Xenharmonic Wiki

53edo: Difference between revisions

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→Intervals: reduce cent values to one decimal place per discussion on Discord; sort ratios by complexity (integer limit); style
Line 32: Line 32:
{| class="wikitable center-all right-2 left-3 left-5"
{| class="wikitable center-all right-2 left-3 left-5"
|-
|-
! #
! #
! Cents
! Cents
! Approximate Ratios<ref group="note">{{sg|limit=no-17's [[19-limit]]}} ''Italics'' represent inconsistent intervals which are mapped by the 19-limit [[patent val]] to their second-closest (as opposed to closest) approximation in 53edo. </ref>
! Approximate ratios<ref group="note">{{sg|limit=no-17's [[19-limit]]}} ''Italics'' represent inconsistent intervals which are mapped by the 19-limit [[patent val]] to their second-closest (as opposed to closest) approximation in 53edo. </ref>
! colspan="3" | [[Ups and downs notation]] ([[Enharmonic unisons in ups and downs notation|EUs]]: v<sup>5</sup>A1 and ^d2)
! colspan="3" | [[Ups and downs notation]] ([[enharmonic unisons in ups and downs notation|EUs]]: v<sup>5</sup>A1 and ^d2)
! colspan="2" | [[Solfege]]s
! colspan="2" | [[Solfege]]s
|-
|-
| 0
| 0
| 0.00
| 0.0
| [[1/1]]
| [[1/1]]
| P1
| P1
Line 48: Line 48:
|-
|-
| 1
| 1
| 22.64
| 22.6
| [[81/80]], [[64/63]], [[50/49]]
| ''[[50/49]]'', [[64/63]], [[81/80]]
| ^1
| ^1
| up unison
| up unison
Line 57: Line 57:
|-
|-
| 2
| 2
| 45.28
| 45.3
| [[49/48]], [[36/35]], [[33/32]], [[128/125]]
| [[33/32]], [[36/35]], [[49/48]], [[128/125]]
| ^^1, vvm2
| ^^1, vvm2
| dup unison, dudminor 2nd
| dup unison, dudminor 2nd
Line 66: Line 66:
|-
|-
| 3
| 3
| 67.92
| 67.9
| [[25/24]], [[28/27]], [[22/21]], [[27/26]], [[26/25]]
| ''[[22/21]]'', [[25/24]], [[26/25]], [[27/26]], [[28/27]]
| vvA1, vm2
| vvA1, vm2
| dudaug 1sn, downminor 2nd
| dudaug 1sn, downminor 2nd
Line 75: Line 75:
|-
|-
| 4
| 4
| 90.57
| 90.6
| [[19/18]], [[20/19]], [[21/20]], [[256/243]]
| [[19/18]], [[20/19]], [[21/20]], [[256/243]]
| vA1, m2
| vA1, m2
Line 84: Line 84:
|-
|-
| 5
| 5
| 113.21
| 113.2
| [[16/15]], [[15/14]]
| [[15/14]], [[16/15]]
| A1, ^m2
| A1, ^m2
| aug 1sn, upminor 2nd
| aug 1sn, upminor 2nd
Line 93: Line 93:
|-
|-
| 6
| 6
| 135.85
| 135.8
| [[14/13]], [[13/12]], [[27/25]]
| [[13/12]], [[14/13]], [[27/25]]
| ^^m2
| ^^m2
| dupminor 2nd
| dupminor 2nd
Line 102: Line 102:
|-
|-
| 7
| 7
| 158.49
| 158.5
| [[35/32]], [[12/11]], [[11/10]], [[57/52]], [[800/729]]
| [[11/10]], [[12/11]], [[35/32]], [[57/52]], [[800/729]]
| vvM2
| vvM2
| dudmajor 2nd
| dudmajor 2nd
Line 111: Line 111:
|-
|-
| 8
| 8
| 181.13
| 181.1
| [[10/9]]
| [[10/9]]
| vM2
| vM2
Line 120: Line 120:
|-
|-
| 9
| 9
| 203.77
| 203.8
| [[9/8]]
| [[9/8]]
| M2
| M2
Line 129: Line 129:
|-
|-
| 10
| 10
| 226.42
| 226.4
| [[8/7]], [[256/225]]
| [[8/7]], [[256/225]]
| ^M2
| ^M2
Line 138: Line 138:
|-
|-
| 11
| 11
| 249.06
| 249.1
| [[15/13]], [[144/125]], [[125/108]]
| [[15/13]], [[125/108]], [[144/125]]
| ^^M2, vvm3
| ^^M2, vvm3
| dupmajor 2nd, dudminor 3rd
| dupmajor 2nd, dudminor 3rd
Line 147: Line 147:
|-
|-
| 12
| 12
| 271.70
| 271.7
| [[7/6]], [[75/64]]
| [[7/6]], [[75/64]]
| vm3
| vm3
Line 156: Line 156:
|-
|-
| 13
| 13
| 294.34
| 294.3
| [[13/11]], [[19/16]], [[32/27]]
| [[13/11]], [[19/16]], [[32/27]]
| m3
| m3
Line 165: Line 165:
|-
|-
| 14
| 14
| 316.98
| 317.0
| [[6/5]]
| [[6/5]]
| ^m3
| ^m3
Line 174: Line 174:
|-
|-
| 15
| 15
| 339.62
| 339.6
| [[11/9]], [[243/200]]
| [[11/9]], [[243/200]]
| ^^m3
| ^^m3
Line 183: Line 183:
|-
|-
| 16
| 16
| 362.26
| 362.3
| [[16/13]], [[100/81]]
| [[16/13]], [[100/81]]
| vvM3
| vvM3
Line 192: Line 192:
|-
|-
| 17
| 17
| 384.91
| 384.9
| [[5/4]]
| [[5/4]]
| vM3
| vM3
Line 201: Line 201:
|-
|-
| 18
| 18
| 407.55
| 407.5
| [[19/15]], [[24/19]], [[81/64]]
| [[19/15]], [[24/19]], [[81/64]]
| M3
| M3
Line 210: Line 210:
|-
|-
| 19
| 19
| 430.19
| 430.2
| [[9/7]], ''[[14/11]]''
| [[9/7]], ''[[14/11]]''
| ^M3
| ^M3
Line 219: Line 219:
|-
|-
| 20
| 20
| 452.83
| 452.8
| [[13/10]], [[125/96]], [[162/125]]
| [[13/10]], [[125/96]], [[162/125]]
| ^^M3, vv4
| ^^M3, vv4
Line 228: Line 228:
|-
|-
| 21
| 21
| 475.47
| 475.5
| [[21/16]], [[25/19]], [[675/512]], [[320/243]]
| [[21/16]], [[25/19]], [[320/243]], [[675/512]]
| v4
| v4
| down 4th
| down 4th
Line 237: Line 237:
|-
|-
| 22
| 22
| 498.11
| 498.1
| [[4/3]]
| [[4/3]]
| P4
| P4
Line 246: Line 246:
|-
|-
| 23
| 23
| 520.75
| 520.8
| [[27/20]]
| [[27/20]]
| ^4
| ^4
Line 255: Line 255:
|-
|-
| 24
| 24
| 543.40
| 543.4
| [[11/8]], [[15/11]], [[26/19]]
| [[11/8]], [[15/11]], [[26/19]]
| ^^4
| ^^4
Line 264: Line 264:
|-
|-
| 25
| 25
| 566.04
| 566.0
| [[18/13]]
| [[18/13]]
| vvA4, vd5
| vvA4, vd5
Line 273: Line 273:
|-
|-
| 26
| 26
| 588.68
| 588.7
| [[7/5]], [[45/32]]
| [[7/5]], [[45/32]]
| vA4, d5
| vA4, d5
Line 282: Line 282:
|-
|-
| 27
| 27
| 611.32
| 611.3
| [[10/7]], [[64/45]]
| [[10/7]], [[64/45]]
| A4, ^d5
| A4, ^d5
Line 291: Line 291:
|-
|-
| 28
| 28
| 633.96
| 634.0
| [[13/9]]
| [[13/9]]
| ^A4, ^^d5
| ^A4, ^^d5
Line 300: Line 300:
|-
|-
| 29
| 29
| 656.60
| 656.6
| [[16/11]], [[19/13]], [[22/15]]
| [[16/11]], [[19/13]], [[22/15]]
| vv5
| vv5
Line 309: Line 309:
|-
|-
| 30
| 30
| 679.25
| 679.2
| [[40/27]]
| [[40/27]]
| v5
| v5
Line 318: Line 318:
|-
|-
| 31
| 31
| 701.89
| 701.9
| [[3/2]]
| [[3/2]]
| P5
| P5
Line 327: Line 327:
|-
|-
| 32
| 32
| 724.53
| 724.5
| [[32/21]], [[38/25]], [[243/160]], [[1024/675]]
| [[32/21]], [[38/25]], [[243/160]], [[1024/675]]
| ^5
| ^5
Line 336: Line 336:
|-
|-
| 33
| 33
| 747.17
| 747.2
| [[20/13]], [[192/125]], [[125/81]]
| [[20/13]], [[125/81]], [[192/125]]
| ^^5, vvm6
| ^^5, vvm6
| dup 5th, dudminor 6th
| dup 5th, dudminor 6th
Line 345: Line 345:
|-
|-
| 34
| 34
| 769.81
| 769.8
| [[14/9]], [[25/16]], ''[[11/7]]''
| ''[[11/7]]'', [[14/9]], [[25/16]]
| vm6
| vm6
| downminor 6th
| downminor 6th
Line 354: Line 354:
|-
|-
| 35
| 35
| 792.45
| 792.5
| [[19/12]], [[30/19]], [[128/81]]
| [[19/12]], [[30/19]], [[128/81]]
| m6
| m6
Line 363: Line 363:
|-
|-
| 36
| 36
| 815.09
| 815.1
| [[8/5]]
| [[8/5]]
| ^m6
| ^m6
Line 372: Line 372:
|-
|-
| 37
| 37
| 837.74
| 837.7
| [[13/8]], [[81/50]]
| [[13/8]], [[81/50]]
| ^^m6
| ^^m6
Line 381: Line 381:
|-
|-
| 38
| 38
| 860.38
| 860.4
| [[18/11]], [[400/243]]
| [[18/11]], [[400/243]]
| vvM6
| vvM6
Line 390: Line 390:
|-
|-
| 39
| 39
| 883.02
| 883.0
| [[5/3]]
| [[5/3]]
| vM6
| vM6
Line 399: Line 399:
|-
|-
| 40
| 40
| 905.66
| 905.7
| [[22/13]], [[27/16]], [[32/19]]
| [[22/13]], [[27/16]], [[32/19]]
| M6
| M6
Line 408: Line 408:
|-
|-
| 41
| 41
| 928.30
| 928.3
| [[12/7]]
| [[12/7]]
| ^M6
| ^M6
Line 417: Line 417:
|-
|-
| 42
| 42
| 950.94
| 950.9
| [[26/15]], [[125/72]], [[216/125]]
| [[26/15]], [[125/72]], [[216/125]]
| ^^M6, vvm7
| ^^M6, vvm7
Line 426: Line 426:
|-
|-
| 43
| 43
| 973.58
| 973.6
| [[7/4]]
| [[7/4]]
| vm7
| vm7
Line 435: Line 435:
|-
|-
| 44
| 44
| 996.23
| 996.2
| [[16/9]]
| [[16/9]]
| m7
| m7
Line 444: Line 444:
|-
|-
| 45
| 45
| 1018.87
| 1018.9
| [[9/5]]
| [[9/5]]
| ^m7
| ^m7
Line 453: Line 453:
|-
|-
| 46
| 46
| 1041.51
| 1041.5
| [[64/35]], [[11/6]], [[20/11]], [[729/400]]
| [[11/6]], [[20/11]], [[64/35]], [[729/400]]
| ^^m7
| ^^m7
| dupminor 7th
| dupminor 7th
Line 462: Line 462:
|-
|-
| 47
| 47
| 1064.15
| 1064.2
| [[13/7]], [[24/13]], [[50/27]]
| [[13/7]], [[24/13]], [[50/27]]
| vvM7
| vvM7
Line 471: Line 471:
|-
|-
| 48
| 48
| 1086.79
| 1086.8
| [[15/8]]
| [[15/8]]
| vM7
| vM7
Line 480: Line 480:
|-
|-
| 49
| 49
| 1109.43
| 1109.4
| [[19/10]], [[36/19]], [[40/21]], [[243/128]]
| [[19/10]], [[36/19]], [[40/21]], [[243/128]]
| M7
| M7
Line 489: Line 489:
|-
|-
| 50
| 50
| 1132.08
| 1132.1
| [[48/25]], [[27/14]], [[21/11]], [[52/27]], [[25/13]]
| ''[[21/11]]'', [[25/13]], [[27/14]], [[52/27]], [[48/25]]
| ^M7
| ^M7
| upmajor 7th
| upmajor 7th
Line 498: Line 498:
|-
|-
| 51
| 51
| 1154.72
| 1154.7
| [[96/49]], [[35/18]], [[64/33]], [[125/64]]
| [[35/18]], [[64/33]], [[96/49]], [[125/64]]
| ^^M7, vv8
| ^^M7, vv8
| dupmajor 7th, dud 8ve
| dupmajor 7th, dud 8ve
Line 507: Line 507:
|-
|-
| 52
| 52
| 1177.36
| 1177.4
| [[160/81]], [[63/32]], [[49/25]]
| ''[[49/25]]'', [[63/32]], [[160/81]]
| v8
| v8
| down 8ve
| down 8ve
Line 516: Line 516:
|-
|-
| 53
| 53
| 1200.00
| 1200.0
| [[2/1]]
| [[2/1]]
| P8
| P8
Line 532: Line 532:
! Quality
! Quality
! [[Kite's color notation|Color]]
! [[Kite's color notation|Color]]
! Monzo Format
! Monzo format
! Examples
! Examples
|-
|-
Line 581: Line 581:
|-
|-
! [[Kite's color notation|Color of the 3rd]]
! [[Kite's color notation|Color of the 3rd]]
! JI Chord
! JI chord
! Notes as Edosteps
! Notes as edosteps
! Notes of C Chord
! Notes of C chord
! Written Name
! Written name
! Spoken Name
! Spoken name
|-
|-
| zo
| zo
Line 629: Line 629:
| C upmajor or C up
| C upmajor or C up
|}
|}
For a more complete list, see [[Ups and downs notation #Chords and Chord Progressions]].
For a more complete list, see [[Ups and downs notation #Chords and chord progressions]].


== Notation ==
== Notation ==
Retrieved from "https://en.xen.wiki/w/53edo"