22edo: Difference between revisions
| Line 35: | Line 35: | ||
! Cents | ! Cents | ||
! Approximate Ratios<ref group="note">{{sg|2.3.5.7.11.17 subgroup}}</ref> | ! Approximate Ratios<ref group="note">{{sg|2.3.5.7.11.17 subgroup}}</ref> | ||
! colspan="3" | [[Ups and Downs Notation]]<br>([[Enharmonic | ! colspan="3" | [[Ups and Downs Notation|Ups and downs notation]]<br>([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>3</sup>A1 and ^^d2) | ||
! colspan="3" | [[SKULO interval names|SKULO notation]] {{nowrap|(K {{=}} 1)}} | ! colspan="3" | [[SKULO interval names|SKULO notation]] {{nowrap|(K {{=}} 1)}} | ||
! Audio | ! Audio | ||
|- | |- | ||
| 0 | | 0 | ||
| 0. | | 0.0 | ||
| [[1/1]] | | [[1/1]] | ||
| perfect unison | | perfect unison | ||
| Line 51: | Line 51: | ||
|- | |- | ||
| 1 | | 1 | ||
| 54. | | 54.5 | ||
| [[36/35]], [[34/33]], [[33/32]], [[32/31]] | | [[36/35]], [[34/33]], [[33/32]], [[32/31]] | ||
| up-unison, minor 2nd | | up-unison, minor 2nd | ||
| Line 62: | Line 62: | ||
|- | |- | ||
| 2 | | 2 | ||
| 109. | | 109.1 | ||
| [[18/17]], [[17/16]], [[16/15]], [[15/14]] | | [[18/17]], [[17/16]], [[16/15]], [[15/14]] | ||
| downaug 1sn, upminor 2nd | | downaug 1sn, upminor 2nd | ||
| Line 73: | Line 73: | ||
|- | |- | ||
| 3 | | 3 | ||
| 163. | | 163.6 | ||
| [[12/11]], [[11/10]], [[10/9]] | | [[12/11]], [[11/10]], [[10/9]] | ||
| aug 1sn, downmajor 2nd | | aug 1sn, downmajor 2nd | ||
| Line 84: | Line 84: | ||
|- | |- | ||
| 4 | | 4 | ||
| 218. | | 218.2 | ||
| [[9/8]], [[17/15]], [[8/7]] | | [[9/8]], [[17/15]], [[8/7]] | ||
| major 2nd | | major 2nd | ||
| Line 95: | Line 95: | ||
|- | |- | ||
| 5 | | 5 | ||
| 272. | | 272.7 | ||
| [[20/17]], [[7/6]] | | [[20/17]], [[7/6]] | ||
| minor 3rd | | minor 3rd | ||
| Line 106: | Line 106: | ||
|- | |- | ||
| 6 | | 6 | ||
| 327. | | 327.3 | ||
| [[6/5]], [[17/14]], [[11/9]] | | [[6/5]], [[17/14]], [[11/9]] | ||
| upminor 3rd | | upminor 3rd | ||
| Line 117: | Line 117: | ||
|- | |- | ||
| 7 | | 7 | ||
| 381. | | 381.8 | ||
| [[5/4]], [[96/77]] | | [[5/4]], [[96/77]] | ||
| downmajor 3rd | | downmajor 3rd | ||
| Line 128: | Line 128: | ||
|- | |- | ||
| 8 | | 8 | ||
| 436. | | 436.4 | ||
| [[14/11]], [[9/7]], [[22/17]] | | [[14/11]], [[9/7]], [[22/17]] | ||
| major 3rd | | major 3rd | ||
| Line 139: | Line 139: | ||
|- | |- | ||
| 9 | | 9 | ||
| 490. | | 490.9 | ||
| [[4/3]] | | [[4/3]] | ||
| perfect 4th | | perfect 4th | ||
| Line 150: | Line 150: | ||
|- | |- | ||
| 10 | | 10 | ||
| 545. | | 545.5 | ||
| [[15/11]], [[11/8]] | | [[15/11]], [[11/8]] | ||
| up-4th, dim 5th | | up-4th, dim 5th | ||
| Line 161: | Line 161: | ||
|- | |- | ||
| 11 | | 11 | ||
| 600. | | 600.0 | ||
| [[7/5]], [[24/17]], [[17/12]], [[10/7]] | | [[7/5]], [[24/17]], [[17/12]], [[10/7]] | ||
| downaug 4th, updim 5th | | downaug 4th, updim 5th | ||
| Line 172: | Line 172: | ||
|- | |- | ||
| 12 | | 12 | ||
| 654. | | 654.5 | ||
| [[16/11]], [[22/15]] | | [[16/11]], [[22/15]] | ||
| aug 4th, down-5th | | aug 4th, down-5th | ||
| Line 183: | Line 183: | ||
|- | |- | ||
| 13 | | 13 | ||
| 709. | | 709.1 | ||
| [[3/2]] | | [[3/2]] | ||
| perfect 5th | | perfect 5th | ||
| Line 194: | Line 194: | ||
|- | |- | ||
| 14 | | 14 | ||
| 763. | | 763.6 | ||
| [[17/11]], [[14/9]], [[11/7]] | | [[17/11]], [[14/9]], [[11/7]] | ||
| minor 6th | | minor 6th | ||
| Line 205: | Line 205: | ||
|- | |- | ||
| 15 | | 15 | ||
| 818. | | 818.2 | ||
| [[8/5]], [[77/48]] | | [[8/5]], [[77/48]] | ||
| upminor 6th | | upminor 6th | ||
| Line 216: | Line 216: | ||
|- | |- | ||
| 16 | | 16 | ||
| 872. | | 872.7 | ||
| [[18/11]], [[28/17]], [[5/3]] | | [[18/11]], [[28/17]], [[5/3]] | ||
| downmajor 6th | | downmajor 6th | ||
| Line 227: | Line 227: | ||
|- | |- | ||
| 17 | | 17 | ||
| 927. | | 927.3 | ||
| [[17/10]], [[12/7]] | | [[17/10]], [[12/7]] | ||
| major 6th | | major 6th | ||
| Line 238: | Line 238: | ||
|- | |- | ||
| 18 | | 18 | ||
| 981. | | 981.8 | ||
| [[7/4]], [[30/17]], [[16/9]] | | [[7/4]], [[30/17]], [[16/9]] | ||
| minor 7th | | minor 7th | ||
| Line 249: | Line 249: | ||
|- | |- | ||
| 19 | | 19 | ||
| 1036. | | 1036.4 | ||
| [[9/5]], [[11/6]], [[20/11]] | | [[9/5]], [[11/6]], [[20/11]] | ||
| upminor 7th, dim 8ve | | upminor 7th, dim 8ve | ||
| Line 260: | Line 260: | ||
|- | |- | ||
| 20 | | 20 | ||
| 1090. | | 1090.9 | ||
| [[28/15]], [[15/8]], [[32/17]], [[17/9]] | | [[28/15]], [[15/8]], [[32/17]], [[17/9]] | ||
| downmajor 7th, updim 8ve | | downmajor 7th, updim 8ve | ||
| Line 271: | Line 271: | ||
|- | |- | ||
| 21 | | 21 | ||
| 1145. | | 1145.5 | ||
| [[31/16]], [[64/33]], [[33/17]], [[35/18]] | | [[31/16]], [[64/33]], [[33/17]], [[35/18]] | ||
| major 7th, down 8ve | | major 7th, down 8ve | ||
| Line 282: | Line 282: | ||
|- | |- | ||
| 22 | | 22 | ||
| 1200. | | 1200.0 | ||
| [[2/1]] | | [[2/1]] | ||
| perfect octave | | perfect octave | ||
| Line 305: | Line 305: | ||
|- | |- | ||
! [[5L 2s|Diatonic Interval Names]] | ! [[5L 2s|Diatonic Interval Names]] | ||
! Note Names | ! Note Names | ||
|- | |- | ||
| 0 | | 0 | ||
| 0. | | 0.0 | ||
| '''Perfect unison (P1)''' | | '''Perfect unison (P1)''' | ||
| '''D''' | | '''D''' | ||
|- | |- | ||
| 1 | | 1 | ||
| 54. | | 54.5 | ||
| Minor second (m2)<br />Up | | Minor second (m2)<br />Up unison (^1) | ||
| Eb<br />^D | | Eb<br />^D | ||
|- | |- | ||
| 2 | | 2 | ||
| 109. | | 109.1 | ||
| Upminor | | Upminor second (^m2)<br />Downaugmented unison (vA1)<br />Diminished third (d3) | ||
| ^Eb<br />vD#<br />Fb | | ^Eb<br />vD#<br />Fb | ||
|- | |- | ||
| 3 | | 3 | ||
| 163. | | 163.6 | ||
| Downmajor second (vM2)<br />Augmented unison (A1) | | Downmajor second (vM2)<br />Augmented unison (A1) | ||
| vE<br />D# | | vE<br />D# | ||
|- | |- | ||
| 4 | | 4 | ||
| 218. | | 218.2 | ||
| '''Major second (M2)'''<br /> | | '''Major second (M2)'''<br />Upaugmented unison (^A1)<br />Downminor third (vm3) | ||
| '''E'''<br />^D#<br />vF | | '''E'''<br />^D#<br />vF | ||
|- | |- | ||
| 5 | | 5 | ||
| 272. | | 272.7 | ||
| Upmajor second (^M2)<br />'''Minor third (m3)''' | | Upmajor second (^M2)<br />'''Minor third (m3)''' | ||
| ^E<br />'''F''' | | ^E<br />'''F''' | ||
|- | |- | ||
| 6 | | 6 | ||
| 327. | | 327.3 | ||
| '''Upminor third (^m3)'''<br />Diminished fourth (d4) | | '''Upminor third (^m3)'''<br />Diminished fourth (d4) | ||
| '''^F'''<br />Gb | | '''^F'''<br />Gb | ||
|- | |- | ||
| 7 | | 7 | ||
| 381. | | 381.8 | ||
| '''Downmajor third (vM3)'''<br />Augmented second (A2)<br /> | | '''Downmajor third (vM3)'''<br />Augmented second (A2)<br />Updiminished fourth (^d4) | ||
| '''vF#'''<br />E#<br />^Gb | | '''vF#'''<br />E#<br />^Gb | ||
|- | |- | ||
| 8 | | 8 | ||
| 436. | | 436.4 | ||
| '''Major third (M3)'''<br /> | | '''Major third (M3)'''<br />Upaugmented second (^A2)<br />Down fourth (v4) | ||
| '''F#'''<br />^E#<br />vG | | '''F#'''<br />^E#<br />vG | ||
|- | |- | ||
| 9 | | 9 | ||
| 490. | | 490.9 | ||
| '''Perfect fourth (P4)''' | | '''Perfect fourth (P4)''' | ||
| '''G''' | | '''G''' | ||
|- | |- | ||
| 10 | | 10 | ||
| 545. | | 545.5 | ||
| Up | | Up fourth (^4)<br />Diminished fifth (d5) | ||
| ^G<br />Ab | | ^G<br />Ab | ||
|- | |- | ||
| 11 | | 11 | ||
| 600. | | 600.0 | ||
| | | Downaugmented fourth (vA4)<br />Updiminished fifth (^d5) | ||
| vG#<br />^Ab | | vG#<br />^Ab | ||
|- | |- | ||
| 12 | | 12 | ||
| 654. | | 654.5 | ||
| Augmented fourth (A4)<br />Down | | Augmented fourth (A4)<br />Down fifth (v5) | ||
| G#<br />vA | | G#<br />vA | ||
|- | |- | ||
| 13 | | 13 | ||
| 709. | | 709.1 | ||
| '''Perfect fifth (P5)''' | | '''Perfect fifth (P5)''' | ||
| '''A''' | | '''A''' | ||
|- | |- | ||
| 14 | | 14 | ||
| 763. | | 763.6 | ||
| Up | | Up fifth (^5)<br />Minor sixth (m6) | ||
| ^A<br />Bb | | ^A<br />Bb | ||
|- | |- | ||
| 15 | | 15 | ||
| 818. | | 818.2 | ||
| | | Downaugmented fifth (vA5)<br />Upminor sixth (^m6) | ||
| vA#<br />^Bb | | vA#<br />^Bb | ||
|- | |- | ||
| 16 | | 16 | ||
| 872. | | 872.7 | ||
| Augmented fifth (A5)<br />'''Downmajor sixth (vM6)''' | | Augmented fifth (A5)<br />'''Downmajor sixth (vM6)''' | ||
| A#<br />'''vB''' | | A#<br />'''vB''' | ||
|- | |- | ||
| 17 | | 17 | ||
| 927. | | 927.3 | ||
| '''Major sixth (M6)'''<br /> | | '''Major sixth (M6)'''<br />Upaugmented fifth (^A5)<br />Downminor seventh (vm7) | ||
| '''B'''<br />^A#<br />vC | | '''B'''<br />^A#<br />vC | ||
|- | |- | ||
| 18 | | 18 | ||
| 981. | | 981.8 | ||
| '''Minor seventh (m7)'''<br />Upmajor sixth (^M6)<br /> | | '''Minor seventh (m7)'''<br />Upmajor sixth (^M6)<br />Downdiminished octave (vd8) | ||
| '''C'''<br />^B<br />vDb | | '''C'''<br />^B<br />vDb | ||
|- | |- | ||
| 19 | | 19 | ||
| 1036. | | 1036.4 | ||
| '''Upminor seventh (^m7)'''<br />Diminished octave (d8) | | '''Upminor seventh (^m7)'''<br />Diminished octave (d8) | ||
| '''^C'''<br />Db | | '''^C'''<br />Db | ||
|- | |- | ||
| 20 | | 20 | ||
| 1090. | | 1090.9 | ||
| Downmajor seventh (vM7)<br /> | | Downmajor seventh (vM7)<br />Updiminished octave (^d8)<br />Augmented sixth (A6) | ||
| vC#<br />^Db<br />B# | | vC#<br />^Db<br />B# | ||
|- | |- | ||
| 21 | | 21 | ||
| 1145. | | 1145.5 | ||
| Major seventh (M7)<br />Down | | Major seventh (M7)<br />Down octave (v8) | ||
| C#<br />vD | | C#<br />vD | ||
|- | |- | ||
| 22 | | 22 | ||
| 1200. | | 1200.0 | ||
| '''Perfect octave (P8)''' | | '''Perfect octave (P8)''' | ||
| '''D''' | | '''D''' | ||
| Line 488: | Line 488: | ||
! [[Degree]] | ! [[Degree]] | ||
! [[Cent]]s | ! [[Cent]]s | ||
! colspan="2" | Superpyth/Porcupine | ! colspan="2" | Superpyth/Porcupine | ||
! colspan="3" | Porcupine | ! colspan="3" | Porcupine | ||
! colspan="3" | Pentatonic | ! colspan="3" | Pentatonic | ||