Onelist Tuning Digest 463
Message: 21
From: Paul H. Erlich
Sent: Wednesday, December 29, 1999 5:59 PM
To: 'tuning@onelist.com'
Subject: RE: [tuning] RE: 11-limit, 31 tones, 9 hexads within 2.7c of just
Anyway, now that we're dealing with 4-d (11-prime limit) ones, a natural
question would be, can we represent Partch's 43-tone scale with a
periodicity block? Following [Erv] Wilson, we'll identify 11/10 and 10/9 as an
equivalent pair (and their inversions as another) so we are dealing with a
41-tone periodicity block, one of whose unison vectors is 100:99. Unlike
the 19- and 31-tone periodicity blocks found so far, this 41-tone one will
not use 81:80 as a unison vector, as several 81:80 pairs appear in
Partch's scale. . . .
Onelist Tuning Digest 464
Message: 11
Date: Thu, 30 Dec 1999 01:54:25 -0500
From: "Paul H. Erlich"
Subject: Partch scale as periodicity block?
100:99 = [22 *] 3-2 * 52 * 70 * 11-1
What unison vectors can we find? By dividing pairs of step sizes, some
simple candidates are:
81:80
----- = 243:242 or 35 * 5 0 * 70 * 11-2
121:120
55:54
----- = 245:243 or 3-5 * 51 * 72 * 110
99:98
45:44
----- = 225:224 or 32 * 52 * 7-1 * 110
56:55
And lo and behold, the determinant of
-2 2 0 -1
5 0 0 -2
-5 1 2 0
2 2 -1 0
is -41! Next, we'll compare the Fokker hyperparallelopiped(?) with Partch's
scale.
Onelist Tuning Digest 465
Message: 8
From: Paul H. Erlich
Sent: Thursday, December 30, 1999 5:08 AM
To: 'tuning@onelist.com'
Subject: RE: [tuning] Partch scale as periodicity block?
Define Fokker2 as the notes in the hyperparallelopiped centered around 1/1
with edge vectors
( 4 0 -1 1 )
( 2 -1 2 -1 )
( -5 1 2 0 )
( -2 2 0 -1 )
in other words, unison vectors
896/891
441/440
245/243
100/99
Observe:
Fokker2 Partch Fokker2/Partch
1 1 1
81/80 81/80 1
28/27 33/32 896/891
21/20 21/20 1
297/280 16/15 891/896
12/11 12/11 1
10/9 11/10 100/99
" 10/9 1
9/8 9/8 1
8/7 8/7 1
7/6 7/6 1
33/28 32/27 891/896
6/5 6/5 1
11/9 11/9 1
5/4 5/4 1
14/11 14/11 1
9/7 9/7 1
21/16 21/16 1
4/3 4/3 1
27/20 27/20 1
11/8 11/8 1
7/5 7/5 1
10/7 10/7 1
16/11 16/11 1
40/27 40/27 1
3/2 3/2 1
32/21 32/21 1
14/9 14/9 1
11/7 11/7 1
8/5 8/5 1
18/11 18/11 1
5/3 5/3 1
56/33 27/16 896/891
12/7 12/7 1
7/4 7/4 1
16/9 16/9 1
9/5 9/5 1
" 20/11 99/100
11/6 11/6 1
560/297 15/8 896/891
40/21 40/21 1
27/14 64/33 891/896
160/81 160/81 1
Onelist Tuning Digest 464
Message: 12
Date: Thu, 30 Dec 1999 02:56:26 -0500
From: "Paul H. Erlich"
Subject: RE: Partch scale as periodicity block?
... Since translating a note of a periodicity block by one or two
unison vectors does not change its important properties, Partch's
scale with Wilson's two equivalencies is a periodicity block.
