12edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" | Subgroup | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning Error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
| Line 305: | Line 305: | ||
{| class="commatable wikitable center-all left-3 right-4 left-6" | {| class="commatable wikitable center-all left-3 right-4 left-6" | ||
|- | |- | ||
! [[Harmonic limit|Prime<br> | ! [[Harmonic limit|Prime<br>Limit]] | ||
! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref> | ! [[Ratio]]<ref>Ratios longer than 10 digits are presented by placeholders with informative hints</ref> | ||
! [[Monzo]] | ! [[Monzo]] | ||
! [[Cent]]s | ! [[Cent]]s | ||
! [[Color name]] | ! [[Color name|Color Name]] | ||
! Name | ! Name | ||
|- | |- | ||
| 3 | | 3 | ||
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| 62.57 | | 62.57 | ||
| Quadgu | | Quadgu | ||
| | | Diminished comma | ||
|- | |- | ||
| 5 | | 5 | ||
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| 41.06 | | 41.06 | ||
| Trigu | | Trigu | ||
| | | Augmented comma | ||
|- | |- | ||
| 5 | | 5 | ||
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| 21.51 | | 21.51 | ||
| Gu | | Gu | ||
| Syntonic | | Syntonic comma | ||
|- | |- | ||
| 5 | | 5 | ||
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| 34.98 | | 34.98 | ||
| Biruyo | | Biruyo | ||
| | | Jubilisma | ||
|- | |- | ||
| 7 | | 7 | ||
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| 27.26 | | 27.26 | ||
| Ru | | Ru | ||
| Septimal comma | | Septimal comma | ||
|- | |- | ||
| 7 | | 7 | ||
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| 13.79 | | 13.79 | ||
| Zotrigu | | Zotrigu | ||
| | | Starling comma | ||
|- | |- | ||
| 7 | | 7 | ||
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| 7.71 | | 7.71 | ||
| Ruyoyo | | Ruyoyo | ||
| | | Marvel comma | ||
|- | |- | ||
| 7 | | 7 | ||
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| 0.18 | | 0.18 | ||
| Bilorugu | | Bilorugu | ||
| Kalisma | | Kalisma | ||
|- | |- | ||
| 13 | | 13 | ||
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{| class="wikitable center-1 center-2" | {| class="wikitable center-1 center-2" | ||
|- | |- | ||
! Periods <br> per | ! Periods <br> per 8ve | ||
! Generator | ! Generator | ||
!Pergen | ! Pergen | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| 1 | | 1 | ||
| 1\12 | | 1\12 | ||
|(P8, P4/5) | | (P8, P4/5) | ||
| [[Ripple]] | | [[Ripple]] | ||
|- | |- | ||
| 1 | | 1 | ||
| 5\12 | | 5\12 | ||
|(P8, P5) | | (P8, P5) | ||
| [[Meantone]] / [[dominant]] | | [[Meantone]] / [[dominant]] | ||
|- | |- | ||
| 2 | | 2 | ||
| 1\12 | | 1\12 | ||
|(P8/2, P5) | | (P8/2, P5) | ||
| [[Srutal]] / [[pajara]] / [[injera]] | | [[Srutal]] / [[pajara]] / [[injera]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 1\12 | | 1\12 | ||
|(P8/3, P5) | | (P8/3, P5) | ||
| [[Augmented]] | | [[Augmented]] | ||
|- | |- | ||
| 4 | | 4 | ||
| 1\12 | | 1\12 | ||
|(P8/4, P5) | | (P8/4, P5) | ||
| [[Diminished]] | | [[Diminished]] | ||
|- | |- | ||
| 6 | | 6 | ||
| 1\12 | | 1\12 | ||
|(P8/6, P5) | | (P8/6, P5) | ||
| [[Hexe]] | | [[Hexe]] | ||
|} | |} | ||
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{{Main| List of MOS scales in 12edo }} | {{Main| List of MOS scales in 12edo }} | ||
The two most common 12edo | The two most common 12edo mos scales are meantone[5] and meantone[7]. | ||
* Diatonic (meantone) 5L2s 2221221 (generator = 7\12) | * Diatonic (meantone) 5L2s 2221221 (generator = 7\12) | ||
* Pentatonic (meantone) 2L3s 22323 (generator = 7\12) | * Pentatonic (meantone) 2L3s 22323 (generator = 7\12) | ||
* Diminished 4L4s 12121212 (generator = 1\12, period = 3\12) | * Diminished 4L4s 12121212 (generator = 1\12, period = 3\12) | ||
=== Non- | === Non-mos scales === | ||
Due to 12edo's dominance, some non- | Due to 12edo's dominance, some non-mos scales are also widely used in many musical practices around the world. | ||
* Harmonic major | * Harmonic major – 2212132 | ||
* Melodic major | * Melodic major – 2212122 | ||
* Hungarian minor | * Hungarian minor – 2131131 | ||
* Maqam | * Maqam hijaz / double harmonic major – 1312131 | ||
* 5-limit tonality diamond | * 5-odd-limit tonality diamond – 3112113 | ||
== Music == | == Music == | ||