Topic: Convex closure of eikosany

3 scales

Thread (1 messages)

From: Gene Ward Smith (2007-02-15)
Subject: Convex closure of eikosany

Here's the ever-popular Eikosany scale:

! Eikosany.scl
!
3)6 1.3.5.7.9.11 Eikosany (1.3.5 
tonic)                                         
 20
!
 33/32
 21/20
 11/10
 9/8
 7/6
 99/80
 77/60
 21/16
 11/8
 7/5
 231/160
 3/2
 63/40
 77/48
 33/20
 7/4
 9/5
 11/6
 77/40
 2/1

Here's a 7-limit version, made by using 384/35 in place of 11 (385/384
approximating):

! eikoseven.scl
Seven-limit version of 385/384-tempered Eikosany
20
!
36/35
21/20
192/175
9/8
7/6
216/175
32/25
21/16
48/35
7/5
36/25
3/2
63/40
8/5
288/175
7/4
9/5
64/35
48/25
2

Here's the convex closure of the above scale in the 7-limit lattice:

! iko7.scl
Seven-limit tuning of ikosany.scl
31
!
36/35
28/27
729/700
16/15
27/25
81/70
7/6
32/27
6/5
243/200
216/175
56/45
729/560
4/3
27/20
112/81
243/175
7/5
36/25
3/2
54/35
14/9
8/5
81/50
224/135
243/140
16/9
9/5
324/175
28/15
2

And here is the above, tuned to 140-et, which tempers out 385/384 and 
also (which turns out to be useful) 5120/5103:

! ikosany.scl
Convex closure of Eikosany in 385/384-tempering, 140-et tuning
31
!
51.428571
60.000000
77.142857
111.428571
137.142857
257.142857
265.714286
291.428571
317.142857
342.857143
368.571429
377.142857
462.857143
497.142857
522.857143
557.142857
574.285714
582.857143
634.285714
702.857143
754.285714
762.857143
814.285714
840.000000
874.285714
960.000000
994.285714
1020.000000
1071.428571
1080.000000
1200.000000

The above "Ikosany" scale has 24 fifths, 12 major thirds, 12 7/4s, 7 
11/8s and 4 13/8s, all in the 140-et tuning. Presented for whatever 
it is worth; the tonality diamond would be another obvious starting 
point for this.