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Meantone: Difference between revisions

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Line 38: Line 38:
|690.225
|690.225
|1/2 Pythagorean comma, Pythagorean dilimma
|1/2 Pythagorean comma, Pythagorean dilimma
|-
|76/51
|690.603
|
|-
|-
|<nowiki>| -19 9 0 2 ></nowiki>
|<nowiki>| -19 9 0 2 ></nowiki>
Line 74: Line 78:
|694.165
|694.165
|2/7 septimal comma
|2/7 septimal comma
|-
|[[14/13]]
|694.34
|Tridecimal Meantone
|-
|-
| [[56/45]]
| [[56/45]]
Line 91: Line 99:
|
|
|-
|-
| [[6/5]]
| [[6/5]], [[25/18]]
| 694.786
| 694.786
| 1/3 comma
| 1/3 comma
|-
|[[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
|-
|-
|<nowiki>| 27 -17 ></nowiki>
|<nowiki>| 27 -17 ></nowiki>
Line 114: Line 130:
| 695.493
| 695.493
| Lucy Tuning
| Lucy Tuning
|-
|[[13/12]]
|695.612
|Tridecimal Meantone
|-
|-
| [[9/7]]
| [[9/7]]
Line 120: Line 140:
|-
|-
| f^4 = 2f + 2
| f^4 = 2f + 2
| 695.630
| 695.63
| Wilson fifth
| Wilson fifth
|-
|-
Line 128: Line 148:
|-
|-
| [[25/24]]
| [[25/24]]
| 695.810
| 695.81
| 2/7 comma
| 2/7 comma
|-
|-
| [[13/10]]
| [[13/10]]
| 695.838
| 695.838
| ratwolf fifth, meanpop eigenmonzo
| ratwolf fifth, Tridecimal Meantone and meanpop eigenmonzo
|-
|[[81/80]]
|695.869
|
|-
|-
| [[36/35]]
| [[36/35]]
Line 146: Line 170:
| 696
| 696
|
|
|-
|16/13
|696.035
|Tridecimal Meantone
|-
|-
|8192/6561
|8192/6561
Line 166: Line 194:
| 696.245
| 696.245
|
|
|-
|19/17
|696.279
|Classical meantone
|-
|-
| [[81edo|47\81]]
| [[81edo|47\81]]
Line 177: Line 209:
| [[48/35]]
| [[48/35]]
| 696.399
| 696.399
|
|-
|39/32
|696.405
|
|
|-
|-
Line 189: Line 225:
| [[5/4]]
| [[5/4]]
| 696.578
| 696.578
| 5- 7- and 9-limit minimax, 1/4 comma
| 5-, 7-, 9- and 11- (Meanpop) limit minimax, 1/4 comma
|-
|-
| 49/48
| 49/48
Line 202: Line 238:
| 696.648
| 696.648
| [[7-limit]] least squares
| [[7-limit]] least squares
|-
|[[11/9]]
|696.713
|11-, 13- and 15- limit (Tridecimal Meantone) minimax
|-
|-
| [[31edo|18\31]]
| [[31edo|18\31]]
Line 217: Line 257:
| [[49/40]]
| [[49/40]]
| 696.959
| 696.959
|
|-
|[[12/11]]
|697.021
|
|
|-
|-
| [[7/5]]
| [[7/5]]
| 697.085
| 697.085
|
|-
|[[15/11]]
|697.158
|
|-
|[[27/22]]
|697.159
|
|
|-
|-
Line 226: Line 278:
| 697.176
| 697.176
|
|
|-
|14/13
|697.242
|13, 15 limit minimax (Grosstone)
|-
|-
|[[2187/2048]]
|[[2187/2048]]
|697.263
|697.263
|1/5 Pythagorean comma, Pythagorean aptome
|1/5 Pythagorean comma, Pythagorean apotome
|-
|13/10
|697.289
|Grosstone
|-
|[[11/8]]
|697.295
|
|-
|-
| [[74edo|43\74]]
| [[74edo|43\74]]
Line 238: Line 302:
| 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 limit minimax (Meridetone)
|-
|[[16/13]]
|696.467
|Grosstone
|-
|[[11/10]]
|697.5
|
|-
|15/13
|697.511
|Grosstone
|-
|13/12
|697.637
|Meridetone
|-
|-
| [[16/15]]
| [[16/15]]
Line 258: Line 346:
| 697.781
| 697.781
|
|
|-
|16/13
|697.797
|Meridetone
|-
|[[14/11]]
|697.812
|
|-
|15/13
|697.83
|Meridetone
|-
|[[18/13]]
|697.966
|Grosstone
|-
|13/10
|698.009
|Meridetone
|-
|-
|[[1024/729]]
|[[1024/729]]
|698.045
|698.045
|1/6 Pythagorean comma, Pythagorean tritone
|1/6 Pythagorean comma, lesser Pythagorean tritone
|-
|-
|<nowiki>| - 17 9 0 1 ></nowiki>
|<nowiki>| - 17 9 0 1 ></nowiki>
Line 273: Line 381:
| [[55edo|32\55]]
| [[55edo|32\55]]
| 698.182
| 698.182
|
|-
|33/28
|698.272
|
|
|-
|-
| [[80/63]]
| [[80/63]]
| 698.303
| 698.303
|
|-
|17/15
|698.331
|
|
|-
|-
Line 290: Line 406:
|698.604
|698.604
|1/7 Pythagorean comma, Pythagorean limma
|1/7 Pythagorean comma, Pythagorean limma
|-
|45/34
|698.661
|
|-
|-
| [[79edo|46\79]]
| [[79edo|46\79]]
| 698.734
| 698.734
|
|
|-
|13/11
|698.801
|Meridetone
|-
|-
|[[135/128]]
|[[135/128]]
Line 311: Line 435:
|
|
|-
|-
|[[18/17]]
|[[18/17|''18/17'']]
|700.209
|''700.209''
|
|-
|''[[19/16]]''
|''700.829''
|
|
|-
|-
| [[53edo|31\53]]
|[[81/80|''81/80'']]
| 701.887
|''701.792''
|
|
|-
|-
| [[3/2]]
| [[53edo|''31\53'']]
| 701.955
| ''701.887''
| [[Pythagorean tuning]]
|
|-
| [[3/2|''3/2'']]
| ''701.955''
| [[Pythagorean tuning|''Pythagorean tuning'']]
|-
|[[64/63|''64/63'']]
|''702.272''
|
|-
|''256/189''
|''702.301''
|
|-
|''33/26''
|''703.186''
|''Tridecimal Meantone''
|-
|''13/11''
|''703.597''
|''Tridecimal Meantone''
|-
|''88/81''
|''710.4335''
|
|}
|}


Line 327: Line 479:


== Links ==
== Links ==
* http://www.kylegann.com/histune.html -- An Introduction to Historical Tunings, by [[Kyle Gann]] [[Category:Meantone| ]] <!-- main article -->
* http://www.kylegann.com/histune.html -- An Introduction to Historical Tunings, by [[Kyle Gann]]   [[Category:Meantone| ]] <!-- main article -->
[[Category:Temperament]]
[[Category:Temperament]]
[[Category:Theory]]
[[Category:Theory]]
Retrieved from "https://en.xen.wiki/w/Meantone"