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38edo: Difference between revisions

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→Intervals: split ratios by subgroup
Line 19: Line 19:
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
|-
! rowspan="2" | Step
! rowspan="3" | Step
! rowspan="2" | Cents
! rowspan="3" | Cents
! colspan="2" | Approximated ratios
! colspan="3" | Approximated ratios
! rowspan="2" colspan="3" | [[Ups and downs notation]]*<br>([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and vvd2)
! rowspan="3" colspan="3" | [[Ups and downs notation]]*<br>([[Enharmonic unisons in ups and downs notation|EUs]]: vvA1 and vvd2)
|-
|-
! 19-odd-limit ratios, patent val
! rowspan="2" | Ratios of the <br>2.3.5.11.17.19 subgroup
! 19-odd-limit ratios,<br>in 38df val
! colspan="2" | Ratios of 7 and 13
|-
! Patent val
! 38df val
|-
|-
| 0
| 0
| 0.0
| 0.0
| [[1/1]]
| [[1/1]]
| [[1/1]]
|  
|
| Perfect 1sn
| Perfect 1sn
| P1
| P1
Line 37: Line 41:
| 1
| 1
| 31.6
| 31.6
|
|
|
|  
|  
| Up 1sn
| Up 1sn
| ^1
| ^1
Line 45: Line 50:
| 2
| 2
| 63.2
| 63.2
|
|
|
|  
|  
| Aug 1sn, dim 2nd
| Aug 1sn, dim 2nd
| A1, d2
| A1, d2
Line 53: Line 59:
| 3
| 3
| 94.7
| 94.7
| 20/19, 19/18, 18/17, 17/16
| [[20/19]], [[19/18]], [[18/17]], [[17/16]]
| [[20/19]], [[19/18]], [[18/17]], [[17/16]]
| ''[[15/14]]''
|
| Upaug 1sn, downminor 2nd
| Upaug 1sn, downminor 2nd
| ^A1, vm2
| ^A1, vm2
Line 61: Line 68:
| 4
| 4
| 126.3
| 126.3
| 16/15, 15/14, 14/13
| [[16/15]]
| [[16/15]], [[15/14]], [[14/13]], [[13/12]]
| [[14/13]]
| [[15/14]], [[14/13]], [[13/12]]
| Minor 2nd
| Minor 2nd
| m2
| m2
Line 69: Line 77:
| 5
| 5
| 157.9
| 157.9
| 13/12, 12/11, 11/10
| [[12/11]], [[11/10]]
| [[12/11]], [[11/10]]
| ''[[13/12]]''
|
| Mid 2nd
| Mid 2nd
| ~2
| ~2
Line 77: Line 86:
| 6
| 6
| 189.5
| 189.5
| 10/9, 19/17, 9/8
| [[10/9]], [[19/17]], [[9/8]]
| [[10/9]], [[19/17]], [[9/8]]
|
|
| Major 2nd
| Major 2nd
| M2
| M2
Line 85: Line 95:
| 7
| 7
| 221.1
| 221.1
| 17/15, 8/7, 15/13
| [[17/15]]
| [[17/15]]
| [[8/7]], ''[[15/13]]''
|
| Upmajor 2nd
| Upmajor 2nd
| ^M2
| ^M2
Line 93: Line 104:
| 8
| 8
| 252.6
| 252.6
| 22/19
| [[22/19]]
| [[8/7]], [[15/13]], [[22/19]], [[7/6]]
|  
| ''[[8/7]]'', [[15/13]], [[7/6]]
| Aug 2nd, Dim 3rd
| Aug 2nd, Dim 3rd
| A2, d3
| A2, d3
Line 101: Line 113:
| 9
| 9
| 284.2
| 284.2
| 7/6, 20/17, 19/16
| [[20/17]], [[19/16]]
| [[20/17]], [[13/11]], [[19/16]]
| ''[[7/6]]''
| [[13/11]]
| Downminor 3rd
| Downminor 3rd
| vm3
| vm3
Line 109: Line 122:
| 10
| 10
| 315.8
| 315.8
| 13/11, 6/5, 17/14
| [[6/5]]
| [[6/5]]
| ''[[13/11]]'', ''[[17/14]]''
|
| Minor 3rd
| Minor 3rd
| m3
| m3
Line 117: Line 131:
| 11
| 11
| 347.4
| 347.4
| 16/13, 11/9
| [[11/9]]
| [[17/14]], [[11/9]]
| [[16/13]]
| [[17/14]]
| Mid 3rd
| Mid 3rd
| ~3
| ~3
Line 125: Line 140:
| 12
| 12
| 378.9
| 378.9
| 5/4
| [[5/4]]
| [[16/13]], [[5/4]]
|  
| ''[[16/13]]''
| Major 3rd
| Major 3rd
| M3
| M3
Line 133: Line 149:
| 13
| 13
| 410.5
| 410.5
| 9/7, 24/19, 19/15
| [[24/19]], [[19/15]]
| [[24/19]], [[19/15]], [[14/11]]
| ''[[9/7]]''
| [[14/11]]
| Upmajor 3rd, Downdim 4th
| Upmajor 3rd, Downdim 4th
| ^M3, vd4
| ^M3, vd4
Line 141: Line 158:
| 14
| 14
| 442.1
| 442.1
| 14/11, 22/17, 17/13
| [[22/17]]
| [[9/7]], [[22/17]], [[13/10]]
| ''[[14/11]]'', ''[[17/13]]''
| [[9/7]], [[13/10]]
| Aug 3rd, dim 4th
| Aug 3rd, dim 4th
| A3, d4
| A3, d4
Line 149: Line 167:
| 15
| 15
| 473.7
| 473.7
| 13/10
|  
| ''[[13/10]]''
| [[17/13]]
| [[17/13]]
| Down 4th
| Down 4th
Line 157: Line 176:
| 16
| 16
| 505.3
| 505.3
| 4/3, 19/14
| [[4/3]]
| [[4/3]]
| ''[[19/14]]''
|
| Perfect 4th
| Perfect 4th
| P4
| P4
Line 165: Line 185:
| 17
| 17
| 536.8
| 536.8
| 15/11, 11/8, 18/13
| [[15/11]], [[11/8]]
| [[19/14]], [[15/11]], [[26/19]], [[11/8]]
| ''[[18/13]]''
| [[19/14]], [[26/19]]
| Up 4th
| Up 4th
| ^4
| ^4
Line 173: Line 194:
| 18
| 18
| 568.4
| 568.4
| 26/19
|  
| ''[[26/19]]''
| [[18/13]], [[7/5]]
| [[18/13]], [[7/5]]
| Aug 4th
| Aug 4th
Line 181: Line 203:
| 19
| 19
| 600.0
| 600.0
| 7/5, 24/17, 17/12, 10/7
| [[24/17]], [[17/12]]
| [[24/17]], [[17/12]]
| [[7/5]], [[10/7]]
|
| Upaug 4th, downdim 5th
| Upaug 4th, downdim 5th
| ^A4, vd5
| ^A4, vd5
Line 189: Line 212:
| 20
| 20
| 631.6
| 631.6
| 19/13
|  
| ''[[19/13]]''
| [[10/7]], [[13/9]]
| [[10/7]], [[13/9]]
| Dim 5th
| Dim 5th
Line 197: Line 221:
| 21
| 21
| 663.2
| 663.2
| 16/11, 22/15, 13/9
| [[16/11]], [[22/15]]
| [[16/11]], [[19/13]], [[22/15]], [[28/19]]
| ''[[13/9]]''
| [[19/13]], [[28/19]]
| Down 5th
| Down 5th
| v5
| v5
Line 205: Line 230:
| 22
| 22
| 694.7
| 694.7
| 3/2, 28/19
| [[3/2]]
| [[3/2]]
| ''[[28/19]]''
|
| Perfect 5th
| Perfect 5th
| P5
| P5
Line 213: Line 239:
| 23
| 23
| 726.3
| 726.3
| 20/13
|  
| ''[[20/13]]''
| [[26/17]]
| [[26/17]]
| Up 5th
| Up 5th
Line 221: Line 248:
| 24
| 24
| 757.9
| 757.9
| 17/11, 11/7, 26/17
| [[17/11]]
| [[20/13]], [[17/11]], [[14/9]]
| ''[[26/17]]'', ''[[11/7]]''
|
| Aug 5th, dim 6th
| Aug 5th, dim 6th
| A5, d6
| A5, d6
Line 229: Line 257:
| 25
| 25
| 789.5
| 789.5
| 14/9, 19/12, 30/19
| [[30/19]], [[19/12]]
| [[11/7]], [[30/19]], [[19/12]]
| ''[[14/9]]''
| [[11/7]]
| Upaug 5th, downminor 6th
| Upaug 5th, downminor 6th
| ^A5, vm6
| ^A5, vm6
Line 237: Line 266:
| 26
| 26
| 821.1
| 821.1
| 8/5
| [[8/5]]
| [[8/5]], [[13/8]]
|
| ''[[13/8]]''
| Minor 6th
| Minor 6th
| m6
| m6
Line 245: Line 275:
| 27
| 27
| 852.6
| 852.6
| 18/11, 13/8
| [[18/11]]
| [[18/11]], [[28/17]]
| [[13/8]]
| [[28/17]]
| Mid 6th
| Mid 6th
| ~6
| ~6
Line 253: Line 284:
| 28
| 28
| 884.2
| 884.2
| 22/13, 5/3, 28/17
| [[5/3]]
| [[5/3]]
| ''[[28/17]]'', ''[[22/13]]''
|
| Major 6th
| Major 6th
| M6
| M6
Line 261: Line 293:
| 29
| 29
| 915.8
| 915.8
| 32/19, 17/10, 12/7
| [[32/19]], [[17/10]]
| [[32/19]], [[22/13]], [[17/10]]
|
|
| Upmajor 6th
| Upmajor 6th
| ^M6
| ^M6
Line 269: Line 302:
| 30
| 30
| 947.4
| 947.4
| 19/11
| [[19/11]]
| [[12/7]], [[19/11]], [[26/15]], [[7/4]]
|
| [[12/7]], [[26/15]], ''[[7/4]]''
| Aug 6th, dim 7th
| Aug 6th, dim 7th
| A6, d7
| A6, d7
Line 277: Line 311:
| 31
| 31
| 978.9
| 978.9
| 30/17, 7/4, 26/15
| [[30/17]]
| [[30/17]]
| ''[[26/15]]'', [[7/4]]
|
| Downminor 7th
| Downminor 7th
| vm7
| vm7
Line 285: Line 320:
| 32
| 32
| 1010.5
| 1010.5
| 9/5, 16/9, 34/19
| [[16/9]], [[34/19]], [[9/5]]
| [[16/9]], [[34/19]], [[9/5]]
|
|
| Minor 7th
| Minor 7th
| m7
| m7
Line 293: Line 329:
| 33
| 33
| 1042.1
| 1042.1
| 11/6, 20/11, 24/13
| [[20/11]], [[11/6]]
| [[20/11]], [[11/6]]
| ''[[24/13]]''
|
| Mid 7th
| Mid 7th
| ~7
| ~7
Line 301: Line 338:
| 34
| 34
| 1073.7
| 1073.7
| 13/7, 15/8, 28/25
| [[15/8]]
| [[24/13]], [[13/7]], [[28/15]], [[15/8]]
| [[13/7]]
| [[24/13]], [[13/7]], [[28/15]]
| Major 7th
| Major 7th
| M7
| M7
Line 309: Line 347:
| 35
| 35
| 1105.3
| 1105.3
| 32/17, 17/9, 36/19, 19/10
| [[32/17]], [[17/9]], [[36/19]], [[19/10]]
| [[32/17]], [[17/9]], [[36/19]], [[19/10]]
| ''[[28/15]]''
|
| Upmajor 7th, Downdim 8ve
| Upmajor 7th, Downdim 8ve
| ^M7, vd8
| ^M7, vd8
Line 317: Line 356:
| 36
| 36
| 1136.8
| 1136.8
|
|
|
|  
|  
| Aug 7th, dim 8ve
| Aug 7th, dim 8ve
| A7, d8
| A7, d8
Line 327: Line 367:
|
|
|
|
|
| Down 8ve
| Down 8ve
| v8
| v8
Line 334: Line 375:
| 1200.0
| 1200.0
| [[2/1]]
| [[2/1]]
| [[2/1]]
|  
|
| Perfect 8ve
| Perfect 8ve
| P8
| P8
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