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Meantone: Difference between revisions

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Make tunings shown by types
→Spectrum of meantone tunings by eigenmonzos: remove 11- and 13-limit eigenmonzos for (1) they're unreadable (2) they're present in meantone vs meanpop
Line 61: Line 61:
| 688.323
| 688.323
| 1/2 septimal comma
| 1/2 septimal comma
|-
| 16/13
| 689.868
| Meanplop
|-
|-
| {{monzo| 16 -10 }}
| {{monzo| 16 -10 }}
Line 81: Line 77:
| 691.202
| 691.202
| 1/2 comma
| 1/2 comma
|-
| 13/12
| 692.285
| Meanplop
|-
|-
| [[26edo|(15\26)]]
| [[26edo|(15\26)]]
Line 97: Line 89:
| 692.867
| 692.867
| 1/3 septimal comma
| 1/3 septimal comma
|-
| 33/26
| 693.178
| Grosstone
|-
| 13/10
| 693.223
| Meanplop
|-
|-
| [[45edo|(26\45)]]
| [[45edo|(26\45)]]
Line 113: Line 97:
| 693.352
| 693.352
| 2/5 comma
| 2/5 comma
|-
| 18/13
| 693.897
| Meanplop
|-
|-
| 19683/16384
| 19683/16384
Line 125: Line 105:
| 694.165
| 694.165
| 2/7 septimal comma
| 2/7 septimal comma
|-
| 15/13
| 694.193
| Meanplop
|-
| [[14/13]]
| 694.340
| Tridecimal meantone
|-
|-
| [[56/45]]
| [[56/45]]
Line 153: Line 125:
| 694.786
| 694.786
| 1/3 comma
| 1/3 comma
|-
| 14/13
| 694.878
| Meanplop
|-
| [[18/13]]
| 695.124
| Tridecimal meantone
|-
|-
| 5103/4095
| 5103/4095
| 695.139
| 695.139
| 1/4 septimal comma
| 1/4 septimal comma
|-
| [[15/13]]
| 695.226
| Tridecimal Meantone
|-
|-
| {{monzo| 27 -17 }}
| {{monzo| 27 -17 }}
Line 185: Line 145:
| 695.493
| 695.493
| Lucy Tuning
| Lucy Tuning
|-
| 39/28
| 695.6095
| Tridecimal meantone, tridecimal meanpop
|-
| [[13/12]]
| 695.612
| Tridecimal meantone
|-
|-
| [[9/7]]
| [[9/7]]
Line 209: Line 161:
| 695.810
| 695.810
| 2/7 comma
| 2/7 comma
|-
| 40/33
| 695.815
| Meanpop
|-
| [[13/10]]
| 695.838
| Ratwolf fifth, tridecimal meantone and meanpop eigenmonzo
|-
|-
| [[81/80]]
| [[81/80]]
Line 237: Line 181:
| 696.000
| 696.000
|
|
|-
| 16/13
| 696.035
| Tridecimal meantone, tridecimal meanpop
|-
| 13/11
| 696.043
| 13- and 15-odd-limit minimax (tridecimal meanpop)
|-
| 11/8
| 696.052
| Meanpop
|-
|-
| 8192/6561
| 8192/6561
| 696.09
| 696.090
| 1/4 Pythagorean comma, Pythagorean diminished fourth
| 1/4 Pythagorean comma, Pythagorean diminished fourth
|-
|-
Line 261: Line 193:
| 696.165
| 696.165
| [[5-odd-limit]] least squares
| [[5-odd-limit]] least squares
|-
| 11/10
| 696.176
| Meanpop
|-
|-
| (8 - φ)\11
| (8 - φ)\11
Line 285: Line 213:
| 696.319
| 696.319
|
|
|-
| 27/22
| 696.3635
| Meanpop
|-
|-
| [[48/35]]
| [[48/35]]
| 696.399
| 696.399
|
|
|-
| 39/32
| 696.405
| Tridecimal meantone, tridecimal meanpop
|-
| 14/11
| 696.413
| Meanpop
|-
|-
| {{Monzo| 19 9 -1 -11 }}
| {{Monzo| 19 9 -1 -11 }}
| 696.436
| 696.436
| 9-odd-limit least squares
| 9-odd-limit least squares
|-
| 12/11
| 696.474
| Meanpop
|-
|-
| 16384/15309
| 16384/15309
Line 329: Line 241:
| 696.648
| 696.648
| [[7-odd-limit]] least squares
| [[7-odd-limit]] least squares
|-
| [[11/9]]
| 696.713
| 11-, 13- and 15-odd-limit (tridecimal meantone) minimax
|-
|-
| [[31edo|(18\31)]]
| [[31edo|(18\31)]]
Line 341: Line 249:
| 696.796
| 696.796
|
|
|-
| 11/9
| 696.839
| Meanpop
|-
|-
| [[8/7]]
| [[8/7]]
Line 353: Line 257:
| 696.959
| 696.959
|
|
|-
| [[12/11]]
| 697.021
| Undecimal meantone
|-
|-
| [[7/5]]
| [[7/5]]
| 697.085
| 697.085
|
|
|-
| [[15/11]]
| 697.158
| rowspan="2" | Undecimal meantone
|-
| [[27/22]]
| 697.159
|-
| 39/32
| 697.168
| Grosstone
|-
|-
| [[75/64]]
| [[75/64]]
| 697.176
| 697.176
|2/9 comma
|2/9 comma
|-
| 22/21
| 697.220
| Undecimal meantone
|-
| 14/13
| 697.242
| 13- and 15-odd-limit minimax (grosstone)
|-
|-
| [[2187/2048]]
| [[2187/2048]]
| 697.263
| 697.263
| 1/5 Pythagorean comma, Pythagorean apotome
| 1/5 Pythagorean comma, Pythagorean apotome
|-
| 13/10
| 697.289
| Grosstone
|-
| [[11/8]]
| 697.295
| Undecimal meantone
|-
|-
| [[74edo|(43\74)]]
| [[74edo|(43\74)]]
Line 404: Line 277:
| 697.344
| 697.344
|
|
|-
| [[13/11]]
| 697.376
| Meridetone
|-
|-
| 45927/32768
| 45927/32768
| 697.411
| 697.411
| 1/6 septimal comma
| 1/6 septimal comma
|-
| 18/13
| 697.465
| 13-, 15-odd-limit minimax (meridetone)
|-
| [[16/13]]
| 696.467
| Grosstone
|-
| [[11/10]]
| 697.500
| Undecimal meantone
|-
| 15/13
| 697.511
| Grosstone
|-
| 13/12
| 697.637
| Meridetone
|-
|-
| [[16/15]]
| [[16/15]]
Line 448: Line 297:
| 697.781
| 697.781
|
|
|-
| 40/33, 16/13
| 697.797
| Undecimal meantone, meridetone
|-
| [[14/11]]
| 697.812
| Undecimal meantone
|-
| 15/13
| 697.830
| Meridetone
|-
| [[18/13]]
| 697.966
| Grosstone
|-
| 13/10
| 698.009
| Meridetone
|-
|-
| [[1024/729]]
| [[1024/729]]
Line 484: Line 313:
| 698.182
| 698.182
|
|
|-
| 33/28
| 698.272
| Undecimal meantone
|-
|-
| [[80/63]]
| [[80/63]]
Line 500: Line 325:
| 698.371
| 698.371
| 1/6 comma
| 1/6 comma
|-
| 33/26
| 698.407
| Meanplop, meridetone
|-
|-
| [[67edo|(39\67)]]
| [[67edo|(39\67)]]
Line 512: Line 333:
| 698.604
| 698.604
| 1/7 Pythagorean comma, Pythagorean limma
| 1/7 Pythagorean comma, Pythagorean limma
|-
| 112/99
| 698.640
| Undecimal meantone
|-
|-
| 45/34
| 45/34
Line 524: Line 341:
| 698.734
| 698.734
|
|
|-
| 13/11
| 698.801
| Meridetone, meanplop
|-
|-
| [[135/128]]
| [[135/128]]
Line 572: Line 385:
| ''702.301''
| ''702.301''
|
|
|-
| ''33/26''
| ''703.186''
| ''Tridecimal meantone''
|-
| ''22/21''
| ''703.356''
| ''Meanpop''
|-
| ''13/11''
| ''703.597''
| ''Tridecimal meantone''
|-
| ''88/81''
| ''707.946''
| ''Meanpop''
|-
| ''88/81''
| ''710.4335''
| ''Undecimal meantone''
|}
|}


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