modulation

Of course, when folks talk of modulation, we can't leave jazz out. I,
for one, enjoy stretching the current limits of jazz by performing it in
19eq...it gives the chord changes a nice twist, familiar but strange,
and is a good challenge for one's technique as well. Starrett and I have
plans for doing standard style jazz in 31. To me, being able to modulate
is the strong suit of eq temps; that's what they do best. I like writing
pieces with lots of chord changes, so eq temps are a natural. On another
note, I rehearsed with a Japanese koto/samisen player yesterday for an
upcoming show...she has a good grasp of the differences in pitch between
Japanese music and Western 12 eq. We are going to do a samisen/fretless
guitar improv, and hearing her play a minor scale with slightly flatted
pitches was a hoot...I plan on learning a lot...Hstick

hello group. Not to argue for the tyranny of equal temperment, but
isn't it necessary for modulation, where you end up needing all 12
tones? cheers, Kelly

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:

> hello group. Not to argue for the tyranny of equal temperment, but
> isn't it necessary for modulation, where you end up needing all 12
> tones? cheers, Kelly

I thought there were 31 tones so you need 31-equal to get all 31
tones. But I could be wrong.

31? Sorry, I'm kind of new to microtonal music. Don't even have
speakers on my computer...I have an old Julian Carrillo microtonal
choral piece somewhere....

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
>
> > hello group. Not to argue for the tyranny of equal temperment,
but
> > isn't it necessary for modulation, where you end up needing all
12
> > tones? cheers, Kelly
>
> I thought there were 31 tones so you need 31-equal to get all 31
> tones. But I could be wrong.

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:

> 31? Sorry, I'm kind of new to microtonal music. Don't even have
> speakers on my computer...I have an old Julian Carrillo microtonal
> choral piece somewhere....

Ah; I thought you might be teasing us a little. My point was that it
makes equally good sense to say we need 31 tones to modulate
"everywhere" as 12. It all depends on what "everywhere" is going to
be--your universe of tonality. But any equal division of the octave
has the property that it is isotropic--that is, from everywhere it
looks the same. Nor can you always argue that you need 12 notes to the
octave to perform common-practice Western music, as sometimes 31 would
actually be historically (as well as intonationally) more accurate.

Hi, "traktus5",

on 8/18/04 3:05 AM, Gene Ward Smith <gwsmith@svpal.org> wrote:

> --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
>
>> 31? Sorry, I'm kind of new to microtonal music. Don't even have
>> speakers on my computer...I have an old Julian Carrillo microtonal
>> choral piece somewhere....
>
> Ah; I thought you might be teasing us a little. My point was that it
> makes equally good sense to say we need 31 tones to modulate
> "everywhere" as 12. It all depends on what "everywhere" is going to
> be--your universe of tonality. But any equal division of the octave
> has the property that it is isotropic--that is, from everywhere it
> looks the same. Nor can you always argue that you need 12 notes to the
> octave to perform common-practice Western music, as sometimes 31 would
> actually be historically (as well as intonationally) more accurate.

Yes, and keep in mind that JI is not necessarily a closed tuning system. In
fact its openness (even infiniteness) is considered by many to be one of its
key features (aside from harmony), so that you are free to go into as large
a lattice of pitches as your music requires. This *is* a potentially
infinite resource, and although finite in any actual use, the finiteness is
sometimes you might say only limited by the length of the piece. And some
pieces do in fact push this pretty far. You can find this for example in
Toby Twining's Crysalid Requiem. Personally I may have never known this by
listening to it but since I read the article on it in the previous issue of
1/1 I know this piece modulates very far from its original set of pitches.

-Kurt

traktus5 wrote:
> hello group. Not to argue for the tyranny of equal temperment, but > isn't it necessary for modulation, where you end up needing all 12 > tones? cheers, Kelly

Why stop at 12 when you can have 26? :-)

http://www.io.com/~hmiller/midi/26tet.mid

Then again, that's still a form of equal temperament. But you can just as easily do modulation with other kinds of symmetrical temperaments.

http://www.io.com/~hmiller/music/ex/lemba.mid

The difference is that you usually can't modulate all the way around the circle and come back to where you started, like you can with equal temperaments. (Although some temperaments do allow you to modulate in circles to a limited extent; there are temperaments that repeat at the quarter octave, for instance.)

Of course, the limits of modulation are only a problem for instruments with a limited number of fixed pitches; you can modulate as far as you like in just intonation with flexible pitch instruments (like fretless strings) or voices. And after a while in a large JI lattice you reach a point where you're so close to your starting point that you can ignore the small difference and treat it as a "unison vector".

hi Kelly,

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:

> 31? Sorry, I'm kind of new to microtonal music.
> Don't even have speakers on my computer...I have an old
> Julian Carrillo microtonal choral piece somewhere....
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
> >
> > > hello group. Not to argue for the tyranny of
> > > equal temperment, but isn't it necessary for modulation,
> > > where you end up needing all 12 tones? cheers, Kelly
> >
> > I thought there were 31 tones so you need 31-equal to get
> > all 31 tones. But I could be wrong.

what Gene meant was that standard musical notation
gives us 31 different notes.

i'm going to use "A" as the reference note, since
historically it obviously was the first reference note
used when letter-notation was invented (otherwise, why
would it be "A"?).

the regular 7-tone diatonic scale is:
A - B - C - D - E - F - G - (A)

each of these can also have a sharp:
A# - B# - C# - D# - E# - F# - G#

or a flat:
Ab - Bb - Cb - Db - Eb - Fb - Gb

then we also have double-sharps:
Ax - Bx - Cx - Dx - Ex - Fx - Gx

and double-flats:
Abb - Bbb - Cbb - Dbb - Ebb - Fbb - Gbb

now some in these last two categories become
awkward, because they bump up against notes which
already have a sharp or flat. for example,
we're used to thinking of Cb as B, but what
about Cbb? is that supposed to be a synonym
for Bb?

as it turns out, modern Euro-centric harmonic theory
evolved within a meantone context, and the particular
variety of meantone was generally assumed to be
1/4-comma (which is the "true" meantone tuning -- i.e.,
it really does have a "tone" [major-2nd] which is
exactly midway in pitch between the two JI major-2nds
of ratios 10/9 and 9/8; other "meantones" are approximately
mean but not exactly).

now if you'll take a look at my 1/4-comma meantone page:

http://tonalsoft.com/enc/index2.htm?1-4cmt.htm

you'll see an explanation, with diagrams, of how
1/4-comma meantone almost closes after 31 notes.
this means that 31edo (31-tone equal-temperament)
gives a good emulation of 1/4-comma meantone.

and you'll see from my explanation that in 1/4-comma
meantone, Cbb does indeed come very close to one of
the other notes already in the scale ... it's not
Bb, but it's Ax.

anyway, the "awkward" double-sharps and double-flats
occur near the points where the basic diatonic scale
only has semitones instead of whole-tones, i.e.,
between E-F and B-C.

so, if i put those "awkward" double-sharps and
double-flats in brackets, the whole system looks
like this:

A - B - C - D - E - F - G
A# - B# - C# - D# - E# - F# - G#
Ab - Bb - Cb - Db - Eb - Fb - Gb
Ax - [Bx] - Cx - Dx - [Ex] - Fx - Gx
Abb - Bbb - [Cbb] - Dbb - Ebb - [Fbb] - Gbb

count them up, and you get 31 different notes.

a handful of modern JI composers have used the
bracketed notes as well as others with 3 or even 4
sharps or flats ... Ben Johnston is actually the
only composer i know of who has done this.

but otherwise, i doubt if you'll ever find a piece
in the standard repertoire which goes beyond these 31.

also see my 31edo page for more:

http://tonalsoft.com/enc/index2.htm?31edo.htm

-monz

Monz, thanks for the detailed, informative reply. _Kelly

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> hi Kelly,
>
>
> --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
>
> > 31? Sorry, I'm kind of new to microtonal music.
> > Don't even have speakers on my computer...I have an old
> > Julian Carrillo microtonal choral piece somewhere....
> >
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > > --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
> > >
> > > > hello group. Not to argue for the tyranny of
> > > > equal temperment, but isn't it necessary for modulation,
> > > > where you end up needing all 12 tones? cheers, Kelly
> > >
> > > I thought there were 31 tones so you need 31-equal to get
> > > all 31 tones. But I could be wrong.
>
>
>
> what Gene meant was that standard musical notation
> gives us 31 different notes.
>
> i'm going to use "A" as the reference note, since
> historically it obviously was the first reference note
> used when letter-notation was invented (otherwise, why
> would it be "A"?).
>
> the regular 7-tone diatonic scale is:
> A - B - C - D - E - F - G - (A)
>
> each of these can also have a sharp:
> A# - B# - C# - D# - E# - F# - G#
>
> or a flat:
> Ab - Bb - Cb - Db - Eb - Fb - Gb
>
> then we also have double-sharps:
> Ax - Bx - Cx - Dx - Ex - Fx - Gx
>
> and double-flats:
> Abb - Bbb - Cbb - Dbb - Ebb - Fbb - Gbb
>
>
> now some in these last two categories become
> awkward, because they bump up against notes which
> already have a sharp or flat. for example,
> we're used to thinking of Cb as B, but what
> about Cbb? is that supposed to be a synonym
> for Bb?
>
>
> as it turns out, modern Euro-centric harmonic theory
> evolved within a meantone context, and the particular
> variety of meantone was generally assumed to be
> 1/4-comma (which is the "true" meantone tuning -- i.e.,
> it really does have a "tone" [major-2nd] which is
> exactly midway in pitch between the two JI major-2nds
> of ratios 10/9 and 9/8; other "meantones" are approximately
> mean but not exactly).
>
>
> now if you'll take a look at my 1/4-comma meantone page:
>
> http://tonalsoft.com/enc/index2.htm?1-4cmt.htm
>
> you'll see an explanation, with diagrams, of how
> 1/4-comma meantone almost closes after 31 notes.
> this means that 31edo (31-tone equal-temperament)
> gives a good emulation of 1/4-comma meantone.
>
> and you'll see from my explanation that in 1/4-comma
> meantone, Cbb does indeed come very close to one of
> the other notes already in the scale ... it's not
> Bb, but it's Ax.
>
>
> anyway, the "awkward" double-sharps and double-flats
> occur near the points where the basic diatonic scale
> only has semitones instead of whole-tones, i.e.,
> between E-F and B-C.
>
> so, if i put those "awkward" double-sharps and
> double-flats in brackets, the whole system looks
> like this:
>
> A - B - C - D - E - F - G
> A# - B# - C# - D# - E# - F# - G#
> Ab - Bb - Cb - Db - Eb - Fb - Gb
> Ax - [Bx] - Cx - Dx - [Ex] - Fx - Gx
> Abb - Bbb - [Cbb] - Dbb - Ebb - [Fbb] - Gbb
>
>
> count them up, and you get 31 different notes.
>
> a handful of modern JI composers have used the
> bracketed notes as well as others with 3 or even 4
> sharps or flats ... Ben Johnston is actually the
> only composer i know of who has done this.
>
> but otherwise, i doubt if you'll ever find a piece
> in the standard repertoire which goes beyond these 31.
>
>
> also see my 31edo page for more:
>
> http://tonalsoft.com/enc/index2.htm?31edo.htm
>
>
>
>
> -monz