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Würschmidt: Difference between revisions

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In the below, octave-reduced harmonics 1–33 are indicated in '''bold'''. All intervals are in the 165-[[odd limit]].
In the below, octave-reduced harmonics 1–33 are indicated in '''bold'''. All intervals are in the 165-[[odd limit]].


{| class="wikitable center-all right-2"
{| class="wikitable center-1 right-2"
|-
|-
! rowspan="2" | # !! rowspan="2" | Cents* !! colspan="2" | Approximate ratios
! rowspan="2" | # !! rowspan="2" | Cents* !! colspan="2" | Approximate ratios
|-
|-
! 2.3.5.23 subgroup !! Add-11 extension
! 2.3.5.23 subgroup !! Add-11 extension
|-
|-
| 0 || 0.00 || '''1/1''' ||
| 0 || 0.0 || '''1/1''' ||
|-
|-
| 1 || 387.652 || '''5/4''', 144/115 || 69/55
| 1 || 387.7 || '''5/4''', 144/115 || 69/55
|-
|-
| 2 || 775.304 || '''25/16''', 36/23 || 69/44
| 2 || 775.3 || '''25/16''', 36/23 || 69/44
|-
|-
| 3 || 1162.956 || 45/23, 125/64 || 88/45, 108/55
| 3 || 1163.0 || 45/23, 125/64 || 88/45, 108/55
|-
|-
| 4 || 350.608 || 92/75 || 11/9, 27/22
| 4 || 350.6 || 92/75 || 11/9, 27/22
|-
|-
| 5 || 738.260 || 23/15, 192/125 || 55/36, 135/88
| 5 || 738.3 || 23/15, 192/125 || 55/36, 135/88
|-
|-
| 6 || 1125.912 || 23/12, 48/25 || 44/23
| 6 || 1125.9 || 23/12, 48/25 || 44/23
|-
|-
| 7 || 313.564 || 6/5, 115/96 || 55/46
| 7 || 313.6 || 6/5, 115/96 || 55/46
|-
|-
| 8 || 701.216 || '''3/2''' || 121/81
| 8 || 701.2 || '''3/2''' || 121/81
|-
|-
| 9 || 1088.868 || '''15/8''', 216/115 ||  
| 9 || 1088.9 || '''15/8''', 216/115 ||  
|-
|-
| 10 || 276.520 || 27/23, 75/64 || 88/75
| 10 || 276.5 || 27/23, 75/64 || 88/75
|-
|-
| 11 || 664.172 || 184/125, 135/92 || 22/15, 81/55
| 11 || 664.2 || 184/125, 135/92 || 22/15, 81/55
|-
|-
| 12 || 1051.824 || 46/25 || 11/6, 81/44
| 12 || 1051.8 || 46/25 || 11/6, 81/44
|-
|-
| 13 || 239.476 || 23/20, 144/125 || 55/48, 132/115
| 13 || 239.5 || 23/20, 144/125 || 55/48, 132/115
|-
|-
| 14 || 627.128 || '''23/16''', 36/25 || 33/23
| 14 || 627.1 || '''23/16''', 36/25 || 33/23
|-
|-
| 15 || 1014.780 || 9/5, 115/64 || 165/92, 242/135
| 15 || 1014.8 || 9/5, 115/64 || 165/92, 242/135
|-
|-
| 16 || 202.432 || '''9/8''' || 121/108
| 16 || 202.4 || '''9/8''' || 121/108
|-
|-
| 17 || 590.084 || 45/32, 162/115 ||  
| 17 || 590.1 || 45/32, 162/115 ||  
|-
|-
| 18 || 977.736 || 81/46 || 44/25
| 18 || 977.7 || 81/46 || 44/25
|-
|-
| 19 || 165.388 || 138/125 || 11/10
| 19 || 165.4 || 138/125 || 11/10
|-
|-
| 20 || 553.040 || 69/50 || '''11/8'''
| 20 || 553.0 || 69/50 || '''11/8'''
|-
|-
| 21 || 940.692 || 69/40, 216/125 || 55/32
| 21 || 940.7 || 69/40, 216/125 || 55/32
|-
|-
| 22 || 128.344 || 27/25, 69/64 || 99/92
| 22 || 128.3 || 27/25, 69/64 || 99/92
|-
|-
| 23 || 515.996 || 27/20 ||  
| 23 || 516.0 || 27/20 ||  
|-
|-
| 24 || 903.648 || '''27/16''' ||  
| 24 || 903.6 || '''27/16''' ||  
|-
|-
| 25 || 91.300 || 135/128 || 132/125
| 25 || 91.3 || 135/128 || 132/125
|-
|-
| 26 || 478.952 || || 33/25
| 26 || 479.0 || || 33/25
|-
|-
| 27 || 866.604 || 207/125 || 33/20
| 27 || 866.6 || 207/125 || 33/20
|-
|-
| 28 || 54.256 ||  || '''33/32'''
| 28 || 54.3 ||  || '''33/32'''
|-
|-
| 29 || 441.908 || 162/125 || 165/128
| 29 || 441.9 || 162/125 || 165/128
|-
|-
| 30 || 829.560 || 81/50 || 121/75
| 30 || 829.6 || 81/50 || 121/75
|-
|-
| 31 || 17.212 || 81/80 || 121/120
| 31 || 17.2 || 81/80 || 121/120
|}
|}
<nowiki />* In 5-limit [[CTE]] tuning
<nowiki/>* In 5-limit [[CTE]] tuning


== Tunings ==
== Tunings ==
Retrieved from "https://en.xen.wiki/w/Würschmidt"