iko7

Seven-limit tuning of ikosany.scl

Open in Scale Workshop Scala analysis Download scl

Properties

Notes	31
Period	1200.0 ¢
Just	7-limit
Source	Mailing lists
Reference	https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_69794.html#69794
Thread	3 scales

Tone	Tone (¢)	Step	Step (¢)
36/35	49	36/35	49
28/27	63	245/243	14
729/700	70	19683/19600	7
16/15	112	2240/2187	41
27/25	133	81/80	22
81/70	253	15/14	119
7/6	267	245/243	14
32/27	294	64/63	27
6/5	316	81/80	22
243/200	337	81/80	22
216/175	364	64/63	27
56/45	379	245/243	14
729/560	457	6561/6272	78
4/3	498	2240/2187	41
27/20	520	81/80	22
112/81	561	2240/2187	41
243/175	568	19683/19600	7
7/5	583	245/243	14
36/25	631	36/35	49
3/2	702	25/24	71
54/35	751	36/35	49
14/9	765	245/243	14
8/5	814	36/35	49
81/50	835	81/80	22
224/135	877	2240/2187	41
243/140	955	6561/6272	78
16/9	996	2240/2187	41
9/5	1018	81/80	22
324/175	1066	36/35	49
28/15	1081	245/243	14
2	1200	15/14	119

Similar scales

File	Notes	Rotation	Max diff (¢)
ikosany	31	0	6.9

Parent scales

File	Notes	Max diff (¢)
septenarian53well	53	5.8
Sp53via19lim	53	6.3
edo-53	53	6.4
amity53pure	53	6.5
SpaRational53Coll	53	6.6
xen18-erlich-hanson-53	53	6.6
xen18-erlich-orwell-53	53	7.0
xen18-erlich-sensipent-46	46	9.5
xen18-erlich-orson-53	53	7.6
xen18-erlich-helmholtz-53	53	7.7

Child scales

File	Notes	Max diff (¢)
al-farabi_chrom2	7	0.0
xen03-wilson-negative-07	7	0.0
xen09-wilson-marwa-04-05	7	0.0
xen09-wilson-marwa-04-09	7	0.0
xen09-wilson-marwa-04-12	7	0.0
xen09-wilson-marwa-04-14	7	0.0
xen09-wilson-marwa-07-12	7	0.0
xen09-wilson-marwa-07-14	7	0.0
xen09-wilson-marwa-08-03	7	0.0
xen09-wilson-marwa-08-04	7	0.0

Mailing list post

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.

Full 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.

Raw file

! 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
!
! https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_69794.html#69794
!
! [info]
! source = Mailing lists
! file = tuning/messages/yahoo_tuning_messages_api_raw_55190-71650.json
! topic_id = 69794
! msg_id = 69794