Xenharmonic Wiki

36edo: Difference between revisions

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→Theory: expand on subsets and supersets
→Intervals: unify to 1 decimal place
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== Intervals  ==
== Intervals  ==
{| class="wikitable center-all right-2"
{| class="wikitable center-1 right-2 center-6 center-7 center-8"
|-
|-
! Degree
! #
! [[cent|Cents]]
! [[Cent]]s
! Approximate<br />ratios of 2.3.7<ref group="note" name="subg">{{sg|limit=2.3.7 or 2.3.7.13.17.19 subgroup}}</ref>
! Approximate<br>ratios of 2.3.7<ref group="note" name="subg">{{sg|limit=2.3.7 or 2.3.7.13.17.19 subgroup}}</ref>
! Additional ratios<br />of 2.3.7.13.17.19<ref group="note" name="subg" />
! Additional ratios<br>of 2.3.7.13.17.19<ref group="note" name="subg" />
! Additional ratios<br />of 2.3.5.7<ref group="note" name="incons">Inconsistent intervals are in ''italics.''</ref>
! Additional ratios<br>of 2.3.5.7<ref group="note" name="incons">Inconsistent intervals are in ''italics.''</ref>
! colspan="3" | [[Ups and Downs Notation|Ups and downs<br />notation]]
! colspan="3" | [[Ups and Downs Notation|Ups and downs<br />notation]]
|-
|-
| 0
| 0
| 0.00
| 0.0
| 1/1
| 1/1
|  
|  
Line 50: Line 50:
|-
|-
| 1
| 1
| 33.33
| 33.3
| 64/63, [[49/48]]
| [[49/48]], [[64/63]]
|  
|  
|  
|  
Line 59: Line 59:
|-
|-
| 2
| 2
| 66.67
| 66.7
| [[28/27]]
| [[28/27]]
|  
|  
Line 68: Line 68:
|-
|-
| 3
| 3
| 100
| 100.0
| 256/243
| 256/243
| [[17/16]], [[18/17]]
| [[17/16]], [[18/17]]
Line 77: Line 77:
|-
|-
| 4
| 4
| 133.33
| 133.3
| 243/224
| 243/224
| [[14/13]], [[13/12]]
| [[14/13]], [[13/12]]
Line 86: Line 86:
|-
|-
| 5
| 5
| 166.67
| 166.7
| [[54/49]]
| [[54/49]]
|  
|  
Line 95: Line 95:
|-
|-
| 6
| 6
| 200
| 200.0
| [[9/8]]
| [[9/8]]
| [[19/17]]
| [[19/17]]
Line 104: Line 104:
|-
|-
| 7
| 7
| 233.33
| 233.3
| [[8/7]]
| [[8/7]]
|  
|  
Line 113: Line 113:
|-
|-
| 8
| 8
| 266.67
| 266.7
| [[7/6]]
| [[7/6]]
|  
|  
Line 122: Line 122:
|-
|-
| 9
| 9
| 300
| 300.0
| [[32/27]]
| [[32/27]]
| [[19/16]]
| [[19/16]]
Line 131: Line 131:
|-
|-
| 10
| 10
| 333.33
| 333.3
| 98/81
| 98/81
| [[17/14]]
| [[17/14]]
Line 140: Line 140:
|-
|-
| 11
| 11
| 366.67
| 366.7
| 243/196
| 243/196
| [[16/13]], [[26/21]], [[21/17]]
| [[16/13]], [[26/21]], [[21/17]]
Line 149: Line 149:
|-
|-
| 12
| 12
| 400
| 400.0
| [[81/64]]
| [[81/64]]
| [[24/19]]
| [[24/19]]
Line 158: Line 158:
|-
|-
| 13
| 13
| 433.33
| 433.3
| [[9/7]]
| [[9/7]]
|  
|  
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|-
|-
| 14
| 14
| 466.67
| 466.7
| [[64/49]], [[21/16]]
| [[64/49]], [[21/16]]
| [[17/13]]
| [[17/13]]
Line 176: Line 176:
|-
|-
| 15
| 15
| 500.00
| 500.0
| [[4/3]]
| [[4/3]]
|  
|  
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|-
|-
| 16
| 16
| 533.33
| 533.3
| [[49/36]]
| [[49/36]]
|  
|  
Line 194: Line 194:
|-
|-
| 17
| 17
| 566.67
| 566.7
|  
|  
| [[18/13]]
| [[18/13]]
Line 203: Line 203:
|-
|-
| 18
| 18
| 600
| 600.0
|  
|  
| [[17/12]], [[24/17]]
| [[17/12]], [[24/17]]
Line 212: Line 212:
|-
|-
| 19
| 19
| 633.33
| 633.3
|  
|  
| [[13/9]]
| [[13/9]]
Line 221: Line 221:
|-
|-
| 20
| 20
| 666.67
| 666.7
| 72/49
| 72/49
|  
|  
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|-
|-
| 21
| 21
| 700
| 700.0
| [[3/2]]
| [[3/2]]
|  
|  
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|-
|-
| 22
| 22
| 733.33
| 733.3
| [[49/32]], [[32/21]]
| [[49/32]], [[32/21]]
| [[26/17]]
| [[26/17]]
Line 248: Line 248:
|-
|-
| 23
| 23
| 766.67
| 766.7
| [[14/9]]
| [[14/9]]
|  
|  
Line 257: Line 257:
|-
|-
| 24
| 24
| 800
| 800.0
| [[128/81]]
| [[128/81]]
| [[19/12]]
| [[19/12]]
Line 266: Line 266:
|-
|-
| 25
| 25
| 833.33
| 833.3
| 392/243
| 392/243
| [[13/8]], [[21/13]], [[34/21]]
| [[13/8]], [[21/13]], [[34/21]]
Line 275: Line 275:
|-
|-
| 26
| 26
| 866.67
| 866.7
| 81/49
| 81/49
| [[28/17]]
| [[28/17]]
Line 284: Line 284:
|-
|-
| 27
| 27
| 900
| 900.0
| [[27/16]]
| [[27/16]]
| [[32/19]]
| [[32/19]]
Line 293: Line 293:
|-
|-
| 28
| 28
| 933.33
| 933.3
| [[12/7]]
| [[12/7]]
|  
|  
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|-
|-
| 29
| 29
| 966.67
| 966.7
| [[7/4]]
| [[7/4]]
|  
|  
Line 311: Line 311:
|-
|-
| 30
| 30
| 1000
| 1000.0
| [[16/9]]
| [[16/9]]
| [[34/19]]
| [[34/19]]
Line 320: Line 320:
|-
|-
| 31
| 31
| 1033.33
| 1033.3
| 49/27
| 49/27
|  
|  
Line 329: Line 329:
|-
|-
| 32
| 32
| 1066.67
| 1066.7
| 448/243
| 448/243
| [[13/7]], [[24/13]]
| [[13/7]], [[24/13]]
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|-
|-
| 33
| 33
| 1100
| 1100.0
| [[243/128]]
| [[243/128]]
| [[32/17]], [[17/9]]
| [[32/17]], [[17/9]]
Line 347: Line 347:
|-
|-
| 34
| 34
| 1133.33
| 1133.3
| [[27/14]]
| [[27/14]]
|  
|  
Line 356: Line 356:
|-
|-
| 35
| 35
| 1166.67
| 1166.7
| 63/32, 96/49
| 63/32, 96/49
|  
|  
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|-
|-
| 36
| 36
| 1200.00
| 1200.0
| 2/1
| 2/1
|  
|  
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|}
|}


Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and Downs Notation#Chords and Chord Progressions|Ups and Downs Notation - Chords and Chord Progressions]].
Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chords and chord progressions]].


== Notation ==
== Notation ==
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