Xenharmonic Wiki

ABACABADABACABA JI scales: Difference between revisions

← Older editNewer edit →
VisualWikitext
Lhearne (talk | contribs)
autopatrolled, emailconfirmed
1,510 edits
Lhearne (talk | contribs)
autopatrolled, emailconfirmed
1,510 edits
No edit summary
Line 71: Line 71:


with an odd-limit of 625, a step pattern of ABACABAADAABACABA, and a mean variety of 4.625.
with an odd-limit of 625, a step pattern of ABACABAADAABACABA, and a mean variety of 4.625.
The final scale has gaps between 28/25 and 5/4, and between 8/5 and 25/14, where a minor third and major 6th 'should' be, which we can fill with intervals of the scale while keeping the odd-limit at 625 by adding A below 5/4 and above 8/5, leading to
1/1 21/20 16/15 28/25 25/21 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 42/25 25/14 15/8 40/21 2/1,
with a step pattern of ABACAABADABAACABA, with a mean variety of 4.625.


== 1225-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c ==
== 1225-limit ABACABADABACABA JI scales with period 2/1, with steps > 20c ==
'Form' is added to the tables below, following the above section on 17-form. The 'form' is the also the smallest [[EDO|edo]] to approximate the scale.


=== Octochord to 4/3 -> D = 9/8 (~203.91c) ===
=== Octochord to 4/3 -> D = 9/8 (~203.91c) ===
Line 88: Line 83:
!Scale
!Scale
!odd-limit of scale intervals
!odd-limit of scale intervals
!Form
|-
|-
|22/21 (~80.54c)
|22/21 (~80.54c)
Line 94: Line 90:
|1/1 22/21 12/11 8/7 7/6 11/9 14/11 4/3 3/2 11/7 18/11 12/7 7/4 11/6 21/11 2/1
|1/1 22/21 12/11 8/7 7/6 11/9 14/11 4/3 3/2 11/7 18/11 12/7 7/4 11/6 21/11 2/1
|441
|441
|17
|-
|-
|24/23 (~73.68c)
|24/23 (~73.68c)
Line 100: Line 97:
|1/1 24/23 23/21 8/7 7/6 28/23 23/18 4/3 3/2 36/23 23/14 12/7 7/4 42/23 23/12 2/1
|1/1 24/23 23/21 8/7 7/6 28/23 23/18 4/3 3/2 36/23 23/14 12/7 7/4 42/23 23/12 2/1
|529
|529
|17
|-
|-
|25/24 (~70.67c)
|25/24 (~70.67c)
Line 106: Line 104:
|1/1 25/24 16/15 10/9 6/5 5/4 32/25 4/3 3/2 25/16 8/5 5/3 9/5 15/8 48/25 2/1
|1/1 25/24 16/15 10/9 6/5 5/4 32/25 4/3 3/2 25/16 8/5 5/3 9/5 15/8 48/25 2/1
|625
|625
|17
|-
|-
|34/33 (~51.68c)
|34/33 (~51.68c)
Line 112: Line 111:
|1/1 34/33 18/17 12/11 11/9 34/27 22/17 4/3 3/2 17/11 27/17 18/11 11/6 17/9 33/17 2/1
|1/1 34/33 18/17 12/11 11/9 34/27 22/17 4/3 3/2 17/11 27/17 18/11 11/6 17/9 33/17 2/1
|1089
|1089
|24
|-
|-
|34/33 (~51.68c)  
|34/33 (~51.68c)  
Line 118: Line 118:
|1/1 34/33 11/10 17/15 20/17 40/33 22/17 4/3 3/2 17/11 33/20 17/10 30/17 20/11 33/17 2/1  
|1/1 34/33 11/10 17/15 20/17 40/33 22/17 4/3 3/2 17/11 33/20 17/10 30/17 20/11 33/17 2/1  
|1089
|1089
|17
|-
|-
|36/35 (~48.77c)
|36/35 (~48.77c)
Line 124: Line 125:
|1/1 36/35 10/9 8/7 7/6 6/5 35/27 4/3 3/2 54/35 5/3 12/7 7/4 9/5 35/18 2/1
|1/1 36/35 10/9 8/7 7/6 6/5 35/27 4/3 3/2 54/35 5/3 12/7 7/4 9/5 35/18 2/1
|1225
|1225
|17
|-
|-
|36/35 (~48.77c)
|36/35 (~48.77c)
Line 130: Line 132:
|1/1 36/35 35/33 12/11 11/9 44/35 35/27 4/3 3/2 54/35 35/22 18/11 11/6 66/35 35/18 2/1
|1/1 36/35 35/33 12/11 11/9 44/35 35/27 4/3 3/2 54/35 35/22 18/11 11/6 66/35 35/18 2/1
|1225
|1225
|24
|}
|}


Line 140: Line 143:
!Scale
!Scale
!odd-limit of scale intervals
!odd-limit of scale intervals
!Form
|-
|21/20 (~84.47c)
|64/63 (~27.26c)
|125/112 (~190.12c)
|1/1 21/20 16/15 28/25 5/4 21/16 4/3 7/5 10/7 3/2 32/21 8/5 25/14 15/8 40/21 2/1
|625
|19
|-
|26/25 (~67.9c)
|175/169 (~60.4c)
|125/112 (~190.12c)
|1/1 26/25 14/13 28/25 5/4 13/10 35/26 7/5 10/7 52/35 20/13 8/5 25/14 13/7 25/13 2/1
|1225
|19
|-
|28/27 (~62.96c)
|729/700 (~70.28c)
|125/112 (~190.12c)
|1/1 28/27 27/25 28/25 5/4 35/27 27/20 7/5 10/7 40/27 54/35 8/5 25/14 50/27 27/14 2/1
|1225
|19
|-
|-
|16/15 (~111.73c)
|16/15 (~111.73c)
|525/512 (~43.41c)
|525/512 (~43.41c)
|36/35 (~48.77c)
|36/35 (~48.77c)
|16/15 35/32 7/6 6/5 32/25 21/16 7/5 10/7 32/21 25/16 5/3 12/7 64/35 15/8 2/1
|1/1 16/15 35/32 7/6 6/5 32/25 21/16 7/5 10/7 32/21 25/16 5/3 12/7 64/35 15/8 2/1
|1225
|-
|35/34 (~50.18c)
|126/121 (~166.50c)
|36/35 (~48.77c)
|1/1 35/34 17/15 7/6 6/5 21/17 34/25 7/5 10/7 25/17 34/21 5/3 12/7 30/17 68/35 2/1
|1225
|1225
|15
|-
|-
|31/30 (~56.77c)
|31/30 (~56.77c)
Line 158: Line 178:
|1/1 31/30 35/31 7/6 6/5 31/25 42/31 7/5 10/7 31/21 50/31 5/3 12/7 62/35 40/31 2/1
|1/1 31/30 35/31 7/6 6/5 31/25 42/31 7/5 10/7 31/21 50/31 5/3 12/7 62/35 40/31 2/1
|1225
|1225
|15
|-
|-
|28/27 (~62.96c)
|35/34 (~50.18c)
|729/700 (~70.28c)
|126/121 (~166.50c)
|125/112 (190.12c)
|36/35 (~48.77c)
|1/1 28/27 27/25 28/25 5/4 35/27 27/20 7/5 10/7 40/27 54/35 8/5 25/14 50/27 27/14 2/1
|1/1 35/34 17/15 7/6 6/5 21/17 34/25 7/5 10/7 25/17 34/21 5/3 12/7 30/17 68/35 2/1
|1225
|-
|26/25 (~67.9c)
|175/169 (~60.4c)
|125/112 (190.12c)
|1/1 26/25 14/13 28/25 5/4 13/10 35/26 7/5 10/7 52/35 20/13 8/5 25/14 13/7 25/13 2/1  
|1225
|1225
|15
|}
|}
Retrieved from "https://en.xen.wiki/w/ABACABADABACABA_JI_scales"