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Meantone family: Difference between revisions

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Phasing out wedgies
Line 18: Line 18:


: mapping generators: ~2, ~3
: mapping generators: ~2, ~3
{{Multival|legend=1| 1 4 4 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 93: Line 91:


{{Mapping|legend=1| 1 0 -4 -13 | 0 1 4 10 }}
{{Mapping|legend=1| 1 0 -4 -13 | 0 1 4 10 }}
{{Multival|legend=1| 1 4 10 4 13 12 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 129: Line 125:


Mapping: {{mapping| 1 0 -4 -13 -25 | 0 1 4 10 18 }}
Mapping: {{mapping| 1 0 -4 -13 -25 | 0 1 4 10 18 }}
Wedgie: {{multival| 1 4 10 18 4 13 25 12 28 16 }}


Optimal tunings:  
Optimal tunings:  
Line 541: Line 535:


: mapping generator: ~2, ~3
: mapping generator: ~2, ~3
{{Multival|legend=1| 1 4 10 -13 4 13 -24 12 -44 -71 }}


Optimal tunings:  
Optimal tunings:  
Line 573: Line 565:


Mapping: {{mapping| 1 0 -4 -13 24 -20 | 0 1 4 10 -13 15 }}
Mapping: {{mapping| 1 0 -4 -13 24 -20 | 0 1 4 10 -13 15 }}
Wedgie: {{multival| 1 4 10 -13 15 4 13 -24 20 12 -44 20 -71 5 100 }}


Optimal tunings:  
Optimal tunings:  
Line 658: Line 648:


Mapping: {{mapping| 1 0 -4 -13 24 10 | 0 1 4 10 -13 -4 }}
Mapping: {{mapping| 1 0 -4 -13 24 10 | 0 1 4 10 -13 -4 }}
{{Multival|legend=1| 1 4 10 -13 -4 4 13 -24 -10 12 -44 -24 -71 -48 34 }}


Optimal tunings:  
Optimal tunings:  
Line 741: Line 729:


Mapping: {{mapping| 1 0 -4 -13 -6 | 0 1 4 10 6 }}
Mapping: {{mapping| 1 0 -4 -13 -6 | 0 1 4 10 6 }}
{{Multival|legend=1| 1 4 10 6 4 13 6 12 0 -18 }}


Optimal tunings:  
Optimal tunings:  
Line 762: Line 748:


Mapping: {{mapping| 1 0 -4 -13 -6 -20 | 0 1 4 10 6 15 }}
Mapping: {{mapping| 1 0 -4 -13 -6 -20 | 0 1 4 10 6 15 }}
{{Multival|legend=1| 1 4 10 6 15 4 13 6 20 12 0 20 -18 5 30 }}


Optimal tunings:  
Optimal tunings:  
Line 1,106: Line 1,090:


{{Mapping|legend=1| 1 0 -4 17 | 0 1 4 -9 }}
{{Mapping|legend=1| 1 0 -4 17 | 0 1 4 -9 }}
{{Multival|legend=1| 1 4 -9 4 -17 -32 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 1,226: Line 1,208:


{{Mapping|legend=1| 1 0 -4 6 | 0 1 4 -2 }}
{{Mapping|legend=1| 1 0 -4 6 | 0 1 4 -2 }}
{{Multival|legend=1| 1 4 -2 4 -6 -16 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 1,470: Line 1,450:


{{Mapping|legend=1| 1 0 -4 -2 | 0 1 4 3 }}
{{Mapping|legend=1| 1 0 -4 -2 | 0 1 4 3 }}
{{Multival|legend=1| 1 4 3 4 2 -4 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 1,557: Line 1,535:


: mapping generators: ~2, ~128/105
: mapping generators: ~2, ~128/105
{{Multival|legend=1| 2 8 -11 8 -23 -48 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 1,590: Line 1,566:


Mapping: {{mapping| 1 1 0 6 2 | 0 2 8 -11 5 }}
Mapping: {{mapping| 1 1 0 6 2 | 0 2 8 -11 5 }}
Wedgie: {{multival| 2 8 -11 5 8 -23 1 -48 -16 52 }}


Optimal tunings:  
Optimal tunings:  
Line 1,730: Line 1,704:


: mapping generators: ~2, ~10/7
: mapping generators: ~2, ~10/7
{{Multival|legend=1| 3 12 11 12 9 -8 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 1,756: Line 1,728:


Mapping: {{mapping| 1 0 -4 -3 4 | 0 3 12 11 -1 }}
Mapping: {{mapping| 1 0 -4 -3 4 | 0 3 12 11 -1 }}
Wedgie: {{multival| 3 12 11 -1 12 9 -12 -8 -44 -41 }}


Optimal tunings:  
Optimal tunings:  
Line 1,788: Line 1,758:


Mapping: {{mapping| 1 0 -4 -3 -5 | 0 3 12 11 16 }}
Mapping: {{mapping| 1 0 -4 -3 -5 | 0 3 12 11 16 }}
Wedgie: {{multival| 3 12 11 16 12 9 15 -8 -4 7 }}


Optimal tunings:  
Optimal tunings:  
Line 1,926: Line 1,894:


: mapping generators: ~2, ~9/7
: mapping generators: ~2, ~9/7
{{Multival|legend=1| 4 16 9 16 3 -24 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 1,954: Line 1,920:


Mapping: {{mapping| 1 3 8 6 7 | 0 -4 -16 -9 -10 }}
Mapping: {{mapping| 1 3 8 6 7 | 0 -4 -16 -9 -10 }}
Wedgie: {{multival| 4 16 9 10 16 3 2 -24 -32 -3 }}


Optimal tunings:  
Optimal tunings:  
Line 2,046: Line 2,010:


Mapping: {{mapping| 1 3 8 6 -4 | 0 -4 -16 -9 21 }}
Mapping: {{mapping| 1 3 8 6 -4 | 0 -4 -16 -9 21 }}
Wedgie: {{multival| 4 16 9 -21 16 3 -47 -24 -104 -90 }}


Optimal tunings:  
Optimal tunings:  
Line 2,067: Line 2,029:


: mapping generators: ~2, ~54/49
: mapping generators: ~2, ~54/49
{{Multival|legend=1| 5 20 7 20 -3 -40 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 2,086: Line 2,046:


Mapping: {{mapping| 1 1 0 2 3 | 0 5 20 7 4 }}
Mapping: {{mapping| 1 1 0 2 3 | 0 5 20 7 4 }}
Wedgie: {{multival| 5 20 7 4 20 -3 -11 -40 -60 -13 }}


Optimal tunings:  
Optimal tunings:  
Line 2,150: Line 2,108:


{{Mapping|legend=1| 1 4 12 12 | 0 -5 -20 -19 }}
{{Mapping|legend=1| 1 4 12 12 | 0 -5 -20 -19 }}
{{Multival|legend=1| 5 20 19 20 16 -12 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 2,190: Line 2,146:


: mapping generators: ~7/5, ~3
: mapping generators: ~7/5, ~3
{{Multival|legend=1| 2 8 8 8 7 -4 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 2,217: Line 2,171:


Mapping: {{mapping| 2 0 -8 -7 -12 | 0 1 4 4 6 }}
Mapping: {{mapping| 2 0 -8 -7 -12 | 0 1 4 4 6 }}
Wedgie: {{Multival| 2 8 8 12 8 7 12 -4 0 6 }}


Optimal tunings:  
Optimal tunings:  
Line 2,402: Line 2,354:


: mapping generators: ~735/512, ~35/24
: mapping generators: ~735/512, ~35/24
{{Multival|legend=1| 4 16 -10 16 -27 -68 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 2,483: Line 2,433:


: mapping generators: ~2401/1728, ~343/288
: mapping generators: ~2401/1728, ~343/288
{{Multival|legend=1| 8 32 6 32 -13 -76 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Line 2,536: Line 2,484:


: mapping generators: ~8/7, ~3
: mapping generators: ~8/7, ~3
{{Multival|legend=1| 5 20 0 20 -14 -56 }}


[[Optimal tuning]]s:  
[[Optimal tuning]]s:  
Retrieved from "https://en.xen.wiki/w/Meantone_family"