Yahoo Tuning Groups Ultimate Backup tuning update on Centaur page

Updated some information about the 12 tone 7 limit Centaur tuning.
One is a chart that shows the 50 different intervals one can find in the 12 tone 7 limit tuning.
http://anaphoria.com/centaur.html
--
It was the first tuning i had on a sustained instrument back in these days when electronic were not an option.
Basically what gave me quite a bit to explore in a few different directions.

I always forget to mention that another advantage it has for a beginner especially is that it has both a major [A] and minor chord {F#] very close to 12ET useful for comparison.

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

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

🔗genewardsmith <genewardsmith@...>

🔗Diogenes23 <kraiggrady@...>

There is definitely some intervals close to others that one could do this.
I had noticed how Riley will use two 16/15 to function as a 8/7

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@> wrote:
> >
> >
> > Updated some information about the 12 tone 7 limit Centaur tuning.
> > One is a chart that shows the 50 different intervals one can
> > find in the 12 tone 7 limit tuning.
> > http://anaphoria.com/centaur.html
>
> I hope I won't upset you my using the dreaded word "temperament", but another fact about Centaur I think worth noting is that if you marvel temper Terry Riley's Harp of New Albion scale, for instance by using 197et, you get a scale which is a transposition of the marvel (197et) tuning of Centaur. Another transposition gives the marvel tempering of what Scala lists as indian_12, "North Indian Gamut, modern Hindustani".
>

🔗Chris Vaisvil <chrisvaisvil@...>

Guys,

You know I'm still just starting out with micro (even though its been well
over a year I've been making serious attempts).

I can see where you can generate the different scales with the Centaur, but
I don't understand how one works *harmony* when you get past using the
Centaur tuning as a JI variant of essentially 12 equal.

When I was at Andrew Heathwaite's Oddmusic Garden I was able to talk to
Denny *Genovese about music built on the harmonic series, specifically
harmonic series sections. His main message was that while common practice
moves essentially the same chord harmonic series music adds and takes away
pitches.

I am trying to wrap my head around this JI thing and I don't *think* Denny's
perspective applies here.

Any ET or psuedo ET is really quite easy to compose in. It is by definition
analogous to 12 ET.

However, what IS one suppose to do with a tuning like Centaur?

It may sound totally dense but I don't get the microtonal practice. One
possible solution I wish to avoid is "forcing" interval combinations such as
one would do when playing meantone in far keys. That doesn't seem to be the
best way to go about anything.

Thanks in advance for your help.

Chris
*

🔗Carl Lumma <carl@...>

Chris!

> When I was at Andrew Heathwaite's Oddmusic Garden I was able
> to talk to Denny Genovese about music built on the harmonic
> series,

You saw Denny in Illinois!? He was my teacher. Last I spoke
with him, he was living in Costa Rica. Has he moved back to
Chicago or something?

> I am trying to wrap my head around this JI thing and I don't
> *think* Denny's perspective applies here.

Denny's idea is to use the modes of the harmonic series to
make music. It's so simple there's nothing really to talk
about, so we never talk about it. It's a great idea though,
and he had a whole band playing instruments tuned to his
scales -- they released 2 albums in the early '90s. By 2002
he'd given the instruments away, but he managed to sample
them from the albums and create a virtual version of his
ensemble in Fruity Loops. He played me some wicked stuff
he was working on, but last I heard he'd shelved the project
and given up music to do real estate in CR!

> Any ET or psuedo ET is really quite easy to compose in.

I disagree with that entirely. 12-ET takes a lifetime to
master and little of the knowledge transfers to other ETs.

> However, what IS one suppose to do with a tuning like Centaur?

I independently discovered Centaur in 1997, tuned my piano
to it, and recorded some improvisations. They were on the
tuning punks site back in the day.

> It may sound totally dense but I don't get the microtonal
> practice.

What's not to get? It's got 4:5:6:7 chords on I and IV.
You play those, along with a few triads (Ab IIRC?) and jam
a melody over top. Well, that's what I did. Maybe Kraig
uses it differently. The point for me is that it's a JI
scale that fits on the piano. My main instrument is piano
and unfortunately it's one of the least microtonally
adaptable instruments in existence. So no, it's not anything
wonderful but it is wonderful compared to most of what you
can put on a piano.

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

Denny is living in Florida now. I tell you Andrew is doing wonderful
things for micromusic!

Andrew had Denny as "composer in residence" for a month. I believe
they were paying his way. Andrew and Jacob were going to do a radio
interview with Denny but I didn't get the podcast or it didn't happen.
Seeing Denny perform was very enlightening. Music seemed to be a
spiritual thing to him - more than most. Perhaps I'm overselling it -
but that was my impression.

http://oddmusicuc.wordpress.com/2010/06/27/oddmusic-instrument-garden-a-program/

On Mon, Aug 23, 2010 at 8:23 PM, Carl Lumma <carl@...> wrote:

> > I am trying to wrap my head around this JI thing and I don't
> > *think* Denny's perspective applies here.
>
> Denny's idea is to use the modes of the harmonic series to
> make music. It's so simple there's nothing really to talk
> about, so we never talk about it. It's a great idea though,
> and he had a whole band playing instruments tuned to his
> scales -- they released 2 albums in the early '90s. By 2002
> he'd given the instruments away, but he managed to sample
> them from the albums and create a virtual version of his
> ensemble in Fruity Loops. He played me some wicked stuff
> he was working on, but last I heard he'd shelved the project
> and given up music to do real estate in CR!

I was aware that he had two active periods where he built instruments
for the entire ensemble. At one point (in between?) he was living with
a group of people in Hawaii from what I gathered. About the modes -
yes indeed that is it. He had a psaltry tuned to harmonic 13 through
20 or something like that. It sounded otherworldly. When I commented
to that effect he said that is what he wanted. :-) It was inspiring
enough to make me want to build a psalty :-) Also he had these
modified recorders (wind instrument) where the head of the recorded
was fitted onto conduit of 3 or sp feet inlength. The instrument could
*only* play the harmonic series. Obviously an easier thing to do than
the psalty - though a psalty looks to be pretty easy to make.

>
> > Any ET or psuedo ET is really quite easy to compose in.
>
> I disagree with that entirely. 12-ET takes a lifetime to
> master and little of the knowledge transfers to other ETs.

I must disagree. Perhaps it is a manner of approach. If you are going
to say it takes a lifetime to write music with the complexity and
rules all of common practice yes. However, when I sit and compose in
*my style* and search for *my* rules I find the process is much the
same but the intervals I can build with are different. I am aware of
huge amounts of scale information out there - Ron Sword has been
amassing scales and modes for every edo you can shake a guitar at. I'm
as of yet unsure how that applies to me because I am not, at this
point, shoving the music into a box (scale) but rather trying to find
where it wants to go. If it happens to be in a particular scale or
mode, so be it. If not... so what?

But - characteristically I asked this question about Centaur
specifically to see if I am wrong in my approach, at least for JI.

>
> > However, what IS one suppose to do with a tuning like Centaur?
>
> I independently discovered Centaur in 1997, tuned my piano
> to it, and recorded some improvisations. They were on the
> tuning punks site back in the day.

I'd love to hear it - if you need hosting you know who to ask...

>
> > It may sound totally dense but I don't get the microtonal
> > practice.
>
> What's not to get? It's got 4:5:6:7 chords on I and IV.
> You play those, along with a few triads (Ab IIRC?) and jam
> a melody over top.
> -Carl

I am working on editing an improvisation in Centaur and I find it
doesn't sound too different from a "perfect" 12 edo, mostly. I'll try
your method. BUT that still leaves me wondering about the 50 intervals
on that webpage.

http://anaphoria.com/centaur.html

Chris

🔗Carl Lumma <carl@...>

Chris wrote:

> I was aware that he had two active periods where he built
> instruments for the entire ensemble. At one point (in between?)
> he was living with a group of people in Hawaii from what I
> gathered. About the modes - yes indeed that is it. He had a
> psaltry tuned to harmonic 13 through 20 or something like
> that. It sounded otherworldly. When I commented to that
> effect he said that is what he wanted. :-) It was inspiring
> enough to make me want to build a psalty :-) Also he had these
> modified recorders (wind instrument) where the head of the
> recorded was fitted onto conduit of 3 or sp feet in length.

Fipple pipes! His invention from his Hawaii days. Get some
friends together with a set of pipes, and you can play scales
by hocketing.

Denny also invented the binary flute, which is described in
Xenharmonikon I.

I lived with Denny in Florida for three months in 1997, during
which time I learned to play and tune many of his instruments.

> > > Any ET or psuedo ET is really quite easy to compose in.
> >
> > I disagree with that entirely. 12-ET takes a lifetime to
> > master and little of the knowledge transfers to other ETs.
>
> I must disagree. Perhaps it is a manner of approach. If you
> are going to say it takes a lifetime to write music with the
> complexity and rules all of common practice yes. However,
> when I sit and compose in *my style* and search for *my*
> rules I find the process is much the same but the intervals
> I can build with are different. I am aware of huge amounts of
> scale information out there - Ron Sword has been amassing
> scales and modes for every edo you can shake a guitar at.
> I'm as of yet unsure how that applies to me because I am not,
> at this point, shoving the music into a box (scale) but
> rather trying to find where it wants to go. If it happens to
> be in a particular scale or mode, so be it. If not... so what?

Yes, I understand and that is fine. For me personally, I'm
seldom moved by music made with this approach.

> But - characteristically I asked this question about Centaur
> specifically to see if I am wrong in my approach, at least
> for JI.

I don't see how you could be wrong...

> > What's not to get? It's got 4:5:6:7 chords on I and IV.
> > You play those, along with a few triads (Ab IIRC?) and jam
> > a melody over top.
>
> I am working on editing an improvisation in Centaur and I find
> it doesn't sound too different from a "perfect" 12 edo, mostly.
> I'll try your method. BUT that still leaves me wondering about
> the 50 intervals on that webpage.

Here's the lattice diagram (use fixed-width font). It
contains everything you need to know.

! A-------------E-------------B
! /:\ /:\ / \
! / : \ / : \ / \
! / : \ / : \ / \
! Ab------------Eb------------Bb \ / \
! `. / ,' \`. \ / ,'/ \`. \ / \
! `. /.' \ `.\ /.' / \ `.\ / \
! `F---------\---C---/-----\---G-------------D
! \ : / \ :
! \ : / \ :
! \:/ \:
! Gb------------Db

I remembered wrong about Ab... it's Gb.

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

On Mon, Aug 23, 2010 at 9:25 PM, Carl Lumma <carl@...> wrote:

I am not,
at this point, shoving the music into a box (scale) but
rather trying to find where it wants to go. If it happens to
be in a particular scale or mode, so be it. If not... so what?

Yes, I understand and that is fine. For me personally, I'm
seldom moved by music made with this approach.

Well, Daniel gave me what he looks for in music - what do you?

Though I will state the piece that I made with voice leading that you
said you liked was made with the same approach.

>
> Here's the lattice diagram (use fixed-width font). It
> contains everything you need to know.
>
> ! A-------------E-------------B
> ! /:\ /:\ / \
> ! / : \ / : \ / \
> ! / : \ / : \ / \
> ! Ab------------Eb------------Bb \ / \
> ! `. / ,' \`. \ / ,'/ \`. \ / \
> ! `. /.' \ `.\ /.' / \ `.\ / \
> ! `F---------\---C---/-----\---G-------------D
> ! \ : / \ :
> ! \ : / \ :
> ! \:/ \:
> ! Gb------------Db
>

I printed it out and I'll see what I can find, thanks!!

Chris

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> Here's the lattice diagram (use fixed-width font). It
> contains everything you need to know.

Unless you think you need to know about the approximate fifths and major thirds, for instance.

> ! A-------------E-------------B
> ! /:\ /:\ / \
> ! / : \ / : \ / \
> ! / : \ / : \ / \
> ! Ab------------Eb------------Bb \ / \
> ! `. / ,' \`. \ / ,'/ \`. \ / \
> ! `. /.' \ `.\ /.' / \ `.\ / \
> ! `F---------\---C---/-----\---G-------------D
> ! \ : / \ :
> ! \ : / \ :
> ! \:/ \:
> ! Gb------------Db
>
> I remembered wrong about Ab... it's Gb.

Here's the marvel-approximated 5-limit lattice:

* * *
* * * * *
* * * *

Note the chain of five fifths in this version. The 7s appear diagonally, since two 16/15s give an 8/7.

🔗Carl Lumma <carl@...>

Hi Chris,

> Well, Daniel gave me what he looks for in music - what do you?

Denny?

I've always approached the piano freely, thinking in terms of
sound rather than form. But embodied in the piano is 12-ET
(better than your average ET) and the diatonic scale (better
than your average scale) and the triads and scales I learned
when I was five, and the weight of five centuries of music
we've all been learning since the womb. My plan has always
been to acquire a generalized keyboard and set it up with a
xenharmonic system of similar power and approach it freely.
But without doing that in advance - finding a scale, thinking
about how it maps to the instrument - I don't think I'd be
doing something analogous to what I do at the piano.

> Though I will state the piece that I made with voice leading
> that you said you liked was made with the same approach.

I've liked a few of your pieces. The ones that come to mind
are:

- one you did in a rank 2 scale (hanson?) where I said
something like "instant success with regular mapping!" but
that ticked you off

- one you did about snow, with the video, in lucytuning
(another rank 2 scale)

- the jazzy one in 17 you did for one of the 60x60 things
(done by ear I think; this was probably my favorite of all)

- a short one in 22 that I liked more than you did (there
were two versions but I only liked the piano version that
sounded nothing like the other one)

But I vaguely remember something about voice leading which
was none of these I think -- or was it?

-Carl

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Gene wrote:
>
> > > Here's the lattice diagram (use fixed-width font). It
> > > contains everything you need to know.
> >
> > Unless you think you need to know about the approximate fifths
> > and major thirds, for instance.
>
> Fifth singular. There are several approx. major thirds and,
> as usual, all minor thirds are playable. But there are far
> better 7-limit JI scales if marvel approximations are desired.
> The point of Centaur is pure 7-limit harmony and strong melody.
> I've tuned up several block-type scales with more consonances
> than Centaur but I've always found them melodically inferior.

That's one theory about Centaur, but two cents worth of error may not microtempering, but it's also not enough to trash the harmony and melody you mention. It's certainly worth taking a listen to see how it compares for you.

🔗Kraig Grady <kraiggrady@...>

Thanks Carl~
I do think it works quite well melodically mainly because of the repeated tetrachords.
One has to not worry so much with sticking to low limit intervals in JI with this few of tones. You can play through the 12 'diatonic' scales and the flat ones will be dark and the sharp will be bright and shimmery. There was a great advantage to have such variety at my fingertips.
It is not good for exact transposition of material . One has to listen to what the scale wants to do in each instance and go with it. This gives one possibilities you don't have with temperment in the same fashion temperment will give you other ones.

I think it is like woodwinds (JI) compared to brass (temp/et).
Brass instrument color is more even throughout it range whereas woodwinds contrast more. each has their advantages. One does not complain that a melody high in the flute does not say the same thing in the low range.

Fifth singular. There are several approx. major thirds and,
as usual, all minor thirds are playable. But there are far
better 7-limit JI scales if marvel approximations are desired.
The point of Centaur is pure 7-limit harmony and strong melody.
I've tuned up several block-type scales with more consonances
than Centaur but I've always found them melodically inferior.

-Carl
--

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

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

🔗christopherv <chrisvaisvil@...>

I would very much like some opinions if my Centaur piece is ... what it *should* be - in other words is Centaur supposed to be relatively non-strident xenharmonic or am I mis-using the tuning?

This goes back to the criticism that I was writing non-xenharmonic music.

So I'm not asking about the quality of the music itself but the "xenhamonicity" of the music. Should it be more xenharmonic?

Thanks,

Chris

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@...> wrote:
>
>
> Thanks Carl~
> I do think it works quite well melodically mainly because of
> the repeated tetrachords.
> One has to not worry so much with sticking to low limit
> intervals in JI with this few of tones. You can play through the
> 12 'diatonic' scales and the flat ones will be dark and the
> sharp will be bright and shimmery. There was a great advantage
> to have such variety at my fingertips.
> It is not good for exact transposition of material . One has
> to listen to what the scale wants to do in each instance and go
> with it. This gives one possibilities you don't have with
> temperment in the same fashion temperment will give you other ones.
>
> I think it is like woodwinds (JI) compared to brass (temp/et).
> Brass instrument color is more even throughout it range
> whereas woodwinds contrast more. each has their advantages. One
> does not complain that a melody high in the flute does not say
> the same thing in the low range.
>
>
> Fifth singular. There are several approx. major thirds and,
> as usual, all minor thirds are playable. But there are far
> better 7-limit JI scales if marvel approximations are desired.
> The point of Centaur is pure 7-limit harmony and strong melody.
> I've tuned up several block-type scales with more consonances
> than Centaur but I've always found them melodically inferior.
>
> -Carl

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗Kraig Grady <kraiggrady@...>

a fine piece.
I don't think one can misuse a tuning if one is using subsets of it in ways that these subsets work.
Like Carl i noticed you were light on the 7 limit intervals but one should not use something if it doesn't fit in with what you are writing.

The tuning was my first JI instrument that could sustain. Couldn't do it electronically at the time, so it was designed to explore a few features of JI and many of the new consonants available as well as some new scales.

I would very much like some opinions if my Centaur piece is ... what it *should*
be - in other words is Centaur supposed to be relatively non-strident
xenharmonic or am I mis-using the tuning?

This goes back to the criticism that I was writing non-xenharmonic music.

So I'm not asking about the quality of the music itself but the "xenhamonicity"
of the music. Should it be more xenharmonic?

Thanks,

Chris
--

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

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

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

a momentary antenna as i turn to water
this evaporates - an island once again

🔗Chris Vaisvil <chrisvaisvil@...>

Oh my - a whole series of emails I missed somehow.

Ok,

Yes it was Daniel off list. Denny and I didn't get that far - at least
as far as I can remember.

On Mon, Aug 23, 2010 at 11:52 PM, Carl Lumma <carl@...> wrote:
>
>
>
> Hi Chris,
>
> > Well, Daniel gave me what he looks for in music - what do you?
>
> Denny?
>
> I've always approached the piano freely, thinking in terms of
> sound rather than form.

I'd be guessing you tried a prepared piano.

> My plan has always
> been to acquire a generalized keyboard and set it up with a
> xenharmonic system of similar power and approach it freely.
> But without doing that in advance - finding a scale, thinking
> about how it maps to the instrument - I don't think I'd be
> doing something analogous to what I do at the piano.

It would seem Carlo has found that with his isomorphic keyboard and
Carlos Gamma.
My impression is that Carlo jumped into Gamma with both feet and is
emerging from the water with impressive chops.
Perhaps like the immersion method of learning languages

>
> > Though I will state the piece that I made with voice leading
> > that you said you liked was made with the same approach.
>
> I've liked a few of your pieces. The ones that come to mind
> are:
>
> - one you did in a rank 2 scale (hanson?) where I said
> something like "instant success with regular mapping!" but
> that ticked you off

If I seemed ticked off I apologize. I can't remember why I would have been.

Here is the Hanson piece that is called Watching it Snow
http://chrisvaisvil.com/?p=82

Thanks for the list of the other ones you like.

I can't identify the 22 ET pair for sure but I'm thinking it may be
http://micro.soonlabel.com/22-ET/mini-piano-22-20100322-study-in-22-electro.mp3
http://micro.soonlabel.com/22-ET/mini-piano-22-20100322-study-in-22.mp3

which is called spiral stairs

> But I vaguely remember something about voice leading which
> was none of these I think -- or was it?
>
> -Carl
>

The voice leading one is Orwellian Cameras
http://notonlymusic.com/board/download/file.php?id=881

Which I am re-working. Though I sometimes think I'd be better off
sticking to solo instruments. I find ensembles *hard* to write for.

🔗Chris Vaisvil <chrisvaisvil@...>

Thank you Carl, Gene, and Kraig for the comments.

I had to consult Doty (p 56) - 7 limit is then (just?) using the
dominant 7th? - or in this tuning, in the key of C, the B flat?
- though I use a *lot* of major 7ths -and (again in the key of C) the
B natural doesn't show up until the 15th harmonic.

I guess I'm a little confused on the meaning of 7-limit. To be fair
I've been stuck on p 29 of Doty for a while (I've not read much
recently) so "continue reading" is as acceptable an answer as any
other.

Chris

On Mon, Aug 30, 2010 at 7:46 AM, Kraig Grady <kraiggrady@...> wrote:
>
>
>
> a fine piece.
> I don't think one can misuse a tuning if one is using subsets of
> it in ways that these subsets work.
> Like Carl i noticed you were light on the 7 limit intervals but
> one should not use something if it doesn't fit in with what you
> are writing.
>

🔗Carl Lumma <carl@...>

Hi Chris,

> Yes it was Daniel off list.

Ah.

> > I've always approached the piano freely, thinking in terms
> > of sound rather than form.
>
> I'd be guessing you tried a prepared piano.

No! I think that's really stupid. Like, objectively stupid.
Sorry if that offends but to me it's like building a $3 billion
rocket and filling the tank with Ovaltine instead of jet fuel.
I was billed alongside one of Cage's prep. piano pieces in
New York and had I had fruit on hand, I would have thrown it.

I meant more along the lines of, discarding fixed meter, not
playing any known genre of music (e.g. funk, jazz...), and
trying to forget what little theory I know.

> > My plan has always
> > been to acquire a generalized keyboard and set it up with a
> > xenharmonic system of similar power and approach it freely.
> > But without doing that in advance - finding a scale, thinking
> > about how it maps to the instrument - I don't think I'd be
> > doing something analogous to what I do at the piano.
>
> It would seem Carlo has found that with his isomorphic keyboard
> and Carlos Gamma.

Yup. He's the guy who's got the best combination of keyboard,
theory, and musicianship in the world right now, that I know of.
Aaron Hunt and several others are up there too. I'll get there
one day. It's probably gonna be until my youngest starts school
in 2014. I really wanted to get the location/money/wife/kids
thing done first. But I still play the piano for about an hour
a week. Microtonality is gaining in popularity and technology
is making everything cheaper, so waiting will probably make
things easier. The only downside is aging. However I've
already lost most of my angry young man wind, so I should be
steady through my 30s & 40s.

> Here is the Hanson piece that is called Watching it Snow
> http://chrisvaisvil.com/?p=82

Wait a second! I thought the Lucytuning piece was
Watching it Snow. With the video. No! That was
Talking 2 God. I have the video here, properly named.
Also have the the Watching it Snow mp3 here, correct.
OK! Yes, a very sweet piece.

> I can't identify the 22 ET pair for sure but I'm thinking it may be
> http://micro.soonlabel.com/22-ET/mini-piano-22-20100322-study-in-
> 22-electro.mp3
> http://micro.soonlabel.com/22-ET/mini-piano-22-20100322-study-
> in-22.mp3
>
> which is called spiral stairs

Those are them! I have the piano version mp3 here. Along with
17-ET Jazz, and Kandahar Poppies. Those are the five I saved
as most memorable.

> The voice leading one is Orwellian Cameras
> http://notonlymusic.com/board/download/file.php?id=881
>
> Which I am re-working. Though I sometimes think I'd be better
> off sticking to solo instruments. I find ensembles *hard* to
> write for.

Yes! I didn't save it because you labeled it a WIP.
To me it sounds great. Just needs a melody over that
(add another instrument!), then wrap it up with one of
Carlo's patented fade-outs (the biggest weakness in his
stuff right now IMO).

-Carl

🔗Carl Lumma <carl@...>

Chris: The easy way to think of "limits" is to be like Denny;
it's all the intervals you get in a harmonic series up to that
number, but (somewhat unlike Denny) with octave extensions
allowed. So 7-limit is harmonics up to 7. And the 7th harmonic
is a lot like a minor 7th in 12-ET. A 4:5:6:7 chord is a lot
like a dominant 7th chord in 12-ET. Barbershop quartets
harmonize everything with dom.7 chords, tuned pure (7-limit)...

Note, one way to remember it is, the diatonic intervals match
the harmonic ones, except the 5th and 3rd are reversed!
1 = unison, 3 = 5th, 5 = 3rd, 7 = m7, 9 = M9, 11= #11 etc.

That's odd limit, and that's usually what's meant when we're
talking about characterizing the consonances in a piece of
music like this. Doty uses PRIME limit though, which is a
bit different. It's what we use to characterize temperaments.
Simple right!? To learn more about prime limits, "continue
reading". :)

-Carl

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Thank you Carl, Gene, and Kraig for the comments.
>
> I had to consult Doty (p 56) - 7 limit is then (just?) using
> the dominant 7th? - or in this tuning, in the key of C, the
> B flat? - though I use a *lot* of major 7ths -and (again in
> the key of C) the B natural doesn't show up until the
> 15th harmonic.
>
> I guess I'm a little confused on the meaning of 7-limit. To be
> fair I've been stuck on p 29 of Doty for a while (I've not read
> much recently) so "continue reading" is as acceptable an answer
> as any other.
>
> Chris