Superpyth: Difference between revisions

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== Interval chains ==
== Interval chains ==
In the following tables, odd harmonics 1–11 are in '''bold'''.  
The following tables show the intervals of {{frac|2|7}} septimal comma superpyth, where the fifth is approximately 709.745{{cent}}. Odd harmonics 1—11 are in '''bold'''.


{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
Line 24: Line 24:
|-
|-
! #
! #
! Note (assuming 1/1 is C)
! Cents*
! Cents*
! Approximate Ratios
! Approximate Ratios
Line 32: Line 33:
|-
|-
| 1
| 1
| 709.6
| 709.745
| '''3/2'''
| '''3/2'''
|-
|-
| 2
| 2
| 219.2
| 219.489
| '''8/7''', '''9/8'''
| '''8/7''', '''9/8'''
|-
|-
| 3
| 3
| 928.8
| 929.234
| 12/7
| 12/7
|-
|-
| 4
| 4
| 438.4
| 438.979
| 9/7
| 9/7
|-
|-
| 5
| 5
| 1148.0
| 1148.724
| 27/14
| 27/14
|-
|-
| 6
| 6
| 657.6
| 658.468
| 72/49, 81/56
| 72/49, 81/56
|-
|-
| 7
| 7
| 167.2
| 168.213
| 54/49
| 54/49
|}
|}
<nowiki>*</nowiki> in 2.3.7-subgroup CTE tuning


{| class="wikitable center-1 right-2 right-4"
{| class="wikitable center-1 right-2 right-4"
Line 73: Line 73:
|-
|-
| 1
| 1
| 708.5
| 709.745
| '''3/2'''
| '''3/2'''
|-
|-
| 2
| 2
| 216.9
| 219.489
| '''8/7''', '''9/8'''
| '''8/7''', '''9/8'''
|-
|-
| 3
| 3
| 925.4
| 929.234
| 12/7
| 12/7
|-
|-
| 4
| 4
| 433.8
| 438.979
| 9/7, 14/11
| 9/7, 14/11
|-
|-
| 5
| 5
| 1142.3
| 1148.724
| 21/11, 27/14, 64/33
| 21/11, 27/14, 64/33
|-
|-
| 6
| 6
| 650.7
| 658.468
| '''16/11'''
| '''16/11'''
|-
|-
| 7
| 7
| 159.2
| 168.213
| 12/11
| 12/11
|}
|}
<nowiki>*</nowiki> in 2.3.7.11-subgroup CTE tuning


{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
Line 120: Line 119:
|-
|-
| 1
| 1
| 709.6
| 709.745
| '''3/2'''
| '''3/2'''
|
|
Line 126: Line 125:
|-
|-
| 2
| 2
| 219.2
| 219.489
| '''8/7''', '''9/8'''
| '''8/7''', '''9/8'''
|
|
Line 132: Line 131:
|-
|-
| 3
| 3
| 928.8
| 929.234
| 12/7
| 12/7
|
|
Line 138: Line 137:
|-
|-
| 4
| 4
| 438.4
| 438.979
| 9/7
| 9/7
|
|
Line 144: Line 143:
|-
|-
| 5
| 5
| 1148.0
| 1148.724
| 27/14, 35/18
| 27/14, 35/18
| 88/45
| 88/45
Line 150: Line 149:
|-
|-
| 6
| 6
| 657.5
| 658.468
| 35/24, 40/27
| 35/24, 40/27
| 22/15
| 22/15
Line 156: Line 155:
|-
|-
| 7
| 7
| 167.1
| 168.213
| 10/9
| 10/9
| 11/10
| 11/10
Line 162: Line 161:
|-
|-
| 8
| 8
| 876.7
| 877.958
| 5/3
| 5/3
| 33/20
| 33/20
Line 168: Line 167:
|-
|-
| 9
| 9
| 386.3
| 387.703
| '''5/4'''
| '''5/4'''
|
|
Line 174: Line 173:
|-
|-
| 10
| 10
| 1095.9
| 1097.447
| 15/8, 40/21
| 15/8, 40/21
|  
|  
Line 180: Line 179:
|-
|-
| 11
| 11
| 605.5
| 607.192
| 10/7
| 10/7
|  
|  
Line 186: Line 185:
|-
|-
| 12
| 12
| 115.1
| 116.937
| 15/14
| 15/14
|  
|  
Line 192: Line 191:
|-
|-
| 13
| 13
| 824.7
| 826.682
| 45/28
| 45/28
| 44/27
| 44/27
Line 198: Line 197:
|-
|-
| 14
| 14
| 334.3
| 336.426
| 60/49
| 60/49
| 11/9
| 11/9
Line 204: Line 203:
|-
|-
| 15
| 15
| 1043.9
| 1046.171
| 50/27
| 50/27
| 11/6
| 11/6
Line 210: Line 209:
|-
|-
| 16
| 16
| 553.5
| 555.916
| 25/18
| 25/18
| '''11/8'''
| '''11/8'''
Line 216: Line 215:
|-
|-
| 17
| 17
| 63.0
| 65.661
| 25/24
| 25/24
| 22/21, 33/32
| 22/21, 33/32
| 45/44
| 45/44
|}
|}
<nowiki>*</nowiki> in 7-limit CTE tuning


== Scales ==
== Scales ==