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Superpyth: Difference between revisions

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→Interval chains: rework for readability
→Interval chains: consolidate tables to make space for 11-limit superpyth
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== Interval chains ==
== Interval chains ==
In the following tables, odd harmonics 1–11 are in '''bold'''.
; Archy (2.3.7)
; Archy (2.3.7)
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2 mw-collapsible mw-collapsed"
|-
|-
! #
! #
! Cents
! Cents*
! Approximate Ratios
! Approximate Ratios
|-
|-
Line 30: Line 32:
|-
|-
| 1
| 1
| 709.3
| 709.6
| '''3/2'''
| '''3/2'''
|-
|-
| 2
| 2
| 218.6
| 219.2
| '''8/7''', '''9/8'''
| '''8/7''', '''9/8'''
|-
|-
| 3
| 3
| 928.0
| 928.8
| 12/7
| 12/7
|-
|-
| 4
| 4
| 437.3
| 438.4
| 9/7
| 9/7
|-
|-
| 5
| 5
| 1146.6
| 1148.0
| 27/14
|}
 
; Full 7-limit superpyth
{| class="wikitable center-1 right-2"
|-
! #
! Cents
! Approximate Ratios
|-
| 0
| 0.0
| '''1/1'''
|-
| 1
| 710.3
| '''3/2'''
|-
| 2
| 220.6
| '''8/7''', '''9/8'''
|-
| 3
| 930.9
| 12/7
|-
| 4
| 441.2
| 9/7
|-
| 5
| 1151.5
| 27/14
| 27/14
|-
|-
| 6
| 6
| 661.7
| 657.6
| 40/27
| 72/49, 81/56
|-
|-
| 7
| 7
| 172.0
| 167.2
| 10/9
| 54/49
|-
| 8
| 882.3
| 5/3
|-
| 9
| 392.6
| '''5/4'''
|-
| 10
| 1102.9
| 15/8
|-
| 11
| 613.2
| 10/7
|}
|}
<nowiki>*</nowiki> in 2.3.7-subgroup CTE tuning


; Supra (2.3.7.11)
; Supra (2.3.7.11)
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2 right-4 mw-collapsible mw-collapsed"
|-
|-
! #
! #
! Cents
! Cents*
! Approximate Ratios
! Approximate Ratios
|-
|-
Line 118: Line 73:
|-
|-
| 1
| 1
| 707.2
| 708.5
| '''3/2'''
| '''3/2'''
|-
|-
| 2
| 2
| 214.4
| 216.9
| '''8/7''', '''9/8'''
| '''8/7''', '''9/8'''
|-
|-
| 3
| 3
| 921.6
| 925.4
| 12/7
| 12/7
|-
|-
| 4
| 4
| 428.8
| 433.8
| 9/7, 14/11
| 9/7, 14/11
|-
|-
| 5
| 5
| 1136.0
| 1142.3
| 27/14, 64/33
| 21/11, 27/14, 64/33
|-
|-
| 6
| 6
| 643.2
| 650.7
| '''16/11'''
| '''16/11'''
|-
|-
| 7
| 7
| 150.4
| 159.2
| 12/11
| 12/11
|-
| 8
| 857.5
| 18/11
|}
|}
<nowiki>*</nowiki> in 2.3.7.11-subgroup CTE tuning


; Full 11-limit suprapyth
; Full 7-limit superpyth
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
|-
! #
! rowspan="2" | #
! Cents
! rowspan="2" | Cents*
! Approximate Ratios
! colspan="3" | Approximate Ratios
|-
! 7-limit
! 11-limit Extension<br>(Superpyth)
! 11-limit Extension<br>(Suprapyth)
|-
|-
| 0
| 0
| 0.0
| 0.0
| '''1/1'''
| '''1/1'''
|
|
|-
|-
| 1
| 1
| 709.5
| 709.6
| '''3/2'''
| '''3/2'''
|
|
|-
|-
| 2
| 2
| 219.0
| 219.2
| '''8/7''', '''9/8'''
| '''8/7''', '''9/8'''
|
|
|-
|-
| 3
| 3
| 928.5
| 928.8
| 12/7
| 12/7
|
|
|-
|-
| 4
| 4
| 438.0
| 438.4
| 9/7, 14/11
| 9/7
|
| 14/11
|-
|-
| 5
| 5
| 1147.5
| 1148.0
| 27/14, 64/33
| 27/14, 35/18
| 88/45
| 21/11, 64/33
|-
|-
| 6
| 6
| 657.0
| 657.5
| '''16/11''', 40/27
| 35/24, 40/27
| 22/15
| '''16/11'''
|-
|-
| 7
| 7
| 166.5
| 167.1
| 10/9, 12/11
| 10/9
| 11/10
| 12/11
|-
|-
| 8
| 8
| 876.0
| 876.7
| 5/3, 18/11
| 5/3
| 33/20
| 18/11
|-
|-
| 9
| 9
| 385.4
| 386.3
| '''5/4''', 27/22
| '''5/4'''
|
| 27/22
|-
|-
| 10
| 10
| 1094.9
| 1095.9
| 15/8
| 15/8, 40/21
|
|
|-
|-
| 11
| 11
| 604.4
| 605.5
| 10/7
| 10/7
|
|
|-
| 12
| 115.1
| 15/14
|
|
|-
| 13
| 824.7
| 45/28
| 44/27
|
|-
| 14
| 334.3
| 60/49
| 11/9
| 40/33
|-
| 15
| 1043.9
| 50/27
| 11/6
| 20/11
|-
| 16
| 553.5
| 25/18
| '''11/8'''
| 15/11
|-
| 17
| 63.0
| 25/24
| 22/21, 33/32
| 45/44
|}
|}
<nowiki>*</nowiki> in 7-limit CTE tuning


== Scales ==
== Scales ==
Retrieved from "https://en.xen.wiki/w/Superpyth"