Xenharmonic Wiki

45edo: Difference between revisions

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→Regular temperament properties: + data and table of rank-2 temps
→Intervals: convert to an ordinary interval table, with ratios approximated thru a val
Line 19: Line 19:


== Intervals ==
== Intervals ==
{| class="wikitable mw-collapsible mw-collapsed right-all center-3 left-6 center-7"
{| class="wikitable center-1 right-2 center-5 center-6"
|-
|-
! rowspan="2" | Step #
! #
! ET
! colspan="2" | Just (JI)
! rowspan="2" | Error<br>(ET−JI)
! colspan="4" rowspan="2" | [[Ups and downs notation]]
|-
! Cents
! Interval
! Cents
! Cents
! Approximate ratios*
! colspan="4" | [[Ups and downs notation]]
|-
|-
| 0
| 0
| 0.000
| 0.0
| [[1/1]]
| [[1/1]]
| 0.000
| 0.000
| Perfect Unison
| Perfect Unison
| P1
| P1
Line 41: Line 34:
|-
|-
| 1
| 1
| 26.666
| 26.7
| [[65/64]]
| [[49/48]], [[50/49]]
| 26.841
| -0.174
| Up unison
| Up unison
| ^1
| ^1
Line 50: Line 41:
|-
|-
| 2
| 2
| 53.333
| 53.3
| [[33/32]]
| [[36/35]], ''[[25/24]]'', ''[[64/63]]''
| 53.273
| 0.060
| Augmented Unison
| Augmented Unison
| A1
| A1
Line 59: Line 48:
|-
|-
| 3
| 3
| 80.000
| 80.0
| [[22/21]]
| [[21/20]]
| 80.537
| -0.537
| Diminished 2nd
| Diminished 2nd
| d2
| d2
Line 68: Line 55:
|-
|-
| 4
| 4
| 106.666
| 106.7
| [[17/16]]
| [[15/14]]
| 104.955
| 1.711
| Downminor 2nd
| Downminor 2nd
|vm2
| vm2
| vEb
| vEb
|-
|-
| 5
| 5
| 133.333
| 133.3
| [[27/25]]
| [[13/12]], [[14/13]], ''[[16/15]]''
| 133.238
| 0.095
| Minor 2nd
| Minor 2nd
| m2
| m2
Line 86: Line 69:
|-
|-
| 6
| 6
| 160.000
| 160.0
| [[11/10]]
| [[54/49]]
| 165.004
| -5.004
| Mid 2nd
| Mid 2nd
| ~2
| ~2
Line 95: Line 76:
|-
|-
| 7
| 7
| 186.666
| 186.7
| [[10/9]]
| [[10/9]], ''[[9/8]]''
| 182.404
| 4.262
| Major 2nd
| Major 2nd
| M2
| M2
Line 104: Line 83:
|-
|-
| 8
| 8
| 213.333
| 213.3
| [[9/8]]
|  
| 203.910
| 9.423
| Upmajor 2nd
| Upmajor 2nd
| ^M2
| ^M2
Line 113: Line 90:
|-
|-
| 9
| 9
| 240.000
| 240.0
| [[8/7]]
| [[8/7]], [[15/13]]
| 231.174
| 8.826
| Augmented 2nd
| Augmented 2nd
| A2
| A2
Line 122: Line 97:
|-
|-
| 10
| 10
| 266.666
| 266.7
| [[7/6]]
| [[7/6]]
| 266.871
| -0.205
| Diminished 3rd
| Diminished 3rd
| d3
| d3
Line 131: Line 104:
|-
|-
| 11
| 11
| 293.333
| 293.3
| [[32/27]]
| [[25/21]]
| 294.135
| -0.802
| Downminor 3rd
| Downminor 3rd
| vm3
| vm3
Line 140: Line 111:
|-
|-
| 12
| 12
| 320.000
| 320.0
| [[6/5]]
| [[6/5]]
| 315.641
| 4.359
| Minor 3rd
| Minor 3rd
| m3
| m3
Line 149: Line 118:
|-
|-
| 13
| 13
| 346.666
| 346.7
| [[11/9]]
| [[49/40]], [[60/49]]
| 347.408
| -0.741
| Mid 3rd
| Mid 3rd
| ~3
| ~3
Line 158: Line 125:
|-
|-
| 14
| 14
| 373.333
| 373.3
| [[5/4]]
| [[5/4]], [[26/21]], ''[[16/13]]''
| 386.314
| -12.980
| Major 3rd
| Major 3rd
| M3
| M3
Line 167: Line 132:
|-
|-
| 15
| 15
| 400.000
| 400.0
| [[63/50]]
| [[63/50]]
| 400.108
| -0.108
| Upmajor 3rd
| Upmajor 3rd
| ^M3
| ^M3
Line 176: Line 139:
|-
|-
| 16
| 16
| 426.666
| 426.7
| [[9/7]]
| [[9/7]]
| 435.084
| -8.418
| Augmented 3rd
| Augmented 3rd
| A3
| A3
Line 185: Line 146:
|-
|-
| 17
| 17
| 453.333
| 453.3
| [[13/10]]
| [[13/10]], ''[[21/16]]''
| 454.294
| -0.961
| Diminished 4th
| Diminished 4th
| d4
| d4
Line 194: Line 153:
|-
|-
| 18
| 18
| 480.000
| 480.0
| [[21/16]]
| ''[[64/49]]''
| 470.781
| 9.219
| Down 4th
| Down 4th
| v4
| v4
Line 203: Line 160:
|-
|-
| 19
| 19
| 506.666
| 506.7
| [[4/3]]
| [[4/3]]
| 498.045
| 8.622
| Perfect 4th
| Perfect 4th
| P4
| P4
Line 212: Line 167:
|-
|-
| 20
| 20
| 533.333
| 533.3
| [[49/36]]
| [[49/36]]
| 533.742
| -0.409
| Up 4th or Mid 4th
| Up 4th or Mid 4th
| ^4, ~4
| ^4, ~4
Line 221: Line 174:
|-
|-
| 21
| 21
| 560.000
| 560.0
| [[18/13]]
| [[18/13]]
| 563.382
| -3.382
| Augmented 4th
| Augmented 4th
| A4
| A4
Line 230: Line 181:
|-
|-
| 22
| 22
| 586.666
| 586.7
| [[7/5]]
| [[7/5]]
| 582.512
| 4.155
| Upaugmented 4th
| Upaugmented 4th
| ^A4
| ^A4
Line 239: Line 188:
|-
|-
| 23
| 23
| 613.333
| 613.3
| [[10/7]]
| [[10/7]]
| 617.488
| -4.155
| Downdiminshed 5th
| Downdiminshed 5th
| vd5
| vd5
Line 248: Line 195:
|-
|-
| 24
| 24
| 640.000
| 640.0
| [[13/9]]
| [[13/9]]
| 636.618
| 3.382
| Diminished 5th
| Diminished 5th
| d5
| d5
Line 257: Line 202:
|-
|-
| 25
| 25
| 666.666
| 666.7
| [[72/49]]
| [[72/49]]
| 666.258
| 0.409
| Down 5th or Mid 5th
| Down 5th or Mid 5th
| v5, ~5
| v5, ~5
Line 266: Line 209:
|-
|-
| 26
| 26
| 693.333
| 693.3
| [[3/2]]
| [[3/2]]
| 701.955
| -8.622
| Perfect 5th
| Perfect 5th
| P5
| P5
Line 275: Line 216:
|-
|-
| 27
| 27
| 720.000
| 720.0
| [[32/21]]
| ''[[49/32]]''
| 729.219
| -9.219
| Up 5th
| Up 5th
| ^5
| ^5
Line 284: Line 223:
|-
|-
| 28
| 28
| 746.666
| 746.7
| [[20/13]]
| [[20/13]], ''[[32/21]]''
| 745.786
| 0.961
| Augmented 5th
| Augmented 5th
| A5
| A5
Line 293: Line 230:
|-
|-
| 29
| 29
| 773.333
| 773.3
| [[14/9]]
| [[14/9]]
| 764.916
| 8.418
| Diminished 6th
| Diminished 6th
| d6
| d6
Line 302: Line 237:
|-
|-
| 30
| 30
| 800.000
| 800.0
| [[100/63]]
| [[100/63]]
| 799.892
| 0.108
| Downminor 6th
| Downminor 6th
| vm6
| vm6
Line 311: Line 244:
|-
|-
| 31
| 31
| 826.666
| 826.7
| [[8/5]]
| [[8/5]], [[21/13]], ''[[13/8]]''
| 813.686
| 12.980
| Minor 6th
| Minor 6th
| m6
| m6
Line 320: Line 251:
|-
|-
| 32
| 32
| 853.333
| 853.3
| [[18/11]]
| [[49/30]], [[80/49]]
| 852.592
| 0.741
| Mid 6th
| Mid 6th
| ~6
| ~6
Line 329: Line 258:
|-
|-
| 33
| 33
| 880.000
| 880.0
| [[5/3]]
| [[5/3]]
| 884.359
| -4.359
| Major 6th
| Major 6th
| M6
| M6
Line 338: Line 265:
|-
|-
| 34
| 34
| 906.666
| 906.7
| [[27/16]]
| [[42/25]]
| 905.865
| 0.802
| Upmajor 6th
| Upmajor 6th
| ^M6
| ^M6
Line 347: Line 272:
|-
|-
| 35
| 35
| 933.333
| 933.3
| [[12/7]]
| [[12/7]]
| 933.129
| 0.205
| Augmented 6th
| Augmented 6th
| A6
| A6
Line 356: Line 279:
|-
|-
| 36
| 36
| 960.000
| 960.0
| [[7/4]]
| [[7/4]], [[26/15]]
| 968.826
| -8.826
| Diminished 7th
| Diminished 7th
| d7
| d7
Line 365: Line 286:
|-
|-
| 37
| 37
| 986.666
| 986.7
| [[16/9]]
|  
| 996.089
| -9.423
| Downminor 7th
| Downminor 7th
| vm7
| vm7
Line 374: Line 293:
|-
|-
| 38
| 38
| 1013.333
| 1013.3
| [[9/5]]
| [[9/5]], ''[[16/9]]''
| 1017.596
| -4.262
| Minor 7th
| Minor 7th
| m7
| m7
Line 383: Line 300:
|-
|-
| 39
| 39
| 1040.000
| 1040.0
| [[20/11]]
| [[49/27]]
| 1034.996
| 5.004
| Mid 7th
| Mid 7th
| ~7
| ~7
Line 392: Line 307:
|-
|-
| 40
| 40
| 1066.666
| 1066.7
| [[50/27]]
| [[13/7]], [[24/13]], ''[[15/8]]''
| 1066.762
| -0.095
| Major 7th
| Major 7th
| M7
| M7
Line 401: Line 314:
|-
|-
| 41
| 41
| 1093.333
| 1093.3
| [[32/17]]
| [[28/15]]
| 1095.044
| -1.711
| Upmajor 7th
| Upmajor 7th
| ^M7
| ^M7
Line 410: Line 321:
|-
|-
| 42
| 42
| 1120.000
| 1120.0
| [[21/11]]
| [[40/21]]
| 1119.463
| 0.537
| Augmented 7th
| Augmented 7th
| A7
| A7
Line 419: Line 328:
|-
|-
| 43
| 43
| 1146.666
| 1146.7
| [[64/33]]
| [[35/18]], ''[[48/25]]'', ''[[63/32]]''
| 1146.727
| -0.060
| Diminished 8ve
| Diminished 8ve
| d8
| d8
Line 428: Line 335:
|-
|-
| 44
| 44
| 1173.333
| 1173.3
| [[128/65]]
| [[49/25]], [[96/49]]
| 1173.158
| 0.174
| Down 8ve
| Down 8ve
| v8
| v8
Line 437: Line 342:
|-
|-
| 45
| 45
| 1200.000
| 1200.0
| [[2/1]]
| [[2/1]]
| 1200.000
| 0.000
| Perfect Octave
| Perfect Octave
| P8
| P8
| D
| D
|}
|}
<nowiki/>* As a 2.3.5.7.13-subgroup temperament, using the 45f val


== Notation ==
== Notation ==
Retrieved from "https://en.xen.wiki/w/45edo"