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12edo: Difference between revisions

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→Intervals: Added higher prime limit intervals to a separate column
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autopatrolled, Sysops
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→Intervals: merged the two columns of JI ratios into one
Line 18: Line 18:
!Cents
!Cents
! colspan="3" |Interval
! colspan="3" |Interval
!7-limit Ratios*
!Approximate JI Ratios*
!Other
|-
|-
|0
|0
Line 27: Line 26:
|D
|D
|1/1
|1/1
|
|-
|-
|1
|1
Line 34: Line 32:
|A1, m2
|A1, m2
|D#, Eb
|D#, Eb
|15/14, 16/15, 21/20, 25/24, 28/27
|15/14, 16/15, 18/17, 21/20, 25/24, 28/27
|18/17
|-
|-
|2
|2
Line 43: Line 40:
|E
|E
|8/7, 9/8, 10/9
|8/7, 9/8, 10/9
|
|-
|-
|3
|3
Line 50: Line 46:
|m3
|m3
|F
|F
|7/6, 6/5
|7/6, 6/5, 19/16
|19/16
|-
|-
|4
|4
Line 59: Line 54:
|F#
|F#
|5/4, 9/7
|5/4, 9/7
|
|-
|-
|5
|5
Line 67: Line 61:
|G
|G
|4/3
|4/3
|
|-
|-
|6
|6
Line 74: Line 67:
|A4, d5
|A4, d5
|G#, Ab
|G#, Ab
|7/5, 10/7
|7/5, 10/7, 17/12, 24/17
|17/12, 12/17
|-
|-
|7
|7
Line 83: Line 75:
|A
|A
|3/2
|3/2
|
|-
|-
|8
|8
Line 91: Line 82:
|Bb
|Bb
|8/5, 14/9
|8/5, 14/9
|
|-
|-
|9
|9
Line 98: Line 88:
|M6
|M6
|B
|B
|5/3, 12/7
|5/3, 12/7, 32/19
|32/19
|-
|-
|10
|10
Line 107: Line 96:
|C
|C
|7/4, 9/5, 16/9
|7/4, 9/5, 16/9
|
|-
|-
|11
|11
Line 114: Line 102:
|M7
|M7
|C#
|C#
|15/8, 28/15, 40/21, 48/25, 27/14
|15/8, 17/9, 28/15, 40/21, 48/25, 27/14
|17/9
|-
|-
|19
|19
Line 123: Line 110:
|D
|D
|2/1
|2/1
|
|}
|}
<nowiki>*</nowiki> based on treating 12-edo as a 2.3.5.7 subgroup temperament; other approaches are possible.
<nowiki>*</nowiki> based on treating 12-edo as a 2.3.5.7.17.19 subgroup temperament; other approaches are possible.


==Rank two temperaments==
==Rank two temperaments==
Line 179: Line 165:
| {{Monzo| 3 4 -4 }}
| {{Monzo| 3 4 -4 }}
| style="text-align:right;" | 62.57
| style="text-align:right;" | 62.57
|Quadgu
| style="text-align:center;" |Quadgu
| style="text-align:center;" | Major Diesis
| style="text-align:center;" | Major Diesis
| style="text-align:center;" | Diminished Comma
| style="text-align:center;" | Diminished Comma
Line 187: Line 173:
| {{Monzo| 2 2 -1 -1 }}
| {{Monzo| 2 2 -1 -1 }}
| style="text-align:right;" | 48.77
| style="text-align:right;" | 48.77
|Rugu
| style="text-align:center;" |Rugu
| style="text-align:center;" | Septimal Quarter Tone
| style="text-align:center;" | Septimal Quarter Tone
| style="text-align:center;" |  
| style="text-align:center;" |  
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| {{Monzo| 7 0 -3 }}
| {{Monzo| 7 0 -3 }}
| style="text-align:right;" | 41.06
| style="text-align:right;" | 41.06
|Trigu
| style="text-align:center;" |Trigu
| style="text-align:center;" | Diesis
| style="text-align:center;" | Diesis
| style="text-align:center;" | Augmented Comma
| style="text-align:center;" | Augmented Comma
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| {{Monzo| 1 0 2 -2 }}
| {{Monzo| 1 0 2 -2 }}
| style="text-align:right;" | 34.98
| style="text-align:right;" | 34.98
|Biruyo
| style="text-align:center;" |Biruyo
| style="text-align:center;" | Tritonic Diesis
| style="text-align:center;" | Tritonic Diesis
| style="text-align:center;" | Jubilisma
| style="text-align:center;" | Jubilisma
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| {{Monzo| 6 -2 0 -1 }}
| {{Monzo| 6 -2 0 -1 }}
| style="text-align:right;" | 27.26
| style="text-align:right;" | 27.26
|Ru
| style="text-align:center;" |Ru
| style="text-align:center;" | Septimal Comma
| style="text-align:center;" | Septimal Comma
| style="text-align:center;" | Archytas' Comma
| style="text-align:center;" | Archytas' Comma
Line 219: Line 205:
| {{Monzo| -19 12 }}
| {{Monzo| -19 12 }}
| style="text-align:right;" | 23.46
| style="text-align:right;" | 23.46
|Lalawa
| style="text-align:center;" |Lalawa
| style="text-align:center;" | Pythagorean Comma
| style="text-align:center;" | Pythagorean Comma
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 227: Line 213:
| {{Monzo| -4 4 -1 }}
| {{Monzo| -4 4 -1 }}
| style="text-align:right;" | 21.51
| style="text-align:right;" | 21.51
|Gu
| style="text-align:center;" |Gu
| style="text-align:center;" | Syntonic Comma
| style="text-align:center;" | Syntonic Comma
| style="text-align:center;" | Didymos Comma
| style="text-align:center;" | Didymos Comma
Line 235: Line 221:
| {{Monzo| 0 -2 5 -3 }}
| {{Monzo| 0 -2 5 -3 }}
| style="text-align:right;" | 21.18
| style="text-align:right;" | 21.18
|Triru-aquinyo
| style="text-align:center;" |Triru-aquinyo
| style="text-align:center;" | Gariboh
| style="text-align:center;" | Gariboh
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 243: Line 229:
| {{Monzo| 11 -4 -2 }}
| {{Monzo| 11 -4 -2 }}
| style="text-align:right;" | 19.55
| style="text-align:right;" | 19.55
|Sagugu
| style="text-align:center;" |Sagugu
| style="text-align:center;" | Diaschisma
| style="text-align:center;" | Diaschisma
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 251: Line 237:
| {{Monzo| -1 -2 -1 1 0 1 }}
| {{Monzo| -1 -2 -1 1 0 1 }}
| style="text-align:right;" | 19.13
| style="text-align:right;" | 19.13
|Thozogu
| style="text-align:center;" |Thozogu
| style="text-align:center;" | Superleap
| style="text-align:center;" | Superleap
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 259: Line 245:
| {{Monzo| 26 -12 -3 }}
| {{Monzo| 26 -12 -3 }}
| style="text-align:right;" | 17.60
| style="text-align:right;" | 17.60
|Sasa-trigu
| style="text-align:center;" |Sasa-trigu
| style="text-align:center;" | Misty Comma
| style="text-align:center;" | Misty Comma
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 267: Line 253:
| {{Monzo| -1 2 0 -2 1 }}
| {{Monzo| -1 2 0 -2 1 }}
| style="text-align:right;" | 17.58
| style="text-align:right;" | 17.58
|Loruru
| style="text-align:center;" |Loruru
| style="text-align:center;" | Mothwellsma
| style="text-align:center;" | Mothwellsma
| style="text-align:center;" |  
| style="text-align:center;" |  
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| {{Monzo| 2 -2 2 0 -1 }}
| {{Monzo| 2 -2 2 0 -1 }}
| style="text-align:right;" | 17.40
| style="text-align:right;" | 17.40
|Luyoyo
| style="text-align:center;" |Luyoyo
| style="text-align:center;" | Ptolemisma
| style="text-align:center;" | Ptolemisma
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 283: Line 269:
| {{Monzo| 1 2 -3 1 }}
| {{Monzo| 1 2 -3 1 }}
| style="text-align:right;" | 13.79
| style="text-align:right;" | 13.79
|Zotrigu
| style="text-align:center;" |Zotrigu
| style="text-align:center;" | Septimal Semicomma
| style="text-align:center;" | Septimal Semicomma
| style="text-align:center;" | Starling Comma
| style="text-align:center;" | Starling Comma
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| {{Monzo| 5 -4 3 -2 }}
| {{Monzo| 5 -4 3 -2 }}
| style="text-align:right;" | 13.47
| style="text-align:right;" | 13.47
|Rurutriyo
| style="text-align:center;" |Rurutriyo
| style="text-align:center;" | Octagar
| style="text-align:center;" | Octagar
| style="text-align:center;" |  
| style="text-align:center;" |  
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| {{Monzo| 4 0 -2 -1 1 }}
| {{Monzo| 4 0 -2 -1 1 }}
| style="text-align:right;" | 9.86
| style="text-align:right;" | 9.86
|Lorugugu
| style="text-align:center;" |Lorugugu
| style="text-align:center;" | Valinorsma
| style="text-align:center;" | Valinorsma
| style="text-align:center;" |  
| style="text-align:center;" |  
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| {{Monzo| 7 -4 0 1 -1 }}
| {{Monzo| 7 -4 0 1 -1 }}
| style="text-align:right;" | 9.69
| style="text-align:right;" | 9.69
|Saluzo
| style="text-align:center;" |Saluzo
| style="text-align:center;" | Pentacircle
| style="text-align:center;" | Pentacircle
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 315: Line 301:
| {{Monzo| -9 8 -4 2 }}
| {{Monzo| -9 8 -4 2 }}
| style="text-align:right;" | 8.04
| style="text-align:right;" | 8.04
|Labizogugu
| style="text-align:center;" |Labizogugu
| style="text-align:center;" | Varunisma
| style="text-align:center;" | Varunisma
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 323: Line 309:
| {{Monzo| -5 2 2 -1 }}
| {{Monzo| -5 2 2 -1 }}
| style="text-align:right;" | 7.71
| style="text-align:right;" | 7.71
|Ruyoyo
| style="text-align:center;" |Ruyoyo
| style="text-align:center;" | Septimal Kleisma
| style="text-align:center;" | Septimal Kleisma
| style="text-align:center;" | Marvel Comma
| style="text-align:center;" | Marvel Comma
Line 331: Line 317:
| {{Monzo| 6 0 -5 2 }}
| {{Monzo| 6 0 -5 2 }}
| style="text-align:right;" | 6.08
| style="text-align:right;" | 6.08
|Zozoquingu
| style="text-align:center;" |Zozoquingu
| style="text-align:center;" | Hemimean
| style="text-align:center;" | Hemimean
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 339: Line 325:
| {{Monzo| 10 -6 1 -1 }}
| {{Monzo| 10 -6 1 -1 }}
| style="text-align:right;" | 5.76
| style="text-align:right;" | 5.76
|Saruyo
| style="text-align:center;" |Saruyo
| style="text-align:center;" | Hemifamity
| style="text-align:center;" | Hemifamity
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 347: Line 333:
| {{Monzo| -3 2 -1 2 -1 }}
| {{Monzo| -3 2 -1 2 -1 }}
| style="text-align:right;" | 3.93
| style="text-align:right;" | 3.93
|Luzozogu
| style="text-align:center;" |Luzozogu
| style="text-align:center;" | Werckisma
| style="text-align:center;" | Werckisma
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 355: Line 341:
| {{Monzo| 25 -14 0 -1 }}
| {{Monzo| 25 -14 0 -1 }}
| style="text-align:right;" | 3.80
| style="text-align:right;" | 3.80
|Sasaru
| style="text-align:center;" |Sasaru
| style="text-align:center;" | Garischisma
| style="text-align:center;" | Garischisma
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 363: Line 349:
| {{Monzo| -15 8 1 }}
| {{Monzo| -15 8 1 }}
| style="text-align:right;" | 1.95
| style="text-align:right;" | 1.95
|Layo
| style="text-align:center;" |Layo
| style="text-align:center;" | Schisma
| style="text-align:center;" | Schisma
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 371: Line 357:
| {{Monzo| -11 2 7 -3 }}
| {{Monzo| -11 2 7 -3 }}
| style="text-align:right;" | 1.63
| style="text-align:right;" | 1.63
|Latriru-asepyo
| style="text-align:center;" |Latriru-asepyo
| style="text-align:center;" | Meter
| style="text-align:center;" | Meter
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 379: Line 365:
| {{Monzo| -4 6 -6 3 }}
| {{Monzo| -4 6 -6 3 }}
| style="text-align:right;" | 0.33
| style="text-align:right;" | 0.33
|Trizogugu
| style="text-align:center;" |Trizogugu
| style="text-align:center;" | Landscape Comma
| style="text-align:center;" | Landscape Comma
| style="text-align:center;" |  
| style="text-align:center;" |  
Line 387: Line 373:
| {{Monzo| -3 4 -2 -2 2 }}
| {{Monzo| -3 4 -2 -2 2 }}
| style="text-align:right;" | 0.18
| style="text-align:right;" | 0.18
|Bilorugu
| style="text-align:center;" |Bilorugu
| style="text-align:center;" | Kalisma
| style="text-align:center;" | Kalisma
| style="text-align:center;" | Gauss' Comma
| style="text-align:center;" | Gauss' Comma
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| {{Monzo| 161 -84 -12 }}
| {{Monzo| 161 -84 -12 }}
| style="text-align:right;" | 0.02
| style="text-align:right;" | 0.02
|Sepbisa-quadtrigu
| style="text-align:center;" |Sepbisa-quadtrigu
| style="text-align:center;" | Atom
| style="text-align:center;" | Atom
| style="text-align:center;" |  
| style="text-align:center;" |  
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