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12edo: Difference between revisions

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→Music: add a brief description
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2,991 edits
→Intervals: four columns is overkill
Line 42: Line 42:
! rowspan="2" | [[Cent]]s
! rowspan="2" | [[Cent]]s
! rowspan="2" | [[Interval region]]
! rowspan="2" | [[Interval region]]
! colspan="4" | Approximated [[JI]] intervals<ref group="note">{{sg|limit=2.3.5.7.17.19 subgroup}}</ref> ([[error]] in [[¢]])
! colspan="2" | Approximated [[JI]] intervals ([[error]] in [[¢]])
! rowspan="2" | Audio
! rowspan="2" | Audio
|-
|-
! [[3-limit]]
! [[5-limit]]
! [[5-limit]]
! [[7-limit]]
! style="width: 330px;" | Higher limits<ref group="note">{{sg|limit=2.3.5.7.17.19 subgroup}}</ref>
! Other
|-
|-
| 0
| 0
Line 54: Line 52:
| Unison (prime)
| Unison (prime)
| [[1/1]] (just)
| [[1/1]] (just)
|
|
|  
|  
| [[File:piano_0_1edo.mp3]]
| [[File:piano_0_1edo.mp3]]
Line 62: Line 58:
| 100
| 100
| Minor second
| Minor second
|  
| [[256/243]] (+9.775)<br>[[25/24]] (+29.328)<br>[[16/15]] (−11.731)
| [[25/24]] (+29.328)<br>[[16/15]] (−11.731)
| [[28/27]] (+37.039), [[21/20]] (+15.533), [[15/14]] (−19.443)<br>[[17/16]] (−4.955), [[18/17]] (+1.045)<br>[[19/18]] (+6.397), [[20/19]] (+11.199)
| [[28/27]] (+37.039)<br>[[21/20]] (+15.533)<br>[[15/14]] (−19.443)
| [[18/17]] (+1.045)<br>[[17/16]] (−4.955)
| [[File:piano_1_12edo.mp3]]
| [[File:piano_1_12edo.mp3]]
|-
|-
Line 71: Line 65:
| 200
| 200
| Major second
| Major second
| [[9/8]] (−3.910)
| [[9/8]] (−3.910)<br>[[10/9]] (+17.596)
| [[10/9]] (+17.596)
| [[8/7]] (−31.174), [[28/25]] (+3.802)<br>[[17/15]] (−16.687), [[19/17]] (+7.442), [[64/57]] (−0.532)
| [[28/25]] (+3.802)<br>[[8/7]] (−31.174)
| [[19/17]] (+7.442)<br>[[55/49]] (+0.020)<br>[[64/57]] (−0.532)<br>[[17/15]] (−16.687)
| [[File:piano_1_6edo.mp3]]
| [[File:piano_1_6edo.mp3]]
|-
|-
Line 80: Line 72:
| 300
| 300
| Minor third
| Minor third
| [[32/27]] (+5.865)
| [[32/27]] (+5.865)<br>[[6/5]] (−15.641)<br>[[75/64]] (+25.418)
| [[6/5]] (−15.641)
| [[7/6]] (+33.129), [[25/21]] (−1.847)<br>[[19/16]] (+2.487)
| [[7/6]] (+33.129)<br>[[25/21]] (−1.847)
| [[19/16]] (+2.487)<br>[[44/37]] (+0.026)
| [[File:piano_1_4edo.mp3]]
| [[File:piano_1_4edo.mp3]]
|-
|-
Line 89: Line 79:
| 400
| 400
| Major third
| Major third
| [[81/64]] (−7.820)
| [[81/64]] (−7.820)<br>[[5/4]] (+13.686)<br> [[32/25]] (-27.373)
| [[5/4]] (+13.686)
| [[63/50]] (−0.108), [[9/7]] (−35.084)<br>[[34/27]] (+0.910), [[24/19]] (−4.442)
| [[63/50]] (−0.108)<br>[[9/7]] (−35.084)
| [[34/27]] (+0.910)<br>[[24/19]] (−4.442)
| [[File:piano_1_3edo.mp3]]
| [[File:piano_1_3edo.mp3]]
|-
|-
Line 98: Line 86:
| 500
| 500
| Fourth
| Fourth
| [[4/3]] (+1.955)
| [[4/3]] (+1.955)<br> [[27/20]] (-19.551)
|  
| [[21/16]] (-29.219)
|
|
| [[File:piano_5_12edo.mp3]]
| [[File:piano_5_12edo.mp3]]
|-
|-
Line 107: Line 93:
| 600
| 600
| [[Tritone]]
| [[Tritone]]
|  
| [[25/18]] (+31.283)<br>[[36/25]] (-31.283)<br>[[45/32]] (+9.776)<br>[[64/45]] (−9.776)
| [[45/32]] (+9.776)<br>[[64/45]] (−9.776)
| [[7/5]] (+17.488), [[10/7]] (−17.488)<br>[[24/17]] (+3.000), [[17/12]] (−3.000)<br>[[99/70]] (−0.088), [[140/99]] (+0.088)
| [[7/5]] (+17.488)<br>[[10/7]] (−17.488)
| [[24/17]] (+3.000)<br>[[99/70]] (−0.088)<br>[[140/99]] (+0.088)<br>[[17/12]] (−3.000)
| [[File:piano_1_2edo.mp3]]
| [[File:piano_1_2edo.mp3]]
|-
|-
Line 116: Line 100:
| 700
| 700
| Fifth
| Fifth
| [[3/2]] (−1.955)
| [[3/2]] (−1.955)<br>[[40/27]] (+19.551)
|  
| [[32/21]] (+29.219)
|
|
| [[File:piano_7_12edo.mp3]]
| [[File:piano_7_12edo.mp3]]
|-
|-
Line 125: Line 107:
| 800
| 800
| Minor sixth
| Minor sixth
| [[128/81]] (+7.820)
| [[128/81]] (+7.820)<br>[[8/5]] (−13.686)<br>[[25/16]] (+27.373)
| [[8/5]] (−13.686)
| [[14/9]] (+35.084), [[100/63]] (+0.108)<br>[[19/12]] (+4.442), [[27/17]] (−0.910)
| [[14/9]] (+35.084)<br>[[100/63]] (+0.108)
| [[19/12]] (+4.442)<br>[[27/17]] (−0.910)
| [[File:piano_2_3edo.mp3]]
| [[File:piano_2_3edo.mp3]]
|-
|-
Line 134: Line 114:
| 900
| 900
| Major sixth
| Major sixth
| [[27/16]] (−5.865)
| [[27/16]] (−5.865)<br>[[5/3]] (+15.641)<br>[[128/75]] (-25.418)
| [[5/3]] (+15.641)
| [[12/7]] (−33.129), [[42/25]] (+1.847)<br>[[32/19]] (−2.487)
| [[42/25]] (+1.847)<br>[[12/7]] (−33.129)
| [[37/22]] (−0.026)<br>[[32/19]] (−2.487)
| [[File:piano_3_4edo.mp3]]
| [[File:piano_3_4edo.mp3]]
|-
|-
Line 143: Line 121:
| 1000
| 1000
| Minor seventh
| Minor seventh
| [[16/9]] (+3.910)
| [[16/9]] (+3.910)<br>[[9/5]] (−17.596)
| [[9/5]] (−17.596)
| [[7/4]] (+31.174), [[25/14]] (−3.802)<br>[[30/17]] (+16.687), [[34/19]] (−7.442)<br>[[57/32]] (+0.532)
| [[7/4]] (+31.174)<br>[[25/14]] (−3.802)
| [[30/17]] (+16.687)<br>[[57/32]] (+0.532)<br>[[98/55]] (−0.020)<br>[[34/19]] (−7.442)
| [[File:piano_5_6edo.mp3]]
| [[File:piano_5_6edo.mp3]]
|-
|-
Line 152: Line 128:
| 1100
| 1100
| Major seventh
| Major seventh
|  
| [[243/128]] (-9.775)<br>[[15/8]] (+11.731)<br>[[48/25]] (−29.328)
| [[15/8]] (+11.731)<br>[[48/25]] (−29.328)
| [[28/15]] (+19.443), [[40/21]] (−15.533), [[27/14]] (−37.039)<br>[[32/17]] (+4.955), [[17/9]] (−1.045)<br>[[36/19]] (-6.397), [[19/10]] (-11.199)
| [[28/15]] (+19.443)<br>[[40/21]] (−15.533)<br>[[27/14]] (−37.039)
| [[32/17]] (+4.955)<br>[[17/9]] (−1.045)
| [[File:piano_11_12edo.mp3]]
| [[File:piano_11_12edo.mp3]]
|-
|-
Line 162: Line 136:
| Octave
| Octave
| [[2/1]] (just)
| [[2/1]] (just)
|
|
|  
|  
| [[File:piano_1_1edo.mp3]]
| [[File:piano_1_1edo.mp3]]
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