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Septischismic: Difference between revisions

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Here is a quick compressed cheat sheet of octave-reduced intervals. This is a simplification with many (infinitely many) intervals left out for the sake of brevity. For every entry here, ratios here represent pitch-classes and their pitch class inverses; so for instance 8/5 pitch class is mapped to 8 fifths - 1 aberschisma step, being the octave inverse of 5/4 pitch class negates the mappings so it is found at -8 fifths + 1 aberschisma step. There are no octave reduced primes or prime inverses with positive fifth step and aberschisma step.   
Here is a quick compressed cheat sheet of octave-reduced intervals. This is a simplification with many (infinitely many) intervals left out for the sake of brevity. For every entry here, ratios here represent pitch-classes and their pitch class inverses; so for instance 8/5 pitch class is mapped to 8 fifths - 1 aberschisma step, being the octave inverse of 5/4 pitch class negates the mappings so it is found at -8 fifths + 1 aberschisma step. There are no octave reduced primes or prime inverses with positive fifth step and aberschisma step.   


{| class="wikitable center-1"
{| class="wikitable center-1 right-2 right-4"
! #
! rowspan="2" | #
! Aberschisma offset -1  
! colspan="2" | Aberschisma offset -1
! Aberschisma offset 0
! colspan="2" | Aberschisma offset 0
|-
! Cents*
! Approx. ratios
! Cents*
! Approx. ratios
|-
|-
| 0
| 0
| 1195.83
| 720/361
| 720/361
| 0.00
| '''1/1'''
| '''1/1'''
|-
|-
| 1
| 1
| 698.06
| 256/171
| 256/171
| 702.23
| '''3/2'''
| '''3/2'''
|-
|-
| 2
| 2
| 200.29
| 64/57
| 64/57
| 204.46
| '''9/8'''
| '''9/8'''
|-
|-
| 3
| 3
| 902.52
| '''32/19'''
| '''32/19'''
| 906.69
| 27/16
| 27/16
|-
|-
| 4
| 4
| 404.75
| 24/19
| 24/19
| 408.92
| 81/64
| 81/64
|-
|-
| 5
| 5
| 1106.98
| 36/19
| 36/19
| 1111.15
| 243/128
| 243/128
|-
|-
| 6
| 6
| 609.21
| 64/45
| 64/45
| 613.38
| 729/512
| 729/512
|-
|-
| 7
| 7
| 111.44
| '''16/15'''
| '''16/15'''
| 115.62
| 77/72
| 77/72
|-
|-
| 8
| 8
| 813.68
| '''8/5'''
| '''8/5'''
| 817.85
| 77/48
| 77/48
|-
|-
| 9
| 9
| 315.91
| 6/5
| 6/5
| 320.08
| 77/64
| 77/64
|-
|-
| 10
| 10
| 1018.14
| 9/5
| 9/5
| 1022.31
| 65/36
| 65/36
|-
|-
| 11
| 11
| 520.37
| 27/20
| 27/20
| 524.54
| 65/48
| 65/48
|-
|-
| 12
| 12
| 22.60
| 81/80
| 81/80
| 26.77
| 64/63
| 64/63
|-
|-
| 13
| 13
| 724.83
| 243/160
| 243/160
| 729.00
| 32/21
| 32/21
|-
|-
| 14
| 14
| 227.06
| 729/640
| 729/640
| 231.23
| '''8/7'''
| '''8/7'''
|-
|-
| 15
| 15
| 929.29
| 416/243
| 416/243
| 933.46
| 12/7
| 12/7
|-
|-
| 16
| 16
| 431.52
| 104/81
| 104/81
| 435.69
| 9/7
| 9/7
|-
|-
| 17
| 17
| 1133.75
| 52/27
| 52/27
| 1137.92
| 27/14
| 27/14
|-
|-
| 18
| 18
| 635.98
| 13/9
| 13/9
| 640.15
| 81/56
| 81/56
|-
|-
| 19
| 19
| 138.21
| 13/12
| 13/12
| 142.38
| 88/81
| 88/81
|-
|-
| 20
| 20
| 840.44
| '''13/8'''
| '''13/8'''
| 844.61
| 44/27
| 44/27
|-
|-
| 21
| 21
| 342.67
| 39/32
| 39/32
| 346.85
| 11/9
| 11/9
|-
|-
| 22
| 22
| 1044.91
| 64/35
| 64/35
| 1049.08
| 11/6
| 11/6
|-
|-
| 23
| 23
| 547.14
| 48/35
| 48/35
| 551.31
| '''11/8'''
| '''11/8'''
|-
|-
| 24
| 24
| 49.37
| 36/35
| 36/35
| 53.54
| 33/32
| 33/32
|}
|}
* In 2.3.5.7.11.13.19-subgroup CWE tuning, octave reduced


== Notation ==
== Notation ==
Retrieved from "https://en.xen.wiki/w/Septischismic"