12 MOS

I have a feeling this question will show how little I know.

Is it possible to construct a MOS scale in 12 equal?

And a 2nd question - if I were to use Greek tetrachords (actually I want Babylonian) does one simply repeat the structure going up or down from the 4 note span?

If this is in the wiki do you know where to look?

This is for a composition project that I'm overdue on so I would greatly appreciate any assistance _ thanks

Chris
*

Hi Chris,

> Is it possible to construct a MOS scale in 12 equal?

Yes. You pick an interval, the "generator", and make a
chain out of it.

A D G C

is a chain of three generators of 500 cents. The chain will
form a MOS, or not, depending on its length. It will never
be a MOS if the interval shares a common factor with the
octave.* The octave is 12 steps, so the generator can't be
2, 3, 4, or 6 steps. In 19-ET, every generator works
because 19 is prime.

In an ET, the chains you get with some generator are the same
as those you get with its octave inversion. So you don't need
to consider generators bigger than half an octave. That's why
I didn't bother saying that 8, 9, and 10 steps were not going
to give MOS in 12-ET -- because those chains are just
inversions of the chains based on 2, 3, and 4 steps.

This won't be a complete answer, but it should get you going.

-Carl

* There's a subtlety here to do with terminology... which is
safe for you to ignore.

--- In tuning@yahoogroups.com, chrisvaisvil@... wrote:
>
> I have a feeling this question will show how little I know.
>
> Is it possible to construct a MOS scale in 12 equal?

I started this wiki page just for you: http://xenharmonic.wikispaces.com/MOS+in+12edo

If anyone has complaints about the terminology, now's your chance...

> And a 2nd question - if I were to use Greek tetrachords (actually I want Babylonian) does one simply repeat the structure going up or down from the 4 note span?

I was under the impression that the usual thing to do is arrange the tetrachords so that the scale repeats at the octave. This requires some "conjunct" tetrachords (which share a note), and some "disjunct" tetrachords (which are separated by 9/8).

So if your tetrachord is D F F# G a possible scale would be:

D F F# G A C C# D F F# G A C C# D
|------| |------|------| |------|
disjunct conjunct disjunct

Keenan

> Is it possible to construct a MOS scale in 12 equal?

I think you're going to be disappointed. The more interesting-looking
MOSs of 12 EDO are the usual scales and modes you're used to.

If you have an ET, you can use Scala to do this instead of doing the
chaining yourself. From the menu:
--> Tools --> Moment of Symmetry

Choose parent size of 12, and then you can show, for example, all
generators and scale sizes. You'll get a lot with a generator of 1
step, or of 11, which gives you such exciting scales as C C# D D# E F
F# G G# A A# C. I don't find those to be particularly interesting, so
I don't consider them. YMMV.

Some of the more interesting ones are the following. (Note: The first
line is the scale steps, the second is the number of steps in
subsequent intervals. Also, I took some stuff out and added the lines
with --> at the front.)

Generator 5:

3: 0 3 5 8 10 12 = 2L+3S
(5) 3 2 3 2 2
--> C Eb F Ab Bb C

4: 0 1 3 5 6 8 10 12 = 5L+2S
(7) 1 2 2 1 2 2 2
--> C Db Eb F Gb Ab Bb C

Generator 7:

3: 0 2 4 7 9 12 = 2L+3S
(5) 2 2 3 2 3
--> C D E G A C

4: 0 2 4 6 7 9 11 12 = 5L+2S
(7) 2 2 2 1 2 2 1
--> C D E F# G A B C

Notice, though, that a mode of an MOS is also an MOS. Also note that
if you have the same step sequences, starting on a different step, you
end up with transpositions.

2L+3S with generator 5 can be considered Cm, minus the 2nd and 5th,
while 2L+3S with generator 7 (even though it starts on a different
note) can be considered Em, minus the 2nd and 5th: In other words,
they're transpositions of modes of each other.

Likewise with 5L+2S.

So you can safely reduce the number of MOSs to two:
C D E G A C
and
C D E F# G A B C
...and their modes. Those are two of the most-used scales in the world.

Does it have to be an MOS, or does it just have to be something
interesting in 12-equal? If you want a bunch of interesting scales
based on 12-equal, you might try this:

Create a new 12-equal scale. (Shift-alt-E, enter "12".)

Hit the "Play" button on the toolbar (it has a little keyboard on it).
That brings up the chromatic clavier.

Hit the "Mode" button on the bottom of the chromatic clavier.

Scala automatically provides a list of modes that fit a scale size of
12, ranging from two notes to all 12. They're not necessarily MOSs,
but they might prove interesting. The Messiaen modes have a unique
sound, for example. And once you've selected one, you can try it on
the clavier before choosing it for your composition.

I hope this helps.

Regards,
Jake

Thank you Carl, Keenan, and Jake

Everything said was invaluable and I really appreciate the page on the wiki
Keenan.

To give a little background - what the (unpaid) commission is for a 5 to 7
minute piece for flute and electronics. Working with the performer's
preference I'm going with alto flute, probably exclusively.
My plan of attack is actually compose in 24 et but keeping the use of
quarter tone fingering in the flute to a minimum since, as I mentioned, I'm
late which means Laura has less time to learn her part.
(I'll share a rendering after the premier on April 29th assuming I complete
this and hopefully I'll eventually be able to share the actual performance
as a recording or video.)

I asked about MOS and Greek tetrachords as a means of pitch organization.
In part I asked because of George Harrison's Blue Jay Way which uses this
interesting scale in 12 equal

C Eb E Gb G A B C with one excursion to a high D (this is as scored in C,
not as I played it - I'm not sure what pitch my 12 string was at)

If you look it up the song on wikipedia you will see some discussion of
Lydian mode and also the Indian ragas Kosalam and Multani.

http://en.wikipedia.org/wiki/Blue_Jay_Way

I covered it for relaxation last weekend
http://alonetone.com/vaisvil/tracks/blue-jay-way-cover

Now to get beyond the 1 minute mark !!

Thanks again!

Chris

The original MOS article uses 12 ET as the first examples.
always best to go to the source.http://anaphoria.com/mos.PDF

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Thank you Carl, Keenan, and Jake
>
> Everything said was invaluable and I really appreciate the page on the wiki
> Keenan.
>
> To give a little background - what the (unpaid) commission is for a 5 to 7
> minute piece for flute and electronics. Working with the performer's
> preference I'm going with alto flute, probably exclusively.
> My plan of attack is actually compose in 24 et but keeping the use of
> quarter tone fingering in the flute to a minimum since, as I mentioned, I'm
> late which means Laura has less time to learn her part.
> (I'll share a rendering after the premier on April 29th assuming I complete
> this and hopefully I'll eventually be able to share the actual performance
> as a recording or video.)
>
> I asked about MOS and Greek tetrachords as a means of pitch organization.
> In part I asked because of George Harrison's Blue Jay Way which uses this
> interesting scale in 12 equal
>
> C Eb E Gb G A B C with one excursion to a high D (this is as scored in C,
> not as I played it - I'm not sure what pitch my 12 string was at)
>
> If you look it up the song on wikipedia you will see some discussion of
> Lydian mode and also the Indian ragas Kosalam and Multani.
>
> http://en.wikipedia.org/wiki/Blue_Jay_Way
>
> I covered it for relaxation last weekend
> http://alonetone.com/vaisvil/tracks/blue-jay-way-cover
>
> Now to get beyond the 1 minute mark !!
>
> Thanks again!
>
> Chris
>