> > love them.
> >
> > -Mike
> >
> > On Sun, May 25, 2008 at 5:08 PM, Kraig Grady <kraiggrady@...
> > <mailto:kraiggrady@...>> wrote:
> >
> > If you go to
> > http://anaphoria.com/wilson.html
<http://anaphoria.com/wilson.html>
> > and look under
> > KEYBOARD DESIGNS/RELATED TO THE SCALE TREE
> > there are quite a few mappings there along with the templates that
> > generate them
> >
> >
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria.com/
> > <http://anaphoria.com/>>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria
> > <http://anaphoriasouth.blogspot.com/
> > <http://anaphoriasouth.blogspot.com/>>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> > Torsten Anders wrote:
> > >
> > > Dear all,
> > >
> > > thanks Charles and Carl for your replies concerning
key-mappings for
> > > this hexagon keyboard. It seems to me that several generalised
> > > keyboards went for a similar key arrangement (e.g., the
TERPSTRA and
> > > the Wilson Generalized Keyboards from Starr Labs). The Scalatron
> > keys
> > > are round, but the arrangement is also similar.
> > >
> > > What key-mappings are used for these keyboards? I understand
that in
> > > principle you can tune them any way you like, but of course some
> > > mappings make more sense than others. In particular, I am
interested
> > > in mappings which allow for 3 to 7 prime limit harmony (or even
> > > beyond). For example, Charles kindly sent a Wilson layout (see
> > > below). I understand that when tuned in 31 ET, this mapping
would
> > > allow for 3 to 7 limit primes. Also the default harmonic table
> > of the
> > > AXiS could be tuned in some non-12 ET way (e.g., in JI).
However, it
> > > appears to me a harmonic table would only allow for 3 and
5-limit
> > > harmony -- or any other two prime factor limits, because the
> > table is
> > > two-dimensional. Are there other typical/common key-mappings for
> > such
> > > a honey-comb key arrangement? Which key-mappings are
suitable for 3,
> > > 5, and 7 limit (or even beyond), for example, by something like
> > 31 ET?
> > >
> > > Sorry if these question is a FAQ.
> > >
> > > Thank you!
> > >
> > > Best
> > > Torsten
> > >
> > > On May 25, 2008, at 12:54 AM, Charles Lucy wrote:
> > > > A diagram of the Bosanquet keyboard can be found here:
> > > >
> > > > http://www.lucytune.com/midi_and_keyboard/hexboard.html
> > <http://www.lucytune.com/midi_and_keyboard/hexboard.html>
> > > <http://www.lucytune.com/midi_and_keyboard/hexboard.html
> > <http://www.lucytune.com/midi_and_keyboard/hexboard.html>>
> > > >
> > >
> > > On May 25, 2008, at 2:13 AM, Carl Lumma wrote:
> > > > > Now, the biggest question for me remains: what are
suitable key
> > > > > mappings?
> > > >
> > > > Sky's the limit! Well that, and the 21-column limit. :)
> > > >
> > > > > You mention a Bosanquet mapping and a "harmonic table"
> > > > > layout. Could you be more specific about the latter?
> > > >
> > > > See their website for info on the harmonic table. The idea
> > > > is to make consonances short on the keyboard and give up
> > > > a left-right ascending pitch axis. Some concertinas work
> > > > like this. You could argue there are too many runs in Byrd.
> > >
> > > --
> > > Torsten Anders
> > > Interdisciplinary Centre for Computer Music Research
> > > University of Plymouth
> > > Office: +44-1752-586227
> > > Private: +44-1752-558917
> > > http://strasheela.sourceforge.net
> > <http://strasheela.sourceforge.net>
> > <http://strasheela.sourceforge.net
> > <http://strasheela.sourceforge.net>>
> > > http://www.torsten-anders.de <http://www.torsten-anders.de>
> > <http://www.torsten-anders.de <http://www.torsten-anders.de>>
> > >
> > >
> >
> >
> >
>

Torsten Anders wrote:

> What key-mappings are used for these keyboards? I understand that in > principle you can tune them any way you like, but of course some > mappings make more sense than others. In particular, I am interested > in mappings which allow for 3 to 7 prime limit harmony (or even > beyond). For example, Charles kindly sent a Wilson layout (see > below). I understand that when tuned in 31 ET, this mapping would > allow for 3 to 7 limit primes. Also the default harmonic table of the > AXiS could be tuned in some non-12 ET way (e.g., in JI). However, it > appears to me a harmonic table would only allow for 3 and 5-limit > harmony -- or any other two prime factor limits, because the table is > two-dimensional. Are there other typical/common key-mappings for such > a honey-comb key arrangement? Which key-mappings are suitable for 3, > 5, and 7 limit (or even beyond), for example, by something like 31 ET?

A two dimensional keyboard can give you 3-limit JI. If you want 5-limit chords either the octaves will be out of tune, or you need to temper, or use an irregular JI mapping. The nice thing about the harmonic layout is that root position triads are the same regardless of what temperament you choose. However, what interval on the keyboard ends up as an octave depends on your choice of temperament class.

Generally speaking, if you want octaves, you need a rank 2 temperament or something like it for a two dimensional keyboard. If you want 7-limit with 31 ET then some suitable temperament classes are meantone, orwell, and miracle, with increasing accuracy. Also, 31 ET belongs to the large family of temperaments where 225:224 vanishes. That means two major thirds of 5:4 are equivalent to 14:9 and 16:15 and 15:14 are equivalent. For this family there'll be a common harmonic mapping of (use a fixed width font):

' 14:9-----7:3-----7:2
' / \ / \ /
' / \ / \ /
' / \ / \ /
' 5:4----15:8----14:5
' / \ / \ /
' / \ / \ /
' / \ / \ /
'1:1-----3:2-----9:4

With so many keys it's useful to have duplications to give you a choice of fingerings. For this you can choose an equal temperament, MOS, or periodicity block. One nice feature of the harmonic layout is that for different layouts consistent with the same ET you finger chords the same way. Some of them might not work, but if they don't it means they can't be played at all in that tuning.

The standard tuning is for 12 ET. So obviously you could replace it with the 12 note tuning of your choice. But there wouldn't be much point because you could have done the same with a standard keyboard. As you mentioned 31 ET, you could try rank 2 temperaments or JI scales consistent with it. I happen to think these keyboards would work very well for 19 note scales if the keys were coloured accordingly...

There are other ways to map hexagonal keyboards and you have links to follow up.

Graham

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--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> I'm talking about a slightly different notion of consistency,
> I think.
>
> It is true that 72 is 17-limit consistent, but most of western
> harmony doesn't work like that. Western 5-limit harmony mainly
> consists of stacked major and minor thirds, which is so obvious
> I'm sure that you would all find it slightly insulting to even
> mention :P. The problem is that when you stack enough fifths or
> major thirds on top of each other, the harmony breaks down in
> 72-tet, like in the case of the #15 chord, where the C# is off.
> Being as jazz especially consists of a lot of quartal voicings,
> and 72-tet is a relatively poor match for a bunch of stacked
> fifths, it is slightly less useful. 5 stacked fifths will
> "break" the consistency of the harmony, as will 3 thirds.

Yes, that's right, but I think what you're complaining about
is that it's not a meantone tuning. What do you make of this
chord in 53-ET?

-Carl

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Thank you Graham.

Best
Torsten

On May 26, 2008, at 4:09 AM, Graham Breed wrote:

> Torsten Anders wrote:
>
> > What key-mappings are used for these keyboards? I understand that in
> > principle you can tune them any way you like, but of course some
> > mappings make more sense than others. In particular, I am interested
> > in mappings which allow for 3 to 7 prime limit harmony (or even
> > beyond). For example, Charles kindly sent a Wilson layout (see
> > below). I understand that when tuned in 31 ET, this mapping would
> > allow for 3 to 7 limit primes. Also the default harmonic table of > the
> > AXiS could be tuned in some non-12 ET way (e.g., in JI). However, it
> > appears to me a harmonic table would only allow for 3 and 5-limit
> > harmony -- or any other two prime factor limits, because the > table is
> > two-dimensional. Are there other typical/common key-mappings for > such
> > a honey-comb key arrangement? Which key-mappings are suitable for 3,
> > 5, and 7 limit (or even beyond), for example, by something like > 31 ET?
>
> A two dimensional keyboard can give you 3-limit JI. If you
> want 5-limit chords either the octaves will be out of tune,
> or you need to temper, or use an irregular JI mapping. The
> nice thing about the harmonic layout is that root position
> triads are the same regardless of what temperament you
> choose. However, what interval on the keyboard ends up as
> an octave depends on your choice of temperament class.
>
> Generally speaking, if you want octaves, you need a rank 2
> temperament or something like it for a two dimensional
> keyboard. If you want 7-limit with 31 ET then some suitable
> temperament classes are meantone, orwell, and miracle, with
> increasing accuracy. Also, 31 ET belongs to the large
> family of temperaments where 225:224 vanishes. That means
> two major thirds of 5:4 are equivalent to 14:9 and 16:15 and
> 15:14 are equivalent. For this family there'll be a common
> harmonic mapping of (use a fixed width font):
>
> ' 14:9-----7:3-----7:2
> ' / \ / \ /
> ' / \ / \ /
> ' / \ / \ /
> ' 5:4----15:8----14:5
> ' / \ / \ /
> ' / \ / \ /
> ' / \ / \ /
> '1:1-----3:2-----9:4
>
> With so many keys it's useful to have duplications to give
> you a choice of fingerings. For this you can choose an
> equal temperament, MOS, or periodicity block. One nice
> feature of the harmonic layout is that for different layouts
> consistent with the same ET you finger chords the same way.
> Some of them might not work, but if they don't it means
> they can't be played at all in that tuning.
>
> The standard tuning is for 12 ET. So obviously you could
> replace it with the 12 note tuning of your choice. But
> there wouldn't be much point because you could have done the
> same with a standard keyboard. As you mentioned 31 ET, you
> could try rank 2 temperaments or JI scales consistent with
> it. I happen to think these keyboards would work very well
> for 19 note scales if the keys were coloured accordingly...
>
> There are other ways to map hexagonal keyboards and you have
> links to follow up.
>
> Graham
>
>
--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586227
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

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"Yes". Quite recently I posted some comments about stacking different
kinds of Just "thirds", using "thirds" very broadly, so of course I
run into what you're talking about quickly. An equal temperament may
have very good approximations of the intervals in question, but when
stacking up, the deviations from Just mean that the later intervals
are no longer acceptable.

In the case of 34 equal, both "6/5" and "5/4" are both almost exactly
2 cents high. So in your chord it's going to overshoot the Just mark
to such an extent that the closest approximation is going to be
almost one degree of 34 high (a misspelling or whatever you want to
call it). Hmmm... I think the amount of deviation from the Just goal
here would be about the same as in 72, if I'm not mistaken- 13 cents
too high when using the nearest, and "wrong", key. And egregiously
off, 20+ cents, using the "right note".

But 34 is screwed from the get-go as far as being a proper
temperament for Just-oriented Western music, in contrast to being a
kind of field of possible intervals or tetrachord divisions or
whatever (where it excels), having no "circle" of fifths, an unlinked
M3, and just not plain not being or sounding meantoney.

Anyway your example is an example of why I was grumbling about the
superiority of the idea of integer limits, rather than prime or odd
limits.

-Cameron Bobro

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...>
wrote:
>
> Sorry, quick correction - the #15 is one syntonic comma HIGHER than
the
> chromatic semitone.
>
> On Mon, May 26, 2008 at 5:27 AM, Mike Battaglia <battaglia01@...>
> wrote:
>
> > I just realized as well, maybe people don't know what chord I'm
talking
> > about -- I'm just referring to 5-limit music here. By alternately
stacking
> > major and minor thirds on top of each other, one will hit the
following
> > scale degrees:
> >
> > 1 3 5 maj7 9 #11 13 #15
> > C E G B D F# A C# (12-tet notation)
> > C E- G B- D F#- A C#- (72-tet notation - what it should be)
> >
> > Classical jazz theory doesn't usually mention 3rd octave chord
extensions,
> > but as someone who is currently studying jazz piano, that chord
is talked
> > about often. I hear it in classical music as well -- maybe not
voiced that
> > way, but at least I hear that #15 note is used fairly often.
Also, the C#
> > that is a #15 here will differ from the normal C# that is a
chromatic
> > semitone by a syntonic comma (the #15 is lower). You would expect
this C# to
> > be accessed in relation to C in 72-tet as a C#-, one step down
from the
> > standard 12-tet C#, but due to accumulated rounding errors, it
actually ends
> > up one 72-tet step higher from where it would be.
> >
> > This is just what I've noticed by playing around with it. 53's
near perfect
> > fifths and thirds actually make this much less of an issue, and
I'm not sure
> > how 41-tet or 34-tet fares. 31-tet is pretty good as well, and
when you get
> > lower the step sizes start to be big enough that accumulated
rounding errors
> > aren't much of an issue (but of course there are other issues).
> >
> > What the "ideal" equal temperament is I don't know, but 72-tet
has some
> > flaws. 72-tet does have huge huge advantages, but having to deal
with
> > accumulated rounding errors in my mind more than nullifies the
ease of
> > conceptual thinking that is a result of it's being derived from
12-tet. It's
> > great to be able to relate everything to the 12 tones that we
know, but who
> > wants to figure out how the rounding errors add up every time
they play an
> > extended chord?
> >
> >
> > On Mon, May 26, 2008 at 5:10 AM, Mike Battaglia <battaglia01@...>
> > wrote:
> >
> >> No... the next sentence right after where you ended quoting me
is me
> >> saying that this is an issue even though 72-tet is not a meantone
> >> temperament.
> >>
> >> What I am saying is that the C#- which is a #15 rounds up a step
to C#.
> >> That simple fact makes 72-tet relatively difficult to use for
relatively
> >> common chords, although they aren't that common in some
contexts. I'm not
> >> talking about the change of step being related to the syntonic
comma here.
> >> I'm talking about the change of step being due to a rounding
error. The
> >> accumulated error of the fifths and thirds builds up to the
point where it
> >> is greater than half of the step size of a single 72-tet step,
and so the
> >> nearest approximation of the note in question is one step off
from where
> >> you'd expect it to be if you look at the intervals making it up.
> >>
> >> If you don't believe me, try it in scala and see! Put in the
numbers above
> >> - 32:40:48:60:72:90:108:135 - which should be C E- G B- D F#- A
C#- and
> >> you'll see the 13.33333 cent rounding error for the 135th
harmonic if you
> >> set it to be a 72-tet approximation (it will be C#, not C#-).
Then, change
> >> the last number to 134 or something just so scala will round
that last note
> >> down to the proper C#-, and you'll hear that it sounds much
worse. 53-tet
> >> handles this chord much better, as the step sizes for each
interval are
> >> consistent, and so it's easier to think about. Being easy to
think about is
> >> supposed to be the primary advantage of 72-tet, and in most
cases it is, but
> >> it breaks down here.
> >>
> >> So it sounds good to say that 72-tet is consistent to the 17-
limit, but
> >> thinking about consistency that way might be misleading when
evaluating a
> >> temperament, especially as most of western harmony consists of
stacked
> >> fifths and thirds For example, 3 stacked fifths, C-G-D-A is
technically a
> >> 27-limit chord. A temperament that is consistent up to the 25-
limit for
> >> example might sound great at first glance, but it means that at
the 27-limit
> >> the consistency of the fifths would break down, and being able
to have 3
> >> fifths on top of each other is pretty important for any
temperament. This
> >> again has nothing to do with meantone temperament or the
syntonic comma in
> >> general -- it's a different phenomenon I'm describing.
> >>
> >> -Mike
> >>
> >>
> >> On Mon, May 26, 2008 at 2:38 AM, Carl Lumma <carl@...> wrote:
> >>
> >>> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>,
"Mike
> >>> Battaglia" <battaglia01@> wrote:
> >>> >
> >>> > I'm talking about a slightly different notion of consistency,
> >>> > I think.
> >>> >
> >>> > It is true that 72 is 17-limit consistent, but most of western
> >>> > harmony doesn't work like that. Western 5-limit harmony mainly
> >>> > consists of stacked major and minor thirds, which is so
obvious
> >>> > I'm sure that you would all find it slightly insulting to even
> >>> > mention :P. The problem is that when you stack enough fifths
or
> >>> > major thirds on top of each other, the harmony breaks down in
> >>> > 72-tet, like in the case of the #15 chord, where the C# is
off.
> >>> > Being as jazz especially consists of a lot of quartal
voicings,
> >>> > and 72-tet is a relatively poor match for a bunch of stacked
> >>> > fifths, it is slightly less useful. 5 stacked fifths will
> >>> > "break" the consistency of the harmony, as will 3 thirds.
> >>>
> >>> Yes, that's right, but I think what you're complaining about
> >>> is that it's not a meantone tuning. What do you make of this
> >>> chord in 53-ET?
> >>>
> >>> -Carl
> >>>
> >>>
> >>>
> >>
> >>
> >
>

Dear Mike,

On May 26, 2008, at 10:27 AM, Mike Battaglia wrote:
> 1 3 5 maj7 9 #11 13 #15
> C E G B D F# A C# (12-tet notation)
> C E- G B- D F#- A C#- (72-tet notation - what it should be)
>
> Classical jazz theory doesn't usually mention 3rd octave chord > extensions, but as someone who is currently studying jazz piano, > that chord is talked about often. I hear it in classical music as > well -- maybe not voiced that way, but at least I hear that #15 > note is used fairly often.

just curious: do you really mean this 8-note chord occurs sometimes in classical music. Certainly, you can have a minor 9th in a chord, but I wonder whether in classical music you would derive it by stacking so many thirds (instead of having some alteration).

Best
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586227
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

Mike Battaglia wrote:
> I'm talking about a slightly different notion of consistency, I think.

It looks like the same kind of consistency but over a different set of intervals.

> It is true that 72 is 17-limit consistent, but most of western harmony > doesn't work like that. Western 5-limit harmony mainly consists of > stacked major and minor thirds, which is so obvious I'm sure that you > would all find it slightly insulting to even mention :P. The problem is > that when you stack enough fifths or major thirds on top of each other, > the harmony breaks down in 72-tet, like in the case of the #15 chord, > where the C# is off. Being as jazz especially consists of a lot of > quartal voicings, and 72-tet is a relatively poor match for a bunch of > stacked fifths, it is slightly less useful. 5 stacked fifths will > "break" the consistency of the harmony, as will 3 thirds. Even in > non-meantone music, I still find this to be an issue.

There's a certain school of harmony that talks about stacked major and minor thirds. But that school usually also talks about 12 note equal temperament. I wouldn't expect such chords to work outside of 12 note equal temperament. If they can be tuned other than 12 note equal temperament I wouldn't assume that it should be with pure 5-limit thirds that add up to complex 5-limit dissonances.

If that is what you're doing, then yes, being 17-limit consistent is irrelevant. And 72-tet isn't the best temperament out there for 5-limit harmony. But it does that the advantage that stacked fifths will give *exactly the same* results as the do in 12-tet.

A chord that could easily be seen as failing outside meantone is the plain old dominant seventh.

G B D F

If this is about stacked 5-limit thirds the interval G-F is 9:5. But if you want it to resolve onto a tonic C major chord it's helpful if C F is 4:3. These two criteria are inconsistent unless you have a meantone. There's no need to go to 15th chords for problems to arise with different tunings.

> So if we view chords like these as musical excursions into the JI > lattice, then you realize that going far enough in any one direction on > the lattice will cause rounding errors in -any- equal temperament, and > 72-tet's tolerance threshold for that is pretty low, especially compared > to 53-tet. This might not bother many people, as a #15 chord is kind of > a new sound even in jazz, but in some later classical works, extremely > extended chords like that are heard quite a bit (take Amaj/C, for > instance). Of course, the option always remains to manually adjust for > the inconsistencies, but I find it makes it extremely difficult to > figure out which note to hit if you're far out in 5-limit JI space when > there are rounding errors and the step sizes are so small. The option > also exists to just ignore the inconsistencies, but I find that it > sounds much better to adjust for them. I find the whole process to be > slightly irritating, although if you don't care so much about chords > like that, then I think 72-tet is incredibly useful.

Yes, any equal temperament with pure octaves will eventually give an inconsistency if the set of intervals you're trying to approximate gets large enough. But why exactly does it matter?

So Amaj/C is C A C# E? I don't see any particular problems with it.

Why do you have to "manually adjust" anything? The intervals of 72-tet are consistent in themselves. The results of stacked fifths are the same as you get in 12-equal. Who do you think's going to notice that C C#- is slightly more than half a step off from the extended JI ratio you're predicting?

> For reference, the #15 chord I'm talking about is > 32:40:48:60:72:90:108:135, or 1/1:5/4:3/2:15/8:9/4:45/16:27/8:135/32. > It's just a set of stacked major and minor thirds from C to C# -- C E G > B D F# A C#, or in 72-tet notation (is it called Sims-maneri notation?) > C E- G B- D F#- A C#-, except at the end the C#- jumps up to C#.

Why does it jump? Who can recognize this ratio of 135:32? The note A is exactly where it would be in 12-tet. The interval A-C# that ends the chord is exactly what you'd expect from a 5-limit interval in 72-tet. The offending interval C C#- is, by my calculations, exactly 0.53 steps (that's 8.8 cents) out. Spell it as C C# and I make it 0.47 steps (7.8 cents) out instead. It's more to the point to say that it's always out of tune, rather than approximated inconsistently.

Remember that minor thirds in 12-tet are over 15 cents out. So if discrepancies of this order are a problem then 12-tet has never been suitable for traditional harmony. If the C#- "jumps" to C# then the interval C C# is exactly where you'd expect it to be from 12-tet and the bad third of A C# is also exactly what it is in 12-tet.

> Again, just my opinion on it. As I am particularly enamored with that > style of composition, I find 72-tet to have some serious shortcomings. > Especially when it's touted as being "easy" for musicians to adjust to > because it has 12-tet as a subset -- it becomes much less easy for > musicians to adjust to when they have to jump up or down a step to deal > with inconsistencies like this.

Well, sure, 72-tet isn't the best 5-limit temperament out there. It's usually promoted as something that takes you *outside* traditional harmony, what with not being a meantone and having all those higher-prime intervals to choose from. If 5-limit harmony is what you want maybe 5-limit JI will do the trick with fewer notes. Or 53-tet. Or schismatic temperament, which is very accurate and should be relatively simple for these chords (probably requiring less than 53 notes).

The good thing about 72-tet is that it divides 12-tet, and instrumentalists can learn to deal with it accordingly. However imperfect it is the best temperament with those properties even in the 5-limit. With the example you gave the musicians have to jump not much more than half a step.

> Just my two cents.

I'm sorry if you feel you've been cheated but, yes, 72-tet has these properties.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

>
> A chord that could easily be seen as failing outside
> meantone is the plain old dominant seventh.
>
> G B D F
>
> If this is about stacked 5-limit thirds the interval G-F is
> 9:5. But if you want it to resolve onto a tonic C major
> chord it's helpful if C F is 4:3. These two criteria are
> inconsistent unless you have a meantone. There's no need to
> go to 15th chords for problems to arise with different tunings.

On the other hand with the acute fourth it sounds suspiciously
familiar to an orchestral or choral V7-I. Even more so when the B is
a 7/5 above the acute fourth (which I suspect may be one of the
original "justifications" of the 12-tET M3, cf relation to the G, or
this may be one source of its acceptance as a legitimate interval,
but anyway).

-Cameron Bobro

Dear Mike,

I may be more bold than most here to say this:
I think you are fundamentally misunderstanding the driving force
behind jazz. Your approach is in some ways analogous to trying to
explain the trance that some dancers go through in certain
music-cultures while not even for a moment questioning the dancer's
claim that the spirit of one of their ancestors has entered their body.
That claim by the dancer may indicate to us something about the state
of consciousness - that they do not feel cognitively conscious and in
control perhaps. But there is no reason to assume that they in fact
know that their claim is true, despite how ardently they may claim it.

A whole culture and history of jazz that is based on piano theory and
claims that they are stacking thirds and fifths is not at all proof
that they are really doing that or experiencing it that way. It may
indicate SOMETHING about the music, but we can't accept the folk claim
as absolutely unquestionably true.

How absolutely important is it in jazz, for instance, for the 13 of a
13 chord to be a third away from an 11? NOT AT ALL, because 11s are
often absent from 13 chords! What about for it to be a perfect fifth
of a 9? Not in that case either, because it could be all sorts of
arrangements, including having no 9 in the chord at all. It is
ridiculous in my view that jazz theory talks about that note as being
a 13. It seems by all accounts that I know of to simply be another
example of the human desire to fit everything into explanations of
simple patterns. I think it is a pure misunderstanding.

I can, on my Tonal Plexus, play very close to exact versions of any of
the options you're mentioning, and the only ones that sound
harmonically reasonable are the harmonic ones. In that case, the 13's
are generally actually tuned like 6ths, and they are actually 5/3
ratios from the root. And the #15, as you call it, is the same note
as a b9, which is a 17th harmonic, which is 17/8 or 17/4 (octave...
whatever) of the root.

Look, jazz players do all sorts of things that don't seem to actually
be stacked thirds or fifths. Really. And yet they *name* every
possible combination AS THOUGH it were stacked thirds and fifths. The
ability to pretend that it relates to that sort of lattice doesn't
make it true in terms of how the music is experienced psychologically
or why any particular note is chosen.

I think jazz harmony is based primarily on voice-leading. Chords that
sound like a crazy mess to a non-jazz listener out of context are to a
jazz listener a reminder of a context in which they hear it before,
and they don't hear a steady harmony, they hear a bunch of notes that
they can imagine various parts of the chord leading around to other
parts until we finally return to simpler harmony.

And jazz vocalists often sing 7th harmonics if they aren't being
forced to math a tempered m7 from an instrument. And there does exist
a history of jazz artists who have worked at getting away from
temperament as well. The bias toward a lattice of fifths and thirds
is not a jazz concept, but something inherent to 12ET that infects any
music played on a standard 12ET piano, whether intended or not.

I will go so far as to say that I accuse you of imposing your
intellectual ideas on the music - that you want the thirds to be
thirds (as opposed to 17/14 intervals and such) because of your
intellectual ideas and not because you would otherwise musically care.
I think that if you want to be consistent with the tuning of
traditional jazz piano, then the answer is simple: play 12ET piano.
The fact that the (erroneous in my view) folk-jazz-theory of chord
names causes problems with any other tuning shows simply enough that
the theory is missing things.

Look at it cognitively: the drive in jazz is a mix between some
relatively stable harmonies, voice-leading, dissonance and consonance,
and just any agreement in melody/improvised parts with background.
The only one of these things that requires precise tuning is the
stable resolve harmonies, which are generally nothing beyond a 9th.
Those harmonies are best tuned near-harmonic. The rest of the
harmonies are really voice-leading issues, and *in context*, which is
what really matters, it is not very important what the precise tuning
is. The fundamental sound is a clustered, unresolved sound that leads
from one place to the next.

At any rate, if you DON'T want the traditional clustered tension of
those chords, the far and away best tuning to make a resolved, stable
chord is a near-harmonic one in which you should aim for matching
harmonics and drop your intellectual hang up about whether they are
normal fifths and thirds.

I sincerely hope no disrespect is taken with my bold assertions here.
Disagreement and disrespect are not the same thing. I have been
accused in the past of similar intellectual dogmatism and in some
cases come to realize the accusation was true. And I simply
reassessed my thinking and don't disrespect myself for going through
that process. I'm grateful to those who made me re-focus and better
understand what is really going on.

Best,
Aaron Wolf

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> I'm talking about a slightly different notion of consistency, I think.
>
> It is true that 72 is 17-limit consistent, but most of western harmony
> doesn't work like that. Western 5-limit harmony mainly consists of
stacked
> major and minor thirds, which is so obvious I'm sure that you would
all find
> it slightly insulting to even mention :P. The problem is that when
you stack
> enough fifths or major thirds on top of each other, the harmony
breaks down
> in 72-tet, like in the case of the #15 chord, where the C# is off.
Being as
> jazz especially consists of a lot of quartal voicings, and 72-tet is a
> relatively poor match for a bunch of stacked fifths, it is slightly less
> useful. 5 stacked fifths will "break" the consistency of the harmony, as
> will 3 thirds. Even in non-meantone music, I still find this to be
an issue.
>
> So if we view chords like these as musical excursions into the JI
lattice,
> then you realize that going far enough in any one direction on the
lattice
> will cause rounding errors in -any- equal temperament, and 72-tet's
> tolerance threshold for that is pretty low, especially compared to
53-tet.
> This might not bother many people, as a #15 chord is kind of a new sound
> even in jazz, but in some later classical works, extremely extended
chords
> like that are heard quite a bit (take Amaj/C, for instance). Of
course, the
> option always remains to manually adjust for the inconsistencies,
but I find
> it makes it extremely difficult to figure out which note to hit if
you're
> far out in 5-limit JI space when there are rounding errors and the step
> sizes are so small. The option also exists to just ignore the
> inconsistencies, but I find that it sounds much better to adjust for
them. I
> find the whole process to be slightly irritating, although if you
don't care
> so much about chords like that, then I think 72-tet is incredibly
useful.
>
> For reference, the #15 chord I'm talking about is
32:40:48:60:72:90:108:135,
> or 1/1:5/4:3/2:15/8:9/4:45/16:27/8:135/32. It's just a set of
stacked major
> and minor thirds from C to C# -- C E G B D F# A C#, or in 72-tet
notation
> (is it called Sims-maneri notation?) C E- G B- D F#- A C#-, except
at the
> end the C#- jumps up to C#.
>
> Again, just my opinion on it. As I am particularly enamored with
that style
> of composition, I find 72-tet to have some serious shortcomings.
Especially
> when it's touted as being "easy" for musicians to adjust to because
it has
> 12-tet as a subset -- it becomes much less easy for musicians to
adjust to
> when they have to jump up or down a step to deal with
inconsistencies like
> this.
>
> Just my two cents.
>
> -Mike
>
> On Sun, May 25, 2008 at 6:20 PM, Carl Lumma <carl@...> wrote:
>
> > Hi Mike,
> >
> > > Furthermore, that has always been my criticism of 72-tet as
> > > well -- I thought it was the greatest thing in the world until
> > > I realized that the saturated #15 chord (C E- G B- D F#- A C#-)
> > > is inconsistent in 72-tet -- rounding errors will cause the
> > > best approximation for the C#- to jump up one step to C#.
> >
> > 72 is 17-limit consistent, so I'm not sure what you're running
> > into. What JI tuning are you trying to hit here? Or maybe
> > you're running into a chord that can't be tuned in JI (which
> > are sometimes called "magic chords").
> >
> > -Carl
> >
> >
> >
>

Dear Aaron,
I do not claim that stacked fifths and thirds represent ALL of harmony
in jazz or any genre at all. But piano players often stack fifths or
thirds on top of each other in "boring old vanilla 5-limit fashion" as
-ONE- particular feeling or harmonic style, and that approach will
break down in 72-tet after you get far enough. I gave you one example
of 72-tet that doesn't hold that is common in jazz, but I'm not saying
it is representative of the genre's entire harmonic sense.

While it is true that jazz incorporates 7-limit and often 11-limit
harmonies, and that these harmonies are often expressed on instruments
other than the piano or even the piano itself, the point is that jazz
as a force often strives to explore -everything-. 72-tet disables the
use of stacking fifths and thirds unless one is willing to manually
adjust for rounding errors. Where is the "misinterpretation of jazz"
in that?

Furthermore, I myself as a jazz pianist screw around with chord
extensions like #15's. The #15 is not where I'd expect it to be in
72-tet, and so it's irritating. If I were in C minor, for example, and
I wanted to play an Ebsus7 chord to imply Phrygian, voiced as Eb+ Ab+
Db+ F (let's say for the sake of argument I have comma-adjusted
everything correctly) -- would any of the notes have to be further
adjusted by a step due to stupid "rounding errors?" Nobody who's
playing fast-paced, spontaneous, improvised music is going to want to
have to think about that.

The point is while jazz itself has obviously extended past the 7 and
11 limits, it still obviously lives in the 5-limit world as well, and
some of the things that jazz pianists like myself enjoy playing are
weird in 72-tet due to these stupid rounding errors. As a jazz pianist
interested in microtonality, I'm looking to find a system that people
would find easy to play and conceptualize so that I can try to
popularize it amongst my friends and create some spontaneous
improvised music out of it, because I haven't really heard jazz mix
with microtonality in that way before, especially from the perspective
of a keyboardist. 72tet I thought was the most amazing invention in
the world until I realized that these "rounding errors" actually exist
and make it considerably more difficult to figure out what step you
want to actually play to get at the note that you want.

If jazz musicians aren't thinking in terms of notes (C to Eb to Gb to
A) they're thinking in terms of intervals (I want to play a pattern
that goes up repeating in minor thirds). They are most likely not
thinking "behind the scenes" of JI ratios and their nearest
approximation and how to round everything up correctly.

Again, my two cents. Don't think I'm being disrespectful either. I am
willing to accept that maybe 72-tet is really all that it's cracked up
to be, but these rounding errors are the dealbreaker for me right now.

> How absolutely important is it in jazz, for instance, for the 13 of a
> 13 chord to be a third away from an 11? NOT AT ALL, because 11s are
> often absent from 13 chords! What about for it to be a perfect fifth
> of a 9? Not in that case either, because it could be all sorts of
> arrangements, including having no 9 in the chord at all. It is
> ridiculous in my view that jazz theory talks about that note as being
> a 13. It seems by all accounts that I know of to simply be another
> example of the human desire to fit everything into explanations of
> simple patterns. I think it is a pure misunderstanding.
The thing you're missing here is that I'm not insinuating that the 13
has to be stacked fifths. I'm saying that stacked fifths sound good,
whether or not they're used as a "13th" or not, and I -CAN'T- do
enough of those in 72-tet and have it sound consistent. Stacking
fifths is something that I think just sounds cool, and I want to be
able to explore that in jazz just like I want to explore higher limit
harmonies (which is why I'm currently on this forum :P) In 72-tet, I
have to manually adjust these things due to mathematics and things I
don't want to have to think about when I'm playing jazz!

> I can, on my Tonal Plexus, play very close to exact versions of any of
> the options you're mentioning, and the only ones that sound
> harmonically reasonable are the harmonic ones. In that case, the 13's
> are generally actually tuned like 6ths, and they are actually 5/3
> ratios from the root. And the #15, as you call it, is the same note
> as a b9, which is a 17th harmonic, which is 17/8 or 17/4 (octave...
> whatever) of the root.
In boring ol' classical jazz theory, which you seem to hate (:P) the
13th and the 6th are given separate names because they often have
separate functions. In Dorian mode (we'll say in D), for example, it
often sounds really cool to play the B as if it were an approximation
to 27/16. It creates a tension that I much like. Furthermore, I
believe that any note in 12tet can be used to approximate any note
near to it, and that the brain will "guess" at the right note due to
context, so that it is possible in D Dorian for the B to be used
either as 27/16 or as 5/3. I've been exploring going a fifth up from
that B too, as an extra tension (that's an F# over D Dorian, which in
standard jazz theory "breaks down"). Unfortunately, going a fifth up
from that B leads me to a note that in 72tet isn't where I'd expect it
to be -- the nearest note to what I want to hear would be one more
step north due to accumulated errors in rounding.

> I will go so far as to say that I accuse you of imposing your
> intellectual ideas on the music - that you want the thirds to be
> thirds (as opposed to 17/14 intervals and such) because of your
> intellectual ideas and not because you would otherwise musically care.
False. See above about Dorian mode.

> I think that if you want to be consistent with the tuning of
> traditional jazz piano, then the answer is simple: play 12ET piano.
> The fact that the (erroneous in my view) folk-jazz-theory of chord
> names causes problems with any other tuning shows simply enough that
> the theory is missing things.
In my experience, it usually signifies that that jazz theory stems
from 12-tet, which is a meantone system. So just like a dominant 7
could be a few different things, b9's could be 17th harmonics and such
as well. I certainly get that. The theory is definitely missing
things. I have imposed a structure of thirds and fifths as -ONE-
possible musical "color," and I can't get that in 72tet without
considerable conceptual difficulty at times. There are other colors in
72tet that I can get very easily that are inaccessible in 12tet.

> Look at it cognitively: the drive in jazz is a mix between some
> relatively stable harmonies, voice-leading, dissonance and consonance,
> and just any agreement in melody/improvised parts with background.
> The only one of these things that requires precise tuning is the
> stable resolve harmonies, which are generally nothing beyond a 9th.
> Those harmonies are best tuned near-harmonic. The rest of the
> harmonies are really voice-leading issues, and *in context*, which is
> what really matters, it is not very important what the precise tuning
> is. The fundamental sound is a clustered, unresolved sound that leads
> from one place to the next.
>
This is I counter accust you of imposing YOUR intellectual ideas on
jazz. :P Stable resolve harmonics often go beyond a 9th (a #11 or 13
for example are used this way). In fact, even if previous jazz
musicians hadn't really gone past the 9th or the #11 doesn't mean that
you COULDN'T do that. So screw what has already been done in jazz --
the whole point of this forum is to find things that have not.

However, if I want to experiment with ending a song in a maj7#11 chord
-- which jazz musicians do ALL THE TIME -- and I want to experiment
with adding yet another fifth on top of that to get what I call a #15,
just because that is for some reason the sound I want -- then the note
I would reach is rounded incorrectly in 72tet. Note that the #11 I
would reach here is different from 11/8 or 11/4.

> At any rate, if you DON'T want the traditional clustered tension of
> those chords, the far and away best tuning to make a resolved, stable
> chord is a near-harmonic one in which you should aim for matching
> harmonics and drop your intellectual hang up about whether they are
> normal fifths and thirds.
Sometimes. Again, the common practice of ending a song on a lydian
chord contradicts this and often sounds really good.

> I sincerely hope no disrespect is taken with my bold assertions here.
> Disagreement and disrespect are not the same thing. I have been
> accused in the past of similar intellectual dogmatism and in some
> cases come to realize the accusation was true. And I simply
> reassessed my thinking and don't disrespect myself for going through
> that process. I'm grateful to those who made me re-focus and better
> understand what is really going on.
No, I value feedback like this. I'm trying to create and eventually
popularize in some grassroots way an easy-to-understand microtonal
system. 72tet I thought was absolutely phenomenal as it just requires
different inflections of 12tet notes until I realized that I couldn't
play my beloved minor #17 or major #15 chord consistently :( And so
there went that. So I'm still looking.

-Mike

--- In tuning@yahoogroups.com, "battaglia01" <battaglia01@...> wrote:
>
> Dear Aaron,
> I do not claim that stacked fifths and thirds represent ALL of harmony
> in jazz or any genre at all. But piano players often stack fifths or
> thirds on top of each other in "boring old vanilla 5-limit fashion" as
> -ONE- particular feeling or harmonic style, and that approach will
> break down in 72-tet after you get far enough. I gave you one example
> of 72-tet that doesn't hold that is common in jazz, but I'm not saying
> it is representative of the genre's entire harmonic sense.
>
> While it is true that jazz incorporates 7-limit and often 11-limit
> harmonies, and that these harmonies are often expressed on instruments
> other than the piano or even the piano itself, the point is that jazz
> as a force often strives to explore -everything-. 72-tet disables the
> use of stacking fifths and thirds unless one is willing to manually
> adjust for rounding errors. Where is the "misinterpretation of jazz"
> in that?
>

That's fair enough - except that there is a point that stacking of
fifths breaks down ACOUSTICALLY (depending on timbre used) regardless
of tuning. And anyway, in that regard, you would really like the
Tonal Plexus and its 205ET, which does not temper out the Pythagorean
comma and which has better fifths than 72ET.

> Furthermore, I myself as a jazz pianist screw around with chord
> extensions like #15's. The #15 is not where I'd expect it to be in
> 72-tet, and so it's irritating.

EXACTLY! It's based on expectations! If you change your
expectations, then you won't be irritated. You're irritated clearly
because you have unrealistic expectations within that system. Anyway,
once again - try the Tonal Plexus and 205ET - it works in these
regards. Download the software from
http://www.h-pi.com/downloads.html to try out a virtual version. And
since it can be retuned to anything, you could adjust it to fit
whatever expectations you want to have.

> If I were in C minor, for example, and
> I wanted to play an Ebsus7 chord to imply Phrygian, voiced as Eb+ Ab+
> Db+ F (let's say for the sake of argument I have comma-adjusted
> everything correctly) -- would any of the notes have to be further
> adjusted by a step due to stupid "rounding errors?" Nobody who's
> playing fast-paced, spontaneous, improvised music is going to want to
> have to think about that.
>

RIGHT- and nobody playing fast-paced music notices commas either,
unless they are in particularly prominent parts of the music.

> The point is while jazz itself has obviously extended past the 7 and
> 11 limits, it still obviously lives in the 5-limit world as well, and
> some of the things that jazz pianists like myself enjoy playing are
> weird in 72-tet due to these stupid rounding errors. As a jazz pianist
> interested in microtonality, I'm looking to find a system that people
> would find easy to play and conceptualize so that I can try to
> popularize it amongst my friends and create some spontaneous
> improvised music out of it, because I haven't really heard jazz mix
> with microtonality in that way before, especially from the perspective
> of a keyboardist. 72tet I thought was the most amazing invention in
> the world until I realized that these "rounding errors" actually exist
> and make it considerably more difficult to figure out what step you
> want to actually play to get at the note that you want.
>
> If jazz musicians aren't thinking in terms of notes (C to Eb to Gb to
> A) they're thinking in terms of intervals (I want to play a pattern
> that goes up repeating in minor thirds). They are most likely not
> thinking "behind the scenes" of JI ratios and their nearest
> approximation and how to round everything up correctly.
>
> Again, my two cents. Don't think I'm being disrespectful either. I am
> willing to accept that maybe 72-tet is really all that it's cracked up
> to be, but these rounding errors are the dealbreaker for me right now.
>

Once again - 205ET does not have the issues you're talking about here.
So that answers your original question. Now that I understand the
question I think that's the answer: that 205ET doesn't have the same
rounding errors as 72 for these instances. But again, try the
software yourself to test it out.

> > How absolutely important is it in jazz, for instance, for the 13 of a
> > 13 chord to be a third away from an 11? NOT AT ALL, because 11s are
> > often absent from 13 chords! What about for it to be a perfect fifth
> > of a 9? Not in that case either, because it could be all sorts of
> > arrangements, including having no 9 in the chord at all. It is
> > ridiculous in my view that jazz theory talks about that note as being
> > a 13. It seems by all accounts that I know of to simply be another
> > example of the human desire to fit everything into explanations of
> > simple patterns. I think it is a pure misunderstanding.
> The thing you're missing here is that I'm not insinuating that the 13
> has to be stacked fifths. I'm saying that stacked fifths sound good,
> whether or not they're used as a "13th" or not, and I -CAN'T- do
> enough of those in 72-tet and have it sound consistent. Stacking
> fifths is something that I think just sounds cool, and I want to be
> able to explore that in jazz just like I want to explore higher limit
> harmonies (which is why I'm currently on this forum :P) In 72-tet, I
> have to manually adjust these things due to mathematics and things I
> don't want to have to think about when I'm playing jazz!
>
>
> > I can, on my Tonal Plexus, play very close to exact versions of any of
> > the options you're mentioning, and the only ones that sound
> > harmonically reasonable are the harmonic ones. In that case, the 13's
> > are generally actually tuned like 6ths, and they are actually 5/3
> > ratios from the root. And the #15, as you call it, is the same note
> > as a b9, which is a 17th harmonic, which is 17/8 or 17/4 (octave...
> > whatever) of the root.
> In boring ol' classical jazz theory, which you seem to hate (:P) the
> 13th and the 6th are given separate names because they often have
> separate functions. In Dorian mode (we'll say in D), for example, it
> often sounds really cool to play the B as if it were an approximation
> to 27/16.

Sure, that's reasonable, but I think the "as if it were" part is in
your mind (which does not make it less significant since the whole
point of music is how we experience it). And because of that, you
can't easily make it be the case in a random listener's mind.

> It creates a tension that I much like. Furthermore, I
> believe that any note in 12tet can be used to approximate any note
> near to it, and that the brain will "guess" at the right note due to
> context, so that it is possible in D Dorian for the B to be used
> either as 27/16 or as 5/3. I've been exploring going a fifth up from
> that B too, as an extra tension (that's an F# over D Dorian, which in
> standard jazz theory "breaks down"). Unfortunately, going a fifth up
> from that B leads me to a note that in 72tet isn't where I'd expect it
> to be -- the nearest note to what I want to hear would be one more
> step north due to accumulated errors in rounding.
>

Once the brain is "guessing" then there's interpretation and the
simple fact is that listeners may interpret in different ways. And
training has a noticeable impact, as well as other cultural things.
Now that I've done enough barbershop singing, I hear a lot more chords
as if they related to pure harmonies...

> > I will go so far as to say that I accuse you of imposing your
> > intellectual ideas on the music - that you want the thirds to be
> > thirds (as opposed to 17/14 intervals and such) because of your
> > intellectual ideas and not because you would otherwise musically care.
> False. See above about Dorian mode.
>

Ok, glad you've clarified. Hope you're not offended at my initial charge.

> > I think that if you want to be consistent with the tuning of
> > traditional jazz piano, then the answer is simple: play 12ET piano.
> > The fact that the (erroneous in my view) folk-jazz-theory of chord
> > names causes problems with any other tuning shows simply enough that
> > the theory is missing things.
> In my experience, it usually signifies that that jazz theory stems
> from 12-tet, which is a meantone system. So just like a dominant 7
> could be a few different things, b9's could be 17th harmonics and such
> as well. I certainly get that. The theory is definitely missing
> things. I have imposed a structure of thirds and fifths as -ONE-
> possible musical "color," and I can't get that in 72tet without
> considerable conceptual difficulty at times. There are other colors in
> 72tet that I can get very easily that are inaccessible in 12tet.
>
> > Look at it cognitively: the drive in jazz is a mix between some
> > relatively stable harmonies, voice-leading, dissonance and consonance,
> > and just any agreement in melody/improvised parts with background.
> > The only one of these things that requires precise tuning is the
> > stable resolve harmonies, which are generally nothing beyond a 9th.
> > Those harmonies are best tuned near-harmonic. The rest of the
> > harmonies are really voice-leading issues, and *in context*, which is
> > what really matters, it is not very important what the precise tuning
> > is. The fundamental sound is a clustered, unresolved sound that leads
> > from one place to the next.
> >
> This is I counter accust you of imposing YOUR intellectual ideas on
> jazz. :P Stable resolve harmonics often go beyond a 9th (a #11 or 13
> for example are used this way). In fact, even if previous jazz
> musicians hadn't really gone past the 9th or the #11 doesn't mean that
> you COULDN'T do that. So screw what has already been done in jazz --
> the whole point of this forum is to find things that have not.
>
> However, if I want to experiment with ending a song in a maj7#11 chord
> -- which jazz musicians do ALL THE TIME -- and I want to experiment
> with adding yet another fifth on top of that to get what I call a #15,
> just because that is for some reason the sound I want -- then the note
> I would reach is rounded incorrectly in 72tet. Note that the #11 I
> would reach here is different from 11/8 or 11/4.
>

Ok, 72 is not a be-all end-all. I've never been a steadfast dogmatic
proponent of it at all.
At any rate, MY experience, and I strongly suspect based on all the
evidence I am currently aware of, is that ending a song on a maj7#11
is a neat way to end WITHOUT full resolve (at least until the silence
after the song). Tons of music chooses not to fully resolve tension,
and because listeners may have an idea of the resolve in their mind,
that is enough and there is a totally expressive value to an
incomplete resolution even at an end. I myself never experience such
chords as a total and utter resolve despite trying very hard to drop
any expectations otherwise. The complexity of the sound and the beats
and buzzes simply are not fully relaxed and resolved, and that's fine.
I really suspect that you and everyone else would acknowledge the
same thing if you do your best to objectively compare the impact of
such an ending compared to a simpler harmony with total resolve.

On the other hand, I could imagine someone being so keenly aware of
each and every note in a chord such that they expect a complete set of
notes at the end, kind of like a polytonal experience. And in that
regard, you will feel the most resolve with the whole crazy chord, but
NOT because of its chordal function, but because of the MELODIC
function of each independent note... But experiencing that would
require a lot of complex setting up of context and would be
excessively challenging to objectively test.

> > At any rate, if you DON'T want the traditional clustered tension of
> > those chords, the far and away best tuning to make a resolved, stable
> > chord is a near-harmonic one in which you should aim for matching
> > harmonics and drop your intellectual hang up about whether they are
> > normal fifths and thirds.
> Sometimes. Again, the common practice of ending a song on a lydian
> chord contradicts this and often sounds really good.
>
>
> > I sincerely hope no disrespect is taken with my bold assertions here.
> > Disagreement and disrespect are not the same thing. I have been
> > accused in the past of similar intellectual dogmatism and in some
> > cases come to realize the accusation was true. And I simply
> > reassessed my thinking and don't disrespect myself for going through
> > that process. I'm grateful to those who made me re-focus and better
> > understand what is really going on.
> No, I value feedback like this. I'm trying to create and eventually
> popularize in some grassroots way an easy-to-understand microtonal
> system. 72tet I thought was absolutely phenomenal as it just requires
> different inflections of 12tet notes until I realized that I couldn't
> play my beloved minor #17 or major #15 chord consistently :( And so
> there went that. So I'm still looking.
>
> -Mike
>

Please seriously consider the Tonal Plexus. I'm thrilled with mine,
and I'm hoping to have more discussion and feedback with a community
of users and I think it'd be a great fit for you.

Best,
Aaron W

Hiya Mike,

> I just realized as well, maybe people don't know what chord I'
> talking about -- I'm just referring to 5-limit music here. By
> alternately stacking major and minor thirds on top of each
> other, one will hit the following scale degrees:
>
> 1 3 5 maj7 9 #11 13 #15
> C E G B D F# A C# (12-tet notation)
> C E- G B- D F#- A C#- (72-tet notation - what it should be)
>
> Classical jazz theory doesn't usually mention 3rd octave chord
> extensions, but as someone who is currently studying jazz
> piano, that chord is talked about often. I hear it in classical
> music as well -- maybe not voiced that way, but at least I hear
> that #15 note is used fairly often. Also, the C# that is a #15
> here will differ from the normal C# that is a chromatic semitone
> by a syntonic comma (the #15 is lower). You would expect this
> C# to be accessed in relation to C in 72-tet as a C#-, one step
> down from the standard 12-tet C#, but due to accumulated
> rounding errors, it actually ends up one 72-tet step higher
> from where it would be. [snip]

To my mind, the only problem would be if the consonances in
this chord couldn't all take their best 72-ET tunings at once.
The consonances are, I presume, 3:2, 5:4, and 6:5. The best
tunings of these in 72-ET are 42, 23, and 19 steps.

First let's examine the chord in 12-ET:
[This is best viewed in a constant-width font - see "message
options" to the right of this message on Yahoo's web site.]
C E G B D F# A C# note name
0 4 7 11 14 18 21 25 steps

The consonances in 12-ET are 7, 4, and 3 steps. So let's
check the 3rds...

C-E should be 4 and is 4
E-G should be 3 and is 3
G-B should be 4 and is 4
B-D should be 3 and is 3
D-F# should be 4 and is 4
F#-A should be 3 and is 3
A-C# should be 4 and is 4

A-OK. Now the 5ths...

C-G should be 7 and is 7
E-B should be 7 and is 7
G-D should be 7 and is 7
B-F# should be 7 and is 7
D-A should be 7 and is 7
F#-C# should be 7 and is 7

Alright. Now let's tune the thirds in 72-ET so they'll be
right...

C E G B D F# A C# note name
M m M m M m M 3rd quality
0 23 42 65 84 107 126 149

...and then check the 5ths...

C-G should be 42 and is 42 *OK*
E-B should be 42 and is 42 *OK*
G-D should be 42 and is 42 *OK*
B-F# should be 42 and is 42 *OK*
D-A should be 42 and is 42 *OK*
F#-C# should be 42 and is 42 *OK*

So I don't see a problem. The chord should work just like
it does in 12-ET, but with the advantage of the better
tunings of 72. If you tune it the way I did (sorry I don't
know Simms notation) does it sound good? Better or worse
than in 12-ET in your opinion?

Can you show us what you find confusing? Are you thinking
in terms of approximating the 135 directly? 135 isn't
itself a consonance, so I wouldn't worry about that.

-Carl

I am seriously considering it. I'm looking for a keyboard to branch
out into this stuff. I may have slightly different goals from a lot of
people here -- I'm looking for a system that is easy to THINK about so
that I can spread it amongst people that haven't done years of
independent research like most of us on the forum have done. 12tet is
a miracle just because of that reason -- it's easy to conceptualize,
and you can get a -HUGE- array of sounds with it. Of course, we all
want to see what more is possible beyond 12tet and 5-limit music (and
the "tip-of-the-iceberg" 7-limit stuff that has evolved), and so I
think that the search for a temperament that is as easy to think about
as 12tet (or only requires a little more work) but enables access to
xenharmonic sounds is a worthy pursuit.

Of course, for me, I can always come up with some rule to adjust for
rounding errors in 72tet, but I think that the average person who has
no idea what a harmonic series is might find it a bit hard to grasp
and so that system might pose a problem. I will look into the Tonal
Plexus though, as it certainly seems to be a useful tool.

> That's fair enough - except that there is a point that stacking of
> fifths breaks down ACOUSTICALLY (depending on timbre used) regardless
> of tuning. And anyway, in that regard, you would really like the
> Tonal Plexus and its 205ET, which does not temper out the Pythagorean
> comma and which has better fifths than 72ET.

I contest this. There is too much of an emphasis on different
intervals as consonant or dissonant based on how they relate to the
ROOT. You can also "stack" consonances on top of each other so that
adjacent notes, while "far out" in JI space from the root, are related
closely to other notes which eventually relate back to the root. This
builds a complicated structure that often sounds really good. This is
why a major 7th chord doesn't sound awful, for instance -- the C-B,
while being a dissonance in its own right, "fits" into the puzzle of
C-E-G-B as the B is related to the G which is related to the C and the
B is also related to the E which is... well you get the point. So even
though you might call that B a dissonance, your brain actually maps
out a set of "consonances" which are all related. To get at this #15,
I'm just continuing the pattern that leads to a major chord, then a
major7 chord, then a major9 chord, then a maj9#11 chord, etc.

> EXACTLY! It's based on expectations! If you change your
> expectations, then you won't be irritated. You're irritated clearly
> because you have unrealistic expectations within that system. Anyway,
> once again - try the Tonal Plexus and 205ET - it works in these
> regards. Download the software from
> http://www.h-pi.com/downloads.html to try out a virtual version. And
> since it can be retuned to anything, you could adjust it to fit
> whatever expectations you want to have.
Yup. I'll have to check it out. Note that my expectations are purely
for 72-tet as a structure, not psychologically or acoustically.

> > If I were in C minor, for example, and
> > I wanted to play an Ebsus7 chord to imply Phrygian, voiced as Eb+ Ab+
> > Db+ F (let's say for the sake of argument I have comma-adjusted
> > everything correctly) -- would any of the notes have to be further
> > adjusted by a step due to stupid "rounding errors?" Nobody who's
> > playing fast-paced, spontaneous, improvised music is going to want to
> > have to think about that.
> >
>
> RIGHT- and nobody playing fast-paced music notices commas either,
> unless they are in particularly prominent parts of the music.
So if the music is slow, then they will notice. Having to "guess"
roughly at where the intervals lie defeats the purpose of having any
kind of tuning "system" to begin with in my mind. Although I suppose
this could be a matter of preference.

> Sure, that's reasonable, but I think the "as if it were" part is in
> your mind (which does not make it less significant since the whole
> point of music is how we experience it). And because of that, you
> can't easily make it be the case in a random listener's mind.

Oh yes you can. If I play the chord C E F# B D#, that D# will be heard
by most people as a major third above the B, because of that F# B D#
upper structure. It will not be heard as a 6/5 Eb above the C. Music
is mainly how to get people to hear things in the way that you want.

> At any rate, MY experience, and I strongly suspect based on all the
> evidence I am currently aware of, is that ending a song on a maj7#11
> is a neat way to end WITHOUT full resolve (at least until the silence
> after the song). Tons of music chooses not to fully resolve tension,
> and because listeners may have an idea of the resolve in their mind,
> that is enough and there is a totally expressive value to an
> incomplete resolution even at an end. I myself never experience such
> chords as a total and utter resolve despite trying very hard to drop
> any expectations otherwise. The complexity of the sound and the beats
> and buzzes simply are not fully relaxed and resolved, and that's fine.
> I really suspect that you and everyone else would acknowledge the
> same thing if you do your best to objectively compare the impact of
> such an ending compared to a simpler harmony with total resolve.

Or you could hear it as a network of fifths and thirds, which is what
a maj7#11 is. Other chords, like the #9 or b9, might be upper-limit
harmonics that work in 12tet. But that maj7#11 is a network of fifths
and thirds.

Simply put, I contest that the consonance of any note in a chord is
determined by its rational-number relation to the root. It can also be
determined by its rational-number relation to any other note in the
chord.

Just some thoughts.
-Mike

> I can, on my Tonal Plexus, play very close to exact versions of any of
> the options you're mentioning, and the only ones that sound
> harmonically reasonable are the harmonic ones. In that case, the 13's
> are generally actually tuned like 6ths, and they are actually 5/3
> ratios from the root. And the #15, as you call it, is the same note
> as a b9, which is a 17th harmonic, which is 17/8 or 17/4 (octave...
> whatever) of the root.

One more thing to mention, this time from your first post:

The #15 is NOT the same thing as a b9. On a 12-tet piano, it is the
same thing. In 72-tet, it is not the same thing. In 53-tet, it is not
the same thing. C# and Db are not necessarily the same thing.

I use the concept of a #15 to mean a note that is close to the 17th
harmonic, but it is not. It is a major third and 3 fifths up from the
root.
The 17th harmonic has a different use and purpose entirely, although
the notes may be very close.

while what they call it is wrong, i do think the 'mistaken' idea did in fact lead to people plying up thirds , i guess caused it worked.
which lead to chords in fourths, then fifths and seconds even.
Even Partch spaced his hexad in thirds, as a left over of this type of thinking

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Aaron Wolf wrote:
>
> Dear Mike,
>
> I may be more bold than most here to say this:
> I think you are fundamentally misunderstanding the driving force
> behind jazz. Your approach is in some ways analogous to trying to
> explain the trance that some dancers go through in certain
> music-cultures while not even for a moment questioning the dancer's
> claim that the spirit of one of their ancestors has entered their body.
> That claim by the dancer may indicate to us something about the state
> of consciousness - that they do not feel cognitively conscious and in
> control perhaps. But there is no reason to assume that they in fact
> know that their claim is true, despite how ardently they may claim it.
>
> A whole culture and history of jazz that is based on piano theory and
> claims that they are stacking thirds and fifths is not at all proof
> that they are really doing that or experiencing it that way. It may
> indicate SOMETHING about the music, but we can't accept the folk claim
> as absolutely unquestionably true.
>
> How absolutely important is it in jazz, for instance, for the 13 of a
> 13 chord to be a third away from an 11? NOT AT ALL, because 11s are
> often absent from 13 chords! What about for it to be a perfect fifth
> of a 9? Not in that case either, because it could be all sorts of
> arrangements, including having no 9 in the chord at all. It is
> ridiculous in my view that jazz theory talks about that note as being
> a 13. It seems by all accounts that I know of to simply be another
> example of the human desire to fit everything into explanations of
> simple patterns. I think it is a pure misunderstanding.
>
> I can, on my Tonal Plexus, play very close to exact versions of any of
> the options you're mentioning, and the only ones that sound
> harmonically reasonable are the harmonic ones. In that case, the 13's
> are generally actually tuned like 6ths, and they are actually 5/3
> ratios from the root. And the #15, as you call it, is the same note
> as a b9, which is a 17th harmonic, which is 17/8 or 17/4 (octave...
> whatever) of the root.
>
> Look, jazz players do all sorts of things that don't seem to actually
> be stacked thirds or fifths. Really. And yet they *name* every
> possible combination AS THOUGH it were stacked thirds and fifths. The
> ability to pretend that it relates to that sort of lattice doesn't
> make it true in terms of how the music is experienced psychologically
> or why any particular note is chosen.
>
> I think jazz harmony is based primarily on voice-leading. Chords that
> sound like a crazy mess to a non-jazz listener out of context are to a
> jazz listener a reminder of a context in which they hear it before,
> and they don't hear a steady harmony, they hear a bunch of notes that
> they can imagine various parts of the chord leading around to other
> parts until we finally return to simpler harmony.
>
> And jazz vocalists often sing 7th harmonics if they aren't being
> forced to math a tempered m7 from an instrument. And there does exist
> a history of jazz artists who have worked at getting away from
> temperament as well. The bias toward a lattice of fifths and thirds
> is not a jazz concept, but something inherent to 12ET that infects any
> music played on a standard 12ET piano, whether intended or not.
>
> I will go so far as to say that I accuse you of imposing your
> intellectual ideas on the music - that you want the thirds to be
> thirds (as opposed to 17/14 intervals and such) because of your
> intellectual ideas and not because you would otherwise musically care.
> I think that if you want to be consistent with the tuning of
> traditional jazz piano, then the answer is simple: play 12ET piano.
> The fact that the (erroneous in my view) folk-jazz-theory of chord
> names causes problems with any other tuning shows simply enough that
> the theory is missing things.
>
> Look at it cognitively: the drive in jazz is a mix between some
> relatively stable harmonies, voice-leading, dissonance and consonance,
> and just any agreement in melody/improvised parts with background.
> The only one of these things that requires precise tuning is the
> stable resolve harmonies, which are generally nothing beyond a 9th.
> Those harmonies are best tuned near-harmonic. The rest of the
> harmonies are really voice-leading issues, and *in context*, which is
> what really matters, it is not very important what the precise tuning
> is. The fundamental sound is a clustered, unresolved sound that leads
> from one place to the next.
>
> At any rate, if you DON'T want the traditional clustered tension of
> those chords, the far and away best tuning to make a resolved, stable
> chord is a near-harmonic one in which you should aim for matching
> harmonics and drop your intellectual hang up about whether they are
> normal fifths and thirds.
>
> I sincerely hope no disrespect is taken with my bold assertions here.
> Disagreement and disrespect are not the same thing. I have been
> accused in the past of similar intellectual dogmatism and in some
> cases come to realize the accusation was true. And I simply
> reassessed my thinking and don't disrespect myself for going through
> that process. I'm grateful to those who made me re-focus and better
> understand what is really going on.
>
> Best,
> Aaron Wolf
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, "Mike > Battaglia" <battaglia01@...> wrote:
> >
> > I'm talking about a slightly different notion of consistency, I think.
> >
> > It is true that 72 is 17-limit consistent, but most of western harmony
> > doesn't work like that. Western 5-limit harmony mainly consists of
> stacked
> > major and minor thirds, which is so obvious I'm sure that you would
> all find
> > it slightly insulting to even mention :P. The problem is that when
> you stack
> > enough fifths or major thirds on top of each other, the harmony
> breaks down
> > in 72-tet, like in the case of the #15 chord, where the C# is off.
> Being as
> > jazz especially consists of a lot of quartal voicings, and 72-tet is a
> > relatively poor match for a bunch of stacked fifths, it is slightly less
> > useful. 5 stacked fifths will "break" the consistency of the harmony, as
> > will 3 thirds. Even in non-meantone music, I still find this to be
> an issue.
> >
> > So if we view chords like these as musical excursions into the JI
> lattice,
> > then you realize that going far enough in any one direction on the
> lattice
> > will cause rounding errors in -any- equal temperament, and 72-tet's
> > tolerance threshold for that is pretty low, especially compared to
> 53-tet.
> > This might not bother many people, as a #15 chord is kind of a new sound
> > even in jazz, but in some later classical works, extremely extended
> chords
> > like that are heard quite a bit (take Amaj/C, for instance). Of
> course, the
> > option always remains to manually adjust for the inconsistencies,
> but I find
> > it makes it extremely difficult to figure out which note to hit if
> you're
> > far out in 5-limit JI space when there are rounding errors and the step
> > sizes are so small. The option also exists to just ignore the
> > inconsistencies, but I find that it sounds much better to adjust for
> them. I
> > find the whole process to be slightly irritating, although if you
> don't care
> > so much about chords like that, then I think 72-tet is incredibly
> useful.
> >
> > For reference, the #15 chord I'm talking about is
> 32:40:48:60:72:90:108:135,
> > or 1/1:5/4:3/2:15/8:9/4:45/16:27/8:135/32. It's just a set of
> stacked major
> > and minor thirds from C to C# -- C E G B D F# A C#, or in 72-tet
> notation
> > (is it called Sims-maneri notation?) C E- G B- D F#- A C#-, except
> at the
> > end the C#- jumps up to C#.
> >
> > Again, just my opinion on it. As I am particularly enamored with
> that style
> > of composition, I find 72-tet to have some serious shortcomings.
> Especially
> > when it's touted as being "easy" for musicians to adjust to because
> it has
> > 12-tet as a subset -- it becomes much less easy for musicians to
> adjust to
> > when they have to jump up or down a step to deal with
> inconsistencies like
> > this.
> >
> > Just my two cents.
> >
> > -Mike
> >
> > On Sun, May 25, 2008 at 6:20 PM, Carl Lumma <carl@...> wrote:
> >
> > > Hi Mike,
> > >
> > > > Furthermore, that has always been my criticism of 72-tet as
> > > > well -- I thought it was the greatest thing in the world until
> > > > I realized that the saturated #15 chord (C E- G B- D F#- A C#-)
> > > > is inconsistent in 72-tet -- rounding errors will cause the
> > > > best approximation for the C#- to jump up one step to C#.
> > >
> > > 72 is 17-limit consistent, so I'm not sure what you're running
> > > into. What JI tuning are you trying to hit here? Or maybe
> > > you're running into a chord that can't be tuned in JI (which
> > > are sometimes called "magic chords").
> > >
> > > -Carl
> > >
> > >
> > >
> >
>
>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Hiya Mike,
>
> > I just realized as well, maybe people don't know what chord I'
> > talking about -- I'm just referring to 5-limit music here. By
> > alternately stacking major and minor thirds on top of each
> > other, one will hit the following scale degrees:
> >
> > 1 3 5 maj7 9 #11 13 #15
> > C E G B D F# A C# (12-tet notation)
> > C E- G B- D F#- A C#- (72-tet notation - what it should be)
> >
> > Classical jazz theory doesn't usually mention 3rd octave chord
> > extensions, but as someone who is currently studying jazz
> > piano, that chord is talked about often. I hear it in classical
> > music as well -- maybe not voiced that way, but at least I hear
> > that #15 note is used fairly often. Also, the C# that is a #15
> > here will differ from the normal C# that is a chromatic semitone
> > by a syntonic comma (the #15 is lower). You would expect this
> > C# to be accessed in relation to C in 72-tet as a C#-, one step
> > down from the standard 12-tet C#, but due to accumulated
> > rounding errors, it actually ends up one 72-tet step higher
> > from where it would be. [snip]
>
> To my mind, the only problem would be if the consonances in
> this chord couldn't all take their best 72-ET tunings at once.
> The consonances are, I presume, 3:2, 5:4, and 6:5. The best
> tunings of these in 72-ET are 42, 23, and 19 steps.
>
> First let's examine the chord in 12-ET:
> [This is best viewed in a constant-width font - see "message
> options" to the right of this message on Yahoo's web site.]
> C E G B D F# A C# note name
> 0 4 7 11 14 18 21 25 steps
>
> The consonances in 12-ET are 7, 4, and 3 steps. So let's
> check the 3rds...
>
> C-E should be 4 and is 4
> E-G should be 3 and is 3
> G-B should be 4 and is 4
> B-D should be 3 and is 3
> D-F# should be 4 and is 4
> F#-A should be 3 and is 3
> A-C# should be 4 and is 4
>
> A-OK. Now the 5ths...
>
> C-G should be 7 and is 7
> E-B should be 7 and is 7
> G-D should be 7 and is 7
> B-F# should be 7 and is 7
> D-A should be 7 and is 7
> F#-C# should be 7 and is 7
>
> Alright. Now let's tune the thirds in 72-ET so they'll be
> right...
>
> C E G B D F# A C# note name
> M m M m M m M 3rd quality
> 0 23 42 65 84 107 126 149
>
> ...and then check the 5ths...
>
> C-G should be 42 and is 42 *OK*
> E-B should be 42 and is 42 *OK*
> G-D should be 42 and is 42 *OK*
> B-F# should be 42 and is 42 *OK*
> D-A should be 42 and is 42 *OK*
> F#-C# should be 42 and is 42 *OK*
>
> So I don't see a problem. The chord should work just like
> it does in 12-ET, but with the advantage of the better
> tunings of 72. If you tune it the way I did (sorry I don't
> know Simms notation) does it sound good? Better or worse
> than in 12-ET in your opinion?
>
> Can you show us what you find confusing? Are you thinking
> in terms of approximating the 135 directly? 135 isn't
> itself a consonance, so I wouldn't worry about that.
>
> -Carl
>

Carl, this is where I claim that psychology trumps math. You are
clearly correct that there is no substantial issue here in terms of
mathematical consonance. However, the significance is that by Mike's
way of thinking about what it should be, he *expected* something
different from what he ended up at. He had a feeling of cognitive
dissonance - that what he was experiencing was not as he expected. I
fully believe it is possible he could change his expectations and
eliminate any issue. However, perhaps the exact experience he desires
is one in which a particular interval or absolute pitch that he
expects in his mind is realized a certain way that 72ET cannot do. In
that case, 72ET fails for his particularly quirky way of creating his
expectations of pitch. There's nothing wrong with him being that way,
but it would be an error if he thought any normal listener would care
or notice or have his particular expectations.

-Aaron W

Aaron wrote...
> Carl, this is where I claim that psychology trumps math.
> You are clearly correct that there is no substantial issue
> here in terms of mathematical consonance. However, the
> significance is that by Mike's way of thinking about what
> it should be, he *expected*

Can we please stop making broad philosophical statements
and turning everything into a holy war with math? I'm trying
to communicate with Mike. I tried to show him how I thought
about it with an example, and asked him why he was confused.
It's an approach you might try more of some time.

-Carl

> > Sure, that's reasonable, but I think the "as if it were" part is in
> > your mind (which does not make it less significant since the whole
> > point of music is how we experience it). And because of that, you
> > can't easily make it be the case in a random listener's mind.
>
> Oh yes you can. If I play the chord C E F# B D#, that D# will be heard
> by most people as a major third above the B, because of that F# B D#
> upper structure. It will not be heard as a 6/5 Eb above the C. Music
> is mainly how to get people to hear things in the way that you want.
>

Mike, this is true to a degree. However, any trained musicians will
impose very substantial bias on their listening, and any untrained
musician will either not notice these things as much or be biased by
their stylistic experience and focus. Timbre plays a large part as
well. Most untrained musicians will not hear that chord as any of the
versions you mention, they won't conceptualize the harmonies at all,
they'll probably think more about the overall tone quality of the
sound - is it restless? Is it relaxing? etc. And most likely the
way they feel the D# will be very strongly - primarily even - based on
what the surrounding context is. And if it is a complex context
within a complex musical style then people used to that style will
relate it to similar experiences in past hearings, and people not used
to the style will probably dislike the whole thing or just not really
judge it and just see it as complex and confusing.

I think something like this discussion came up right when I'd just got
the TPX and hadn't learned to operate it yet... I just played around
with your example chord, and I can be certain that while you are
generally correct the major third on top takes prominence, the whole
chord, played as a big chunk sounds vague and uncertain. I have to
clarify things by playing pieces of it or arpeggiating to kind of
focus my mind around the harmony.

Anyway, I agree about the root issue as you mentioned it. A stack of
fifths does relate each to the next and not necessarily to the root,
but you're now talking about chords that are many octaves wide.
There's no chance it is experienced as a fused, unified singular chord
by the average listener. They will hear both the little harmonies
between notes and they will hear a complex whole ensemble sound and
they'll hear the independent notes. Trying to name it as a single
chord is not really descriptive in my mind. If we play two recorded
songs at once, or say a jazz bass line and a flute solo at the same
time that have no particular pattern... it may be very interesting.
But it doesn't create unambiguous unified chord sounds.

The idea of hearing a tempered note as though it were a just harmony
is valid to a degree, but it is very open to interpretation and
influence based on expectations. Beyond that, it may remind someone
of the right note, just like a blurry photo can remind someone of an
object, but it is not ever the same experience as seeing the real
object or a clear photo of it. The restlessness of beats for any
temperament do impact the overall experience and no
guess-interpretation of what it should be will eliminate that.

-AW

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> > I can, on my Tonal Plexus, play very close to exact versions of any of
> > the options you're mentioning, and the only ones that sound
> > harmonically reasonable are the harmonic ones. In that case, the 13's
> > are generally actually tuned like 6ths, and they are actually 5/3
> > ratios from the root. And the #15, as you call it, is the same note
> > as a b9, which is a 17th harmonic, which is 17/8 or 17/4 (octave...
> > whatever) of the root.
>
> One more thing to mention, this time from your first post:
>
> The #15 is NOT the same thing as a b9. On a 12-tet piano, it is the
> same thing. In 72-tet, it is not the same thing. In 53-tet, it is not
> the same thing. C# and Db are not necessarily the same thing.
>
> I use the concept of a #15 to mean a note that is close to the 17th
> harmonic, but it is not. It is a major third and 3 fifths up from the
> root.
> The 17th harmonic has a different use and purpose entirely, although
> the notes may be very close.
>

Mike, since those names come from a world of 7-note diatonic scales
that are either interpreted as pythagorean, 12ET, or 5-limit, there is
no way to absolutely claim that your #15 name means anything different
from b9, except the addition of one more octave. Neither of those
names are clear on tuning at all. They just identify a general range
within a 7-note diatonic scale.

I originally claimed it as the same because not only are they
interchangeable on a 12ET piano, but they are both best harmonically
tuned as 17th harmonic, therefore the same. Any other tuning creates
less of a sense of single unified chord.

Let me put it this way: these names are thoroughly inadequate to
express subtly tunings. By bothering to name something as a chord, it
seems to me that it should make a unified concordant sound. If it
does not, then it must have some other function, which is possibly
voice-leading or possibly something else. Though your stacks of
fifths ideas are valid, there is no way you can claim that traditional
jazz chord names are or are not that tuning versus a harmonic tuning.
All they really do is tell you which piano notes are included and
they don't say much at all about the function of the chord. I wish
they did but there simply is not enough consistency in the jazz world
to truly use them that way. I'd be interested if you have any real
evidence of these names meaning any more than my simplistic reduction
of them. Sure, some people like you may claim they imply other
things, but if there's no consistency, then I think it just just a
false intellectual exercise.

To summarize: your musical ideas are fine. Insisting that a jazz
number chord name means something specific about your ideas seems
erroneous to me.

-AW

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> while what they call it is wrong, i do think the 'mistaken' idea did in
> fact lead to people plying up thirds , i guess caused it worked.
> which lead to chords in fourths, then fifths and seconds even.
> Even Partch spaced his hexad in thirds, as a left over of this type of
> thinking
>

Right! But that doesn't say much because we could make up other
'mistaken' ideas that could lead to other conceptual ideas... and in
the end those ideas would work too because people would find some way
to be expressive with them or adapt them into some more extended
expressive context. Therefore, none of this gets at explaining what
factors actually shape the experience and what harmonies or whatever
are heard in what way. There are limiting factors, but they're not
related to any of these 'mistaken' ideas - except that once a style
starts being based around some conceptual framework, it creates a
unified consistency within the style that people start to get used to.

-AW

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Aaron wrote...
> > Carl, this is where I claim that psychology trumps math.
> > You are clearly correct that there is no substantial issue
> > here in terms of mathematical consonance. However, the
> > significance is that by Mike's way of thinking about what
> > it should be, he *expected*
>
> Can we please stop making broad philosophical statements
> and turning everything into a holy war with math? I'm trying
> to communicate with Mike. I tried to show him how I thought
> about it with an example, and asked him why he was confused.
> It's an approach you might try more of some time.
>
> -Carl
>

Ok, sorry. But since music is totally useless without a
psychologically active listener, the math on its own really is a
dead-end. Math in relation to experience of music is useful.

My point isn't that he wasn't confused, but that even if he was/is
confused his experience of listening to the music and being confused
is a particular affective experience - and that it overrides any
actual physical math within the pitches. My further point is that
math can show a lot of things, but we should give credence the areas
in which the things the math shows actually impact our experience
enough to be demonstrable.

-AW

Mike Battaglia wrote:
> I am seriously considering it. I'm looking for a keyboard to branch
> out into this stuff. I may have slightly different goals from a lot of
> people here -- I'm looking for a system that is easy to THINK about so
> that I can spread it amongst people that haven't done years of
> independent research like most of us on the forum have done. 12tet is
> a miracle just because of that reason -- it's easy to conceptualize,
> and you can get a -HUGE- array of sounds with it. Of course, we all
> want to see what more is possible beyond 12tet and 5-limit music (and
> the "tip-of-the-iceberg" 7-limit stuff that has evolved), and so I
> think that the search for a temperament that is as easy to think about
> as 12tet (or only requires a little more work) but enables access to
> xenharmonic sounds is a worthy pursuit.

There are a number of systems that might meet that criterion, or at least come close to it, but there are always trade-offs to consider. If meantone fifths are good enough, 31tet is a reasonable choice, with its variety of 7- and 11-limit approximations and a familiar notation system. For a better approximation of JI with the same number of notes, miracle[31] is a good choice (although the structure of the tuning system may take some getting used to).

If 31-ET is too many notes, there's always 22-ET -- which opens up new possibilities for harmony but at the same time is incompatible with many traditional chord progressions that take advantage of the 81/80 syntonic comma. Miracle[21] and orwell[22] are a couple of possible temperaments in this size range. One of the things that makes ET's easier to think about, on the other hand, is the fact that you can take any interval and start it on any note in the scale; you don't have to worry about how close you are to one end of the chain or the other.

Bosanquet's keyboard is a nice design because it can be so easily adapted for many of these ET's (12, 19, 22, 31, 41, 43, 53...) but there are other options. The Wilson Archives has a paper describing Larry Hanson's keyboard (http://www.anaphoria.com/hanson.PDF), which may be a better option for 15-, 34-, and 72-ET.

Mike wrote...

> I use the concept of a #15 to mean a note that is close to the
> 17th harmonic, but it is not. It is a major third and 3 fifths
> up from the root.

Oh, are you wanting the C# to be a 17/8? Then your criticism
makes sense to me. 12-ET tempers out 136/135, but it's one
step in 72-ET. So your complaint isn't about consistency, but
about wanting 136/135 "in the kernel" as some would say.

The thing about going outside 12-ET is, you have to give up
something. If you had all the same commas vanish, you'd
have 12-ET! So you have to decide which commas of 12 (if any)
are important to you. Can't do without 81/80? Then you
can get better accuracy and extended harmony with 31. But
you'll lose 648/625 (4 min 3rds = octave).

Here are all the ETs that temper out 136/135:

(2 10 12 14 17 20 22 24 32 34 36 44 46 51 54 56 58 66 68
70 78 80 85 90 92 97 102 107 112 114 119 124 126 131 136
148 160 165 177)

Maybe Graham or one of our resident minor geniuses can tell
us which of these are contorsional. 58 looks like an
excellent choice to me.

-Carl

I do think there is a reason stacked thirds work better than stacked 2nds. one is that we are used to triads in the first place and anything in that ballpark i imagine we can take as a 'variation' thereof. The mind is very elastic and has enough fuzzy circuit to do this , in fact relies on it.
Jazz harmony seems more about color than anything. One does not care weather one chord follows another and we have crossing of voices per se. It is more an extension of Saties way of hearing harmonies than Ravels or Debussy ( although this stuff was being played in New Orleans). Since Harmony is so non functional, one wonders why it concerns us more than say, melody. And here is where i have trouble with the JI world. I mean i can accept any combination of diatonic notes as harmony, and most everyone else can although i imagine Copland is too much for someone. i say let it take care of itself, except in cases where we are using to add color to the line itself, as above.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Aaron Wolf wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > while what they call it is wrong, i do think the 'mistaken' idea did in
> > fact lead to people plying up thirds , i guess caused it worked.
> > which lead to chords in fourths, then fifths and seconds even.
> > Even Partch spaced his hexad in thirds, as a left over of this type of
> > thinking
> >
>
> Right! But that doesn't say much because we could make up other
> 'mistaken' ideas that could lead to other conceptual ideas... and in
> the end those ideas would work too because people would find some way
> to be expressive with them or adapt them into some more extended
> expressive context. Therefore, none of this gets at explaining what
> factors actually shape the experience and what harmonies or whatever
> are heard in what way. There are limiting factors, but they're not
> related to any of these 'mistaken' ideas - except that once a style
> starts being based around some conceptual framework, it creates a
> unified consistency within the style that people start to get used to.
>
> -AW
>
>

--- In tuning@yahoogroups.com, "Aaron Wolf" <wolftune@...> wrote:

> > Can we please stop making broad philosophical statements
> > and turning everything into a holy war with math? I'm trying
> > to communicate with Mike. I tried to show him how I thought
> > about it with an example, and asked him why he was confused.
> > It's an approach you might try more of some time.
>
> Ok, sorry. But since music is totally useless without a
> psychologically active listener, the math on its own really is a
> dead-end.

Glad to see you've reformed! ;)

> My point isn't that he wasn't confused, but that even if he was/is
> confused his experience of listening to the music and being confused
> is a particular affective experience - and that it overrides any
> actual physical math within the pitches. My further point is that
> math can show a lot of things, but we should give credence the areas
> in which the things the math shows actually impact our experience
> enough to be demonstrable.

Well I just posted a list of tunings that may allow him to
express this chord in a logical manner and with better
consonance than in 12-ET. Let's see if hitting that 17th
harmonic is really what he was after.

-Carl

contorsional?
sorry don't know that word

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Carl Lumma wrote:
>
>
>
> Maybe Graham or one of our resident minor geniuses can tell
> us which of these are contorsional. 58 looks like an
> excellent choice to me.
>
> -Carl
>
>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Aaron Wolf" <wolftune@> wrote:
>
> > > Can we please stop making broad philosophical statements
> > > and turning everything into a holy war with math? I'm trying
> > > to communicate with Mike. I tried to show him how I thought
> > > about it with an example, and asked him why he was confused.
> > > It's an approach you might try more of some time.
> >
> > Ok, sorry. But since music is totally useless without a
> > psychologically active listener, the math on its own really is a
> > dead-end.
>
> Glad to see you've reformed! ;)
>

Yeah, I was admittedly a JI-fundamentalist at one time...
I still believe, as a teacher especially, that we need to at least
display something close to the 'ideal' that we are supposed to relate
to in order to best understand temperament and dissonance. I really
am annoyed about my couple years in "aural skills" class in college in
which everyone was supposed to make broad assumptions and
identifications about intervals while listening only to piano (and not
always recently tuned either).

Furthermore, I'm still shocked how few of my music professors even
understood the issues or knew the locations of harmonics past 8.
And I also do still believe that smoother resolve, better tuned major
chords and such, actually do promote a more relaxed and healthy society...
But I understand the complexities now and I have to admit to still
liking all sorts of music, including tons of 12ET music.

-AW

> > My point isn't that he wasn't confused, but that even if he was/is
> > confused his experience of listening to the music and being confused
> > is a particular affective experience - and that it overrides any
> > actual physical math within the pitches. My further point is that
> > math can show a lot of things, but we should give credence the areas
> > in which the things the math shows actually impact our experience
> > enough to be demonstrable.
>
> Well I just posted a list of tunings that may allow him to
> express this chord in a logical manner and with better
> consonance than in 12-ET. Let's see if hitting that 17th
> harmonic is really what he was after.
>
> -Carl
>

I can see I've opened the can of worms here.

> Mike, since those names come from a world of 7-note diatonic scales
> that are either interpreted as pythagorean, 12ET, or 5-limit, there is
> no way to absolutely claim that your #15 name means anything different
> from b9, except the addition of one more octave. Neither of those
> names are clear on tuning at all. They just identify a general range
> within a 7-note diatonic scale.

Yeah, there is a way. It's just how I'm using it. A b9 would be a
minor sixth up from the fourth scale degree. A #15 would be a major
third and 3 fifths up from the root. A minor sixth up from a fourth is
4/3 * 8/5 = 32/15. A major third and 3 fifths up from the root is 5/4
* 3/2 * 3/2 * 3/2 = 135/32. Put in the same octave, 16/15 != 135/128.

In my opinion, calling 17/8 a "b9" is like calling 7/4 a "dominant 7."
They are roughly in the ballpark, but there is a difference. There is
a system to jazz harmony. That's not to say that you can't use 17:8 in
a b9 chord.

Actually, I just realized while typing this, who cares? Jazz numbering
wasn't invented with microtonality in mind. I am drawing a distinction
between a b2 and a b9 and a #15 because they all represent comma
adjustments to me, just like a 6th and a 13 is a comma adjustment. If
you don't like my numbering system, then for purposes of
communication, we'll just abandon it. The main point that I am making
about 72-tet is that this chord:

32:40:48:60:72:90:108:135

Is inconsistent in 72-tet, and I like that chord and I play it a lot.
It is made up of alternately stacked major and minor thirds. If you
put that chord into scala and round it to the nearest 72-tet
approximation, you will see the pattern break down at 135. Accumulated
rounding errors will have that note "jump" up to the next step. It
bad. Me no like. Make think hard. If you keep the 72-tet approximation
on, and change the last number to 134, so the chord becomes this:

32:40:48:60:72:90:108:134

just for the purpose of having scala round the last note "down" to the
72-tet step before it, just so you can hear what it sounds like, it
doesn't sound as clean. Also, being as jazz tends to go way way out
into 5-limit JI space, then I assume there are other chords that will
run into the same problem, and nobody is going to want to have to
think about that. In my mind, that more than nullifies the advantages
of "easy thinking" that 72-tet is supposed to provide. I haven't
looked at 205-tet yet, and it might be consistent enough that it
doesn't have this problem.

> I originally claimed it as the same because not only are they
> interchangeable on a 12ET piano, but they are both best harmonically
> tuned as 17th harmonic, therefore the same. Any other tuning creates
> less of a sense of single unified chord.

I want the interval that is one major third and 3 fifths up from the
root. That interval is best tuned as that interval, not as the 17th
harmonic. Big numbers don't necessarily mean "dissonant." You are
basically saying that dominant 7 chords have to always be tune to
4:5:6:7, which is not the case. Having 7/4 in there is one chord,
having 16/9 as the seventh is another chord, and having 9/5 as the
seventh is another chord. Why do you insist that there is only one
correct way to tune this chord? It's like comparing 5/4 to 81/64.
81/64 is not an out of tune 5/4. 5/4 is just 5/4, and 81/64 is 81/64.
If I have learned how to use 135/64, then there is no need to pretend
that it's dissonant because it's a 3 digit number and that I "really"
want 17/8.

> Let me put it this way: these names are thoroughly inadequate to
> express subtly tunings. By bothering to name something as a chord, it
> seems to me that it should make a unified concordant sound. If it
> does not, then it must have some other function, which is possibly
> voice-leading or possibly something else. Though your stacks of
> fifths ideas are valid, there is no way you can claim that traditional
> jazz chord names are or are not that tuning versus a harmonic tuning.
> All they really do is tell you which piano notes are included and
> they don't say much at all about the function of the chord. I wish
> they did but there simply is not enough consistency in the jazz world
> to truly use them that way. I'd be interested if you have any real
> evidence of these names meaning any more than my simplistic reduction
> of them. Sure, some people like you may claim they imply other
> things, but if there's no consistency, then I think it just just a
> false intellectual exercise.

On the contrary. I'm saying that there is no such thing as what the
"jazz chords" are supposed to be. I'm just saying I want a major 3rd
and 3 fifths on top of it. The 17th harmonic won't give me that note.

I just followed the major 3rd/minor third stacking pattern and found
out that the #15 was the next logical step.

C E G B D F# A C# = 1 3 5 maj7 9 #11 13 ______? #15 seems to be the
continuation of the pattern. b9 would imply a different usage.

I suppose there are other things that #15 could signify, but having
the chord with the 17th harmonic CALLED the b9 chord seems erroneous
to me, as these chord names have in fact come out of boring old
5-limit meantone diatonic scale theory. We need another name for the
chord you are describing, in order to avoid communication explosions
like the one that we've had, in my opinion. Or call it a b9. But we
need some distinction between THAT chord and the one that is a bunch
of stacked fifths and thirds and fourths.

I believe that any interval on a piano can be psychologically
interpreted as a whole bunch of different ratios depending on the
context. You are absolutely right though, in stating that musicians
put their own bias onto it. I would say that biasing the note that is
C# to always be 17:8 is the kind of bias you speak of.

-Mike

To Herman:

Yeah. I would really like to find a bosanquet keyboard MIDI controler
that I could change on the fly from 12-tet to 19-tet to 31-tet to
34-tet to 41-tet to 53-tet. That is like the holy grail of life to me
right now.

So far I've found that 53-tet is absolutely amazing, but it's a ton of
notes. 19-tet never seemed like all it was cracked up to be, since it
doesn't distinguish between 7/6 and 8/7, and the compressed major
chord (the third and fifth are BOTH flat) sounds weird to my ears. But
the more I just play with it, the more I like it, as I guess I'm used
to playing on out of tune pianos (or are they microtonal?), and it's
not THAT bad. 31-tet's flat fifths were kind of annoying at first, but
you sort of adjust to that as well. I've never heard anything in
22-tet -- do you know any links to recordings online that have been
done in this temperament?

-Mike

> Oh, are you wanting the C# to be a 17/8? Then your criticism
> makes sense to me. 12-ET tempers out 136/135, but it's one
> step in 72-ET. So your complaint isn't about consistency, but
> about wanting 136/135 "in the kernel" as some would say.

Not quite... I don't want C# to be a 17/8. I want the C# to be 135/32.
In my experience, even though the numbers are huge, that interval
sounds consonant if you play it like so:

C E G B D F# A C#

And I already apologize about the stupid naming system that has
already caused so many communication errors, but it's supposed to be a
bunch of stacked major and minor thirds. Like so:

5/4 - 6/5 - 5/4 - 6/5 - etc.

Or, in just intonation,

32:40:48:60:72:90:108:135

In my experience, even though 135/32 looks at first glance like it
would be incredibly dissonant, when you put it into the pattern I've
described, you can relate the 135/32 down to the note before it to the
note before that to the note before that and so on back to the root.
It sounds really good. So numbers don't always give an immediate
indicator of dissonance.

It's like a major 7th chord: 8:10:12:15. 15/8 seems like it would be
dissonant, but since you can feel the relation between the 15 and the
12 and the 15 and the 10, and then from the 10 and the 12 back to the
8, you can then map out the 15 to the 8. This is how the ear learns to
hear new ratios as being consonant that might seem dissonant if you
just look at the numbers.

Anyways, if you put this chord into scala or the tuning software of
your choice, and you look at the nearest 72-tet approximation of the
chord, you'll see that the last note -- the 135 -- jumps up a step to
the next note due to rounding errors that have built up as more fifths
and thirds are stacked up. It is a pain to have to think about that
while playing. In addition, what about other chords that are just as
far out into JI space as that chord is? Where do they "jump" from step
to step? I don't want to have to think about mathematical rounding
errors when I'm playing. That's the disadvantage of 72-tet for me.

Compare for yourself:

32:40:48:60:72:90:108:135
32:40:48:60:72:90:108:134

Put both of these chords in scala and use the 72-tet approximation of
each. Forget the number values, and never mind the 134 at the end,
just do it so that scala will round the last note down a step to where
it "should" be for that 135. You'll hear that the first one sounds a
lot better. So just ignoring the rounding errors and acting as if they
didn't exist usually translates to a loss in chord purity, which
defeats the purpose of 72-tet to begin with.

Just some thoughts.

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> contorsional?
> sorry don't know that word

I don't really know it either. But I think it's like
two temperaments superimposed. 24-ET in the 5-limit is the
favorite example. You never actually get to the extra notes.
Graham can explain better.

-Carl

--- In tuning@yahoogroups.com, "Aaron Wolf" <wolftune@...> wrote:

> > > > Can we please stop making broad philosophical statements
> > > > and turning everything into a holy war with math? I'm trying
> > > > to communicate with Mike. I tried to show him how I thought
> > > > about it with an example, and asked him why he was confused.
> > > > It's an approach you might try more of some time.
> > >
> > > Ok, sorry. But since music is totally useless without a
> > > psychologically active listener, the math on its own really
> > > is a dead-end.
> >
> > Glad to see you've reformed! ;)
>
> Yeah, I was admittedly a JI-fundamentalist at one time...

No, I meant with that comment "math on its own really is
a dead-end". That kind of thing has incited riots here
many times.

> And I also do still believe that smoother resolve, better
> tuned major chords and such, actually do promote a more
> relaxed and healthy society...

It sure seems like they might. Certainly I think a capella
singing could, but smooth chords are only one aspect of that.

> But I understand the complexities now and I have to admit
> to still liking all sorts of music, including tons of
> 12ET music.

Ain't it the truth. There ain't nobody alive who's done
more than scratch the surface of this stuff.

-Carl

Ji or ET - it all uses math. Except for those who remain 'more advanced', using only their ears without measuring at all.
Unfortunately this might leave undue influence to mere muscle memory combined with unintentional instrumental design artifacts. The latter at least leaves more room for the unexpected at least.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Aaron Wolf wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, "Carl > Lumma" <carl@...> wrote:
> >
> > --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, > "Aaron Wolf" <wolftune@> wrote:
> >
> > > > Can we please stop making broad philosophical statements
> > > > and turning everything into a holy war with math? I'm trying
> > > > to communicate with Mike. I tried to show him how I thought
> > > > about it with an example, and asked him why he was confused.
> > > > It's an approach you might try more of some time.
> > >
> > > Ok, sorry. But since music is totally useless without a
> > > psychologically active listener, the math on its own really is a
> > > dead-end.
> >
> > Glad to see you've reformed! ;)
> >
>
> Yeah, I was admittedly a JI-fundamentalist at one time...
> I still believe, as a teacher especially, that we need to at least
> display something close to the 'ideal' that we are supposed to relate
> to in order to best understand temperament and dissonance. I really
> am annoyed about my couple years in "aural skills" class in college in
> which everyone was supposed to make broad assumptions and
> identifications about intervals while listening only to piano (and not
> always recently tuned either).
>
> Furthermore, I'm still shocked how few of my music professors even
> understood the issues or knew the locations of harmonics past 8.
> And I also do still believe that smoother resolve, better tuned major
> chords and such, actually do promote a more relaxed and healthy society...
> But I understand the complexities now and I have to admit to still
> liking all sorts of music, including tons of 12ET music.
>
> -AW
>
> > > My point isn't that he wasn't confused, but that even if he was/is
> > > confused his experience of listening to the music and being confused
> > > is a particular affective experience - and that it overrides any
> > > actual physical math within the pitches. My further point is that
> > > math can show a lot of things, but we should give credence the areas
> > > in which the things the math shows actually impact our experience
> > > enough to be demonstrable.
> >
> > Well I just posted a list of tunings that may allow him to
> > express this chord in a logical manner and with better
> > consonance than in 12-ET. Let's see if hitting that 17th
> > harmonic is really what he was after.
> >
> > -Carl
> >
>
>

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> > Oh, are you wanting the C# to be a 17/8? Then your criticism
> > makes sense to me. 12-ET tempers out 136/135, but it's one
> > step in 72-ET. So your complaint isn't about consistency, but
> > about wanting 136/135 "in the kernel" as some would say.
>
> Not quite... I don't want C# to be a 17/8. I want the C# to be
> 135/32. In my experience, even though the numbers are huge,
> that interval sounds consonant if you play it like so:
>
> C E G B D F# A C#

It's not the 135/32-ness that's generating consonance here.
It's all the 5ths and 3rds. 135/32 itself is not a consonance.
You can't tune it by ear. 17/8 is.

> And I already apologize about the stupid naming system that
> has already caused so many communication errors, but it's
> supposed to be a bunch of stacked major and minor thirds.
> Like so:
>
> 5/4 - 6/5 - 5/4 - 6/5 - etc.

Yes -- did you see my prior post about this?
/tuning/topicId_76549.html#76648
72-ET handles this just fine.

> In my experience, even though 135/32 looks at first glance like
> it would be incredibly dissonant, when you put it into the pattern
> I've described, you can relate the 135/32 down to the note before
> it to the note before that to the note before that and so on back
> to the root. It sounds really good. So numbers don't always give
> an immediate indicator of dissonance.

What are you actually experiencing here? You don't like
the sound of the chord 0 23 42 65 84 107 126 149 in 72-ET?
You prefer the sound of the chord 0 23 42 65 84 107 126 148?
Or....??

> It's like a major 7th chord: 8:10:12:15. 15/8 seems like it
> would be dissonant

No, 15 is a reasonable number. I can tune 15/8 by ear,
with a bit of luck and a spritz of Vitalis.

> but since you can feel the relation between the 15 and the
> 12 and the 15 and the 10, and then from the 10 and the 12 back
> to the 8, you can then map out the 15 to the 8. This is how
> the ear learns to hear new ratios as being consonant that
> might seem dissonant if you just look at the numbers.

Yes, it's more consonant in the chord than by itself.

> Anyways, if you put this chord into scala or the tuning
> software of your choice, and you look at the nearest 72-tet
> approximation of the chord, you'll see that the last note --
> the 135 -- jumps up a step to the next note due to rounding
> errors that have built up as more fifths and thirds are
> stacked up. It is a pain to have to think about that
> while playing.

Gotcha. But I don't think you do have to think about it.
If you like 0 23 42 65 84 107 126 148 better it isn't anything
to do with 135/32.

> Compare for yourself:
>
> 32:40:48:60:72:90:108:135
> 32:40:48:60:72:90:108:134
>
> Put both of these chords in scala and use the 72-tet
> approximation of each. Forget the number values, and never
> mind the 134 at the end, just do it so that scala will round
> the last note down a step to where it "should" be for
> that 135. You'll hear that the first one sounds a lot better.

So you do like the obvious chord better! So there's no
problem at all! It's you who're creating the problem by
worrying about the numbers!

> So just ignoring the rounding errors and acting as if they
> didn't exist usually translates to a loss in chord purity,
> which defeats the purpose of 72-tet to begin with.

But it sounds like exactly the opposite thing is happening
here!!!!???

-Carl

The can of worms;-)

Over the years I have given considerable thought to how to tune "Jazz" chords for guitar.

This page was prepared quite a few years ago, yet may still throw some new light for you on one practical way of considering, tuning and playing complex "Jazz" chords.

http://www.lucytune.com/new_to_lt/chords.html

(sarcasm from Carl anticipated;-)

On 27 May 2008, at 01:27, Mike Battaglia wrote:

> I can see I've opened the can of worms here.
>
> > Mike, since those names come from a world of 7-note diatonic scales
> > that are either interpreted as pythagorean, 12ET, or 5-limit, > there is
> > no way to absolutely claim that your #15 name means anything > different
> > from b9, except the addition of one more octave. Neither of those
> > names are clear on tuning at all. They just identify a general range
> > within a 7-note diatonic scale.
>
> Yeah, there is a way. It's just how I'm using it. A b9 would be a
> minor sixth up from the fourth scale degree. A #15 would be a major
> third and 3 fifths up from the root. A minor sixth up from a fourth is
> 4/3 * 8/5 = 32/15. A major third and 3 fifths up from the root is 5/4
> * 3/2 * 3/2 * 3/2 = 135/32. Put in the same octave, 16/15 != 135/128.
>
> In my opinion, calling 17/8 a "b9" is like calling 7/4 a "dominant 7."
> They are roughly in the ballpark, but there is a difference. There is
> a system to jazz harmony. That's not to say that you can't use 17:8 in
> a b9 chord.
>
> Actually, I just realized while typing this, who cares? Jazz numbering
> wasn't invented with microtonality in mind. I am drawing a distinction
> between a b2 and a b9 and a #15 because they all represent comma
> adjustments to me, just like a 6th and a 13 is a comma adjustment. If
> you don't like my numbering system, then for purposes of
> communication, we'll just abandon it. The main point that I am making
> about 72-tet is that this chord:
>
> 32:40:48:60:72:90:108:135
>
> Is inconsistent in 72-tet, and I like that chord and I play it a lot.
> It is made up of alternately stacked major and minor thirds. If you
> put that chord into scala and round it to the nearest 72-tet
> approximation, you will see the pattern break down at 135. Accumulated
> rounding errors will have that note "jump" up to the next step. It
> bad. Me no like. Make think hard. If you keep the 72-tet approximation
> on, and change the last number to 134, so the chord becomes this:
>
> 32:40:48:60:72:90:108:134
>
> just for the purpose of having scala round the last note "down" to the
> 72-tet step before it, just so you can hear what it sounds like, it
> doesn't sound as clean. Also, being as jazz tends to go way way out
> into 5-limit JI space, then I assume there are other chords that will
> run into the same problem, and nobody is going to want to have to
> think about that. In my mind, that more than nullifies the advantages
> of "easy thinking" that 72-tet is supposed to provide. I haven't
> looked at 205-tet yet, and it might be consistent enough that it
> doesn't have this problem.
>
> > I originally claimed it as the same because not only are they
> > interchangeable on a 12ET piano, but they are both best harmonically
> > tuned as 17th harmonic, therefore the same. Any other tuning creates
> > less of a sense of single unified chord.
>
> I want the interval that is one major third and 3 fifths up from the
> root. That interval is best tuned as that interval, not as the 17th
> harmonic. Big numbers don't necessarily mean "dissonant." You are
> basically saying that dominant 7 chords have to always be tune to
> 4:5:6:7, which is not the case. Having 7/4 in there is one chord,
> having 16/9 as the seventh is another chord, and having 9/5 as the
> seventh is another chord. Why do you insist that there is only one
> correct way to tune this chord? It's like comparing 5/4 to 81/64.
> 81/64 is not an out of tune 5/4. 5/4 is just 5/4, and 81/64 is 81/64.
> If I have learned how to use 135/64, then there is no need to pretend
> that it's dissonant because it's a 3 digit number and that I "really"
> want 17/8.
>
> > Let me put it this way: these names are thoroughly inadequate to
> > express subtly tunings. By bothering to name something as a chord, > it
> > seems to me that it should make a unified concordant sound. If it
> > does not, then it must have some other function, which is possibly
> > voice-leading or possibly something else. Though your stacks of
> > fifths ideas are valid, there is no way you can claim that > traditional
> > jazz chord names are or are not that tuning versus a harmonic > tuning.
> > All they really do is tell you which piano notes are included and
> > they don't say much at all about the function of the chord. I wish
> > they did but there simply is not enough consistency in the jazz > world
> > to truly use them that way. I'd be interested if you have any real
> > evidence of these names meaning any more than my simplistic > reduction
> > of them. Sure, some people like you may claim they imply other
> > things, but if there's no consistency, then I think it just just a
> > false intellectual exercise.
>
> On the contrary. I'm saying that there is no such thing as what the
> "jazz chords" are supposed to be. I'm just saying I want a major 3rd
> and 3 fifths on top of it. The 17th harmonic won't give me that note.
>
> I just followed the major 3rd/minor third stacking pattern and found
> out that the #15 was the next logical step.
>
> C E G B D F# A C# = 1 3 5 maj7 9 #11 13 ______? #15 seems to be the
> continuation of the pattern. b9 would imply a different usage.
>
> I suppose there are other things that #15 could signify, but having
> the chord with the 17th harmonic CALLED the b9 chord seems erroneous
> to me, as these chord names have in fact come out of boring old
> 5-limit meantone diatonic scale theory. We need another name for the
> chord you are describing, in order to avoid communication explosions
> like the one that we've had, in my opinion. Or call it a b9. But we
> need some distinction between THAT chord and the one that is a bunch
> of stacked fifths and thirds and fourths.
>
> I believe that any interval on a piano can be psychologically
> interpreted as a whole bunch of different ratios depending on the
> context. You are absolutely right though, in stating that musicians
> put their own bias onto it. I would say that biasing the note that is
> C# to always be 17:8 is the kind of bias you speak of.
>
> -Mike
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

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--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> I can see I've opened the can of worms here.
>
> > Mike, since those names come from a world of 7-note diatonic scales
> > that are either interpreted as pythagorean, 12ET, or 5-limit, there is
> > no way to absolutely claim that your #15 name means anything different
> > from b9, except the addition of one more octave. Neither of those
> > names are clear on tuning at all. They just identify a general range
> > within a 7-note diatonic scale.
>
> Yeah, there is a way. It's just how I'm using it. A b9 would be a
> minor sixth up from the fourth scale degree. A #15 would be a major
> third and 3 fifths up from the root. A minor sixth up from a fourth is
> 4/3 * 8/5 = 32/15. A major third and 3 fifths up from the root is 5/4
> * 3/2 * 3/2 * 3/2 = 135/32. Put in the same octave, 16/15 != 135/128.
>
> In my opinion, calling 17/8 a "b9" is like calling 7/4 a "dominant
> 7."

Sorry, Mike. These things are ALL not specific. I generally do think
of 7/4 as a dominant 7, as do many others here.

And saying that a b9 is a minor sixth up for the fourth doesn't mean
anything much because there is no consensus that the term "minor
sixth" necessarily means 8/5 versus other tunings in that range. If
you stick with Pythagorean tuning, you call 408 cents a "major third"
and if you use meantone, you call 386 cents a "major third." These
terms are all related to scale and are general. They basically say
which note we're at in a melodic order of some set pitches. They
don't say what these set pitches are.

> They are roughly in the ballpark, but there is a difference. There is
> a system to jazz harmony. That's not to say that you can't use 17:8 in
> a b9 chord.
>
> Actually, I just realized while typing this, who cares? Jazz numbering
> wasn't invented with microtonality in mind. I am drawing a distinction
> between a b2 and a b9 and a #15 because they all represent comma
> adjustments to me, just like a 6th and a 13 is a comma adjustment. If
> you don't like my numbering system, then for purposes of
> communication, we'll just abandon it.

Ok, thanks. We can stick with mentioning it, but it has to remain
open to interpretation because there is no consensus about these terms
meaning anything specific. It is FINE for you to talk about a #15,
and fine for you to say that YOU would like it to be tuned a
particular way.

> The main point that I am making
> about 72-tet is that this chord:
>
> 32:40:48:60:72:90:108:135
>
> Is inconsistent in 72-tet, and I like that chord and I play it a lot.
> It is made up of alternately stacked major and minor thirds. If you
> put that chord into scala and round it to the nearest 72-tet
> approximation, you will see the pattern break down at 135. Accumulated
> rounding errors will have that note "jump" up to the next step. It
> bad. Me no like. Make think hard. If you keep the 72-tet approximation
> on, and change the last number to 134, so the chord becomes this:
>
> 32:40:48:60:72:90:108:134
>
> just for the purpose of having scala round the last note "down" to the
> 72-tet step before it, just so you can hear what it sounds like, it
> doesn't sound as clean. Also, being as jazz tends to go way way out
> into 5-limit JI space, then I assume there are other chords that will
> run into the same problem, and nobody is going to want to have to
> think about that. In my mind, that more than nullifies the advantages
> of "easy thinking" that 72-tet is supposed to provide. I haven't
> looked at 205-tet yet, and it might be consistent enough that it
> doesn't have this problem.
>

Ok, I think I understand. You want each third to be as close to 5/4
and 6/5 as possible, and yet you don't want let accumulated errors get
as big as 135/134 which is nearly 13 cents, thus making the
accumulated errors in 72 necessitate either a bad 135/32 or compromise
one of the thirds.

Now, in my view you really shouldn't care about the 135/32 ratio,
because it doesn't sound that special. It is not much different on
its own that 134/32. It is the harmonic support of each third
supporting each other that is important, and so you should not
compromise the thirds, just don't worry about the tuning of the
outside harmony. If you stop using scala to enter the exact ratios to
get approximations of 7ET you won't have a problem. If you had a 72ET
keyboard, you would just be sure that each third is the same
consistent number of steps and ignore how the outside parts of the
chord relate - they're pretty far away anyway.

What I can tell you, however, about 205ET is that it does NOT have the
problems you're finding in 72ET. The accuracy of thirds and fifths in
205 is better than that of 72. I can play on my Tonal Plexus the
exact chord you're talking about, and I can do it with alternating
thirds of consistently the same shape on the keyboard. The final tone
C# is the precise key that is closest to the actual ratio 135/32. It
is about 1.5 cents off from the exact ratio.

Fact is, for your purposes it sounds like the Tonal Plexus and 205ET
is actually more ideal than even for my purposes. The thirds and
fifths are particularly accurate, and the whole layout is designed
primarily around Pythagorean tuning, meaning biased toward accurate
fifths above all else, though it definitely isn't limited to that.
So the TPX would do it for you, none of the issues you're bringing up
here. I checked.

>
> > I originally claimed it as the same because not only are they
> > interchangeable on a 12ET piano, but they are both best harmonically
> > tuned as 17th harmonic, therefore the same. Any other tuning creates
> > less of a sense of single unified chord.
>
> I want the interval that is one major third and 3 fifths up from the
> root. That interval is best tuned as that interval, not as the 17th
> harmonic. Big numbers don't necessarily mean "dissonant." You are
> basically saying that dominant 7 chords have to always be tune to
> 4:5:6:7, which is not the case. Having 7/4 in there is one chord,
> having 16/9 as the seventh is another chord, and having 9/5 as the
> seventh is another chord. Why do you insist that there is only one
> correct way to tune this chord? It's like comparing 5/4 to 81/64.
> 81/64 is not an out of tune 5/4. 5/4 is just 5/4, and 81/64 is 81/64.
> If I have learned how to use 135/64, then there is no need to pretend
> that it's dissonant because it's a 3 digit number and that I "really"
> want 17/8.
>

Fair enough mostly. Except dissonance is not something completely open
to opinion. Dissonance is related to beats and a few related ideas.
135/64 has more beats than 17/4, though they are far enough apart that
it depends on timbre. A sound that has a strong 17th harmonic will
obviously blend well with 17/4 and not so well with 135/64. However,
if you build it up as you do with a series of fifths and then a major
chord, then yes, 135 is less dissonant.

>
> > Let me put it this way: these names are thoroughly inadequate to
> > express subtly tunings. By bothering to name something as a chord, it
> > seems to me that it should make a unified concordant sound. If it
> > does not, then it must have some other function, which is possibly
> > voice-leading or possibly something else. Though your stacks of
> > fifths ideas are valid, there is no way you can claim that traditional
> > jazz chord names are or are not that tuning versus a harmonic tuning.
> > All they really do is tell you which piano notes are included and
> > they don't say much at all about the function of the chord. I wish
> > they did but there simply is not enough consistency in the jazz world
> > to truly use them that way. I'd be interested if you have any real
> > evidence of these names meaning any more than my simplistic reduction
> > of them. Sure, some people like you may claim they imply other
> > things, but if there's no consistency, then I think it just just a
> > false intellectual exercise.
>
> On the contrary. I'm saying that there is no such thing as what the
> "jazz chords" are supposed to be. I'm just saying I want a major 3rd
> and 3 fifths on top of it. The 17th harmonic won't give me that note.
>
> I just followed the major 3rd/minor third stacking pattern and found
> out that the #15 was the next logical step.
>
> C E G B D F# A C# = 1 3 5 maj7 9 #11 13 ______? #15 seems to be the
> continuation of the pattern. b9 would imply a different usage.
>

Ok, to you it has a different implication. Here's what I think: I
think that schooled jazz musicians who are told to think about
stacking thirds end up thinking the way you do. I think jazz or
jazz-related musicians who rely less on theory and use their ears end
up using the same piano chords, call them the same name, and really do
not use them as stacked thirds in terms of the composition of the
music. I think that in the ambiguous world of 12ET, these chords
generally are just used in two ways: 1. voice leading, and 2. just
extra "color" sounds that don't really care which way you think of it,
they just add extra sounds and make things denser in various ways.

Therefore, I think that your idea of naming and implication COULD be
sensible, but it just in fact not an accurate description of what is
going on in most real music.

> I suppose there are other things that #15 could signify, but having
> the chord with the 17th harmonic CALLED the b9 chord seems erroneous
> to me, as these chord names have in fact come out of boring old
> 5-limit meantone diatonic scale theory. We need another name for the
> chord you are describing, in order to avoid communication explosions
> like the one that we've had, in my opinion. Or call it a b9. But we
> need some distinction between THAT chord and the one that is a bunch
> of stacked fifths and thirds and fourths.
>

I agree we need distinction. However, it seems clear from lots of
usage that many if not most "b9" chords are functioning as solid
harmonic units, implying the harmony 8:10:12:14:17. But that is up
for debate I admit.

My beef with your statement is the idea that 5-limit theory is
informing jazz. How can you possibly make that claim knowing that
from the history of jazz to today the creators of this style had no
option to choose anything other than 12ET theoretically. Maybe they
were trying for 7/4 and 17/4 and even possibly the 11th harmonic and
just calling them by the 5-limit classical names that they appeared to
be on the piano. How can we possibly know? They didn't, for the most
part, realize that these distinctions exist! If someone doesn't know
the word "orange" and describes their style of painting as being
entirely about the patterns between "red" and "blue" how can anyone
say that they certainly meant red and not orange? We can conjecture,
but we can't know. It is simply rash to assume that a jazz piano
instructor, master, professor, whatever means exactly what you think
he means harmonically when he explains jazz piano theory - if we also
know that he doesn't know that these various intervals exist.

The real answer would only be to find really knowledgeable, old
experienced jazz pianist with a really open mind who understand all
the tuning theory, and can explain exactly how they experience jazz
piano in relation to these harmonic alternatives. My guess: they
would say that 12ET works the way it does because it is vague and
slightly dissonant and so it obscures a lot of these things and
creates some tension that drives the music differently from any of the
other harmonic options and they would refuse to either support or deny
the traditional stacked thirds viewpoint.

> I believe that any interval on a piano can be psychologically
> interpreted as a whole bunch of different ratios depending on the
> context. You are absolutely right though, in stating that musicians
> put their own bias onto it. I would say that biasing the note that is
> C# to always be 17:8 is the kind of bias you speak of.
>
> -Mike

I totally agree with this last statement with one exception: the piano
intervals *can* also be interpreted (or non-interpreted if you will)
as not being any ratio, but as being tempered, slightly dissonant
sounds that are what they are and are distinct from any ratio.

Interesting discussion. Glad to hear your views. I was always very
critical of jazz theory because I wasn't sure anyone actually really
did stacking like this in jazz, I thought they just explained things
that way because it was an easy pattern explanation based on the piano.

Best,
Aaron Wolf

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> > Oh, are you wanting the C# to be a 17/8? Then your criticism
> > makes sense to me. 12-ET tempers out 136/135, but it's one
> > step in 72-ET. So your complaint isn't about consistency, but
> > about wanting 136/135 "in the kernel" as some would say.
>
> Not quite... I don't want C# to be a 17/8. I want the C# to be 135/32.
> In my experience, even though the numbers are huge, that interval
> sounds consonant if you play it like so:
>
> C E G B D F# A C#
>
> And I already apologize about the stupid naming system that has
> already caused so many communication errors, but it's supposed to be a
> bunch of stacked major and minor thirds. Like so:
>
> 5/4 - 6/5 - 5/4 - 6/5 - etc.
>
> Or, in just intonation,
>
> 32:40:48:60:72:90:108:135
>
> In my experience, even though 135/32 looks at first glance like it
> would be incredibly dissonant, when you put it into the pattern I've
> described, you can relate the 135/32 down to the note before it to the
> note before that to the note before that and so on back to the root.
> It sounds really good. So numbers don't always give an immediate
> indicator of dissonance.
>

To be sure, 135/32 doesn't look to be incredibly dissonant. Any time
you have a really large number and a smaller number - basically any
interval over a couple octaves, is rarely as dissonant as closer
intervals.

> It's like a major 7th chord: 8:10:12:15. 15/8 seems like it would be
> dissonant, but since you can feel the relation between the 15 and the
> 12 and the 15 and the 10, and then from the 10 and the 12 back to the
> 8, you can then map out the 15 to the 8. This is how the ear learns to
> hear new ratios as being consonant that might seem dissonant if you
> just look at the numbers.
>
> Anyways, if you put this chord into scala or the tuning software of
> your choice, and you look at the nearest 72-tet approximation of the
> chord, you'll see that the last note -- the 135 -- jumps up a step to
> the next note due to rounding errors that have built up as more fifths
> and thirds are stacked up. It is a pain to have to think about that
> while playing. In addition, what about other chords that are just as
> far out into JI space as that chord is? Where do they "jump" from step
> to step? I don't want to have to think about mathematical rounding
> errors when I'm playing. That's the disadvantage of 72-tet for me.
>
> Compare for yourself:
>
> 32:40:48:60:72:90:108:135
> 32:40:48:60:72:90:108:134
>
> Put both of these chords in scala and use the 72-tet approximation of
> each. Forget the number values, and never mind the 134 at the end,
> just do it so that scala will round the last note down a step to where
> it "should" be for that 135. You'll hear that the first one sounds a
> lot better. So just ignoring the rounding errors and acting as if they
> didn't exist usually translates to a loss in chord purity, which
> defeats the purpose of 72-tet to begin with.
>
> Just some thoughts.
>

The 135 doesn't sound better because 135 is better, it sounds better
because the top pair are a good 5/4.if you take away the 90 and the
108, you won't notice much difference in the 135 or 134 options any
more. Which is also to say that your stacking ideas are definitely valid.

Anyway, see my other response about 205ET working better for this.
-Aaron Wolf

Aaron wrote...

> To be sure, 135/32 doesn't look to be incredibly dissonant. Any
> time you have a really large number and a smaller number -
> basically any interval over a couple octaves, is rarely as
> dissonant as closer intervals.

Right. Dissonance and consonance are not inverses. You
can have neither. 135/64 is stupendously non-consonant
in and of itself.

-Carl

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
> Ji or ET - it all uses math. Except for those who remain 'more
> advanced', using only their ears without measuring at all.
> Unfortunately this might leave undue influence to mere muscle memory
> combined with unintentional instrumental design artifacts. The
latter at
> least leaves more room for the unexpected at least.
>

Hey, I'm not saying math doesn't exist. I'm saying that applying our
mathematical concepts to music can sometimes involve focusing too
strictly on only one aspect of musical experience.

The muscle memory and other issues you mention... those are real. The
point I'm making is that in the end music doesn't DO anything beyond
entertain or coordinate or affect people. Other than maybe the
mathematics of brain chemistry, there are aspects to musical
experience that cannot be described purely in tuning math. These are
the somewhat extramusical aspects such as association with memories or
particular mindset or mood when listening, etc etc. In the end, the
whole point is about how listeners experience it.

-AW

>
> Yes -- did you see my prior post about this?
> /tuning/topicId_76549.html#76648
> 72-ET handles this just fine.
>

Carl, Mike's complaint is that when he enters the ratios PURELY as
extended JI, then the last note is rounded flat from what would be
good in 72ET. You are totally correct that it works in 72, such as if
you treat each interval as a "major third" and "minor third" WITHIN
72. What he's done is to treat them as pure instead and then take the
whole thing and try to approximate each to a note in 72.

If I had a 72ET keyboard, and I played each interval as a good third,
I'd end up just fine, as you say. And it would sound fine, because
135 in and of itself doesn't really matter. But you see where he's
getting confused. I think it's because he doesn't have a keyboard,
he's entering bunches of ratios into scala. A 72ET keyboard would
work for him, as would the Tonal Plexus. Since you think 72 is better
- you ought to go ahead as you said earlier and get working on making
physical 72ET keyboards practical for people - whether using existing
hardware and software or not. I think people would appreciate that.

Best,
AW

I wholly agree that musical experience or even perception cannot to quantified.
As i have mentioned, i am a musical hedonist and i like the way it affects me.
While not limited to emotional states, even these more than music expressing them, i think make some possible.
We likewise are quite fascinated though how different cultures will use music differently and have different experiences with it which are not wholly cultural.
Its affect on brain wave activity and those range of experiences while they differ are included under trance states.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

Aaron Wolf wrote:
>
> --- In tuning@yahoogroups.com <mailto:tuning%40yahoogroups.com>, Kraig > Grady <kraiggrady@...> wrote:
> >
> > Ji or ET - it all uses math. Except for those who remain 'more
> > advanced', using only their ears without measuring at all.
> > Unfortunately this might leave undue influence to mere muscle memory
> > combined with unintentional instrumental design artifacts. The
> latter at
> > least leaves more room for the unexpected at least.
> >
>
> Hey, I'm not saying math doesn't exist. I'm saying that applying our
> mathematical concepts to music can sometimes involve focusing too
> strictly on only one aspect of musical experience.
>
> The muscle memory and other issues you mention... those are real. The
> point I'm making is that in the end music doesn't DO anything beyond
> entertain or coordinate or affect people. Other than maybe the
> mathematics of brain chemistry, there are aspects to musical
> experience that cannot be described purely in tuning math. These are
> the somewhat extramusical aspects such as association with memories or
> particular mindset or mood when listening, etc etc. In the end, the
> whole point is about how listeners experience it.
>
> -AW
>
>

Have you put the chord in Scala or some software? Do you not see what
I am talking about?

The obvious chord sounds WORSE than the one with the rounding error skip.

32:40:48:60:72:90:108:135

In 72-tet, that chord SHOULD BE

C E- G B- D F#- A C#-

C#-. Note the -. That means it is one 72-tet step flat of the C# that
is in 12-tet.

BUT

due to the fact that errors in rounding add up and accumulate as you
stack more and more fifths,

the best 72-tet approximation of the WHOLE CHORD from just intonation
to 72-tet is this:

C E- G B- D F#- A C#

C#! no minus! The C# is one 72-tet step up of where it should be!

I assume your question is how I'm running into this weird C#, and why
it isn't C#- like I'd expect?

Well, the actual JI cent values from the root for that chord is this:

C:E- 386.314 5/4
E-:G 315.641 6/5
G:B- 386.314 5/4
B-:D 315.641 6/5
D:F#- 386.314 5/4
F#-:A 315.641 6/5
A:C#- 386.314 5/4

The TOTAL is 2492.179. From the C to the C#- slightly more than 2
octaves up, the total amount of cents is 2492.179. 72-tet has 16.6667
step size. The two step sizes around 2492.179 are 2500 cents and
2483.333 cents.

|2483.333 cents - 2492.179 cents| = 8.846 cents
|2500 cents - 2492.179 cents| = 7.821 cents

So as you can see, 2500 cents is the better match up for this interval.

So to recap, the best match up for a JI major third and three JI
perfect fifths, which is that C#, is 2500 cents. That amounts to 150
72-tet steps.

The best match up for a JI major third in 72-tet is 383.333 cents,
which is 23 72-tet steps
The best match up for a JI perfect fifth in 72-tet is 700.000 cents,
which is 42 72-tet steps.

Does the math work out? Let's see.

1 major third + 3 perfect fifths = 23 steps + 3 * 42 steps = 149 steps.

So herein lies the problem: 72-tet's best approximation for the
interval that is one major third and three perfect fifths wide is one
step wider than the sum total of 72-tet's best approximations for the
interval of one major third and three times one perfect fifth. I find
this extremely annoying, and if this error exists here, then I assume
it will exist elsewhere as well. Using chords that have their basis in
low-integer overtones, such as 17 or 19, doesn't fix the issue itself,
which is that 72-tet is inconsistent for fairly common chords.

I hope I've explained it right this time.

-Mike

Haha, in the time it took me to write that last post, there were three
more posts. Oh well.

Aaron and Carl: At this point I think we're all mostly in agreement. I
don't think most jazz musicians think of tuning at all -- I myself
have just done some listening tests to hear what I think retains most
of the flavor of the original chords. I found that in a lot of cases,
the chords are merely stacked fifths and thirds. There are other cases
where I find 11-limit harmonies are appropriate, and other cases where
I find 17 or 19-limit harmonies appropriate. I just found it to be the
case that a lot of times, it really is just stacked fifths and thirds.

I happened upon this way of thinking when I tried to figure out why
the melodic minor scale and its modes had a completely different feel
from the diatonic major scale and its modes. The only explanation that
made sense to me was that the melodic minor scale has two directly
stacked major thirds in it, which the major scale doesn't have. For
example, here's the lydian augmented scale, which is the 3rd mode of
the melodic minor scale:

C D E F# G# A B C

The C and the E and the G# are two directly stacked major thirds. This
creates the feeling of there being a 25/16 interval -- although you
could interpret it to be a number of different things, I suppose. To
me, it intuitively feels like 25/16. And that could be why the scale
is considerably more dissonant than lydian mode:

C D E F# G A B C

which is its diatonic "counterpart." Also, the modes of the harmonic
minor and major scale have their uses as well:

C D# E F# G A B C - Lydian #9
C D# E F# G# A B C - Lydian Augmented #9

Ignoring the names and numbres, both of these scales have a note that
COULD be reached by going up two major thirds and a fifth -- and that
is the D#. The lydian #9 scale has the normal fifth in the scale, and
the lydian augmented #9 replaces the fifth with the major third on top
of the major third.

Again, I think we're all saying here that any of these notes could
approximate anything, but you certainly can't approximate [1, 2 > with
any of the notes in the major scale. And that is the difference.

Of course, I've also found that the lydian dominant scale:

C D E F# G A Bb C

Is very well approximated by treating Bb as 7/4 and F# as 11/8, even
though those intervals are up to a quartertone away from the original.
So don't think I'm "biased" towards 5-limit music -- the reason I am
here is that I am not. :) I'm just trying to recognize 5-limit music
when I hear it, and figure out what a hypothetical 5-limit structure
COULD BE, and 72-tet doesn't hold up very well for that at times.

So it isn't that I'm getting confused. I've compared the two chords -
C E- G B- D F#- A C#- and C E- G B- D F#- A C# -- and the second one
to me sounds better. Futhermore, I'm not sure how this rounding
"bubble" goes outward to other chords and upper structure triads as
well, and I think that would be a pain for anyone to think about. Or,
they could just not think about it, as you said, but I find that
sometimes it legitimately sounds worse.

-Mike

On Mon, May 26, 2008 at 10:32 PM, Mike Battaglia <battaglia01@...> wrote:
> Have you put the chord in Scala or some software? Do you not see what
> I am talking about?
>
> The obvious chord sounds WORSE than the one with the rounding error skip.
>
> 32:40:48:60:72:90:108:135
>
> In 72-tet, that chord SHOULD BE
>
> C E- G B- D F#- A C#-
>
> C#-. Note the -. That means it is one 72-tet step flat of the C# that
> is in 12-tet.
>
> BUT
>
> due to the fact that errors in rounding add up and accumulate as you
> stack more and more fifths,
>
> the best 72-tet approximation of the WHOLE CHORD from just intonation
> to 72-tet is this:
>
> C E- G B- D F#- A C#
>
> C#! no minus! The C# is one 72-tet step up of where it should be!
>
> I assume your question is how I'm running into this weird C#, and why
> it isn't C#- like I'd expect?
>
> Well, the actual JI cent values from the root for that chord is this:
>
> C:E- 386.314 5/4
> E-:G 315.641 6/5
> G:B- 386.314 5/4
> B-:D 315.641 6/5
> D:F#- 386.314 5/4
> F#-:A 315.641 6/5
> A:C#- 386.314 5/4
>
> The TOTAL is 2492.179. From the C to the C#- slightly more than 2
> octaves up, the total amount of cents is 2492.179. 72-tet has 16.6667
> step size. The two step sizes around 2492.179 are 2500 cents and
> 2483.333 cents.
>
> |2483.333 cents - 2492.179 cents| = 8.846 cents
> |2500 cents - 2492.179 cents| = 7.821 cents
>
> So as you can see, 2500 cents is the better match up for this interval.
>
> So to recap, the best match up for a JI major third and three JI
> perfect fifths, which is that C#, is 2500 cents. That amounts to 150
> 72-tet steps.
>
> The best match up for a JI major third in 72-tet is 383.333 cents,
> which is 23 72-tet steps
> The best match up for a JI perfect fifth in 72-tet is 700.000 cents,
> which is 42 72-tet steps.
>
> Does the math work out? Let's see.
>
> 1 major third + 3 perfect fifths = 23 steps + 3 * 42 steps = 149 steps.
>
> So herein lies the problem: 72-tet's best approximation for the
> interval that is one major third and three perfect fifths wide is one
> step wider than the sum total of 72-tet's best approximations for the
> interval of one major third and three times one perfect fifth. I find
> this extremely annoying, and if this error exists here, then I assume
> it will exist elsewhere as well. Using chords that have their basis in
> low-integer overtones, such as 17 or 19, doesn't fix the issue itself,
> which is that 72-tet is inconsistent for fairly common chords.
>
> I hope I've explained it right this time.
>
> -Mike
>

Damn, I've started a holy war.

That chord was the first one that I could think of. As to the
allegations that that chord either "sounds bad" or "isn't used," I
guarantee you it is used (it's a more modern chord, but it's used). To
be honest, I just picked the first chord that I could remember having
that issue in 72-tet. It also just raises the question of what other
chords have this problem, especially extended voicing chords in jazz
that go outside of the traditional #9/b9/13 whatever chord structure.
Believe it or not, jazz musicians usually don't think about chord
voicing numbers when they're playing. They usually just play, and
sometimes they can end up pretty far "out" from the home key, but in a
harmonically related way (and sometimes not in a harmonically related
way). Are there inconsistencies in rounding there as well?

And let me be clear: I don't think in any way that harmony is nothing
but a set of stacked 5/4 and 6/5 major and minor thirds. I'm just
saying that sometimes, chords ARE just a set of stacked 5/4 and 6/5
major thirds. And sometimes, 72-tet doesn't handle that well. That is
all.

I assume that the consistency issues will become more prominent when
people try to build chords from other intervals, such as if someone
tries to build a harmonic 7th chord off of the harmonic 7th of the
root. Or something like that. 72-tet is fairly good with its 3-limit
and 5-limit consistency levels except for these flaws that I've been
mentioning, but I assume it fares much worse with its 7-limit and
11-limit consistency levels.

I've got to check out 205-ET I think, it seems promising, if not a
little daunting.

Mike, we both (Carl and I) understood long ago. And I assume any other
reader here did as well. You are the one missing something. Here's my
guess about your confusion:

The value of 135 being exactly 135 is NIL. Nobody will hear the
difference in terms of that absolute.
Just intonation matters in terms of CLOSELY RELATED harmonies. Simple
ratios. High ratios are not perceptible as being just intonation. In
that regard, why should we ever use them? Well, because maybe over
time I do exactly what you're saying - but not all at once.

Let me explain further. Let's say I play each interval - each third
of your chord ONE AFTER ANOTHER as a series, not at once. And let's
say I tune each to pure JI.
Then I might want a variation, I might have a set tonal center C note.
And I might want to jump from it to the 135 note, and play each third
as a series one-at-a-time in descending order, and then end up back
where I started. Clearly if I chose any note other than the 135 and
still used pure JI, I would end up not where I started. Hence the 135
is important to this example.

However, 135 as a harmony is totally not worth caring about or
discussing. It doesn't make any particularly special harmony on its
own. It only makes audible harmony when the rest of the notes in your
chord are included. And EVEN STILL, it isn't relevant how it relates
to the root, only how it relates to its harmonically nearby neighbors.

So the point is: it is not *crazy* for you to insist on not accepting
the 72ET fifth error FOR EACH fifth - although most people think it
sounds fine. It is not crazy for you to say that the thirds in 72ET
aren't JI-enough for you, but again most people think they are alright.
BUT - if you are willing to accept the 72ET fifths and thirds as being
on-their-own good enough for you - then you are simply making an error
to be using 72ET but then calculating the whole chord example in JI.
You should simply be calculating it using your already acceptable 72ET
fifths and thirds, and it will add up just fine that way. And there
will be NO PROBLEM with the chord because each fifth and third will
sound fine. And the sound of that chord is TOTALLY IRRELEVANT
regarding the 135, the only factor that makes that chord work is the
blending of each third and fifth.

I'll put it another way. If you used a different temperament that had
the same fifths and thirds errors as 72ET but they were reversed
(sharp instead of flat errors), your chord would probably for the most
part sound fundamentally the same. You could even mix them up. You
could tune one third a little flat, another a little sharp, and it
doesn't matter what they add up to. The whole sound of your chord is
the sound of a series of acceptable thirds. Comparing any two notes
in the chord that are more than an ninth away from each other is
comparing two notes that the listener is not hearing as directly
interacting. You're comparing notes that aren't relevant to the
listener's experience.

There is no reason that you should be entering the JI chord into scala
and then being frustrated. Just don't do that. Either use each
interval as itself already part of 72ET, or perhaps choose to stay
with pure JI and NEVER adjust it to 72ET, just play it on your
computer in pure JI! There's no reason to do one step in one tuning
and the other in the other tuning. Why are you trying to give
yourself a headache?

Ok, look, I do sympathize. You figured out some math of ratios and
you see it creating a bad sound in 72ET although it sounds good in
pure JI. That's fair enough.

The real error is thinking that chords of "stacking" add up to unified
wholes. They do not. Stacked chords like that add up to an
interesting blend in which we can perceive each interval and they
can't be totally pulled away from the whole, but the listener does not
hear it as a unified, fused, single sound. Harmonic chords, where
every note is directly related to a single, simple harmonic series -
those blend purely and fuse into a single sound when played in pure
JI. Your stack chords don't do that. They don't do it in pure JI,
and they don't do it in 72ET or 205ET. They just don't. So with
THOSE chords, all that matters is that each diad in the series is an
acceptable harmony. It isn't relevant that it is *possible* to
express it as a whole ratio series with giant numbers like 135. They
do sound neat. Go ahead and use them. But don't bother calculating
their unified ratios, because that isn't how they are heard. That's
not how they work.

If you're still confused, let us know, but please trust us - we
understood all along as soon as you clarified what #15 meant to you.

Best,
Aaron W

Aaron Wolf wrote:

> Carl, Mike's complaint is that when he enters the ratios PURELY as
> extended JI, then the last note is rounded flat from what would be
> good in 72ET. You are totally correct that it works in 72, such as if
> you treat each interval as a "major third" and "minor third" WITHIN
> 72. What he's done is to treat them as pure instead and then take the
> whole thing and try to approximate each to a note in 72.

The solution seems to be not to do that.

> If I had a 72ET keyboard, and I played each interval as a good third,
> I'd end up just fine, as you say. And it would sound fine, because
> 135 in and of itself doesn't really matter. But you see where he's
> getting confused. I think it's because he doesn't have a keyboard,
> he's entering bunches of ratios into scala. A 72ET keyboard would
> work for him, as would the Tonal Plexus. Since you think 72 is better
> - you ought to go ahead as you said earlier and get working on making
> physical 72ET keyboards practical for people - whether using existing
> hardware and software or not. I think people would appreciate that.

A Ztar works well as a 72ET or miracle-31 keyboard. I have one, although not with me. No reason other people can't get one.

For the type of chords Mikes talking about, schismatic-29 might do the trick. Here are my instructions:

http://x31eq.com/schv12.htm

I think you need a bit more than 5 keyboard-octaves for the 15th chord to work. And tape to hold the keys down.

Graham

"Mike Battaglia" <battaglia01@...> wrote:

> Have you put the chord in Scala or some software? Do you not
> see what I am talking about?

I keep asking you but you keep replying with confusing language
such as "the chord with the rounding error" (both chords have
them if there's a consistency issue), "the obvious chord" (what's
obvious to you may not be obvious to me), stuff in Simms notation
that two people have said they can't read, and stuff in JI which
doesn't help because we're talking about approximations. So
please, use degrees of 72-ET.

> Does the math work out? Let's see.
>
> 1 major third + 3 perfect fifths = 23 steps + 3 * 42 steps = 149
> steps.
>
> So herein lies the problem: 72-tet's best approximation for the
> interval that is one major third and three perfect fifths wide
> is one step wider than the sum total of 72-tet's best
> approximations for the interval of one major third and three
> times one perfect fifth. I find this extremely annoying, and if
> this error exists here, then I assume it will exist elsewhere
> as well. Using chords that have their basis in low-integer
> overtones, such as 17 or 19, doesn't fix the issue itself,
> which is that 72-tet is inconsistent for fairly common chords.
>
> I hope I've explained it right this time.

Everyone is telling you that directly approximating 135 doesn't
matter and that what the top note of the chord SHOULD BE is 149.
Is that or is it not the chord you prefer?

-Carl

--- In tuning@yahoogroups.com, "Mike Battaglia" <battaglia01@...> wrote:
>
> Haha, in the time it took me to write that last post, there were three
> more posts. Oh well.
>
> Aaron and Carl: At this point I think we're all mostly in agreement.

Ok, sorry - I just wrote a darn long response to your claim that we
were still confused before I saw this post. But there may have been
SOMETHING useful in my post anyway, so I won't kick myself TOO hard
for wasting the time.

> I happened upon this way of thinking when I tried to figure out why
> the melodic minor scale and its modes had a completely different feel
> from the diatonic major scale and its modes. The only explanation that
> made sense to me was that the melodic minor scale has two directly
> stacked major thirds in it, which the major scale doesn't have.

AHA! So you admit to coming up with a hypothesis and then formulating
music around it as though it were true - before rigorously testing the
hypothesis and trying to disprove it! You are definitely in the
jazz-theory tradition in that regard.

That's how I think jazz theory started - someone hypothesized that the
whole reason even 7th chords existed was that they were
every-other-note on the piano. That is a totally unconvincing and
empty hypothesis, but since it appeared to simply allow many things to
have an explanation they went with it. And when it didn't work so
well (11 chords aren't the most popular) they just made up exceptions
like please consider leaving out the 11 when playing 13 chords...

And yet, some interesting music and harmonies did come into play as a
result of blind faith in this crappy original explanation.

Ok, that's a little simplistic of a history - but you see how you were
doing the same thing? In a way?

> C D E F# G# A B C
>
> The C and the E and the G# are two directly stacked major thirds. This
> creates the feeling of there being a 25/16 interval -- although you
> could interpret it to be a number of different things, I suppose. To
> me, it intuitively feels like 25/16. And that could be why the scale
> is considerably more dissonant than lydian mode:
>

No - I think it intuitively feels to you that E and G# are - in
certain contexts - a 5/4 implication. I agree. That doesn't make G#
imply a 25/16. It just doesn't. See, that's the "magic" of
temperament. C to E can imply 5/4, but actually be a little sharp.
When you then play E to G# it also implies 5/4, but there ISN'T any
implication that the root E is flatter than the audible note you
actually are playing. The E of E-G# is definitely sharper than 5/4.
So the implication you get from these three notes is the feeling of
5/4 in two places, but at the same time a feeling of being sharper,
and of the G# being a MELODIC leading tone into the A, which is
exactly why it is there in a scale called the melodic minor!

And the reason the scale has its feeling might be more related to how
the notes lead into each other than it does to any aspect of harmony.

I think the whole problem is that in trying to think of temperament
and how it implies things, you are ignoring actual aspects of th
temperament that also make it distinct from JI. Fact is, though some
implications and relations are possible, nothing in a temperament
sounds like JI, and JI can never sound like a temperament. They are
not the same experience.

Best,
AW

Mike Battaglia wrote:
> Have you put the chord in Scala or some software? Do you not see what
> I am talking about?

Why do we need Scala to *see* the problem? How does the problem arise when you're making music in 72-tet?

> The obvious chord sounds WORSE than the one with the rounding error skip.
> > 32:40:48:60:72:90:108:135

What's obvious about the other one?

> In 72-tet, that chord SHOULD BE
> > C E- G B- D F#- A C#-

Yes, obviously. There are two chains of fifths from 12-tet:

C G D A
E- B- F#- C#-

The thirds are all reduced a comma relative to 12-tet. I don't need Scala to tell me this and I'm not confused.

> C#-. Note the -. That means it is one 72-tet step flat of the C# that
> is in 12-tet.

Yes.

> BUT
> > due to the fact that errors in rounding add up and accumulate as you
> stack more and more fifths,
> > the best 72-tet approximation of the WHOLE CHORD from just intonation
> to 72-tet is this:
> > C E- G B- D F#- A C#

No, that's the best approximation of each interval relative to the root, where intervals are taken as extended 5-limit JI. If this is all Scala gives maybe there's a problem with Scale. But maybe Scala can do the approximation different ways -- I'm not familiar with Scala.

> C#! no minus! The C# is one 72-tet step up of where it should be!

Yes, obviously.

> I assume your question is how I'm running into this weird C#, and why
> it isn't C#- like I'd expect?

*My* question is, if C#- is what you expect, and C#- is what sounds best, what's the problem?

<snip>
> So herein lies the problem: 72-tet's best approximation for the
> interval that is one major third and three perfect fifths wide is one
> step wider than the sum total of 72-tet's best approximations for the
> interval of one major third and three times one perfect fifth. I find
> this extremely annoying, and if this error exists here, then I assume
> it will exist elsewhere as well. Using chords that have their basis in
> low-integer overtones, such as 17 or 19, doesn't fix the issue itself,
> which is that 72-tet is inconsistent for fairly common chords.

FWIW, here are the mappings of the simplest equal temperaments that are consistent for this chord (the first number is the number of steps to the octave):

[12, 19, 28]
[19, 30, 44]
[22, 35, 51]
[29, 46, 67]
[31, 49, 72]
[34, 54, 79]
[41, 65, 95]
[46, 73, 107]
[53, 84, 123]
[65, 103, 151]
[77, 122, 179]
[84, 133, 195]
[87, 138, 202]
[94, 149, 218]
[99, 157, 230]
[111, 176, 258]
[118, 187, 274]
[140, 222, 325]
[142, 225, 330]
[147, 233, 341]
[152, 241, 353]
[164, 260, 381]
[171, 271, 397]
[176, 279, 409]
[183, 290, 425]
[193, 306, 448]
[200, 317, 464]
[205, 325, 476]
[217, 344, 504]
[224, 355, 520]

Note that 205 is indeed in the list. But so is 84, which is a multiple of 12. So if you're happy dividing your semitones into 7 equal parts...

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> Aaron Wolf wrote:
>
> > Carl, Mike's complaint is that when he enters the ratios PURELY as
> > extended JI, then the last note is rounded flat from what would be
> > good in 72ET. You are totally correct that it works in 72, such as if
> > you treat each interval as a "major third" and "minor third" WITHIN
> > 72. What he's done is to treat them as pure instead and then take the
> > whole thing and try to approximate each to a note in 72.
>
> The solution seems to be not to do that.
>

Yeah, exactly.

> > If I had a 72ET keyboard, and I played each interval as a good third,
> > I'd end up just fine, as you say. And it would sound fine, because
> > 135 in and of itself doesn't really matter. But you see where he's
> > getting confused. I think it's because he doesn't have a keyboard,
> > he's entering bunches of ratios into scala. A 72ET keyboard would
> > work for him, as would the Tonal Plexus. Since you think 72 is better
> > - you ought to go ahead as you said earlier and get working on making
> > physical 72ET keyboards practical for people - whether using existing
> > hardware and software or not. I think people would appreciate that.
>
> A Ztar works well as a 72ET or miracle-31 keyboard. I have
> one, although not with me. No reason other people can't get
> one.
>

Interesting... for some reason I never took the Ztar's seriously. I
thought of them as just like MIDI-guitars, guitars for MIDI control,
just more dedicated than a set up on a real guitar. What would it
actually be like to use a Ztar for 72ET?

Any further elaboration would be interesting...

> Believe it or not, jazz musicians usually don't think about chord
> voicing numbers when they're playing. They usually just play, and
> sometimes they can end up pretty far "out" from the home key, but in a
> harmonically related way (and sometimes not in a harmonically related
> way).

My point exactly. So theorists after the fact conjecturing that these
chords are stacked chords and not harmonic implications are just
[insert not especially complementary term in plural] who don't
sometimes even know that the harmonic series exists, and they're just
pushing the most seemingly apparent (but actually very impoverished)
explanations onto music they don't really understand. And then these
get taught by intellectual, dogmatic teachers who just parrot what
they learned. All the while, the music is being made just as you say
above.

-AW

> I keep asking you but you keep replying with confusing language
> such as "the chord with the rounding error" (both chords have
> them if there's a consistency issue), "the obvious chord" (what's
> obvious to you may not be obvious to me), stuff in Simms notation
> that two people have said they can't read, and stuff in JI which
> doesn't help because we're talking about approximations. So
> please, use degrees of 72-ET.

See here:

> So you do like the obvious chord better! So there's no
> problem at all! It's you who're creating the problem by
> worrying about the numbers!

You're the one who even started the phrase "the obvious chord." It's a
two way street. I am just as confused by some of the things that you
say as you are by what I say.

"Who is miscommunicating" is a pointless argument. I gave you a chord
and a thought on how that chord is inconsistently approximated by
72-tet, and I you responded by saying that 72-tet approximates it
correctly. I had no idea where the communication broke down until
people told me they couldn't read the Sims-maneri notation, and so I
then explained it instead in terms of 72-tet steps and cents.

>> Does the math work out? Let's see.
>>
>> 1 major third + 3 perfect fifths = 23 steps + 3 * 42 steps = 149
>> steps.
>>
>> So herein lies the problem: 72-tet's best approximation for the
>> interval that is one major third and three perfect fifths wide
>> is one step wider than the sum total of 72-tet's best
>> approximations for the interval of one major third and three
>> times one perfect fifth. I find this extremely annoying, and if
>> this error exists here, then I assume it will exist elsewhere
>> as well. Using chords that have their basis in low-integer
>> overtones, such as 17 or 19, doesn't fix the issue itself,
>> which is that 72-tet is inconsistent for fairly common chords.
>>
>> I hope I've explained it right this time.
>
> Everyone is telling you that directly approximating 135 doesn't
> matter and that what the top note of the chord SHOULD BE is 149.
> Is that or is it not the chord you prefer?

I do NOT prefer the sound of the chord at 149. I prefer the sound of
the chord at 150. I especially prefer it if you continue the pattern
of major and minor thirds PAST the C#, and there are many many many
other chords that have the same rounding problem. Admittedly the
149-150 difference is minor -- it becomes much more apparent if you
continue the pattern even more, and there are other chords in which
the inconsistencies become apparent more quickly.

As for what "matters" and what doesn't "matter," this seems like a
pointless debate. I have compared the chords with the C# being at 150
and the C# being at 149. The C# being at 150 to my ears generally
sounds more like that JI version, ESPECIALLY if you continue the
pattern of major and minor thirds past the C#, when the
inconsistencies become even more annoying and more obvious. I don't
know why I'm supposed to believe that it "doesn't matter" when I can
hear to myself that "it matters." If the sound of it doesn't bother
you, then fine. But it bothers me, and that is all I am saying -- that
is one of my reasons for disliking 72-tet.

And Aaron: I am not "confused," nor is there anything "I don't get."
It is very easy to see that you are recommending that I just ignore
the inconsistencies because you think that the end interval from the C
to the C# is going to be irrelevant, and only the relative consonances
will matter. As I have said a few times, I have tried that approach,
and it doesn't SOUND as good.

Furthermore, it is extremely arrogant to think that I am "confused"
simply because I have a different preference for something than you
do. You have given me YOUR "theory" as to what "matters" and doesn't
matter and how dissonance and consonance works, which I only partially
agree with. Furthermore, your applying this mental structure to music
and trying to fit everything into it is the same kind of
"intellectualizing behavior" that you have accused me of trying to
apply. Please try to be a bit more-self aware next time you start
acting as if I can't come up with my own theories on how things work
-- at least I'm not trying to impose them on others via "clever"
allegations as though they were "confused."

> Ok, sorry - I just wrote a darn long response to your claim that we
> were still confused before I saw this post. But there may have been
> SOMETHING useful in my post anyway, so I won't kick myself TOO hard
> for wasting the time.

I suppose that makes sense. I thought your post was in response to my
post right before it, in which I was quite irritated to discover that
you thought I was in some way "confused." I suppose you will respond
to that post before I respond to this post, and the pattern will
continue all night.

>> I happened upon this way of thinking when I tried to figure out why
>> the melodic minor scale and its modes had a completely different feel
>> from the diatonic major scale and its modes. The only explanation that
>> made sense to me was that the melodic minor scale has two directly
>> stacked major thirds in it, which the major scale doesn't have.
>
> AHA! So you admit to coming up with a hypothesis and then formulating
> music around it as though it were true - before rigorously testing the
> hypothesis and trying to disprove it! You are definitely in the
> jazz-theory tradition in that regard.

No. I came up with a hypothesis and tested it to see if it was
plausible. It seemed, sounded, and intuitively felt plausible. This
has really nothing to do with the concept of using 17 or 19-limit
chords to imply b9 or #9 chords. That is another way to spell out
those chords, and this is one way to spell out the melodic minor
scale.

What I'm saying is that the melodic minor scale could be ANYTHING. It
could be a LOT of things. You could look at as a rational intonation
version that approximates equal temperament, or you could look at it
as irrational intervals, or whatever. You could also look at it as
containing two stacked 5/4 thirds, which is just as valid an approach
as the rest of these.

In my mind, the context that the notes are used psychologically clues
you in to what JI interval they approximate, or if they even
approximate a JI interval at all. And by screwing around with JI
chords that incorporate 25/16, I get the same "feeling" that I do with
the equal tempered melodic minor scale.

> That's how I think jazz theory started - someone hypothesized that the
> whole reason even 7th chords existed was that they were
> every-other-note on the piano. That is a totally unconvincing and
> empty hypothesis, but since it appeared to simply allow many things to
> have an explanation they went with it. And when it didn't work so
> well (11 chords aren't the most popular) they just made up exceptions
> like please consider leaving out the 11 when playing 13 chords...

Correct. I am studying jazz piano at school, and this is predominantly
how it is taught, and it is extremely irritating. Why 11 chords sound
so weird is something I'm currently trying to figure out.

> And yet, some interesting music and harmonies did come into play as a
> result of blind faith in this crappy original explanation.
>
> Ok, that's a little simplistic of a history - but you see how you were
> doing the same thing? In a way?

Again, I never said that I was taking all of music theory and fitting
it into the narrow view that is stacked major and minor thirds. I'm
saying that stacked major and minor thirds exist, and thus they should
be explored. You for some reason think that I'm excluding higher limit
harmonies or something, which I keep saying that I am not.

>> C D E F# G# A B C
>>
>> The C and the E and the G# are two directly stacked major thirds. This
>> creates the feeling of there being a 25/16 interval -- although you
>> could interpret it to be a number of different things, I suppose. To
>> me, it intuitively feels like 25/16. And that could be why the scale
>> is considerably more dissonant than lydian mode:
>>
>
> No - I think it intuitively feels to you that E and G# are - in
> certain contexts - a 5/4 implication. I agree. That doesn't make G#
> imply a 25/16. It just doesn't. See, that's the "magic" of
> temperament. C to E can imply 5/4, but actually be a little sharp.
> When you then play E to G# it also implies 5/4, but there ISN'T any
> implication that the root E is flatter than the audible note you
> actually are playing. The E of E-G# is definitely sharper than 5/4.
> So the implication you get from these three notes is the feeling of
> 5/4 in two places, but at the same time a feeling of being sharper,
> and of the G# being a MELODIC leading tone into the A, which is
> exactly why it is there in a scale called the melodic minor!

I don't see why C-G# can't imply a 25/16. If C-Bb can in certain
contexts psychologically imply 7/4, even on a piano, then why can't
C-G# imply a 25/16? The only structural difference between the melodic
minor modes and the diatonic scale modes is that the melodic minor
modes contain in them two stacked equal tempered major thirds. It is
not too much of a stretch to see what the corresponding JI scale
sounds like with two stacked 5/4 major thirds. In my experience, they
sound similar, but obviously not equivalent.

I assume you think that I'm some kind of JI nazi :P I am not. I don't
think JI is the end-all be-all of everything. I was only picking one
specific instance where I was trying to de-approximate 12tet to a
theoretical JI root, of which there are a few. Take the ionian
augmented scale:

C D E F G# A B C

You can play C E G#, which is an augmented chord, or F G#/Ab C, which
is a minor chord. So relative to the root, the G# could be translated
into JI as 25/16, or it could be translated into JI 24/15 as F Ab C.

> And the reason the scale has its feeling might be more related to how
> the notes lead into each other than it does to any aspect of harmony.
>
> I think the whole problem is that in trying to think of temperament
> and how it implies things, you are ignoring actual aspects of th
> temperament that also make it distinct from JI. Fact is, though some
> implications and relations are possible, nothing in a temperament
> sounds like JI, and JI can never sound like a temperament. They are
> not the same experience.

I don't think so. I'm currently really interested in Charles Lucy's
ideas on irrational numbers being the basis for intervals sounding
good. That being said, it is still possible to attempt to work
"backwards" from temperament to JI, as long as you realize that there
is more than one way to work backwards. So it's like, I keep picking
one possible way to work backwards, and you keep telling me that I'm
saying it's the ONLY way to work backwards, which I'm not.

Aaron Wolf wrote:

> Interesting... for some reason I never took the Ztar's seriously. I
> thought of them as just like MIDI-guitars, guitars for MIDI control,
> just more dedicated than a set up on a real guitar. What would it
> actually be like to use a Ztar for 72ET?
> > Any further elaboration would be interesting...

They're *designed* as MIDI guitars, and that's useful because they're tried and tested musical instruments rather than specialist microtonal input devices. But they still work as microtonal input devices because you have 144 total keys (or 150 if you include the open strings).

It is more comfortable to hold it like a guitar. There's a "tapping" mode where it works like a keyboard, so you hit a key and it sends the note, rather than having to use the string triggers. There's also a Mini-Z that doesn't have the triggers, and so makes more sense as a keyboard. And there's a Z-Board which has two fretboards arranged to be a keyboard. I don't like that idea because the keys are the wrong shape to hit from the front.

For 72ET the obvious way is to tune each string to 12ET and space them a single step of 72 apart. That's simple to implement in a synthesizer if it can tune each channel differently -- no need for tuning tables.

You can also use miracle to get a subset of 72ET (or other tunings). The best way I found for this is to tune each string a quomma (2 degrees of 72) apart, and each fret two secors (totalling 14 degrees of 72) apart. But with fudging so that you keep within the 31 note miracle scale: get a secor (7 degrees of 72) between three strings and round up 5 frets to be an octave. (In fact you only get 30 notes so you need to do something clever with a pedal to really get all 31.) This may sound complicated, but it's based around decimal notation, so the mapping is

0v 0 0^ 1v 1 1^
2v 2 2^ 3v 3 3^
4v 4 4^ 5v 5 5^
...

and so on. There are good melodic intervals between the frets, you get inflections between strings so you can adjust the spelling, and the octaves are easy to stretch. Each chord has interval has four different shapes because of the inequality in the mapping, but the intervals in each direction still sound the same melodically.

Another way is a harmonic mapping, following my 7-limit neutral-third lattices, which I mention here:

http://x31eq.com/lattice.htm#11limit

Graham

Yeah.

Meanwhile, in my limited little musical bubble, I find that adjusting
for the JI rounding errors that come up in 72-tet SOUNDS better. Beats
less, sounds more stable, etc. And it is extra work that I don't think
will "catch on" easily, unless people just ignore it, which I suppose
is a matter of personal preference. But therein lies my problem with
72-tet.

My question is, is there any other temperament that can get at
higher-limit intervals without having this problem? 53 is fairly
decent, but it's 7 and 11-limit resolution is supposedly not the
best... I hear decent things about 41 though.

On Mon, May 26, 2008 at 11:48 PM, Aaron Wolf <wolftune@...> wrote:
>
>> Believe it or not, jazz musicians usually don't think about chord
>> voicing numbers when they're playing. They usually just play, and
>> sometimes they can end up pretty far "out" from the home key, but in a
>> harmonically related way (and sometimes not in a harmonically related
>> way).
>
> My point exactly. So theorists after the fact conjecturing that these
> chords are stacked chords and not harmonic implications are just
> [insert not especially complementary term in plural] who don't
> sometimes even know that the harmonic series exists, and they're just
> pushing the most seemingly apparent (but actually very impoverished)
> explanations onto music they don't really understand. And then these
> get taught by intellectual, dogmatic teachers who just parrot what
> they learned. All the while, the music is being made just as you say
> above.
>
> -AW
>
>

Mike wrote...

> You're the one who even started the phrase "the obvious chord."
> It's a two way street. I am just as confused by some of the
> things that you say as you are by what I say.
>
> "Who is miscommunicating" is a pointless argument.

For sure, for sure, and doubly true for tuning theory. I didn't
mean to play the blame game.

> > Everyone is telling you that directly approximating 135 doesn't
> > matter and that what the top note of the chord SHOULD BE is 149.
> > Is that or is it not the chord you prefer?
>
> I do NOT prefer the sound of the chord at 149. I prefer the sound
> of the chord at 150.

OK! (whew) So we have an experience that is at odds with
the one predicted by 5-limit theory.

> As for what "matters" and what doesn't "matter," this seems like a
> pointless debate. I have compared the chords with the C# being at
> 150 and the C# being at 149. The C# being at 150 to my ears
> generally sounds more like that JI version,

OK. I'd better do some listening.

> ESPECIALLY if you continue the pattern of major and minor
> thirds past the C#, when the inconsistencies become even more
> annoying and more obvious.

Well then we've got a whole 'nother chord to break apart.
Let's stick to what we've got so far for now.

> I don't know why I'm supposed to believe that it "doesn't
> matter" when I can hear to myself that "it matters."

I'm not telling you there isn't a difference, but I am
telling you it isn't because of 135.

> Furthermore, it is extremely arrogant to think that I am
> "confused" simply because I have a different preference for
> something than you do.

I don't know for sure how that got started but I thought
you initially said you found the inconsistency confusing
when playing.

-Carl

> Mike Battaglia wrote:
>> Have you put the chord in Scala or some software? Do you not see what
>> I am talking about?
>
> Why do we need Scala to *see* the problem? How does the
> problem arise when you're making music in 72-tet?
>
>> The obvious chord sounds WORSE than the one with the rounding error skip.
>>
>> 32:40:48:60:72:90:108:135
>
> What's obvious about the other one?

All of the above was actually directed at Carl.

<snip>

>> due to the fact that errors in rounding add up and accumulate as you
>> stack more and more fifths,
>>
>> the best 72-tet approximation of the WHOLE CHORD from just intonation
>> to 72-tet is this:
>>
>> C E- G B- D F#- A C#
>
> No, that's the best approximation of each interval relative
> to the root, where intervals are taken as extended 5-limit
> JI.

Is that not what the whole point of the concept of "consistency" is?

> *My* question is, if C#- is what you expect, and C#- is what
> sounds best, what's the problem?

C#- is what I'd expect, yet C# is what sounds best. Admittedly my
example here was more of a theoretical demonstration than a purely
practical one. The C# that is in JI is actually around midway of a
72-tet step, as you have pointed out. However, there are definitely
more chords and extended "out" voicings in which this problem arises
than this one chord I've pointed out. The problem is that you can see
that if you work in 5-limit JI and go "out" enough, you run into these
inconsistencies when approximating to 72-tet. Jazz musicians often
like to go up in patterns of fifths and thirds and such, and as such
this turns into a bit of a problem. There are times when the rounding
errors bring it much closer to a full step than in this case, where it
turns out to be about half of a step. And adjusting for the rounding
errors is tricky and annoying to do manually, but it sounds much
better in the end to my ears. Or at least, it sounds different... more
beatless, pure, etc., which is partially what attracted me to 72-tet
in the first place. The other thing that attracted me to 72-tet is
that it is simple to think about as it builds off of 24-tet (which is
what most people think in) and consequently 12-tet (which is what most
people know how to play) -- but in my experience, thinking about these
rounding errors is annoying enough that it more than makes up for the
ease of adjustment from 12-tet.

Again, if you don't think that the chords sound bad even with the
rounding errors -- then use 72-tet! I am just voicing my opinion.
Obviously there are only certain areas in which these rounding errors
become a problem at all, but I am becoming wary of small-step equal
temperaments now for precisely this reason -- it makes rounding errors
easy.

> FWIW, here are the mappings of the simplest equal
> temperaments that are consistent for this chord (the first
> number is the number of steps to the octave):
>
> [12, 19, 28]
> [19, 30, 44]
> [22, 35, 51]
> [29, 46, 67]
> [31, 49, 72]
> [34, 54, 79]
> [41, 65, 95]
> [46, 73, 107]
> [53, 84, 123]
> [65, 103, 151]
> [77, 122, 179]
> [84, 133, 195]
> [87, 138, 202]
> [94, 149, 218]
> [99, 157, 230]
> [111, 176, 258]
> [118, 187, 274]
> [140, 222, 325]
> [142, 225, 330]
> [147, 233, 341]
> [152, 241, 353]
> [164, 260, 381]
> [171, 271, 397]
> [176, 279, 409]
> [183, 290, 425]
> [193, 306, 448]
> [200, 317, 464]
> [205, 325, 476]
> [217, 344, 504]
> [224, 355, 520]
>
> Note that 205 is indeed in the list. But so is 84, which is
> a multiple of 12. So if you're happy dividing your
> semitones into 7 equal parts...
>
> Graham

I'm not sure how to interpret that chart... What do the rows vs. the
columns mean?

Also, what exactly do you mean by "interpreting the chord
consistently" if not that the widest interval is the sum of the inner
ones? Because that is the definition of consistency I've been using,
and under that definition, 72-tet does NOT approximate the chord
consistently.

-Mike

>> You're the one who even started the phrase "the obvious chord."
>> It's a two way street. I am just as confused by some of the
>> things that you say as you are by what I say.
>>
>> "Who is miscommunicating" is a pointless argument.
>
> For sure, for sure, and doubly true for tuning theory. I didn't
> mean to play the blame game.

Haha, yeah. This got hostile pretty quickly between everyone, which is
kind of weird, but it's all good

>> > Everyone is telling you that directly approximating 135 doesn't
>> > matter and that what the top note of the chord SHOULD BE is 149.
>> > Is that or is it not the chord you prefer?
>>
>> I do NOT prefer the sound of the chord at 149. I prefer the sound
>> of the chord at 150.
>
> OK! (whew) So we have an experience that is at odds with
> the one predicted by 5-limit theory.

I'm not sure what you mean by 5-limit theory... From using 5-limit JI
to built that chord, the last note rounds up to a different note in
72-tet than you would expect by adding up the sum of the intervals.
It's like a stained glass pattern: You have a shape behind the stained
glass, which in this case represents the chord in question. And the
stained glass in this case has 72 "panes" per yard, which represents
an octave. And the panes seem to be lit up in a pattern of one every
23 steps, followed by one every 19 steps, which is where the shape
behind the panes "comes out" through the glass. But the weird thing
is, by the time you get to the last "block" in the shape, or note in
the chord, the pane in the stained glass window in which that block
appears is one pane over than you would expect by continuing the
pattern, because the shape behind the glass happens to come out there
instead, because every pane has been slightly off with the shape in
the background. Or something.

I need to get a 72-tet MIDI controller and screw around with it a lot
more before I make my FINAL judgement on it. But from trying to
compose with it, I found these rounding errors to be a huge annoyance,
and calculating when to adjust for them to be pretty annoying as well
(but worth the effort in the end). It just led me to abandon 72 as not
being all that it's cracked up to be, although my ear adjusted to
19-tet pretty quickly (and I thought that it sounded -HORRIBLE- in the
beginning), so maybe I'll give it another chance.

I'm just curious though, to Aaron: where exactly did 205-tet, of all
things, come into this? Why did the tonal plexus pick that particular
ET to use?

Mike Battaglia wrote:
>>> due to the fact that errors in rounding add up and accumulate as you
>>> stack more and more fifths,
>>>
>>> the best 72-tet approximation of the WHOLE CHORD from just intonation
>>> to 72-tet is this:
>>>
>>> C E- G B- D F#- A C#
>> No, that's the best approximation of each interval relative
>> to the root, where intervals are taken as extended 5-limit
>> JI.
> > Is that not what the whole point of the concept of "consistency" is?

It's the definition. But the point is that you want consonances to be consistent. The problem here is that the 135 isn't approximated consistently, but most of us don't see that as a problem because we don't see 135 as an independent interval.

>> *My* question is, if C#- is what you expect, and C#- is what
>> sounds best, what's the problem?
> > C#- is what I'd expect, yet C# is what sounds best. Admittedly my
> example here was more of a theoretical demonstration than a purely
> practical one. The C# that is in JI is actually around midway of a
> 72-tet step, as you have pointed out. However, there are definitely
> more chords and extended "out" voicings in which this problem arises
> than this one chord I've pointed out. The problem is that you can see
> that if you work in 5-limit JI and go "out" enough, you run into these
> inconsistencies when approximating to 72-tet. Jazz musicians often
> like to go up in patterns of fifths and thirds and such, and as such
> this turns into a bit of a problem. There are times when the rounding
> errors bring it much closer to a full step than in this case, where it
> turns out to be about half of a step. And adjusting for the rounding
> errors is tricky and annoying to do manually, but it sounds much
> better in the end to my ears. Or at least, it sounds different... more
> beatless, pure, etc., which is partially what attracted me to 72-tet
> in the first place. The other thing that attracted me to 72-tet is
> that it is simple to think about as it builds off of 24-tet (which is
> what most people think in) and consequently 12-tet (which is what most
> people know how to play) -- but in my experience, thinking about these
> rounding errors is annoying enough that it more than makes up for the
> ease of adjustment from 12-tet.

Okay, sorry then, I misunderstood you on that. I have to agree with Carl that your results disagree with your 5-limit theory. If the point were to stack 5-limit thirds you should prefer the best thirds regardless of how the errors add up. As you don't it looks much more like you're hearing 17 than 135. The way to test it is to try 94 note equal temperament. That's consistent both for this extended 5-limit chord and for 17-limit just intonation. So you can try the 5-limit version and see what it sounds like when you raise the C# a degree. And try all kinds of other experiments!

> Again, if you don't think that the chords sound bad even with the
> rounding errors -- then use 72-tet! I am just voicing my opinion.
> Obviously there are only certain areas in which these rounding errors
> become a problem at all, but I am becoming wary of small-step equal
> temperaments now for precisely this reason -- it makes rounding errors
> easy.
> > >> FWIW, here are the mappings of the simplest equal
>> temperaments that are consistent for this chord (the first
>> number is the number of steps to the octave):
>>
>> [12, 19, 28]
>> [19, 30, 44]
>> [22, 35, 51]
>> [29, 46, 67]
>> [31, 49, 72]
>> [34, 54, 79]
>> [41, 65, 95]
>> [46, 73, 107]
>> [53, 84, 123]
<snip>

> I'm not sure how to interpret that chart... What do the rows vs. the
> columns mean?

Each row is an equal temperament. The first column is the number of steps to an octave (2:1). The next column is the number of steps to a 3:1 and then 5:1.

> Also, what exactly do you mean by "interpreting the chord
> consistently" if not that the widest interval is the sum of the inner
> ones? Because that is the definition of consistency I've been using,
> and under that definition, 72-tet does NOT approximate the chord
> consistently.

Er, when did I say that? I'll need the context.

Graham

Er, sorry, I misread your chart. 72-tet isn't in the chart.

The question is, sir, how did you generate that chart? :P Whatever
software you used, hook it up, because I would find it -extremely-
useful.

On Tue, May 27, 2008 at 1:30 AM, Graham Breed <gbreed@...> wrote:
> Mike Battaglia wrote:
>>>> due to the fact that errors in rounding add up and accumulate as you
>>>> stack more and more fifths,
>>>>
>>>> the best 72-tet approximation of the WHOLE CHORD from just intonation
>>>> to 72-tet is this:
>>>>
>>>> C E- G B- D F#- A C#
>>> No, that's the best approximation of each interval relative
>>> to the root, where intervals are taken as extended 5-limit
>>> JI.
>>
>> Is that not what the whole point of the concept of "consistency" is?
>
> It's the definition. But the point is that you want
> consonances to be consistent. The problem here is that the
> 135 isn't approximated consistently, but most of us don't
> see that as a problem because we don't see 135 as an
> independent interval.
>
>>> *My* question is, if C#- is what you expect, and C#- is what
>>> sounds best, what's the problem?
>>
>> C#- is what I'd expect, yet C# is what sounds best. Admittedly my
>> example here was more of a theoretical demonstration than a purely
>> practical one. The C# that is in JI is actually around midway of a
>> 72-tet step, as you have pointed out. However, there are definitely
>> more chords and extended "out" voicings in which this problem arises
>> than this one chord I've pointed out. The problem is that you can see
>> that if you work in 5-limit JI and go "out" enough, you run into these
>> inconsistencies when approximating to 72-tet. Jazz musicians often
>> like to go up in patterns of fifths and thirds and such, and as such
>> this turns into a bit of a problem. There are times when the rounding
>> errors bring it much closer to a full step than in this case, where it
>> turns out to be about half of a step. And adjusting for the rounding
>> errors is tricky and annoying to do manually, but it sounds much
>> better in the end to my ears. Or at least, it sounds different... more
>> beatless, pure, etc., which is partially what attracted me to 72-tet
>> in the first place. The other thing that attracted me to 72-tet is
>> that it is simple to think about as it builds off of 24-tet (which is
>> what most people think in) and consequently 12-tet (which is what most
>> people know how to play) -- but in my experience, thinking about these
>> rounding errors is annoying enough that it more than makes up for the
>> ease of adjustment from 12-tet.
>
> Okay, sorry then, I misunderstood you on that. I have to
> agree with Carl that your results disagree with your 5-limit
> theory. If the point were to stack 5-limit thirds you
> should prefer the best thirds regardless of how the errors
> add up. As you don't it looks much more like you're hearing
> 17 than 135. The way to test it is to try 94 note equal
> temperament. That's consistent both for this extended
> 5-limit chord and for 17-limit just intonation. So you can
> try the 5-limit version and see what it sounds like when you
> raise the C# a degree. And try all kinds of other experiments!
>
>> Again, if you don't think that the chords sound bad even with the
>> rounding errors -- then use 72-tet! I am just voicing my opinion.
>> Obviously there are only certain areas in which these rounding errors
>> become a problem at all, but I am becoming wary of small-step equal
>> temperaments now for precisely this reason -- it makes rounding errors
>> easy.
>>
>>
>>> FWIW, here are the mappings of the simplest equal
>>> temperaments that are consistent for this chord (the first
>>> number is the number of steps to the octave):
>>>
>>> [12, 19, 28]
>>> [19, 30, 44]
>>> [22, 35, 51]
>>> [29, 46, 67]
>>> [31, 49, 72]
>>> [34, 54, 79]
>>> [41, 65, 95]
>>> [46, 73, 107]
>>> [53, 84, 123]
> <snip>
>
>> I'm not sure how to interpret that chart... What do the rows vs. the
>> columns mean?
>
> Each row is an equal temperament. The first column is the
> number of steps to an octave (2:1). The next column is the
> number of steps to a 3:1 and then 5:1.
>
>> Also, what exactly do you mean by "interpreting the chord
>> consistently" if not that the widest interval is the sum of the inner
>> ones? Because that is the definition of consistency I've been using,
>> and under that definition, 72-tet does NOT approximate the chord
>> consistently.
>
> Er, when did I say that? I'll need the context.
>
> Graham
>
>