Yahoo Tuning Groups Ultimate Backup tuning 15 EDO

> Before I come up with my own creation for 15 EDO, I was wondering
> if the staff for 15 EDO has already been establihed. Any help would
> be appreciated. Thanks.

If I understand your question, Blackwood wrote the book on 15 with
his Microtonal Etude and subsequent guitar suite, both on a single
CD available from Cedille Records. On the web, IMHO by far the
most important work in 15 is Herman Miller's Mizarian Porcupine
Overture (google).

[...tests google]

Wow, I've never seen this page before (the 1st result!)...

http://www.io.com/~hmiller/furry/PorcupineOpera.html

Rad!

I believe this is the page I was thinking about...

ftp://ftp.io.com/pub/usr/hmiller/music/

-Carl

🔗stephenszpak <stephen_szpak@hotmail.com>

🔗monz <monz@attglobal.net>

hi Stephen,

--- In tuning@yahoogroups.com, "stephenszpak" <stephen_szpak@h...>
wrote:

> Thanks Carl for getting back to me. This was my first
> post anywhere about anything, so you get a gold star.
> The staff for 15 EDO has NOT been established from what
> I can see so far. I'm not sure if I can take Herman Miller's
> tongue and cheek staff seriously. If Blackwood uses a
> staff I haven't as yet found a image of it. Regardless,
> two composers using 15 EDO, even if they use the same
> staff does not convince me it is a "standard" that should
> be accepted by future musicians. Thanks.

Blackwood's notations for all the EDOs between 13 and 24
use the regular 5-line staff, with unique accidentals for
each tuning.

i have the score of his _Microtonal Etudes_, but unfortunately
my old scanner doesn't work with my new computer.

-monz

🔗Carl Lumma <ekin@lumma.org>

>Thanks Carl for getting back to me. This was my first post anywhere
>about anything, so you get a gold star. The staff for 15 EDO has NOT
>been established from what I can see so far. I'm not sure if I can
>take Herman Miller's tongue and cheek staff seriously. If Blackwood
>uses a staff I haven't as yet found a image of it. Regardless, two
>composers using 15 EDO, even if they use the same staff does not
>convince me it is a "standard" that should be accepted by future
>musicians. Thanks.

Sorry, I'm not sure I'm understanding "staff". What is a "staff"?

I think the Mizarian Porcupine Overture is a great piece of music,
which I would not hesitate to put with the average work of a
Romantic master. I feel the same way about Blackwood's 15-tET
stuff, YMMV.

I'm not aware of anyone proposing 15-tET as a standard. This
group is generally fairly anti-standard. The whole point is to
explore the vast virgin universe of alternate tunings. In 100
years maybe a standard will emerge.

-Carl

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

/tuning/topicId_50122.html#50144

> >Thanks Carl for getting back to me. This was my first post anywhere
> >about anything, so you get a gold star. The staff for 15 EDO has
NOT
> >been established from what I can see so far. I'm not sure if I can
> >take Herman Miller's tongue and cheek staff seriously. If Blackwood
> >uses a staff I haven't as yet found a image of it. Regardless, two
> >composers using 15 EDO, even if they use the same staff does not
> >convince me it is a "standard" that should be accepted by future
> >musicians. Thanks.
>
> Sorry, I'm not sure I'm understanding "staff". What is a "staff"?
>
> I think the Mizarian Porcupine Overture is a great piece of music,
> which I would not hesitate to put with the average work of a
> Romantic master. I feel the same way about Blackwood's 15-tET
> stuff, YMMV.
>
> I'm not aware of anyone proposing 15-tET as a standard. This
> group is generally fairly anti-standard. The whole point is to
> explore the vast virgin universe of alternate tunings. In 100
> years maybe a standard will emerge.
>
> -Carl

***I think there is a little confusion about this, with the
assumption by the poster that composers use different kinds of staves
for different ETs and such like. Well, in some cases this is true,
such as Monzo's use of a special 1/4 tone staff notation (see Monzo
site), but in many cases it's just a matter of assigning *pitches* to
our "regular" 5-line staff as will be shown by the Blackwood excerpt
of 15-tET I put up over in "Tuning Files..."

/tuning_files/files/Pehrson/

Joseph Pehrson

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

🔗monz <monz@attglobal.net>

hi Peter,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
<sault@c...>
> > wrote:
> >
> > > Silly question I know, so all hang on to your seats.
> > >
> > > What is 15 EDO?
> >
> > Division of the octave into 15 equal parts.
> > There's also 15-et (or tet), which is the same
> > considered as a temperament.
>
> Thankyou Gene.
>
> Is 15-EDO anything more than just a theoretical curiosity?
> How does one manage without a '5th'? Why 15?

haven't you seen the recent posts about 15edo music?
the two following pieces have been discussed quite a
bit just in the last few days:

i think the two most prominent pieces in this tuning are
Easley Blackwood's 15edo etude from _Microtonal Etudes_,
which i don't think is on the internet anywhere; and
Herman Miller's _Mizarian Porcupine Overture_.

http://www.io.com/~hmiller/midi/porcupine.mid

Herman also has a page about "Porcupine Temperament",
which we named after his piece:

http://www.io.com/~hmiller/music/temp-porcupine.html

15edo also works as an "augmented" temperament.
http://www.io.com/~hmiller/music/temp-augmented.html

every EDO offers its own set of "vanishing commas"
(also known as "tempered-out unison-vectors"), and
thus its own possibilities for what we call "punning".

you can graphically see some of the possibilities as
they relate to 5-limit JI, here:

http://www.tonalsoft.com/enc/bingo.htm

and there's a table of composers who have used or advocated
various EDOs (or ETs) here:

http://tonalsoft.com/enc/eqtemp.htm

in which you can see that in addition to Herman Miller and
Easley Blackwood, 15edo has also been used/advocated by:

R. M. A. Kusumadinata (Sunda), Augusto Novaro, Joe Zawinul
(with the group Weather Report), Easley Blackwood,
Clem Fortuna, Rndy Winchester, Paul Erlich (with the
group MAD DUXX), and Francesco Caratozzolo.

-monz

🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Thankyou Gene.
> >
> >Is 15-EDO anything more than just a theoretical curiosity? How does
> >one manage without a '5th'? Why 15?
>
> Before you attempt to understand it theoretically, I strongly suggest
> you listen to the Mizarian Porcupine Overture...
>
> ftp://ftp.io.com/pub/usr/hmiller/music/

After doing that, you can check out the following analytical
comparison of 12 with 15.

As Joe mentioned, they have different commas (intervals which they
temper out.) In the 5-limit, 12-et tempers out all product of
81/80 and 128/125, and 15-et all products of 128/125 and 250/243; they
have in common that they temper out 128/125, making the major third a
third of an octave, or 400 cents.

In the 7-limit, 12-et tempers out all products of 36/35, 50/49 and
64/63, while 15-et tempers out all products of 28/27, 49/48, 126/125.
While this looks (and is) quite different, they do have in common that
they both temper out all products of 64/63 and 126/125. These together
give the "tripletone" temperament, which is most characteristic of
27-et, and for which the 12 and 15 note scales may be considered the
equivalent of the black and white keys.

I've been using cents since this is a case where it makes much more
sense than using the intervals themselves, particularly since the
scale steps are in both cases integer amounts of cents. Here is a
table giving the 7-limit consonances 7/6, 5/4, 7/5, 3/2, 5/3 and 7/4,
their size in cents, and the corresponding cents values for both 12
and 15. As you can see, the fifth is quite sharp in 15-et, but the
major sixth/minor thirds and the 7/4 and 8/7 are much improved.

7/6 266.870906 300 240
5/4 386.313714 400 400
7/5 582.512193 600 560
3/2 701.955001 700 720
5/3 884.358713 900 880
7/4 968.825906 1000 960

The Riemann-Siegal goodness values (higher is better) are 1.269599 for
12 and 1.104057 for 15. Discussion of how these are defined is more
appropriate to tuning-math.

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Kurt Bigler <kkb@breathsense.com>

on 12/20/03 6:05 PM, Gene Ward Smith <gwsmith@svpal.org> wrote:

> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
>> I thought he did do a MIDI MPO, but as we know MIDI files aren't as
>> good as mp3 files, unless you have the same equipment as the author.
>
> I'm confident I can make a good version if I can get a midi version
> to render from.

Hey, it might be useful to set up a server with a page that takes a MIDI url
and creates an mp3 from it on the fly. This of course would be less
customizable than what Gene or others would do. But the goal would be to
make sure that the pitch accuracy is excellent, thus eliminating that nasty
source of uncertainty.

The end result would be a page anyone can go to containing a place to enter
a URL, which would then provide a download link to play the resulting MP3.
Maybe 2 clicks would be needed. One to enter the URL and start the
conversion. Another to play the result.

If someone can knows of software that can run under FreeBSD on intel
hardware to do the rendering, I'll set it up on my server. I can take care
of the control page details if someone can tell me of a MIDI rendering
engine with good defaults and accurate pitch that can run under
FreeBSD/intel.

-Kurt

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Thanks Carl for getting back to me. This was my first post anywhere
> >about anything, so you get a gold star. The staff for 15 EDO has NOT
> >been established from what I can see so far. I'm not sure if I can
> >take Herman Miller's tongue and cheek staff seriously. If Blackwood
> >uses a staff I haven't as yet found a image of it. Regardless, two
> >composers using 15 EDO, even if they use the same staff does not
> >convince me it is a "standard" that should be accepted by future
> >musicians. Thanks.
>
> Sorry, I'm not sure I'm understanding "staff". What is a "staff"?
>
> I think the Mizarian Porcupine Overture is a great piece of music,
> which I would not hesitate to put with the average work of a
> Romantic master. I feel the same way about Blackwood's 15-tET
> stuff, YMMV.
>
> I'm not aware of anyone proposing 15-tET as a standard. This
> group is generally fairly anti-standard. The whole point is to
> explore the vast virgin universe of alternate tunings. In 100
> years maybe a standard will emerge.
>
> -Carl

Carl,

I think Stephen was referring to standard notations for 15-tET
(15-EDO), not 15-tET _as_ a standard tuning. I think you will agree
that although the idea of any kind of standard tuning is anathema,
we're quite interested in standardising
terminology/notation/nomenclature whenever possible, so we can
actually understand each other when we attempt to communicate about
various tunings. So saying we're "anti-standard" could be misconstrued.

Stephen,

In a forthcoming paper on the sagittal notation system there are two
notations proposed for 15-tET. One uses the scale's best approximation
of a fifth (9/15 oct or 720 c) between the nominals CGDAE, and the
5-comma up and down accidentals for one degree either side of these.

C C/ D\ D D/ E\ E E/ G\ G G/ A\ A A/ C\

I expect this is identical to someone else's earlier proposal with the
substitution of the specifically sagittal 5-comma symbol (which adds
vertical shafts to the above slashes to turn them into half-arrows
that unambiguously indicate the direction of pitch change).

The other one uses more accidentals and notates 15-tET as every fourth
step of 60-tET (which is of course a multiple of 12-tET). Again, I
won't be surprised if someone else has done this too, modulo the
specifically sagittal accidentals which I can only crudely approximate
with ASCII characters.

Legend for 60-ET notation (ASCII shorthand):
A-G,#,b as for 12-ET
y fifth-tone up (55-comma up)
? tenth-tone up (7:11-comma up)
j tenth-tone down (7:11-comma down)
k fifth-tone down (55-comma down)

C C#j Dk Dy Eb? E Fj F#k F#y G? G#(or Ab) Aj Bbk Bby B?

These do not show the pure-sagittal symbols or any alternative
spellings for modulations, but I can post more on these if you are
interested.

Joseph,

Thanks for posting Blackwood's notation, but without some explanatory
text, I'm not sure I've figured it out. I don't understand what looks
like two different nominals for many degrees, with the same
accidentals against them in some cases. I suppose these are alternate
notations for the same degree, but they seem rather odd, being
apparently a semitone apart. It seems most similar to the first
sagittal notation above.

Regards,
-- Dave Keenan

🔗Herman Miller <hmiller@IO.COM>

On Sat, 20 Dec 2003 13:18:34 -0800, Carl Lumma <ekin@lumma.org> wrote:

>>Thankyou Gene.
>>
>>Is 15-EDO anything more than just a theoretical curiosity? How does
>>one manage without a '5th'? Why 15?
>
>Before you attempt to understand it theoretically, I strongly suggest
>you listen to the Mizarian Porcupine Overture...
>
>ftp://ftp.io.com/pub/usr/hmiller/music/
>
>Waitaminute, 48Kbps mono? Herman Miller, that will not do!

Unfortunately, I didn't save any of the MP3s I sent to the Tuning Punks.
However, I still have the original WAV file of the Mizarian Porcupine
Overture, and (barely) enough disk quota left, so I uploaded a 128kbps
stereo MP3 version to replace the mono version.

ftp://ftp.io.com/pub/usr/hmiller/music/porcupine-overture.mp3

This was done with a SoundBlaster AWE32 and a custom 15-ET sound font, so
the original MIDI version wouldn't be very useful by itself. There's the
new Scala-tuned MIDI version, but in some places there are too many notes
to retune at the same time, so the tuning isn't perfect, and the General
MIDI timbres aren't very close to the original.

http://www.io.com/~hmiller/midi/porcupine.mid

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Peter,
>
>
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
>
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > > --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
> <sault@c...>
> > > wrote:
> > >
> > > > Silly question I know, so all hang on to your seats.
> > > >
> > > > What is 15 EDO?
> > >
> > > Division of the octave into 15 equal parts.
> > > There's also 15-et (or tet), which is the same
> > > considered as a temperament.
> >
> > Thankyou Gene.
> >
> > Is 15-EDO anything more than just a theoretical curiosity?
> > How does one manage without a '5th'? Why 15?
>
>
>
> haven't you seen the recent posts about 15edo music?
> the two following pieces have been discussed quite a
> bit just in the last few days:
>
>
> i think the two most prominent pieces in this tuning are
> Easley Blackwood's 15edo etude from _Microtonal Etudes_,
> which i don't think is on the internet anywhere; and
> Herman Miller's _Mizarian Porcupine Overture_.
>
> http://www.io.com/~hmiller/midi/porcupine.mid
>
>
> Herman also has a page about "Porcupine Temperament",
> which we named after his piece:
>
> http://www.io.com/~hmiller/music/temp-porcupine.html
>
>

WinAmp reports "Error opening MID file".

> 15edo also works as an "augmented" temperament.
> http://www.io.com/~hmiller/music/temp-augmented.html
>
>
>
> every EDO offers its own set of "vanishing commas"
> (also known as "tempered-out unison-vectors"), and
> thus its own possibilities for what we call "punning".
>

Isn't that what I've been talking about all along concerning the
nature of the dual tritone in JI? I'm not sure what you mean,
exactly. Could you be a little more explicit?

> you can graphically see some of the possibilities as
> they relate to 5-limit JI, here:
>
> http://www.tonalsoft.com/enc/bingo.htm
>
>

Utterly impenetrable. However, I'm sure you must know what you're
talking about. You and others on this group have been developing your
ideas for a long time and you appear to have developed your own
language to talk about them. When I try to comprehend the terms by
following up the links I find that your definitions are sometimes
highly personal. For example, you equate 'periodicity'
with 'frequency'. You will have to pardon me if I find that a bit of
a brick wall.

In trying to understand the term 'periodicity-block' I find I must
first understand the terms 'lattice' and 'lattice diagram'. However,
your explanation of these items is somewhat lacking. Could you
explain to me, in simple terms, how to construct a 'lattice diagram'?
The instructions for doing this seem to be missing from your
definition and I cannot find any link to a 'how-to'. Would you show
me a lattice diagram for the octachord (which must surely be the
simplest possible) and how this can be developed to include other
intervals?

Peter

>
> and there's a table of composers who have used or advocated
> various EDOs (or ETs) here:
>
> http://tonalsoft.com/enc/eqtemp.htm
>
>
> in which you can see that in addition to Herman Miller and
> Easley Blackwood, 15edo has also been used/advocated by:
>
> R. M. A. Kusumadinata (Sunda), Augusto Novaro, Joe Zawinul
> (with the group Weather Report), Easley Blackwood,
> Clem Fortuna, Rndy Winchester, Paul Erlich (with the
> group MAD DUXX), and Francesco Caratozzolo.
>
>
>
> -monz

🔗Herman Miller <hmiller@IO.COM>

On Thu, 18 Dec 2003 21:01:48 -0800, Carl Lumma <ekin@lumma.org> wrote:

>> Before I come up with my own creation for 15 EDO, I was wondering
>> if the staff for 15 EDO has already been establihed. Any help would
>> be appreciated. Thanks.
>
>If I understand your question, Blackwood wrote the book on 15 with
>his Microtonal Etude and subsequent guitar suite, both on a single
>CD available from Cedille Records. On the web, IMHO by far the
>most important work in 15 is Herman Miller's Mizarian Porcupine
>Overture (google).
>
>[...tests google]
>
>Wow, I've never seen this page before (the 1st result!)...
>
>http://www.io.com/~hmiller/furry/PorcupineOpera.html
>
>Rad!

That's a **really** old page, from way back when I was just starting to
play around with 15-ET. The links to the defunct Tripod and Netscape sites
are seriously broken, but here's a copy of the original 8-second excerpt
that went with that page:

http://www.io.com/~hmiller/mp3/opera.mp3

That was all done in Cool Edit, so don't expect anything spectacular. As
far as notation, the only part of the overture that I ever wrote down was
in scordatura, showing the keys you play on a 15-ET-tuned keyboard to get
the notes. Most of it was done with the Cakewalk piano roll and custom
sound fonts, and was never written down in any form. But I'd probably use
something like the Scala 15-ET notation if I wanted to start notating 15-ET
music.

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

/tuning/topicId_50122.html#50216

> Joseph,
>
> Thanks for posting Blackwood's notation, but without some
explanatory
> text, I'm not sure I've figured it out. I don't understand what
looks
> like two different nominals for many degrees, with the same
> accidentals against them in some cases. I suppose these are
alternate
> notations for the same degree, but they seem rather odd, being
> apparently a semitone apart. It seems most similar to the first
> sagittal notation above.
>
> Regards,
> -- Dave Keenan

***Hello Dave!

Actually, there is not a lot of information in the score about this,
except that at the beginning he mentions that many of the pieces
use "enharmonics..."

My *guess* is that Blackwood really does substitute these
various "enharmonics" for one another as he trys to find *diatonic* -
sounding chord progressions in them.

Much of his music, as you probably know, is heavily derivative of 12-
equal and, particularly, of the diatonic subset of 12-equal. (I'm
not really disparaging the music here; it's just a fact....)

The only information given in the preface is this, which I have also
placed in the Tuning Files forum:

/tuning/files/Pehrson/

(Blackwood Etudes Preface.jpg)

Joseph

🔗Herman Miller <hmiller@IO.COM>

On Sat, 20 Dec 2003 19:54:28 -0000, "monz" <monz@attglobal.net> wrote:

>15edo also works as an "augmented" temperament.
>http://www.io.com/~hmiller/music/temp-augmented.html

That's why the Moonlight Sonata works as well as it does in 15; it doesn't
make much use of the syntonic comma (except in the 2nd movement), but it
does use the 128/125. Originally I was playing around with a kleismic
version of the 3rd movement, which worked pretty well except for this
problem; since the versatile 15-ET also works as a kleismic temperament,
that led me to the 15-ET version.

>in which you can see that in addition to Herman Miller and
>Easley Blackwood, 15edo has also been used/advocated by:
>
>R. M. A. Kusumadinata (Sunda), Augusto Novaro, Joe Zawinul
>(with the group Weather Report), Easley Blackwood,
>Clem Fortuna, Rndy Winchester, Paul Erlich (with the
>group MAD DUXX), and Francesco Caratozzolo.

Didn't Rick McGowan once have a 15-ET ballet excerpt on the Tuning Punks
site?

🔗Carl Lumma <ekin@lumma.org>

>>ftp://ftp.io.com/pub/usr/hmiller/music/
>>
>>Waitaminute, 48Kbps mono? Herman Miller, that will not do!
>
>Unfortunately, I didn't save any of the MP3s I sent to the Tuning Punks.

Well I still have it if you want it for some reason.

>However, I still have the original WAV file of the Mizarian Porcupine
>Overture, and (barely) enough disk quota left, so I uploaded a 128kbps
>stereo MP3 version to replace the mono version.
>
>ftp://ftp.io.com/pub/usr/hmiller/music/porcupine-overture.mp3

Aha, great.

By the way, there's no reason anyone should lack for storage space in
this day and age. It's like saying you don't have enough toothpaste,
or something.

http://www.io.com/

Hmm, 100MB upgrade costs $9/month if you buy it by the year. Whaddda
rip. I take back the toothpaste remark. And it looks like you can't
even get a static IP address to host it yourself unless you buy a T1
line. I feel like I'm living in a cave, in Soviet Russia.

-Carl

🔗Carl Lumma <ekin@lumma.org>

🔗Peter Wakefield Sault <sault@cyberware.co.uk>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Kurt Bigler <kkb@breathsense.com>

on 12/20/03 9:33 PM, Carl Lumma <ekin@lumma.org> wrote:

>>> ftp://ftp.io.com/pub/usr/hmiller/music/
>>>
>>> Waitaminute, 48Kbps mono? Herman Miller, that will not do!
>>
>> Unfortunately, I didn't save any of the MP3s I sent to the Tuning Punks.
>
> Well I still have it if you want it for some reason.
>
>> However, I still have the original WAV file of the Mizarian Porcupine
>> Overture, and (barely) enough disk quota left, so I uploaded a 128kbps
>> stereo MP3 version to replace the mono version.
>>
>> ftp://ftp.io.com/pub/usr/hmiller/music/porcupine-overture.mp3
>
> Aha, great.
>
> By the way, there's no reason anyone should lack for storage space in
> this day and age. It's like saying you don't have enough toothpaste,
> or something.
>
> http://www.io.com/
>
> Hmm, 100MB upgrade costs $9/month if you buy it by the year. Whaddda
> rip. I take back the toothpaste remark. And it looks like you can't
> even get a static IP address to host it yourself unless you buy a T1
> line. I feel like I'm living in a cave, in Soviet Russia.

You can still get static IP's with some DSL services, but they are more
expensive than normal "consumer" DSL, like maybe $80/month. That's a lot
less than a T1, but still out of range for most of us.

-Kurt

>
> -Carl

🔗Kurt Bigler <kkb@breathsense.com>

🔗kraig grady <kraiggrady@anaphoria.com>

Dear Veterans of this list!
Here is as perfect example of my objection to this 'specialized' language and how it works.
It doesn't. Utterly impenetrable says it all!

>
> From: "Peter Wakefield Sault" <sault@cyberware.co.uk>
> Subject: Re: 15 EDO
>
>
> Utterly impenetrable. However, I'm sure you must know what you're
> talking about. You and others on this group have been developing your
> ideas for a long time and you appear to have developed your own
> language to talk about them. When I try to comprehend the terms by
> following up the links I find that your definitions are sometimes
> highly personal. For example, you equate 'periodicity'
> with 'frequency'. You will have to pardon me if I find that a bit of
> a brick wall.
>
> In trying to understand the term 'periodicity-block' I find I must
> first understand the terms 'lattice' and 'lattice diagram'. However,
> your explanation of these items is somewhat lacking. Could you
> explain to me, in simple terms, how to construct a 'lattice diagram'?
> The instructions for doing this seem to be missing from your
> definition and I cannot find any link to a 'how-to'. Would you show
> me a lattice diagram for the octachord (which must surely be the
> simplest possible) and how this can be developed to include other
> intervals?
>
> Peter
>
> >
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

🔗Aaron K. Johnson <akjmicro@comcast.net>

On Saturday 20 December 2003 11:42 pm, Peter Wakefield Sault wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > >Thankyou Gene.
> > >
> > >Is 15-EDO anything more than just a theoretical curiosity? How
>
> does
>
> > >one manage without a '5th'? Why 15?
> >
> > Before you attempt to understand it theoretically, I strongly
>
> suggest
>
> > you listen to the Mizarian Porcupine Overture...
> >
> > ftp://ftp.io.com/pub/usr/hmiller/music/
> >
> > Waitaminute, 48Kbps mono? Herman Miller, that will not do!
> >
> > -Carl
>
> Such experiments are very valid although there can be no absolute
> judgment of the results in the scientific sense. Mr Miller has
> evidently put a great deal of thought and work into this one. To me
> it forms a very persuasive argument for sticking with 12-EDO. I
> accept that that is a very subjective and narrow opinion and that the
> champions of in-your-face bizarro tonalities undoubtedly love it for
> what it represents rather than for its lack of aesthetic content.

Well, even if you don't like it, it's still an aesthetic, and it's still got
'content', no?

But, I agree that 15-tet is not as interesting to me as the beautiful 19-tet
or 31-tet meantone varieties, with there better JI approximations of thirds
than the normal 12-tet....

I'm also partial to the stuctural presence of fifths and fourths, I must say,
and if you put a gun to my head and asked me if I could write music without
it, I'd say 'yes I could, but I prefer you shoot me'. That doesn't include
necessarily what noisy fun things I would do on a synth where pitch is less
important, or more accidental a parameter, than say timbre......but, from
what I just said, I'd rather right in a tuning with good fifths but no good
thirds in the JI sense (17-tet) than I would vice versa..

Best,
Aaron.

OCEAN, n. A body of water occupying about two-thirds of a world made
for man -- who has no gills. -Ambrose Bierce 'The Devils Dictionary'

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>

/tuning/topicId_50122.html#50233

wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > >Thankyou Gene.
> > >
> > >Is 15-EDO anything more than just a theoretical curiosity? How
> does
> > >one manage without a '5th'? Why 15?
> >
> > Before you attempt to understand it theoretically, I strongly
> suggest
> > you listen to the Mizarian Porcupine Overture...
> >
> > ftp://ftp.io.com/pub/usr/hmiller/music/
> >
> > Waitaminute, 48Kbps mono? Herman Miller, that will not do!
> >
> > -Carl
>
> Such experiments are very valid although there can be no absolute
> judgment of the results in the scientific sense. Mr Miller has
> evidently put a great deal of thought and work into this one. To me
> it forms a very persuasive argument for sticking with 12-EDO. I
> accept that that is a very subjective and narrow opinion and that
the
> champions of in-your-face bizarro tonalities undoubtedly love it
for
> what it represents rather than for its lack of aesthetic content.

***Well, personally, Peter, I enjoyed the "bizarro" sound of it, and
that seemed very integrated with the structural content, which seemed
pretty successful to me... It *couldn't* be done in 12-tET (or 12-
EDO) and sound like that, of course.

Joseph P.

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

/tuning/topicId_50122.html#50240

> on 12/20/03 9:33 PM, Carl Lumma <ekin@l...> wrote:
>
> >>> ftp://ftp.io.com/pub/usr/hmiller/music/
> >>>
> >>> Waitaminute, 48Kbps mono? Herman Miller, that will not do!
> >>
> >> Unfortunately, I didn't save any of the MP3s I sent to the
Tuning Punks.
> >
> > Well I still have it if you want it for some reason.
> >
> >> However, I still have the original WAV file of the Mizarian
Porcupine
> >> Overture, and (barely) enough disk quota left, so I uploaded a
128kbps
> >> stereo MP3 version to replace the mono version.
> >>
> >> ftp://ftp.io.com/pub/usr/hmiller/music/porcupine-overture.mp3
> >
> > Aha, great.
> >
> > By the way, there's no reason anyone should lack for storage
space in
> > this day and age. It's like saying you don't have enough
toothpaste,
> > or something.
> >
> > http://www.io.com/
> >
> > Hmm, 100MB upgrade costs $9/month if you buy it by the year.
Whaddda
> > rip. I take back the toothpaste remark. And it looks like you
can't
> > even get a static IP address to host it yourself unless you buy a
T1
> > line. I feel like I'm living in a cave, in Soviet Russia.
>
> You can still get static IP's with some DSL services, but they are
more
> expensive than normal "consumer" DSL, like maybe $80/month. That's
a lot
> less than a T1, but still out of range for most of us.
>
> -Kurt
>
> >
> > -Carl

***This is why I am very much in favor of services like SoundClick,
which stream an *unlimited* number of files. You pay a little bit if
you don't want any ads at all on the site, but I find the ads pretty
non-intrusive...

http://www.soundclick.com/

Joseph P.

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Aaron K. Johnson" <akjmicro@c...>

/tuning/topicId_50122.html#50257

wrote:
> On Saturday 20 December 2003 11:42 pm, Peter Wakefield Sault wrote:
> > --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > > >Thankyou Gene.
> > > >
> > > >Is 15-EDO anything more than just a theoretical curiosity? How
> >
> > does
> >
> > > >one manage without a '5th'? Why 15?
> > >
> > > Before you attempt to understand it theoretically, I strongly
> >
> > suggest
> >
> > > you listen to the Mizarian Porcupine Overture...
> > >
> > > ftp://ftp.io.com/pub/usr/hmiller/music/
> > >
> > > Waitaminute, 48Kbps mono? Herman Miller, that will not do!
> > >
> > > -Carl
> >
> > Such experiments are very valid although there can be no absolute
> > judgment of the results in the scientific sense. Mr Miller has
> > evidently put a great deal of thought and work into this one. To
me
> > it forms a very persuasive argument for sticking with 12-EDO. I
> > accept that that is a very subjective and narrow opinion and that
the
> > champions of in-your-face bizarro tonalities undoubtedly love it
for
> > what it represents rather than for its lack of aesthetic content.
>
> Well, even if you don't like it, it's still an aesthetic, and it's
still got
> 'content', no?
>
> But, I agree that 15-tet is not as interesting to me as the
beautiful 19-tet
> or 31-tet meantone varieties, with there better JI approximations
of thirds
> than the normal 12-tet....
>
> I'm also partial to the stuctural presence of fifths and fourths, I
must say,
> and if you put a gun to my head and asked me if I could write music
without
> it, I'd say 'yes I could, but I prefer you shoot me'. That doesn't
include
> necessarily what noisy fun things I would do on a synth where pitch
is less
> important, or more accidental a parameter, than say
timbre......but, from
> what I just said, I'd rather right in a tuning with good fifths but
no good
> thirds in the JI sense (17-tet) than I would vice versa..
>
> Best,
> Aaron.
>

***Well, it all depends what you want to do with it. Brian McLaren
really is the composer who has the broadest view of microtonality and
the possibilities. Actually, he seems pretty "tame" considering what
has been "going down" around here lately...

J. Pehrson

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > >Thanks Carl for getting back to me. This was my first post
anywhere
> > >about anything, so you get a gold star. The staff for 15 EDO has
NOT
> > >been established from what I can see so far. I'm not sure if I
can
> > >take Herman Miller's tongue and cheek staff seriously. If
Blackwood
> > >uses a staff I haven't as yet found a image of it. Regardless,
two
> > >composers using 15 EDO, even if they use the same staff does not
> > >convince me it is a "standard" that should be accepted by future
> > >musicians. Thanks.
> >
> > Sorry, I'm not sure I'm understanding "staff". What is a "staff"?
> >
> > I think the Mizarian Porcupine Overture is a great piece of music,
> > which I would not hesitate to put with the average work of a
> > Romantic master. I feel the same way about Blackwood's 15-tET
> > stuff, YMMV.
> >
> > I'm not aware of anyone proposing 15-tET as a standard. This
> > group is generally fairly anti-standard. The whole point is to
> > explore the vast virgin universe of alternate tunings. In 100
> > years maybe a standard will emerge.
> >
> > -Carl
>
> Carl,
>
> I think Stephen was referring to standard notations for 15-tET
> (15-EDO), not 15-tET _as_ a standard tuning. I think you will agree
> that although the idea of any kind of standard tuning is anathema,
> we're quite interested in standardising
> terminology/notation/nomenclature whenever possible, so we can
> actually understand each other when we attempt to communicate about
> various tunings. So saying we're "anti-standard" could be
misconstrued.
>
> Stephen,
>
> In a forthcoming paper on the sagittal notation system there are two
> notations proposed for 15-tET. One uses the scale's best
approximation
> of a fifth (9/15 oct or 720 c) between the nominals CGDAE, and the
> 5-comma up and down accidentals for one degree either side of these.
>
> C C/ D\ D D/ E\ E E/ G\ G G/ A\ A A/ C\
>
> I expect this is identical to someone else's earlier proposal with
the
> substitution of the specifically sagittal 5-comma symbol (which adds
> vertical shafts to the above slashes to turn them into half-arrows
> that unambiguously indicate the direction of pitch change).
>
> The other one uses more accidentals and notates 15-tET as every
fourth
> step of 60-tET (which is of course a multiple of 12-tET). Again, I
> won't be surprised if someone else has done this too, modulo the
> specifically sagittal accidentals which I can only crudely
approximate
> with ASCII characters.
>
> Legend for 60-ET notation (ASCII shorthand):
> A-G,#,b as for 12-ET
> y fifth-tone up (55-comma up)
> ? tenth-tone up (7:11-comma up)
> j tenth-tone down (7:11-comma down)
> k fifth-tone down (55-comma down)
>
> C C#j Dk Dy Eb? E Fj F#k F#y G? G#(or Ab) Aj Bbk Bby B?
>
> These do not show the pure-sagittal symbols or any alternative
> spellings for modulations, but I can post more on these if you are
> interested.
>

***It looks, Stephen, as though Dave Keenan has given you some really
good ideas as to how to notate 15-EDO. If you have any question on
the graphics for Sagittal, I'm sure he will direct you to the
appropriate web pages, as some are posted.

I use Sagittal now myself, or rather a *derivative* of it, since it
didn't at first correspond to my needs but was "adjusted..."

Dave and George Secor are, without at doubt, at the very forefront of
notating microtonal music, and I would take any suggestions they
might have very seriously.

Joseph Pehrson

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

/tuning/topicId_50122.html#50216

> The other one uses more accidentals and notates 15-tET as every
fourth
> step of 60-tET (which is of course a multiple of 12-tET). Again, I
> won't be surprised if someone else has done this too, modulo the
> specifically sagittal accidentals which I can only crudely
approximate
> with ASCII characters.
>
> Legend for 60-ET notation (ASCII shorthand):
> A-G,#,b as for 12-ET
> y fifth-tone up (55-comma up)
> ? tenth-tone up (7:11-comma up)
> j tenth-tone down (7:11-comma down)
> k fifth-tone down (55-comma down)
>
> C C#j Dk Dy Eb? E Fj F#k F#y G? G#(or Ab) Aj Bbk Bby B?
>
> These do not show the pure-sagittal symbols or any alternative
> spellings for modulations, but I can post more on these if you are
> interested.
>

***Oh, I neglected to add, Stephen, that I am *very* much in favor of
Dave's *SECOND* suggestion, that is based on 60-ET notation... since
it is compatible with our "good ol' regular" 12-tET.

I've had good success with 72-tET which is, similarly, based on 12-
equal. (Or, rather, *includes* 12-equal...)

So, Stephen, I really think you have the solution here, and you use
our "regular" 5-line staff to notate 15-EDO, using the Sagittal
symbols that Dave will show you...

J. Pehrson

🔗Afmmjr@aol.com

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:

/tuning/topicId_50122.html#50252

> >
>
> Dear Veterans of this list!
> Here is as perfect example of my objection to this 'specialized'
language and how it works.
> It doesn't. Utterly impenetrable says it all!
>

***Oh, I just wanted to clarify that, on our response to challenging
list topics, I was mentioning Joe Monzo's "Bingo Card Lattice" page:

http://tonalsoft.com/enc/bingo.htm

which was inscrutable for me for some time, and then later became
clearer, and *not* to Paul Erlich's explanation of Periodicity
Blocks, although, admittedly, that was a teeny-tiny bit inscrutable
for also, a period of time. Paul's "Gentle Introduction..."

(That's "Gentle" Introduction, Peter, and not "Gentile" Introduction,
so don't worry...)

which explains lattices and how adding pitches from a lattice until
one finds a "comma" which is tempered out in, logically
enough, "temperaments" became clearer and clearer over time, and Paul
did his best to help gently explain even the "Gentle Introduction..."

http://sonic-arts.org/td/erlich/intropblock1.htm

So, if anybody wants to understand this topic (although I think Peter
is going to "Peter-out" of this list), the Gentle Introduction would
be a good place to start... and Paul is quite patient in explaining
things.

Joseph Pehrson

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Kurt Bigler <kkb@breathsense.com>

on 12/20/03 11:31 PM, kraig grady <kraiggrady@anaphoria.com> wrote:

>>
>
> Dear Veterans of this list!
> Here is as perfect example of my objection to this 'specialized' language and
> how it works.
> It doesn't. Utterly impenetrable says it all!

The thing is that we each create things that are sometimes "impenetrable".
These things are some of what comes to us, and I think we'd better not
censor them just because they are likely "impenetrable" to others.

It is also up to *us* to be penetrable, not things *out there*. Things that
can not be understood must penetrate us, and that process requires opennes
to the unknown. If only the known (or obvious) is admissable then the new
thing that is a bit far away from previous experience will not penetrate.
It requires much tolerance for the unknown in order for something really new
to penetrate.

Crystalizations of experience have their limitation and also their beauty,
and their capacity to inspire. For those who love these things (I include
myself) we will be drawn right through the opacity to eventually discover
the meaning.

Paul's graphics on this page:

http://tonalsoft.com/enc/eqtemp.htm

are a primary example of something that is relatively opaque at first, but
highly awe-inspiring in its beauty. The beauty draws me in to learn more.
And I am compelled by the indication of the infinite and also the
demonstration that the infinite has a structure which preceeded those who
discovered it.

So to me this is also art, and I like to have a lot of such art hanging
around to inspire me. I do not ask it to be penetrable.

This is not to say that only this one extreme should be represented. But it
should not be excluded, and I think the overall balance should not be
judged, although it could perhaps be improved. Clear explanations which
require "no previous experience" are another side of the picture, and I am
all for this.

Perhaps this list is oriented too much toward what is impenetrable by (to?)
many, but that is only a part of the balance, and besides, it happens
organically because of the "critical mass" inspiration shared by some that
are here. This is already balanced by much tolerance of a lot of different
"levels" of use of language here.

-Kurt

>
>
>>
>> From: "Peter Wakefield Sault" <sault@cyberware.co.uk>
>> Subject: Re: 15 EDO
>>
>>
>> Utterly impenetrable. However, I'm sure you must know what you're
>> talking about. You and others on this group have been developing your
>> ideas for a long time and you appear to have developed your own
>> language to talk about them. When I try to comprehend the terms by
>> following up the links I find that your definitions are sometimes
>> highly personal. For example, you equate 'periodicity'
>> with 'frequency'. You will have to pardon me if I find that a bit of
>> a brick wall.
>>
>> In trying to understand the term 'periodicity-block' I find I must
>> first understand the terms 'lattice' and 'lattice diagram'. However,
>> your explanation of these items is somewhat lacking. Could you
>> explain to me, in simple terms, how to construct a 'lattice diagram'?
>> The instructions for doing this seem to be missing from your
>> definition and I cannot find any link to a 'how-to'. Would you show
>> me a lattice diagram for the octachord (which must surely be the
>> simplest possible) and how this can be developed to include other
>> intervals?
>>
>> Peter
>>
>>>
>>
>>
>
> -- -Kraig Grady
> North American Embassy of Anaphoria Island
> http://www.anaphoria.com
> The Wandering Medicine Show
> KXLU 88.9 FM WED 8-9PM PST
>
>
> You do not need web access to participate. You may subscribe through
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>
>

🔗Maximiliano G. Miranda Zanetti <giordanobruno76@yahoo.com.ar>

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:
>
> Utterly impenetrable. However, I'm sure you must know what you're
> talking about. You and others on this group have been developing
your
> ideas for a long time and you appear to have developed your own
> language to talk about them. When I try to comprehend the terms by
> following up the links I find that your definitions are sometimes
> highly personal. For example, you equate 'periodicity'
> with 'frequency'. You will have to pardon me if I find that a bit
of
> a brick wall.
>
> In trying to understand the term 'periodicity-block' I find I must
> first understand the terms 'lattice' and 'lattice diagram'.
However,
> your explanation of these items is somewhat lacking. Could you
> explain to me, in simple terms, how to construct a 'lattice
diagram'?
> The instructions for doing this seem to be missing from your
> definition and I cannot find any link to a 'how-to'. Would you show
> me a lattice diagram for the octachord (which must surely be the
> simplest possible) and how this can be developed to include other
> intervals?
>
> Peter
>

Have you read:

http://tonalsoft.com/enc/lattice.htm

http://tonalsoft.com/monzo/lattices/lattices.htm#5-limit

So, though lattice diagrams' designs vary, they try to show
graphically the relation between the ratios of a given scale. They
are meant to represent odd or prime-limit connections.

Usually conceived as n-dimensional graphics, where n is the number of
prime or odd numbers involved (apart from 2).

So, the ratios 4/3 1 5/3 3/2 6/5 5/4 8/5 would form part of a 5-prime-
limit bidimensional lattice, in which one "direction" implies 3-prime
factorization, and the other 5-prime. The directions could be x-y
axis or so, or any other vectorial directions (linearly-independent!).

If you take the x-y axis approach for a 5-prime-limit lattice, with x-
direction for powers of 3, and y-axis respectively for powers of 5,
then you may have 1 as your central note. Next to it, to the right,
would stand 3/2 (a "fifth" up). Similarly, 4/3 would be the note next
to the left of 1 (one "fifth" down). Above the central note it's
where 5/4 would stand, and below 8/5. 9/8 would be to the right of
3/2, and so on...

If you think in terms of cartesian powers of 3 and 5, the point (2,0)
is 9/8, (1,-1) is 5/3, etc.

This of course is just one way to conceive lattices, you may also see
Erlich's approach in

http://www-math.cudenver.edu/~jstarret/22ALL.pdf

and any other lattice on the posts of the group.

Hope this helps,

Max.

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Kurt Bigler <kkb@breathsense.com>

🔗monz <monz@attglobal.net>

hi Joe,

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> ***Oh, I just wanted to clarify that, on our response
> to challenging list topics, I was mentioning Joe Monzo's
> "Bingo Card Lattice" page:
>
> http://tonalsoft.com/enc/bingo.htm
>
> which was inscrutable for me for some time, and then later
> became clearer, and *not* to Paul Erlich's explanation of
> Periodicity Blocks, although, admittedly, that was a
> teeny-tiny bit inscrutable for also, a period of time.
> Paul's "Gentle Introduction..."
>
> (That's "Gentle" Introduction, Peter, and not "Gentile"
> Introduction, so don't worry...)

funny!

> which explains lattices and how adding pitches from a
> lattice until one finds a "comma" which is tempered out in,
> logically enough, "temperaments" became clearer and clearer
> over time, and Paul did his best to help gently explain even
> the "Gentle Introduction..."
>
> http://sonic-arts.org/td/erlich/intropblock1.htm

i'm currently in the process of transforming the old
Dictionary of Tuning Terms, at the Sonic Arts site,
in the Tonalsoft Encyclopaedia of Tuning. the correct
new URL for Paul's "Gentle Introduction..." is:

http://tonalsoft.com/td/erlich/intropblock1.htm

> So, if anybody wants to understand this topic (although
> I think Peter is going to "Peter-out" of this list), the
> Gentle Introduction would be a good place to start...
> and Paul is quite patient in explaining things.

yeah, when he's around.

-monz

🔗daniel_anthony_stearns <daniel_anthony_stearns@yahoo.com>

exactly right, TIMING AND CADENCE, and--ignoring all else for the
moment--McLaren at his best is clearly one of the best of the micro
writers I've read in this regard, Kyle Gann too.
--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> /tuning/topicId_50122.html#50296
> >
> > There's a thought! Imagine Brian McLaren vs. Peter Wakefield
Sault.
> > There's probably a law against it. ;-)
> >
> > Check out this vintage McLaren, entitled
> >
> > "Unsavory habits of the musical intelligentsia -- or -- the 12-TET
> > musical elite have a point, but if they comb their hair properly,
it
> > won't show"
> >
> > http://www.microtonal.freeservers.com/mclaren/post108.html
> >
> > Hilarious stuff.
>
>
> ***McLaren writes *very* well, there is no doubt about it. What he
> has is a sense of *timing* and *cadence*, which is applicable in
> writing just as it is in music composition...
>
> J. Pehrson

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> Thanks for posting Blackwood's notation, but without some
explanatory
> text, I'm not sure I've figured it out. I don't understand what
looks
> like two different nominals for many degrees, with the same
> accidentals against them in some cases. I suppose these are
alternate
> notations for the same degree, but they seem rather odd, being
> apparently a semitone apart.

Dave, why are you not understanding this? It's exactly what happens
in 15-equal sagittal too -- E=F, B=C, E#=F#, etc.

> It seems most similar to the first
> sagittal notation above.

Carl should have explained Blackwood's desideratum, which (IIRC) was
to have the 15-equal augmented triads, since they have the same
intervals as 12-equal augmented triads, to be spelled the way 12-
equal augmented triads would be most commonly spelled. This is the
part of Blackwood's notation system that comes into direct conflict
with sagittal (or any "'consistent'") notation, and shows Blackwood's
desire to cling to as many 12-equal habits as he could.

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Paul Erlich <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
> --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> > Dave, why are you not understanding this? It's exactly what
happens
> > in 15-equal sagittal too -- E=F, B=C, E#=F#, etc.
>
> Paul, if you're going to respond to all these old messages
> individually, it could get very tedious. How about reading the whole
> thread before replying.

I actually printed out a huge stack of messages and took them home to
read before replying to any of them, hoping to avoid exactly this
type of situation. Unfortunately, the right side of all the messages
was truncated, so I may have missed a few things. Not to mention that
my memory may have been slightly impaired by illness.

> By the way, it's good to have you back.

It's good to have you back too!!