decatonic scales in Partchian terms

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Carl Lumma wrote me, privately, regarding my 22-tET paper:

>I recommend cutting the indian scale bit, and instead write
>about the just versions of the decatonic scales using standard
Partchian terms.

Did you mean something like this?

Let's start with the familiar diatonic (heptatonic) scale in JI.

1. 1/1
2. 10/9 or 9/8
3. 5/4
4. 4/3
5. 3/2
6. 5/3
7. 15/8

Mode 1 is major, mode 6 is minor. The tuning of note 2 depends on the
chordal context. The following chords are complete through the 5-limit:

1,3,5 = 1/1:5/4:3/2 (1/1-O)
2,4,6 = 10/9:4/3:5/3 (5/3-U)
3,5,7 = 5/4:3/2:15/8 (15/8-U)
4,6,1 = 4/3:5/3:1/1 (4/3-O)
5,7,2 = 3/2:15/8:9/8 (3/2-O)
6,1,3 = 5/3:1/1:5/4 (5/4-U)
7,2,4 = X

A meantone tuning, including 12-, 19-, or 31-tET, allows a single pitch
to be used for note 2.

Now the pentachordal (so named because it is built of pentachords
instead of tetrachords) decatonic scale in JI:

1. 1/1
2. 21/20 or 15/14
3. 9/8
4. 5/4
5. 21/16
6. 10/7
7. 3/2
8. 5/3
9. 7/4 or 50/28
0. 15/8

Mode 1 is standard major, mode 4 is standard minor, mode 6 is alternate
major, mode 9 is alternate minor. The following chords are complete
through the 7-limit:

1,4,7,9 = 1/1:5/4:3/2:7/4 (1/1-O)
2,5,8,0 = X
3,6,9,1 = X
4,7,0,2 = 5/4:3/2:15/8:15/14 (15/8-U)
5,8,1,3 = X
6,9,2,4 = 10/7:50/28:15/14:5/4 (10/7-O)
7,0,3,5 = 3/2:15/8:9/8:21/16 (3/2-O)
8,1,4,6 = 5/3:1/1:5/4:10/7 (5/4-U)
9,2,5,7 = 7/4:21/20:21/16:3/2 (21/16-U)
0,3,6,8 = X

The symmetrical decatonic scale has at least two equally economical
representations in JI:

REPRESENTATION 1:

1. 1/1 or 63/64
2. 21/20 or 15/14
3. 9/8
4. 5/4
5. 21/16 or 75/56
6. 45/32 or 10/7
7. 3/2
8. 63/40 or 45/28
9. 7/4 or 50/28
0. 15/8

REPRESENTATION 2:

1. 1/1 or 63/64
2. 21/20 or 15/14
3. 9/8
4. 49/40 or 5/4
5. 21/16
6. 7/5 or 45/32
7. 3/2
8. 63/40 or 45/28
9. 7/4
0. 147/80 or 15/8

Modes 1 and 6 are static major, modes 2 and 7 are dynamic major, modes 5
and 0 are static minor, and modes 4 and 9 are dynamic minor. The
following chords are complete through the 7-limit:

REPRESENTATION 1:

1,4,7,9 = 1/1:5/4:3/2:7/4 (1/1-O)
2,5,8,0 = 15/14:75/56:45/28:15/8 (15/14-O)
3,6,9,1 = X
4,7,0,2 = 5/4:3/2:15/8:15/14 (15/8-U)
5,8,1,3 = 21/16:63/40:63/64:9/8 (63/64-U)
6,9,2,4 = 10/7:5/4:15/14:5/4 (10/7-O)
7,0,3,5 = 3/2:15/8:9/8:21/16 (3/2-O)
8,1,4,6 = X
9,2,5,7 = 7/4:21/20:21/16:3/2 (21/16-U)
0,3,6,8 = 15/8:9/8:45/32:45/28 (45/32-U)

REPRESENTATION 2:

1,4,7,9 = 1/1:5/4:3/2:7/4 (1/1-O)
2,5,8,0 = 21/20:21/16:63/40:147/80 (21/20-O)
3,6,9,1 = X
4,7,0,2 = 5/4:3/2:15/8:15/14 (15/8-U)
5,8,1,3 = 21/16:63/40:63/64:9/8 (63/64-U)
6,9,2,4 = 7/5:7/4:21/20:49/40 (7/5-O)
7,0,3,5 = 3/2:15/8:9/8:21/16 (3/2-O)
8,1,4,6 = X
9,2,5,7 = 7/4:21/20:21/16:3/2 (21/16-U)
0,3,6,8 = 15/8:9/8:45/32:45/28 (45/32-U)

22-tET allows a single pitch to be used for each note in the decatonic
scales.

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Drew Skyfyre wrote

>I use a Mac and I can't think of anything but Max that would allow
>programming this sort of thing. There is always the not so happy option
>of using a regular ascii style programming language, like Java , I
>suppose ?
>Has anyone here used Java to write this type of thing ? Anyone know if
>the shareware/freeware "Megalomania" can be used for this ?

I don't have full details of Java Sound, but I bet it won't allow
low-level access to the MIDI ports. I wrote my Windows program in C++. I
don't know much about Macintosh, but I'm sure the same thing could be done
for it. Unfortunately, graphical and multimedia code is highly machine
specific, so I can't do a quick conversion.

What's "Megalomania" then?

Graham Breed
gbreed@cix.co.uk www.cix.co.uk/~gbreed/

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Graham Breed wrote
> I don't have full details of Java Sound, but I bet it won't allow
> low-level access to the MIDI ports. I wrote my Windows program in C++. I

Java is an evolving environment. Today's Java API only plays mono, 8K AU
files. The Java sound API has been proposed but not released. It is supposed
to be released sometime after JDK 1.2. The current JDK is at version 1.1. It
takes another year or so for each new version of the JDK to be incorporated
into the most popular browsers.

You can read more about the Java Sound API from the following URL. I believe
that it will handle most of your sound card tuning needs.

http://java.sun.com/marketing/collateral/java_sound_ds.html

Mr. Touchless

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