Xenharmonic Wiki

104edo: Difference between revisions

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VisualWikitext
→Theory: +octave stretch
→Intervals: reduce cent values to one decimal place, per discussion on Discord; sort ratios; -some excessively complex ratios
Line 157: Line 157:


== Intervals ==
== Intervals ==
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
|-
! rowspan="2" | #
! rowspan="2" | #
! rowspan="2" | Cents
! rowspan="2" | Cents
! colspan="3" | Approximate Ratios
! colspan="3" | Approximate ratios
|-
|-
! Of 2.3.7.11.13.17.19.25<br />subgroup
! Of 2.3.7.11.13.17.19.25<br>subgroup
! Additional ratios of 5<br />tending sharp (104c val)
! Additional ratios of 5<br>tending sharp (104c val)
! Additional ratios of 5<br />tending flat (patent val)
! Additional ratios of 5<br>tending flat (patent val)
|-
|-
| 0
| 0
| 0.000
| 0.0
| [[1/1]]
| [[1/1]]
| ''[[126/125]]''
|  
| ''[[225/224]]'', ''[[100/99]]''
|  
|-
|-
| 1
| 1
| 11.538
| 11.5
| [[225/224]], [[100/99]]
| [[100/99]], [[225/224]]
|
|
|
|
|-
|-
| 2
| 2
| 23.077
| 23.1
| [[64/63]]
| [[64/63]]
| [[81/80]], ''[[225/224]]''
| [[81/80]], ''[[225/224]]''
Line 187: Line 186:
|-
|-
| 3
| 3
| 34.615
| 34.6
| [[49/48]], [[50/49]]
| [[49/48]], [[50/49]]
|
|
Line 193: Line 192:
|-
|-
| 4
| 4
| 46.154
| 46.2
|
|
| [[36/35]], ''[[50/49]]''
| [[36/35]], ''[[50/49]]''
Line 199: Line 198:
|-
|-
| 5
| 5
| 57.692
| 57.7
| ''[[28/27]]'', [[33/32]]
| ''[[28/27]]'', [[33/32]]
|
|
Line 205: Line 204:
|-
|-
| 6
| 6
| 69.231
| 69.2
| [[25/24]]
| [[25/24]]
|
|
Line 211: Line 210:
|-
|-
| 7
| 7
| 80.769
| 80.8
| [[22/21]]
| [[22/21]]
| ''[[25/24]]'', [[21/20]]
| [[21/20]], ''[[25/24]]''
| ''[[20/19]]''
| ''[[20/19]]''
|-
|-
| 8
| 8
| 92.308
| 92.3
| [[19/18]]
| [[19/18]]
| [[20/19]]
| [[20/19]]
Line 223: Line 222:
|-
|-
| 9
| 9
| 103.846
| 103.8
| [[17/16]], [[18/17]]
| [[17/16]], [[18/17]]
| ''[[16/15]]''
| ''[[16/15]]''
Line 229: Line 228:
|-
|-
| 10
| 10
| 115.385
| 115.4
|
|
|
|
Line 235: Line 234:
|-
|-
| 11
| 11
| 126.923
| 126.9
| [[14/13]]
| [[14/13]]
| ''[[15/14]]''
| ''[[15/14]]''
Line 241: Line 240:
|-
|-
| 12
| 12
| 138.462
| 138.5
| [[13/12]]
| [[13/12]]
|
|
Line 247: Line 246:
|-
|-
| 13
| 13
| 150.000
| 150.0
| [[12/11]]
| [[12/11]]
|
|
Line 253: Line 252:
|-
|-
| 14
| 14
| 161.538
| 161.5
|
|
| [[11/10]]
| [[11/10]]
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|-
|-
| 15
| 15
| 173.077
| 173.1
| [[21/19]]
| [[21/19]]
|
|
Line 265: Line 264:
|-
|-
| 16
| 16
| 184.615
| 184.6
|
|
| [[10/9]]
| [[10/9]]
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|-
|-
| 17
| 17
| 196.154
| 196.2
| [[28/25]], [[19/17]]
| [[19/17]], [[28/25]]
|
|
|
|
|-
|-
| 18
| 18
| 207.692
| 207.7
| [[9/8]]
| [[9/8]]
| ''[[17/15]]''
| ''[[17/15]]''
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|-
|-
| 19
| 19
| 219.231
| 219.2
| [[25/22]]
| [[25/22]]
|
|
Line 289: Line 288:
|-
|-
| 20
| 20
| 230.769
| 230.8
| [[8/7]]
| [[8/7]]
|
|
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|-
|-
| 21
| 21
| 242.308
| 242.3
|
|
|
|
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|-
|-
| 22
| 22
| 253.846
| 253.8
| [[22/19]]
| [[22/19]]
| ''[[15/13]]''
| ''[[15/13]]''
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|-
|-
| 23
| 23
| 265.385
| 265.4
| [[7/6]]
| [[7/6]]
|
|
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|-
|-
| 24
| 24
| 276.923
| 276.9
| [[75/64]]
| [[75/64]]
|
|
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|-
|-
| 25
| 25
| 288.462
| 288.5
| [[32/27]], [[13/11]]
| [[32/27]], [[13/11]]
| ''[[20/17]]''
| ''[[20/17]]''
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|-
|-
| 26
| 26
| 300.000
| 300.0
| [[25/21]], [[19/16]]
| [[25/21]], [[19/16]]
|
|
Line 331: Line 330:
|-
|-
| 27
| 27
| 311.538
| 311.5
|
|
| [[6/5]]
| [[6/5]]
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|-
|-
| 28
| 28
| 323.077
| 323.1
|
|
|
|
Line 343: Line 342:
|-
|-
| 29
| 29
| 334.615
| 334.6
| [[17/14]]
| [[17/14]]
| [[40/33]]
| [[40/33]]
Line 349: Line 348:
|-
|-
| 30
| 30
| 346.154
| 346.2
| [[11/9]], [[39/32]]
| [[11/9]], [[39/32]]
|
|
Line 355: Line 354:
|-
|-
| 31
| 31
| 357.692
| 357.7
| [[27/22]], [[16/13]]
| [[16/13]], [[27/22]]
|
|
|
|
|-
|-
| 32
| 32
| 369.231
| 369.2
| [[26/21]], [[21/17]]
| [[21/17]], [[26/21]]
|
|
|
|
|-
|-
| 33
| 33
| 380.769
| 380.8
|
|
|
|
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|-
|-
| 34
| 34
| 392.308
| 392.3
|
|
| ''[[5/4]]''
| ''[[5/4]]''
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|-
|-
| 35
| 35
| 403.846
| 403.8
| [[63/50]], [[24/19]]
| [[24/19]], [[63/50]]
| [[19/15]]
| [[19/15]]
|
|
|-
|-
| 36
| 36
| 415.385
| 415.4
| [[81/64]], [[14/11]]
| [[14/11]]
|
|
| ''[[19/15]]''
| ''[[19/15]]''
|-
|-
| 37
| 37
| 426.923
| 426.9
| [[32/25]]
| [[32/25]]
|
|
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|-
|-
| 38
| 38
| 438.462
| 438.5
| [[9/7]]
| [[9/7]]
|
|
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|-
|-
| 39
| 39
| 450.000
| 450.0
| [[22/17]]
| [[22/17]]
| [[13/10]]
| [[13/10]]
Line 409: Line 408:
|-
|-
| 40
| 40
| 461.538
| 461.5
| [[17/13]]
| [[17/13]]
|
|
Line 415: Line 414:
|-
|-
| 41
| 41
| 473.077
| 473.1
| [[21/16]]
| [[21/16]]
|
|
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|-
|-
| 42
| 42
| 484.615
| 484.6
|
|
|
|
Line 427: Line 426:
|-
|-
| 43
| 43
| 496.154
| 496.2
| [[4/3]]
| [[4/3]]
|
|
Line 433: Line 432:
|-
|-
| 44
| 44
| 507.692
| 507.7
|
|
|
|
Line 439: Line 438:
|-
|-
| 45
| 45
| 519.231
| 519.2
|
|
| [[27/20]]
| [[27/20]]
Line 445: Line 444:
|-
|-
| 46
| 46
| 530.769
| 530.8
| [[19/14]]
| [[19/14]]
|
|
Line 451: Line 450:
|-
|-
| 47
| 47
| 542.308
| 542.3
| [[26/19]]
| [[26/19]]
| [[15/11]]
| [[15/11]]
Line 457: Line 456:
|-
|-
| 48
| 48
| 553.846
| 553.8
| [[11/8]]
| [[11/8]]
|
|
Line 463: Line 462:
|-
|-
| 49
| 49
| 565.385
| 565.4
| [[18/13]]
| [[18/13]]
|
|
Line 469: Line 468:
|-
|-
| 50
| 50
| 576.923
| 576.9
|
|
| [[7/5]]
| [[7/5]]
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|-
|-
| 51
| 51
| 588.462
| 588.5
|
|
|
|
| [[45/32]], ''[[7/5]]''
| ''[[7/5]]'', [[45/32]]
|-
|-
| 52
| 52
| 600.000
| 600.0
| [[17/12]], [[24/17]]
| [[17/12]], [[24/17]]
| ''[[45/32]]'', ''[[64/45]]''
| ''[[45/32]]'', ''[[64/45]]''
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