17-tone PB and Justin White's question

Forwarded is a question from Justin White.

He refers to <http://www.anaphoria.com/genus.PDF>. On the bottoms of pages
15, 19, 20, and 23, there is a lattice of Wilson's famous 17-tone scale,
which is clearly a periodicity block with unison vectors schisma and
chromatic semitone; i.e.,

[8 1]

and

[-1 2].

Anyone like to tackle Justin's question below? Justin, if you're reading
this, you might like to join tuning-math to see what responses this
generates!

-----Original Message-----
From: Justin White [mailto:justin.white@davidjones.com.au]
Sent: Monday, May 14, 2001 3:53 AM
To: Paul H. Erlich
Subject: Re: adaptive tuning. Can a computer pick a melody from the
harmony ?

Hello Paul, Thanks for your offer of assistance with this one. Have you read
Erv
Wilsons paper "Some Basic Patterns Underlying Genus 12 & 17"?

--- In tuning@y..., "Justin White" <justin.white@d...> wrote:
>>
>> Yes I was attracted to this scale. I thought of creating a scale in
the smae
>> manner using a septimal tetrachord...I haven't found a tetrachord
that will give
>> me the tetrad s I want yet.

>Can you explain what you're trying to do? Maybe I can help.

What I want to do is use the same methodology to create a [septimal] subset
of
the scale I have posted below.

0. 1/1
1 25/24
2. 135/128
3. 35/32
4. 9/8
5. 7/6
6. 75/64
7. 1215/1024
8. 6/5
9. 315/256
10. 5/4
11. 81/64
12. 21/16
13. 675/512
14. 4/3
15. 7/5
16. 45/32
17. 35/24
18. 189/128
19. 3/2
20. 25/16
21. 405/256
22. 8/5
23. 105/64
24. 5/3
25. 27/16
26. 7/4
27. 225/128
28. 9/5
29. 945/512
30. 15/8
31. 243/128
32. 63/32
33. 2/1

Note how Wilsons genus 17 [see below] contains mostly notes from the above
superset [B&C's blue melodic reference]

0. 1/1
1. 135/128
2. 10/9
3. 9/8
4. 1215
5. 5/4
6. 81/80
7. 4/3
8. 45/32.
9. 729/512
10 .3/2
11. 405/256
12. 5/3
13. 27/16
14. 3645/2048
15. 15/8
16. 243/128
17. 2/1

The columns below are to indicate what ratios are more important than
others.
The notes in the left hand column should be used before the notes in the
right
hand column. [This is to do with th e chain of reference used in that
scale.]

1/1
9/8 45/32 135/128 405/256
1215/1024
7/6 35/24
6/5
5/4 25/16 75/64 225/128
675/256
4/3
7/5 21/16 63/32
189/128
3/2 15/8
8/5 25/24
5/3
7/4 35/32 105/64 315/256
945/512
9/5 27/16 81/64
243/128

I'd be interested to see what you make of it all.

Best wishes,

Justin White