Yahoo Tuning Groups Ultimate Backup makemicromusic Maple Leaf Rag in 5-edo and 7-edo...

Hello MMM,

One of the things I've been thinking about is ways to "map"
or translate from one tuning/temperament to another.
Of course, when both tunings have the same number of
notes serving analogous functions, there isn't any problem.
But when the tunings have different cardinalities,
it's not so obvious what to do.
For example, say a piece begins in 12-edo, what strategies
are there for performing it in 17-edo or 7-edo?

Here are a couple of pieces that use an oddball idea
of mapping directly from an audio file... mapping all the
sounding partials of a soundfile to a template derived
from the target or destination. So for example, these
pieces begin with a "dixieland-style" performance of
Scott Joplin's Maple Leaf Rag. The "destination" is chosen
to be 5-edo and a template is chosen which consists of
all the scale steps of 5-edo. Then every partial is
moved/transposed individually to the nearest scale step.

As you can hear, it does some odd things to the timbres,
but it does (more-or-less) restrict the pitches to the
chosen 5-edo scale:

http://www.cae.wisc.edu/~sethares/MLR5edo.mp3

Here is the "same thing" but with a destination of
7-edo:

http://www.cae.wisc.edu/~sethares/MLR7edo.mp3

Comments/questions/criticisms are welcome about the pieces,
about the mapping strategy, and also about other
mapping strategies people have tried out...

Bill Sethares

🔗Carl Lumma <ekin@...>

Cool idea. How are you identifying partials in the source?
I assume you're using a performance without the drums, and
then adding them in later?

I often wish you would use more ETs like 15, 22, 26, 27
than 5, 7, or 10.

-Carl

At 08:43 AM 3/21/2007, you wrote:
>Hello MMM,
>
>One of the things I've been thinking about is ways to "map"
>or translate from one tuning/temperament to another.
>Of course, when both tunings have the same number of
>notes serving analogous functions, there isn't any problem.
>But when the tunings have different cardinalities,
>it's not so obvious what to do.
>For example, say a piece begins in 12-edo, what strategies
>are there for performing it in 17-edo or 7-edo?
>
>Here are a couple of pieces that use an oddball idea
>of mapping directly from an audio file... mapping all the
>sounding partials of a soundfile to a template derived
>from the target or destination. So for example, these
>pieces begin with a "dixieland-style" performance of
>Scott Joplin's Maple Leaf Rag. The "destination" is chosen
>to be 5-edo and a template is chosen which consists of
>all the scale steps of 5-edo. Then every partial is
>moved/transposed individually to the nearest scale step.
>
>As you can hear, it does some odd things to the timbres,
>but it does (more-or-less) restrict the pitches to the
>chosen 5-edo scale:
>
>http://www.cae.wisc.edu/~sethares/MLR5edo.mp3
>
>Here is the "same thing" but with a destination of
>7-edo:
>
>http://www.cae.wisc.edu/~sethares/MLR7edo.mp3
>
>Comments/questions/criticisms are welcome about the pieces,
>about the mapping strategy, and also about other
>mapping strategies people have tried out...
>
>Bill Sethares

🔗Rick McGowan <rick@...>

🔗Doctor Oakroot <doctor@...>

🔗Jon Szanto <jszanto@...>

🔗Doctor Oakroot <doctor@...>

🔗Herman Miller <hmiller@...>

Bill Sethares wrote:

> As you can hear, it does some odd things to the timbres,
> but it does (more-or-less) restrict the pitches to the
> chosen 5-edo scale:
> > http://www.cae.wisc.edu/~sethares/MLR5edo.mp3
> > Here is the "same thing" but with a destination of
> 7-edo:
> > http://www.cae.wisc.edu/~sethares/MLR7edo.mp3
> > Comments/questions/criticisms are welcome about the pieces, > about the mapping strategy, and also about other > mapping strategies people have tried out...

The 7-edo version is more recognizable than the 5-edo version, which might be what you might expect, but it seems that the mapping for the 5-edo version blurs the notes together so that it's hard to get a sense of the original rhythm and general outline of the melody.

This reminds me of a warping I did back in 2002 when I was exploring keemun temperament (the 11-note chain-of-minor thirds temperament, or kleismic as it was called back then).

http://www.io.com/~hmiller/midi/mlrag-keemun.mid

I simply mapped each note of 12-ET to the 11-note keemun scale, which one note duplicated. Not very sophisticated; sometimes it works well and other times it produces an awful mess. In between are some interesting near misses.

🔗Carl Lumma <ekin@...>

🔗Bill Sethares <sethares@...>

Carl wrote:

> Cool idea. How are you identifying partials in the source?

It's basically a running short-time Fourier transform.
In other words, divide up the audio stream into 4K segments
(obviously this number may vary) and take the FFT of each segment.
To find peaks, the program uses the magnitude of the spectrum
and finds local maxima that are above the noise floor.
(This rules out some small local max caused by noise).

> I assume you're using a performance without the drums, and
> then adding them in later?

The original piece is "flute," "clarinet,", "bassoon," and
"bass guitar," and percussion (all synthesized versions).
So I started with five tracks and processed them (did the
mapping of the paritals) independently. Then I
glued them back together, removing parts that didn't seem
to work.

> I often wish you would use more ETs like 15, 22, 26, 27
> than 5, 7, or 10.

Well, I did post a ppiece in 31 ET last week... but in this case there
was good reason to use the smaller ones. When I tried
the same technique with higher ETs, not much happened... meaning,
in a tuning like 15 or 22 there are *lots* of destinations
that are very close to the partials (no matter where they
they may be). Hence the changes are subtle, and not at all what
I think of when I imagine changing a piece from (say) 12-ET to
15-ET...

--Bill Sethares

🔗Bill Sethares <sethares@...>

--- In MakeMicroMusic@yahoogroups.com, Rick McGowan <rick@...> wrote:

> Interesting sounds!...
>
> > Comments/questions/criticisms are welcome about the pieces,
>
> I'd like of like to hear (at least part of) the source from which you
> derived these...

Hi Rick, sure thing... the original is now here:

http://www.cae.wisc.edu/~sethares/MLRdixie.mp3

and the mutated 5 and 7 versions are:

http://www.cae.wisc.edu/~sethares/MLR5edo.mp3
http://www.cae.wisc.edu/~sethares/MLR7edo.mp3

(I hadn't thought to post the original because it's not microtonal --
it's a version of the MLR that I had made a few years ago for
other purposes).

One thing you can see by comparing is that most of the editing
was to remove/delete parts -- for example, while the flute
plays constantly through the original, it appears only in
sections in the mapped versions. Oh yes -- and to Carl,
the percussion was put through the same processing, but I
only kept it in parts, and superimposed the mapped drums
onto the original (you can hear this in some places where
the cymbals and other drums phase against each other).

--Bill Sethares

🔗Bill Sethares <sethares@...>

--- In MakeMicroMusic@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> The 7-edo version is more recognizable than the 5-edo version, which
> might be what you might expect, but it seems that the mapping for the
> 5-edo version blurs the notes together so that it's hard to get a sense
> of the original rhythm and general outline of the melody.

When I was "reconstructing" the piece, I was aiming more for
"interesting sounds" than for "preserving the original" so some
of this may be editing choices. That said, I agree that
there is more of the original in the 7-edo version than the
5-edo, i.e., it was easier to preserve things.

One of the subtleties of the mapping procedure is how to
handle redundancies. For example, say there are two partials
in the original that are both close to a single 5-edo partial --
so both want to map to the same place. Obviously, there is a loss
of information... the particular choice I made was to sum
them, that is, the total energy in the destination is the sum
of the energies of all partials that want to map there.
The problem is that you are adding complex numbers (magnitude
and phase) and so it's not obvious what the best way of combining
them. In the past, I had tried the following:

(1) add the two as complex numbers
(2) add the magnitudes and use the phase corresponding to
the partial with largest magnitude
(3) add the magnitudes and average the phases
(4) use just the mag and phase of the one with
the largest magnitude (and throw away the smaller)

They all sound subtly different -- I have been using (1),
and this does do things to the coherence of the sounds.

> This reminds me of a warping I did back in 2002 when I was exploring
> keemun temperament (the 11-note chain-of-minor thirds temperament, or
> kleismic as it was called back then).
>
> http://www.io.com/~hmiller/midi/mlrag-keemun.mid
>
> I simply mapped each note of 12-ET to the 11-note keemun scale, which
> one note duplicated. Not very sophisticated; sometimes it works well
and
> other times it produces an awful mess. In between are some interesting
> near misses.

OK -- this is one kind of mapping. I suppose the sound would
change depending on which note you chose to duplicate...
Another kind that is easy to do in MIDI is to start
with a piece in one tuning (like 12-edo) and then play it
on synth with a tuning table (re)tuned to something else.
It's pretty hard to retain coherence this way, but it
certainly is a breeding ground for happy accidents!

--Bill Sethares

🔗Bill Sethares <sethares@...>

🔗hstraub64 <hstraub64@...>

--- In MakeMicroMusic@yahoogroups.com, "Bill Sethares" <sethares@...>
wrote:
>
> Hello MMM,
>
> One of the things I've been thinking about is ways to "map"
> or translate from one tuning/temperament to another.
> Of course, when both tunings have the same number of
> notes serving analogous functions, there isn't any problem.
> But when the tunings have different cardinalities,
> it's not so obvious what to do.
> For example, say a piece begins in 12-edo, what strategies
> are there for performing it in 17-edo or 7-edo?
>
> Here are a couple of pieces that use an oddball idea
> of mapping directly from an audio file... mapping all the
> sounding partials of a soundfile to a template derived
> from the target or destination. So for example, these
> pieces begin with a "dixieland-style" performance of
> Scott Joplin's Maple Leaf Rag. The "destination" is chosen
> to be 5-edo and a template is chosen which consists of
> all the scale steps of 5-edo. Then every partial is
> moved/transposed individually to the nearest scale step.
>
> As you can hear, it does some odd things to the timbres,
> but it does (more-or-less) restrict the pitches to the
> chosen 5-edo scale:
>
> http://www.cae.wisc.edu/~sethares/MLR5edo.mp3
>
> Here is the "same thing" but with a destination of
> 7-edo:
>
> http://www.cae.wisc.edu/~sethares/MLR7edo.mp3
>
> Comments/questions/criticisms are welcome about the pieces,
> about the mapping strategy, and also about other
> mapping strategies people have tried out...
>

Heh heh, the very idea is cool!

Sounds very exotic... Something, however, that seems not so
advantageous in this approach is that quite a big part of the partials
seems to be always there - which creates the impression of music
staying on one single chord all the time. Especially in the 5edo
version, but in the 7edo version, too.
--
Hans Straub

🔗Carl Lumma <ekin@...>

At 07:23 AM 3/22/2007, you wrote:
>Carl wrote:
>
>> Cool idea. How are you identifying partials in the source?
>
>It's basically a running short-time Fourier transform.
>In other words, divide up the audio stream into 4K segments
>(obviously this number may vary) and take the FFT of each segment.
>To find peaks, the program uses the magnitude of the spectrum
>and finds local maxima that are above the noise floor.
>(This rules out some small local max caused by noise).

You wrote this yourself using... Lemur, Max/MSP...?

>> I assume you're using a performance without the drums, and
>> then adding them in later?
>
>The original piece is "flute," "clarinet,", "bassoon," and
>"bass guitar," and percussion (all synthesized versions).
>So I started with five tracks and processed them (did the
>mapping of the paritals) independently. Then I
>glued them back together, removing parts that didn't seem
>to work.

Check.

>> I often wish you would use more ETs like 15, 22, 26, 27
>> than 5, 7, or 10.
>
>Well, I did post a piece in 31 ET last week... but in this case
>there was good reason to use the smaller ones. When I tried
>the same technique with higher ETs, not much happened... meaning,
>in a tuning like 15 or 22 there are *lots* of destinations
>that are very close to the partials (no matter where they
>they may be). Hence the changes are subtle, and not at all what
>I think of when I imagine changing a piece from (say) 12-ET to
>15-ET...

Mmm.

Thanks for explaining,

-Carl

🔗Carl Lumma <ekin@...>

🔗Gene Ward Smith <genewardsmith@...>

🔗monz <monz@...>

Hi Doctor Oakroot,

--- In MakeMicroMusic@yahoogroups.com, "Doctor Oakroot" <doctor@...>
wrote:

> Thanks - I thought that was the meaning from context,
> but wasn't getting what it referred to.
>
> > Dr.,
> >
> > {you wrote...}
> >
> > > What does -edo mean?
> >
> > Equal Divisions of the Octave. Some people prefer using
> > this to the older and more common term ET (Equal Temperment),
> > as in most of these applications it really is a more
> > accurate term, in spite of being less well-known.

The last part of Jon's answer might leave a reader wonder
*why* "edo" is a more accurate term, and that prompted me
to add a new paragraph to my Encyclopedia entry which
explains it.

http://tonalsoft.com/enc/e/edo.aspx

(Thanks, Jon! -- that's an update which should have been
made a *long* time ago!)

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Bill Sethares <sethares@...>

Hans Straub wrote:

>Heh heh, the very idea is cool!

> Sounds very exotic... Something, however, that seems not so
> advantageous in this approach is that quite a big part of the partials
> seems to be always there - which creates the impression of music
> staying on one single chord all the time. Especially in the 5edo
> version, but in the 7edo version, too.

Yes... this is due (at least in part) to the fact
that the 5 (and 7) scale steps are quite
far apart, especially in the upper frequency regions.
This causes many upper partials to be mapped to the
same scale location and helps to cause the "single chord"
percept.

I wrote:

>>It's basically a running short-time Fourier transform.
>>In other words, divide up the audio stream into 4K segments
>>(obviously this number may vary) and take the FFT of each segment.
>>To find peaks, the program uses the magnitude of the spectrum
>>and finds local maxima that are above the noise floor.
>>(This rules out some small local max caused by noise).

And Carl asked:

> You wrote this yourself using... Lemur, Max/MSP...?

Not as simple a question as you might imagine.
The first version of all my programs is in Matlab.
But I'm in the process of transferring into Max/MSP,
where things can be done real-time (rather than off-line).
So this stuff started as one way I was testing the Max/MSP
patches: I ran them through the Matlab and then through
the Max/MSP patches... when they differed, I knew
I had errors... so what you hear is an amalgamation of
the two...

And thanks to both Carl and Gene for the links/references
to the mapping procedures... I need to study these...
I will probably return with some questions...

--Bill

🔗Carl Lumma <ekin@...>

🔗Doctor Oakroot <doctor@...>

Hmmm.. that's a little like objecting to calling the ninth month September
because it originally meant "seventh month" (The Roman calendar started in
March).

The modern word octave means a 2:1 interval and hasn't been etymologically
correct since accidentals were invented.

Of course, I could make the same argument about prefering edo over ET, lol.

>>The last part of Jon's answer might leave a reader wonder
>>*why* "edo" is a more accurate term, and that prompted me
>>to add a new paragraph to my Encyclopedia entry which
>>explains it.
>>
>>http://tonalsoft.com/enc/e/edo.aspx
>
> However, some of us feel that EDO is a less accurate
> term, because of the word "octave", which implies the use
> of the diatonic (or at lesat, a 7-tone, octave-repeating)
> scale.
>
> -Carl
>
>

--
http://DoctorOakroot.com - Rough-edged songs on homemade GIT-tars.

🔗monz <monz@...>

Hi Oakroot,

--- In MakeMicroMusic@yahoogroups.com, "Doctor Oakroot" <doctor@...>
wrote:

> > > The last part of Jon's answer might leave a reader wonder
> > > *why* "edo" is a more accurate term, and that prompted me
> > > to add a new paragraph to my Encyclopedia entry which
> > > explains it.
> > >
> > > http://tonalsoft.com/enc/e/edo.aspx
> >
> >
> > Carl wrote:
> >
> > However, some of us feel that EDO is a less accurate
> > term, because of the word "octave", which implies the use
> > of the diatonic (or at lesat, a 7-tone, octave-repeating)
> > scale.
>
>
> Hmmm.. that's a little like objecting to calling the
> ninth month September because it originally meant
> "seventh month" (The Roman calendar started in March).

What you say is true, but think about it, does it really
make any sense to still call the 9th month "September"?
The name should have been changed when the beginning of
the year was changed, but it wasn't and now we all have
to deal with the illogicality of it.

> The modern word octave means a 2:1 interval and hasn't
> been etymologically correct since accidentals were invented.

I suppose that for the calendar it's no big deal, but
in music we have these same kinds of illogicalities and
they are sometimes a big deal, especially when a student
is first learning about music. I'm a music teacher, and
every time i get a new student i have to go thru the
business of explaining how "octave" means "8th" but it's
really the 12th note. Actually i don't mind doing this,
because it gives me the opportunity to sneak in a little
bit of tuning math during the lesson, which not only
opens the door to that student learning about microtonality,
but also helps them with their math schoolwork.

But actually Carl is making a very valid point, and
it's one that i still have not addressed in my Encyclopedia.
Some microtonalists have used the term "ed2" instead of "edo"
to represent equal divisions of the 2:1 ratio, and this
is very good. The example i give on my webpage about the
Bohlen-Pierce tuning could be called "19-ed3".

Some other microtonalists have devised tunings which are
equal divisions of other interval-ratios ... i remember
that Jeff Smith composed a piece in something like 10-ed(5/3).
(Sorry i can't remember exactly what it was, and i've been
googling but can't find Jeff's webpage.)

My friend Brink has composed in many phi-based tunings,
one example of which is his "phinocchio" tuning which
maps the 5th root of phi onto the black keys of the
Halberstadt keyboard, and the 7th root of phi onto the
white keys, so it can be described as 5+7-ed(phi).
You can read a more detailed description of it here:

http://tonalsoft.com/enc/b/brinko.aspx

> Of course, I could make the same argument about prefering
> edo over ET, lol.

But hopefully you can see why the "ed-" terminology can
be much more useful and descriptive -- and correct -- than
simply "ET".

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Austin Butts <metroidman192@...>

--- In MakeMicroMusic@yahoogroups.com, "monz" <monz@...> wrote:
> But actually Carl is making a very valid point, and
> it's one that i still have not addressed in my Encyclopedia.
> Some microtonalists have used the term "ed2" instead of "edo"
> to represent equal divisions of the 2:1 ratio, and this
> is very good. The example i give on my webpage about the
> Bohlen-Pierce tuning could be called "19-ed3".

Interesting proposition. Make perfect since to me, considering there
are other equal temperaments that do not use an equal division of 2:1
and have potential for common use (at least in the MakeMicroMusic
community).

Funny thing how "edo" was meant to define a subset of all rank one
regular temperaments (et in general), but turned out to be a rather
confusing term indeed.

I'd also like to ask one particular question in light of redefining
old vocabulary. A few of my peers understand how intervals are
measured logarithmically and questioned why we use the current
"cent", even in microtuning. I somewhat realized the bias
1200-divisions of a 2:1 ratio presents, but then again the same thing
can be said about 1700, 1900, 5300, etc. It seems to me the term
"cent" is more readily accepted than "octave", but still I hate to not
see any argument other than "it's just based off the old stuff". So
can someone clarify if there is or in not unbiased logic in using 1200
cents dividing a 2:1 ratio?

🔗Rozencrantz the Sane <rozencrantz@...>

Conventions don't ever have a logical basis. Inertia is the only
reason anyone really needs to keep doing what they've been doing.

1200 works quite well as an analysis interval, and if you need more
precision you can use hundredths or thousandths of a cent or smaller
still. Since there is no pragmatic need for another division, the one
that is currently most popular will remain most popular.

On 3/23/07, Austin Butts <metroidman192@...> wrote:

> I'd also like to ask one particular question in light of redefining
> old vocabulary. A few of my peers understand how intervals are
> measured logarithmically and questioned why we use the current
> "cent", even in microtuning. I somewhat realized the bias
> 1200-divisions of a 2:1 ratio presents, but then again the same thing
> can be said about 1700, 1900, 5300, etc. It seems to me the term
> "cent" is more readily accepted than "octave", but still I hate to not
> see any argument other than "it's just based off the old stuff". So
> can someone clarify if there is or in not unbiased logic in using 1200
> cents dividing a 2:1 ratio?

--Tristan
http://dolor-sit-amet.deviantart.com

🔗Graham Breed <gbreed@...>

monz wrote:
> Hi Oakroot,
> > > --- In MakeMicroMusic@yahoogroups.com, "Doctor Oakroot" <doctor@...>
> wrote:

>>Hmmm.. that's a little like objecting to calling the
>>ninth month September because it originally meant
>>"seventh month" (The Roman calendar started in March).
> > What you say is true, but think about it, does it really
> make any sense to still call the 9th month "September"?
> The name should have been changed when the beginning of
> the year was changed, but it wasn't and now we all have
> to deal with the illogicality of it.

It doesn't make sense but most people don't care. In some languages the name does involve "9". In English this is too far established for us to do anything about it -- same as with "octave".

>>The modern word octave means a 2:1 interval and hasn't
>>been etymologically correct since accidentals were invented.
> > I suppose that for the calendar it's no big deal, but
> in music we have these same kinds of illogicalities and
> they are sometimes a big deal, especially when a student
> is first learning about music. I'm a music teacher, and
> every time i get a new student i have to go thru the
> business of explaining how "octave" means "8th" but it's > really the 12th note. Actually i don't mind doing this, > because it gives me the opportunity to sneak in a little
> bit of tuning math during the lesson, which not only > opens the door to that student learning about microtonality,
> but also helps them with their math schoolwork.

Music teachers who use numerical notation (and there are a lot of them) will have no problem explaining an octave as the 8th note. Any other number really would confuse. So there's nothing at all illogical in this case. It's only a choice of perspective and you can't please everybody.

Graham

🔗monz <monz@...>

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

> > [Doctor Oakroot wrote:]
> >
> > > The modern word octave means a 2:1 interval and hasn't
> > > been etymologically correct since accidentals were invented.
> >
> > I suppose that for the calendar it's no big deal, but
> > in music we have these same kinds of illogicalities and
> > they are sometimes a big deal, especially when a student
> > is first learning about music. I'm a music teacher, and
> > every time i get a new student i have to go thru the
> > business of explaining how "octave" means "8th" but it's
> > really the 12th note. Actually i don't mind doing this,
> > because it gives me the opportunity to sneak in a little
> > bit of tuning math during the lesson, which not only
> > opens the door to that student learning about microtonality,
> > but also helps them with their math schoolwork.
>
> Music teachers who use numerical notation (and there are
> a lot of them) will have no problem explaining an octave
> as the 8th note. Any other number really would confuse.
> So there's nothing at all illogical in this case. It's
> only a choice of perspective and you can't please everybody.

I was in a hurry when i wrote that paragraph, and what i
left out is that explaining the 8-vs-12 thing to young
students actually also gives me the opportunity to indulge
in some of the most interesting, fun, and fascinating aspects
of my lessons with them: teaching them some music history.

For all my students, even the youngest ones, i explain
how "a really long time ago" there were no flats or sharps
and the only notes used were the ones with the letters.

For the students who are old enough to appreciate it, i
can go all the way back to ancient Greek tetrachord theory,
and for the ones who really get interested i can push back
further to my ideas about the Sumerians. ;-)

In fact, one of the things i really enjoy about teaching
the youngest ones (the 4-year-olds) their first few lessons,
is in explaining to them "how easy it is to learn music",
because they are right at the age where they are having fun
learning the alphabet, and i show them how in music we only
need 7 letters and not the whole 26. I teach them my own
version of the A-B-C song (the one everyone knows, to the
tune of "Twinkle Twinkle Little Star" ... i just have to
change two of the half-notes in the middle section to two
quarter-notes each), which has these lyrics:

A B C D E F G, A B C D E F G
A B C D E F G, A B C D E F G
A B C D E F G, A B C D E F G

They always get a big kick out of that. ;-)

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗monz <monz@...>

Hi Austin,

--- In MakeMicroMusic@yahoogroups.com, "Austin Butts"
<metroidman192@...> wrote:

> I'd also like to ask one particular question in light of
> redefining old vocabulary. A few of my peers understand
> how intervals are measured logarithmically and questioned
> why we use the current "cent", even in microtuning. I
> somewhat realized the bias 1200-divisions of a 2:1 ratio
> presents, but then again the same thing can be said about
> 1700, 1900, 5300, etc. It seems to me the term "cent" is
> more readily accepted than "octave", but still I hate to not
> see any argument other than "it's just based off the old stuff".
> So can someone clarify if there is or in not unbiased logic
> in using 1200 cents dividing a 2:1 ratio?

In music, the term "octave" is much older than "cents",
which should be obvious from the fact that it simply means
"8th" but even today instead of using the English term we
retain the old Latin one. The same is true of "prime" which
means "1st" (when it refers to the "unison" interval),
whereas all other intervals use their English names or
(as i always do) the abbreviation utilizing the Arabic numeral.

The concept and term "cent" was initiated by Alexander Ellis
in his English translation of Helmholtz's _On The Sensations
of Tone..._, in 1875. It was the simple idea of dividing
a 12-edo semitone into 100 logarithmically equal parts.

There have been many, many other divisions used for the
measurement of small intervals, but "cent" is by far the
most common in Western usage. See my webpage which has a
list of some of the most notable units, and follow the
links to the individual pages for more detail on each unit:

http://tonalsoft.com/enc/u/unit-of-interval-measurement.aspx

Manuel also has a good page about it:

http://www.xs4all.nl/~huygensf/doc/measures.html

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Kraig Grady <kraiggrady@...>

as far as i know , no acoustic instrument has been built in a non 1200 cent instrument except those that are near this interval.
This could also include music even written for acoustical instruments.
Almost exclusive the non 1200 octave occurs in non western countries. Still we refer to them as stretched or shrunk .
These list have a conceit that they are representative of tuning practice when in fact it is only a small cross section of the active movement.
If their were a true movement of non octave tunings, except for the purpose of one time experimentation, i think there would be more a case.
i am totally against all this obscure terminology which does nothing more than makes hinders an intelligible language to new comers.
It does nothing more than alienate the very ideas it wish to promote.
i am wary of learning the meaning of every single new name for a tuning.
Most which do not explain anything except in retrospect. Most remain theoretical

Edo most educated musicians will recognize as a period of Japanese music.

Partch used the word octave even though hardly a single one of his instruments had even one of them of any ratio.
let us look at the case of pentatonics in the field of Ethnomusicology.
They have not found any reason to change the terms away from the octave even though there is not 8 tones to the octave.
We still call CD stores record stores even though they have no records.
and many of the companies who make them have the word records in them.
the term performance art is used less as the practice grew and people just refer to it as theater, even when the defining idea was that it was an autobiographical statement.
In the future i surmise that the term octave will define any interval in which a set of intervals are repeated.
Language is filled with old words that are forced to take on new meanings.
>
> -- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

🔗Doctor Oakroot <doctor@...>

While we're on the topic of inaccurate language, what about the word
"microtonal"?

When I hit a 4th, bend it up to a slightly flat tritone, let it slip back
to the 4th and resolve to a minor third and every little pitch variation
means something... that's microtonal. (The melody described is a
stereotypical blues sound that you would immediately recognize)

5-edo or 13-edo or some JI is just another scale and is no more microtonal
than 12 ET.

> Hi Oakroot,
>
>
> --- In MakeMicroMusic@yahoogroups.com, "Doctor Oakroot" <doctor@...>
> wrote:
>
>> > > The last part of Jon's answer might leave a reader wonder
>> > > *why* "edo" is a more accurate term, and that prompted me
>> > > to add a new paragraph to my Encyclopedia entry which
>> > > explains it.
>> > >
>> > > http://tonalsoft.com/enc/e/edo.aspx
>> >
>> >
>> > Carl wrote:
>> >
>> > However, some of us feel that EDO is a less accurate
>> > term, because of the word "octave", which implies the use
>> > of the diatonic (or at lesat, a 7-tone, octave-repeating)
>> > scale.
>>
>>
>> Hmmm.. that's a little like objecting to calling the
>> ninth month September because it originally meant
>> "seventh month" (The Roman calendar started in March).
>
>
> What you say is true, but think about it, does it really
> make any sense to still call the 9th month "September"?
> The name should have been changed when the beginning of
> the year was changed, but it wasn't and now we all have
> to deal with the illogicality of it.
>
>
(snip for brevity)

--
http://DoctorOakroot.com - Rough-edged songs on homemade GIT-tars.

🔗Austin Butts <metroidman192@...>

Thanks for the links. I'll look into them in detail whenever I can.

I think for all terms and purposes, the cent is a magnificent way to
measure both rational and irrational intervals. When I was first
learning about microtuning, I always understood "cent" because I could
apply it to a context which I understood. However, unlike "semitones
(12-ed2 ones of course)" or "steps" or any other similar term, we are
not limited to using whole numbers of cents, of which we can take to
as many decimals as we please. Therefore, it does not limit us as
12-ed2 has done, even though it is based off of it. My argument
against cents in my previous post was merely me being devil's advocate
in response to a question I couldn't answer without sounding like a
hypocrite.

I realized cent was a much newer innovation, but not exactly how new,
when compared to the octave. A little historical background is always
appreciated in my book.

-Austin

--- In MakeMicroMusic@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Austin,
>
>
> --- In MakeMicroMusic@yahoogroups.com, "Austin Butts"
> <metroidman192@> wrote:
>
> > I'd also like to ask one particular question in light of
> > redefining old vocabulary. A few of my peers understand
> > how intervals are measured logarithmically and questioned
> > why we use the current "cent", even in microtuning. I
> > somewhat realized the bias 1200-divisions of a 2:1 ratio
> > presents, but then again the same thing can be said about
> > 1700, 1900, 5300, etc. It seems to me the term "cent" is
> > more readily accepted than "octave", but still I hate to not
> > see any argument other than "it's just based off the old stuff".
> > So can someone clarify if there is or in not unbiased logic
> > in using 1200 cents dividing a 2:1 ratio?
>
>
> In music, the term "octave" is much older than "cents",
> which should be obvious from the fact that it simply means
> "8th" but even today instead of using the English term we
> retain the old Latin one. The same is true of "prime" which
> means "1st" (when it refers to the "unison" interval),
> whereas all other intervals use their English names or
> (as i always do) the abbreviation utilizing the Arabic numeral.
>
> The concept and term "cent" was initiated by Alexander Ellis
> in his English translation of Helmholtz's _On The Sensations
> of Tone..._, in 1875. It was the simple idea of dividing
> a 12-edo semitone into 100 logarithmically equal parts.
>
> There have been many, many other divisions used for the
> measurement of small intervals, but "cent" is by far the
> most common in Western usage. See my webpage which has a
> list of some of the most notable units, and follow the
> links to the individual pages for more detail on each unit:
>
> http://tonalsoft.com/enc/u/unit-of-interval-measurement.aspx
>
>
> Manuel also has a good page about it:
>
> http://www.xs4all.nl/~huygensf/doc/measures.html
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

🔗Gene Ward Smith <genewardsmith@...>

--- In MakeMicroMusic@yahoogroups.com, "Austin Butts"
<metroidman192@...> wrote:

> > The example i give on my webpage about the
> > Bohlen-Pierce tuning could be called "19-ed3".

> Interesting proposition. Make perfect since to me, considering
there
> are other equal temperaments that do not use an equal division of
2:1
> and have potential for common use (at least in the MakeMicroMusic
> community).

There is no such consensus about the potential of no-twos tuning
systems such as Bohlen-Pierce, but 19-ed3 is just a tuning of 12-edo
with octaves of size 3^(12/19), a cent sharp. I think calling it by a
special name without at the same time relating it to 12 is asking for
confusion. In any case, I regard 19-ed3 and 12-edo, used for 5-limit
harmony, as the same temperament, but I'm afraid I might also in some
cases call 19-ed3 as 12-edo. In fact, if you look I just did.

> Funny thing how "edo" was meant to define a subset of all rank one
> regular temperaments (et in general), but turned out to be a rather
> confusing term indeed.

Is that what it was suppose to be? Why do you say that?

Well, it's a logarithm. If they understand that intervals are
measured logarithmically, it seems to me they've answered their own
question.

> So
> can someone clarify if there is or in not unbiased logic in using
1200
> cents dividing a 2:1 ratio?

It's convention. Everyone does it. When I was working by myself, I
used to divide 2 into 612 parts, but that's not what everyone else
was doing.

Here's a question: why do you say "a 2:1 ratio" and not 2? You can
take a log of 2, but the only way to take the log of a ratio is to
assume that means it is a number. I would really like, now that we
are on terminology, to get theorists to accept rational numbers as
good things.

🔗Carl Lumma <ekin@...>

🔗Gene Ward Smith <genewardsmith@...>

🔗monz <monz@...>

Hi Austin,

--- In MakeMicroMusic@yahoogroups.com, "Austin Butts"
<metroidman192@...> wrote:
>
> Thanks for the links. I'll look into them in detail whenever I can.

In fact, i thought i already had a webpage listing the
units of interval measurement, but found upon replying
to your post that i didn't have one, so i made it right
then and there. But because i spent some time on that,
i forgot to mention one thing i had wanted to say,
which i'll say below ...

> I think for all terms and purposes, the cent is a
> magnificent way to measure both rational and irrational
> intervals. When I was first learning about microtuning,
> I always understood "cent" because I could apply it to
> a context which I understood.

Certainly that's why Ellis decided to use it. By 1875
Western musical culture had pretty much accepted 12-edo
as a standard tuning ... with the exception that 1/6-comma
meantone continued to be used in orchestral practice at
least to some extent.

> However, unlike "semitones (12-ed2 ones of course)" or
> "steps" or any other similar term, we are not limited to
> using whole numbers of cents, of which we can take to
> as many decimals as we please. Therefore, it does not
> limit us as 12-ed2 has done, even though it is based off
> of it.

Funny you should say that, because actually, Ellis himself
did not use decimal places with most of his cents measurements,
preferring to use what he called "cyclical cents", which are
simply the integer values.

Anyway, the thing i had forgotten to mention before was
that some tuning theorists like to use "millioctaves"
instead of cents, precisely because it focuses on a
decimal division of the 2:1 ratio and avoids any reference
to 12-edo. But it hasn't really caught on -- most folks
still prefer cents.

What you'll find when you learn more about the history
of this kind of thing is that music theorists divide
whatever interval happens to matter to them the most
within the context of the music they're most familiar with.
Thus, turk-sents are based on a smaller division of 53-edo
because 53-edo has been widely used in Turkish theory,
Cleonides in his discussion of Aristoxenos's theory relied
on 30 divisions of the 4:3 ratio, because the 4:3 was
the fundamental reference point for the ancient Greeks, etc.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Austin Butts <metroidman192@...>

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:

> There is no such consensus about the potential of no-twos tuning
> systems such as Bohlen-Pierce

That statement of mine you are referring to was all fluff. Advocation
for non 2 tuning can be implied by that statement, but it was not my
intended message.

> I think calling it by a
> special name without at the same time relating it to 12 is asking for
> confusion.

Can you please elaborate on that? Who would it mainly confuse?

> In any case, I regard 19-ed3 and 12-edo, used for 5-limit
> harmony, as the same temperament, but I'm afraid I might also in some
> cases call 19-ed3 as 12-edo. In fact, if you look I just did.

I just realized that 19-ed3 isn't even the Bohlen-Pierce scale. It
should be 13-ed3. Nonetheless, what you say is true. "19-ed3" bears
a stark similarity to 12-ed2 in terms of 5-limit harmony (which set
off an alarm in my mind, because the Just-Intonation Bohlen-Pierce
scale contains intervals with limits higher than 5).

> > Funny thing how "edo" was meant to define a subset of all rank one
> > regular temperaments (et in general), but turned out to be a rather
> > confusing term indeed.
>
> Is that what it was suppose to be? Why do you say that?

I'm glad I shortened my response to this point. It went nowhere fast
as I was typing it out. (Sorry Gene, was my fault, not yours. So
unbelievably tired at this point.)

Long story short, I need a clear cut definition and explanation for
"octave" and "2:1", if they are in any way related and, if so, how?
Disassociation between octave and period across the board would also
be much appreciated if it is deemed proper to do so.

Please pardon my unsupported statement in my previous post. I was
subliminally referring to thoughts I did not mention (and for the most
part, still unmentioned >_>).

> > I'd also like to ask one particular question in light of redefining
> > old vocabulary. A few of my peers understand how intervals are
> > measured logarithmically and questioned why we use the current
> > "cent", even in microtuning.
>
> Well, it's a logarithm. If they understand that intervals are
> measured logarithmically, it seems to me they've answered their own
> question.

I really was referring to the value of a cent, not the concept of it.

> Here's a question: why do you say "a 2:1 ratio" and not 2? You can
> take a log of 2, but the only way to take the log of a ratio is to
> assume that means it is a number. I would really like, now that we
> are on terminology, to get theorists to accept rational numbers as
> good things.

The word "ratio" does seem a bit rediculous placed after rational
numbers. After all, "rational" is derived from "ratio" (or vice
versa, not exactly sure).

However, I think taking the log of a ratio doesn't necessarily mean
the ratio itself is a number. The log of a "ratio" between two
numbers should be the same thing as the "logarithmic difference"
between two numbers.

🔗Austin Butts <metroidman192@...>

--- In MakeMicroMusic@yahoogroups.com, "monz" <monz@...> wrote:
> with the exception that 1/6-comma
> meantone continued to be used in orchestral practice at
> least to some extent.

Interesting. Any other historical information on 1/6-comma meantone?

> > However, unlike "semitones (12-ed2 ones of course)" or
> > "steps" or any other similar term, we are not limited to
> > using whole numbers of cents, of which we can take to
> > as many decimals as we please. Therefore, it does not
> > limit us as 12-ed2 has done, even though it is based off
> > of it.
>
>
> Funny you should say that, because actually, Ellis himself
> did not use decimal places with most of his cents measurements,
> preferring to use what he called "cyclical cents", which are
> simply the integer values.

This seems to be a case where a term evolved out of it's original
intentions. True, he used integer values, but later tuning practices
saw it useful to divide it further, but this time using the same term,
just in smaller parts.

> Anyway, the thing i had forgotten to mention before was
> that some tuning theorists like to use "millioctaves"
> instead of cents, precisely because it focuses on a
> decimal division of the 2:1 ratio and avoids any reference
> to 12-edo. But it hasn't really caught on -- most folks
> still prefer cents.

I originally looking for something like that. (But then again, I
revise my question in why we adhere to 1200 cents. There are other
things besides cents to use after all, depending on context and
audience group.)

> What you'll find when you learn more about the history
> of this kind of thing is that music theorists divide
> whatever interval happens to matter to them the most
> within the context of the music they're most familiar with.

Took the words right out of my mouth. (Didn't even realize you said
that until I got to the bottom. Funny how stuff like that works out.)

🔗Austin Butts <metroidman192@...>

Gene said...

I said...

> However, I think taking the log of a ratio doesn't necessarily mean
> the ratio itself is a number. The log of a "ratio" between two
> numbers should be the same thing as the "logarithmic difference"
> between two numbers.

What exactly do you mean by that, Gene? I fear I misinterpreted your
statement and I need to get on the same page. Are you implying all
ratios are indeed numbers or that it is merely assumed to be true?

🔗monz <monz@...>

--- In MakeMicroMusic@yahoogroups.com, "Austin Butts"
<metroidman192@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "monz" <monz@> wrote:
> > with the exception that 1/6-comma
> > meantone continued to be used in orchestral practice at
> > least to some extent.
>
> Interesting. Any other historical information on
> 1/6-comma meantone?

I made a whole webpage on it and its close relative 55-edo:

http://tonalsoft.com/enc/number/55edo/55edo.htm

(That page is a bit of mess at this point, and it's been
like that for awhile ... someday i'll get around to
editing it.)

When i first made that webpage, because of the fact that
it's based on the evidence that Mozart taught intervals
tuning according to a subset of 55-edo, i made a MIDI file
of the beginning of his 40th Symphony. I was stunned when
i first played it because it sounded *exactly* like what
i remember of hearing the first electrically recorded
performance of it, from 1924.

When i mentioned this in a tuning list post at the time,
Johnny Reinhard corroborated that this tuning was indeed
still used in orchestral playing well into the 20th century.
It seems that it was World War 2 which finally killed it off
in favor of all 12-edo all the time.

> > Funny you should say that, because actually, Ellis himself
> > did not use decimal places with most of his cents measurements,
> > preferring to use what he called "cyclical cents", which are
> > simply the integer values.
>
> This seems to be a case where a term evolved out of it's
> original intentions. True, he used integer values, but
> later tuning practices saw it useful to divide it further,
> but this time using the same term, just in smaller parts.

Well, sure, when someone wants precision all they have to
do is add decimal places. Ellis felt that 1200 divisions
per octave was already accurate enough for most of his
(and Helmholtz's) purposes.

> > Anyway, the thing i had forgotten to mention before was
> > that some tuning theorists like to use "millioctaves"
> > instead of cents, precisely because it focuses on a
> > decimal division of the 2:1 ratio and avoids any reference
> > to 12-edo. But it hasn't really caught on -- most folks
> > still prefer cents.
>
> I originally looking for something like that. (But then
> again, I revise my question in why we adhere to 1200 cents.
> There are other things besides cents to use after all,
> depending on context and audience group.)

In case you haven't noticed, something like 99% (or more)
of the musical world is locked into 12-edo thinking.
We microtonalists, since we now have internet forums
in which we associate on a daily basis, tend to forget
that sometimes.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Herman Miller <hmiller@...>

Austin Butts wrote:

> Long story short, I need a clear cut definition and explanation for
> "octave" and "2:1", if they are in any way related and, if so, how? > Disassociation between octave and period across the board would also
> be much appreciated if it is deemed proper to do so.

A period isn't necessarily an octave, although it frequently is. It can be a fraction of an octave, or some other interval not connected with an octave (you can have a tetrachord-based scale that repeats at the interval of a fifth, for instance). Some of my favorite temperaments have two periods to the octave, where a period is in the approximate range of 600 cents.

Opinions are divided on whether an "octave" always has to be an exact 2:1 interval. My preference is to use "octave" for either an exact 2:1 or its tempered equivalent. Certainly in the case of piano tuning, the interval between notes that have the same name is still referred to as an "octave" even though pianos are tuned with octaves stretched wider than 1200.0 cents.

But in the case of "EDO", I believe it was generally accepted that the "octave" being divided equally is defined as 1200.0 cents. (One reason I don't often use the term is that I don't want to limit octaves to only being 1200.0 cents; another is that in my own usage, I'm always thinking of the tuning as some form of temperament, even if it isn't always a consistent one, so the older usage "ET" is more applicable to my tonal approach to using these tunings.)

🔗monz <monz@...>

--- In MakeMicroMusic@yahoogroups.com, "monz" <monz@...> wrote:

> Some other microtonalists have devised tunings which are
> equal divisions of other interval-ratios ... i remember
> that Jeff Smith composed a piece in something like 10-ed(5/3).
> (Sorry i can't remember exactly what it was, and i've been
> googling but can't find Jeff's webpage.)

I just found it:

http://www.nonoctave.com/tunes/jigsaw.html

On his album "5-dimensional jigsaw puzzle", Jeff Smith
used 14ed(12/7) for several pieces, and 13ed(7/5) for one.

Now this points up something else: using "ed" to describe
a tuning like this, it's almost the same as writing the
actual mathematical description -- so 14ed(12/7) is
(12/7)^(1/14), etc.

BTW, note that Jeff's 14ed(12/7) tuning is almost exactly
the same as 18-edo.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Gene Ward Smith <genewardsmith@...>

--- In MakeMicroMusic@yahoogroups.com, "Austin Butts"
<metroidman192@...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
> <genewardsmith@> wrote:

> > I think calling it by a
> > special name without at the same time relating it to 12 is asking
for
> > confusion.
>
> Can you please elaborate on that? Who would it mainly confuse?

It would mainly confuse anyone who didn't realize how close (a tenth
of a cent of difference) 2^(1/12) and 3^(1/19) are.

> I just realized that 19-ed3 isn't even the Bohlen-Pierce scale. It
> should be 13-ed3.

Oh. I thought you intended to talk about two different things!

> Long story short, I need a clear cut definition and explanation for
> "octave" and "2:1", if they are in any way related and, if so, how?

A pure octave is a frequency ratio of 2:1, which of course you know.
But octaves, like other intervals, do not need to be tuned pure to
deserve the name.

So long as you take the difference to positive, I suppose. More the
logarithmic distance, therefore.

In general, I think ratios are used too much in tuning theory, in
situations where rational numbers would be just fine.

🔗monz <monz@...>

Hi Gene,

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, "monz" <monz@> wrote:
>
> > When i mentioned this in a tuning list post at the time,
> > Johnny Reinhard corroborated that this tuning was indeed
> > still used in orchestral playing well into the 20th century.
> > It seems that it was World War 2 which finally killed it off
> > in favor of all 12-edo all the time.
>
> I wouldn't say "finally", as the authentic performace movement
> arose after WW2.

Yes, thanks, you're certainly correct about that.

Actually, i don't think there was too much thought
about microtonally-informed "authentic performance"
until right about the time that Johnny Reinhard's AFMM
started getting some attention in the New York press
in the 1980s.

So what i really meant was that orchestral playing
practice shifted pretty much universally to 12-edo
during the period of about 1940 to 1990 or so.

I know that academia is a little more interested in
microtonality now than it was when i was a part of
it in the early 1980s ... but only a *little*. Even
today most orchestral musicians only know how to play
in 12-edo or something close to it.

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Michael Sheiman <djtrancendance@...>

Just interested...do any of you know what combination of scale/instruments(IE overtone structures...including synthesized harmonics/instruments) yields the most notes per scale (while sounding fairly tonal/consonant)?

From what I've read it seems even the 19-TET scale, for example / in reality, can be played tonally using combinations of about 7 notes (in its modes).
This, at a glance, appears to make it about as flexible (in terms of how many chords per mode are possible, for example) as 12-TET, albeit with different sets of tones and more possibilities for mode-to-mode modulations. I'm just wondering if there's a trick to get around this.

---------------------------------
Now that's room service! Choose from over 150,000 hotels
in 45,000 destinations on Yahoo! Travel to find your fit.

[Non-text portions of this message have been removed]

🔗monz <monz@...>

Hi Michael,

--- In MakeMicroMusic@yahoogroups.com, Michael Sheiman
<djtrancendance@...> wrote:
>
> Just interested...do any of you know what combination
> of scale/instruments(IE overtone structures...including
> synthesized harmonics/instruments) yields the most notes
> per scale (while sounding fairly tonal/consonant)?
>
> From what I've read it seems even the 19-TET scale,
> for example / in reality, can be played tonally using
> combinations of about 7 notes (in its modes).
> This, at a glance, appears to make it about as flexible
> (in terms of how many chords per mode are possible,
> for example) as 12-TET, albeit with different sets of
> tones and more possibilities for mode-to-mode modulations.
> I'm just wondering if there's a trick to get around this.

Not really sure exactly what you're asking in the first
paragraph, or what you mean by "a trick to get around this".
But i can say a few things about 19-edo (which is what i'm
sure you're referring to by "19-TET") that might shed some
light on it for you.

First, since i mention "edo", i'll say that i'm using that
because i want to be clear that i'm talking about 19 equal
steps per octave. See my webpage:

http://tonalsoft.com/enc/e/edo.aspx

Next: yes, it's simple to use 19-edo tonally by using
7-note scales. In fact, you can play all tonal music
written following the rules of the "common practice" period
(roughly 1600 to 1900) in 19-edo, without having to change
anything other than the tuning.

This is because 19-edo, like 12-edo, belongs to the meantone
family of tunings. All equal-temperaments belong to several
different tuning families, and some of the ones belonging
to the meantone family are 12, 19, 31, 43, and 55 -- these
are all of the historically important ones. See my pages:

http://tonalsoft.com/enc/f/family.aspx

http://tonalsoft.com/enc/m/meantone.aspx

The reason why you can play any "common practice" music
in any of these tunings is because all of that music was
written with meantone tuning in mind. In fact, much of it
was composed before 12-edo became adopted as the nearly
universal standard -- most composers during that era would
have expected something closer to 55-edo to be used as the
tuning for their orchestral music (keyboard music is a
different matter). It's only *because* 12-edo belongs to
the meantone family that this music works OK in 12. See:

http://tonalsoft.com/enc/number/19edo.aspx

http://tonalsoft.com/enc/number/12edo.aspx

http://tonalsoft.com/enc/number/55edo/55edo.htm

One composer who has been working in 19-edo and who
has done some really interesting modulations is John Starrett.
He came up with a technique he calls "deceptive diatonicity",
and his music has a great sense of humor, largely because
of his use of that technique:

http://tonalsoft.com/enc/d/deceptive-diatonicity.aspx

If you're interested in experimenting with these tunings
or any others you can dream up, you're welcome to download
my Tonescape software (you need a Windows XP system), which
is available in its current (unfinished) form as a free demo:

http://tonalsoft.com/downloads/redist/Tonescape_Studio_Den_Haag.exe

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗monz <monz@...>

Hi Michael,

First, since i mention "edo", i'll say that i'm using that
because i want to be clear that i'm talking about 19 equal
steps per octave. See my webpage:

http://tonalsoft.com/enc/e/edo.aspx

http://tonalsoft.com/enc/f/family.aspx

http://tonalsoft.com/enc/m/meantone.aspx

http://tonalsoft.com/enc/number/19edo.aspx

http://tonalsoft.com/enc/number/12edo.aspx

http://tonalsoft.com/enc/number/55edo/55edo.htm

http://tonalsoft.com/enc/d/deceptive-diatonicity.aspx

http://tonalsoft.com/downloads/redist/Tonescape_Studio_Den_Haag.exe

-monz
http://tonalsoft.com
Tonescape microtonal music software

🔗Michael Sheiman <djtrancendance@...>

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