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51edo: Difference between revisions

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→Intervals: Add columns for additional ratios of 5 and 11 tending {flat/sharp}; move relevant ratios from main approximate ratios column to these; revert subgroup description to original specification.
Line 25: Line 25:
! [[Cent]]s
! [[Cent]]s
! Approximate ratios*
! Approximate ratios*
!Additional ratios of
5 and/or 11 tending
flat (51 patent val)
!Additional ratios of
5 and/or 11 tending
sharp (51ce val)
! colspan="3" | [[Ups and downs notation]]
! colspan="3" | [[Ups and downs notation]]
|-
|-
Line 30: Line 36:
| 0.0
| 0.0
| [[1/1]]
| [[1/1]]
|
|
| Perfect 1sn
| Perfect 1sn
| P1
| P1
Line 36: Line 44:
| 1
| 1
| 23.5
| 23.5
| ''[[49/48]]'', [[64/63]]
| [[64/63]], ''[[49/48]]''
|
|[[81/80]]
| Up 1sn
| Up 1sn
| ^1
| ^1
Line 44: Line 54:
| 47.1
| 47.1
| ''[[28/27]]''
| ''[[28/27]]''
|
|
| Downminor 2nd
| Downminor 2nd
| vm2
| vm2
Line 51: Line 63:
| 70.6
| 70.6
| [[27/26]]
| [[27/26]]
|
|
| Minor 2nd
| Minor 2nd
| m2
| m2
Line 58: Line 72:
| 94.1
| 94.1
|  
|  
|[[135/128]]
|
| Upminor 2nd
| Upminor 2nd
| ^m2
| ^m2
Line 65: Line 81:
| 117.6
| 117.6
| [[14/13]]
| [[14/13]]
|[[16/15]]
|
| Downmid 2nd
| Downmid 2nd
| v~2
| v~2
Line 72: Line 90:
| 141.2
| 141.2
| [[13/12]]
| [[13/12]]
|
|[[12/11]]
| Mid 2nd
| Mid 2nd
| ~2
| ~2
Line 78: Line 98:
| 7
| 7
| 164.7
| 164.7
| [[11/10]]
|
|[[11/10]]
|11/10
| Upmid 2nd
| Upmid 2nd
| ^~2
| ^~2
Line 86: Line 108:
| 188.2
| 188.2
|  
|  
|
|
| Downmajor 2nd
| Downmajor 2nd
| vM2
| vM2
Line 93: Line 117:
| 211.8
| 211.8
| [[9/8]]
| [[9/8]]
|
|
| Major 2nd
| Major 2nd
| M2
| M2
Line 100: Line 126:
| 235.3
| 235.3
| [[8/7]]
| [[8/7]]
|
|
| Upmajor 2nd
| Upmajor 2nd
| ^M2
| ^M2
Line 107: Line 135:
| 258.8
| 258.8
| [[7/6]]
| [[7/6]]
|
|
| Downminor 3rd
| Downminor 3rd
| vm3
| vm3
Line 114: Line 144:
| 282.4
| 282.4
| ''[[32/27]]''
| ''[[32/27]]''
|
|[[13/11]]
| Minor 3rd
| Minor 3rd
| m3
| m3
Line 121: Line 153:
| 305.9
| 305.9
|  
|  
|
|[[6/5]]
| Upminor 3rd
| Upminor 3rd
| ^m3
| ^m3
Line 127: Line 161:
| 14
| 14
| 329.4
| 329.4
| [[40/33]]
|
|[[40/33]]
|40/33
| Downmid 3rd
| Downmid 3rd
| v~3
| v~3
Line 135: Line 171:
| 352.9
| 352.9
| [[16/13]], [[39/32]]
| [[16/13]], [[39/32]]
|
|
| Mid 3rd
| Mid 3rd
| ~3
| ~3
Line 142: Line 180:
| 376.5
| 376.5
| [[26/21]]
| [[26/21]]
|[[5/4]]
|
| Upmid 3rd
| Upmid 3rd
| ^~3
| ^~3
Line 149: Line 189:
| 400.0
| 400.0
|  
|  
|
|''5/4''
| Downmajor 3rd
| Downmajor 3rd
| vM3
| vM3
Line 156: Line 198:
| 423.5
| 423.5
| ''[[81/64]]''
| ''[[81/64]]''
|
|
| Major 3rd
| Major 3rd
| M3
| M3
Line 163: Line 207:
| 447.1
| 447.1
| ''[[9/7]]''
| ''[[9/7]]''
|
|
| Upmajor 3rd
| Upmajor 3rd
| ^M3
| ^M3
Line 170: Line 216:
| 470.6
| 470.6
| [[21/16]]
| [[21/16]]
|
|
| Down 4th
| Down 4th
| v4
| v4
Line 177: Line 225:
| 494.1
| 494.1
| [[4/3]]
| [[4/3]]
|
|
| Perfect 4th
| Perfect 4th
| P4
| P4
Line 184: Line 234:
| 517.6
| 517.6
|  
|  
|
|
| Up 4th
| Up 4th
| ^4
| ^4
Line 190: Line 242:
| 23
| 23
| 541.2
| 541.2
| [[15/11]]
|
|[[11/8]], [[15/11]]
|15/11
| Downdim 5th
| Downdim 5th
| vd5
| vd5
Line 198: Line 252:
| 564.7
| 564.7
| [[18/13]]
| [[18/13]]
|
|''11/8''
| Dim 5th
| Dim 5th
| d5
| d5
Line 205: Line 261:
| 588.2
| 588.2
| [[39/28]]
| [[39/28]]
|
|
| Updim 5th
| Updim 5th
| ^d5
| ^d5
Line 212: Line 270:
| 611.8
| 611.8
| [[56/39]]
| [[56/39]]
|
|
| Downaug 4th
| Downaug 4th
| vA4
| vA4
Line 219: Line 279:
| 635.3
| 635.3
| [[13/9]]
| [[13/9]]
|
|''16/11''
| Aug 4th
| Aug 4th
| A4
| A4
Line 225: Line 287:
| 28
| 28
| 658.8
| 658.8
| [[22/15]]
|
|[[16/11]], [[22/15]]
|22/15
| Upaug 4th
| Upaug 4th
| ^A4
| ^A4
Line 233: Line 297:
| 682.4
| 682.4
|  
|  
|
|
| Down 5th
| Down 5th
| v5
| v5
Line 240: Line 306:
| 705.9
| 705.9
| [[3/2]]
| [[3/2]]
|
|
| Perfect 5th
| Perfect 5th
| P5
| P5
Line 247: Line 315:
| 729.4
| 729.4
| [[32/21]]
| [[32/21]]
|
|
| Up 5th
| Up 5th
| ^5
| ^5
Line 254: Line 324:
| 752.9
| 752.9
| ''[[14/9]]''
| ''[[14/9]]''
|
|
| Downminor 6th
| Downminor 6th
| vm6
| vm6
Line 261: Line 333:
| 776.5
| 776.5
| ''[[128/81]]''
| ''[[128/81]]''
|
|
| Minor 6th
| Minor 6th
| m6
| m6
Line 268: Line 342:
| 800.0
| 800.0
|  
|  
|
|''8/5''
| Upminor 6th
| Upminor 6th
| ^m6
| ^m6
Line 275: Line 351:
| 823.5
| 823.5
| [[21/13]]
| [[21/13]]
|[[8/5]]
|
| Downmid 6th
| Downmid 6th
| v~6
| v~6
Line 282: Line 360:
| 847.1
| 847.1
| [[13/8]], [[64/39]]
| [[13/8]], [[64/39]]
|
|
| Mid 6th
| Mid 6th
| ~6
| ~6
Line 288: Line 368:
| 37
| 37
| 870.6
| 870.6
| [[33/20]]
|
|[[33/20]]
|33/20
| Upmid 6th
| Upmid 6th
| ^~6
| ^~6
Line 296: Line 378:
| 894.1
| 894.1
|  
|  
|
|[[5/3]]
| Downmajor 6th
| Downmajor 6th
| vM6
| vM6
Line 303: Line 387:
| 917.6
| 917.6
| ''[[27/16]]''
| ''[[27/16]]''
|
|[[22/13]]
| Major 6th
| Major 6th
| M6
| M6
Line 310: Line 396:
| 941.2
| 941.2
| [[12/7]]
| [[12/7]]
|
|
| Upmajor 6th
| Upmajor 6th
| ^M6
| ^M6
Line 317: Line 405:
| 964.7
| 964.7
| [[7/4]]
| [[7/4]]
|
|
| Downminor 7th
| Downminor 7th
| vm7
| vm7
Line 324: Line 414:
| 988.2
| 988.2
| [[16/9]]
| [[16/9]]
|
|
| Minor 7th
| Minor 7th
| m7
| m7
Line 331: Line 423:
| 1011.8
| 1011.8
|  
|  
|
|
| Upminor 7th
| Upminor 7th
| ^m7
| ^m7
Line 337: Line 431:
| 44
| 44
| 1035.3
| 1035.3
| [[20/11]]
|
|[[20/11]]
|20/11
| Downmid 7th
| Downmid 7th
| v~7
| v~7
Line 345: Line 441:
| 1058.8
| 1058.8
| [[24/13]]
| [[24/13]]
|
|[[11/6]]
| Mid 7th
| Mid 7th
| ~7
| ~7
Line 352: Line 450:
| 1082.4
| 1082.4
| [[13/7]]
| [[13/7]]
|[[15/8]]
|
| Upmid 7th
| Upmid 7th
| ^~7
| ^~7
Line 359: Line 459:
| 1105.9
| 1105.9
|  
|  
|[[256/135]]
|
| Downmajor 7th
| Downmajor 7th
| vM7
| vM7
Line 366: Line 468:
| 1129.4
| 1129.4
| [[52/27]]
| [[52/27]]
|
|
| Major 7th
| Major 7th
| M7
| M7
Line 373: Line 477:
| 1152.9
| 1152.9
| ''[[27/14]]''
| ''[[27/14]]''
|
|
| Upmajor 7th
| Upmajor 7th
| ^M7
| ^M7
Line 380: Line 486:
| 1176.5
| 1176.5
| [[63/32]], ''[[96/49]]''
| [[63/32]], ''[[96/49]]''
|
|[[160/81]]
| Down 8ve
| Down 8ve
| v8
| v8
Line 387: Line 495:
| 1200.0
| 1200.0
| [[2/1]]
| [[2/1]]
|
|
| Perfect 8ve
| Perfect 8ve
| P8
| P8
| D
| D
|}
|}
<nowiki>*</nowiki> As a 2.3.7.13-subgroup temperament, with the addition of selected intervals of 5 and 11; inconsistent intervals in italic.
<nowiki>*</nowiki> As a 2.3.7.13-subgroup temperament; inconsistent intervals in italic.


== Notation ==
== Notation ==
Retrieved from "https://en.xen.wiki/w/51edo"