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Huygens vs meanpop: Difference between revisions

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==Spectrum of Undecimal Meantone Tunings by Eigenmonzos==
==Spectrum of Undecimal Meantone Tunings by Eigenmonzos==


11-limit commas: 81/80, 99/98, 126/125
{| class="wikitable"
{| class="wikitable"
|-
|-
Line 102: Line 103:
|-
|-
| | 5/4
| | 5/4
| | 696.578
| | 696.578 (5, 7, 9 limit minimax)
|-
|-
| | 11/9
| | 11/9
| | 696.713 (minimax tuning)
| | 696.713 (11 limit minimax)
|-
|-
| | 8/7
| | 8/7
Line 124: Line 125:
| | 14/11
| | 14/11
| | 697.812
| | 697.812
|-
| | 4/3
| | 701.955
|}
===Tridecimal meantone===
13-limit commas: 66/65, 81/80, 99/98, 105/104
{| class="wikitable"
|-
! | Eigenmonzo
! | Fifth
|-
| | 10/9
| | 691.202
|-
| | 14/13
| | 694.340
|-
| | 6/5
| | 694.786
|-
| | 18/13
| | 695.124
|-
| | 15/13
| | 695.226
|-
| | 13/12
| | 695.612
|-
| | 9/7
| | 695.614
|-
| | 13/10
| | 695.838
|-
| | 16/13
| | 696.035
|-
| | 15/14
| | 696.111
|-
| | 7/6
| | 696.319
|-
| | 5/4
| | 696.578 (5, 7, 9 limit minimax)
|-
| | 11/9
| | 696.713 (11, 13, 15 limit minimax)
|-
| | 8/7
| | 696.883
|-
| | 12/11
| | 697.021
|-
| | 7/5
| | 697.085
|-
| | 15/11
| | 697.158
|-
| | 11/8
| | 697.295
|-
| | 11/10
| | 697.500
|-
| | 16/15
| | 697.654
|-
| | 14/11
| | 697.812
|-
| | 4/3
| | 701.955
|-
| | 13/11
| | 703.597
|}
===Grosstone===
13-limit commas: 81/80, 99/98, 126/125, 144/143
{| class="wikitable"
|-
! | Eigenmonzo
! | Fifth
|-
| | 10/9
| | 691.202
|-
| | 6/5
| | 694.786
|-
| | 9/7
| | 695.614
|-
| | 15/14
| | 696.111
|-
| | 7/6
| | 696.319
|-
| | 5/4
| | 696.578 (5, 7, 9 limit minimax)
|-
| | 11/9
| | 696.713 (11 limit minimax)
|-
| | 8/7
| | 696.883
|-
| | 12/11
| | 697.021
|-
| | 7/5
| | 697.085
|-
| | 15/11
| | 697.158
|-
| | 14/13
| | 697.242 (13, 15 limit minimax)
|-
| | 13/10
| | 697.289
|-
| | 11/8
| | 697.295
|-
| | 13/11
| | 697.376
|-
| | 16/13
| | 697.467
|-
| | 11/10
| | 697.500
|-
| | 15/13
| | 697.511
|-
| | 16/15
| | 697.654
|-
| | 13/12
| | 697.731
|-
| | 14/11
| | 697.812
|-
| | 18/13
| | 697.966
|-
| | 4/3
| | 701.955
|}
===Meridetone===
13-limit commas: 78/77, 81/80, 99/98, 126/125
{| class="wikitable"
|-
! | Eigenmonzo
! | Fifth
|-
| | 10/9
| | 691.202
|-
| | 6/5
| | 694.786
|-
| | 9/7
| | 695.614
|-
| | 15/14
| | 696.111
|-
| | 7/6
| | 696.319
|-
| | 5/4
| | 696.578 (5, 7, 9 limit minimax)
|-
| | 11/9
| | 696.713 (11 limit minimax)
|-
| | 8/7
| | 696.883
|-
| | 12/11
| | 697.021
|-
| | 7/5
| | 697.085
|-
| | 15/11
| | 697.158
|-
| | 11/8
| | 697.295
|-
| | 18/13
| | 697.465 (13, 15 limit minimax)
|-
| | 11/10
| | 697.500
|-
| | 13/12
| | 697.637
|-
| | 16/15
| | 697.654
|-
| | 16/13
| | 697.797
|-
| | 14/11
| | 697.812
|-
| | 15/13
| | 697.830
|-
| | 13/10
| | 698.009
|-
| | 14/13
| | 698.335
|-
| | 13/11
| | 698.801
|-
|-
| | 4/3
| | 4/3
Line 130: Line 365:


==Spectrum of Meanpop Tunings by Eigenmonzos==
==Spectrum of Meanpop Tunings by Eigenmonzos==
11-limit commas: 81/80, 126/125, 385/384
13-limit commas: 81/80, 105/104, 126/125, 144/143


{| class="wikitable"
{| class="wikitable"
Line 138: Line 376:
| | 10/9
| | 10/9
| | 691.202
| | 691.202
|-
| | 14/13
| | 694.340
|-
|-
| | 6/5
| | 6/5
| | 694.786
| | 694.786
|-
| | 18/13
| | 695.124
|-
| | 15/13
| | 695.226
|-
| | 13/12
| | 695.612
|-
|-
| | 9/7
| | 9/7
| | 695.614
| | 695.614
|-
| | 13/10
| | 695.838
|-
| | 16/13
| | 696.035
|-
| | 13/11
| | 696.043 (13, 15 limit minimax)
|-
|-
| | 11/8
| | 11/8
| | 696.052
| | 696.052
|-
| | 15/14
| | 696.111
|-
|-
| | 11/10
| | 11/10
Line 159: Line 421:
| | 12/11
| | 12/11
| | 696.474
| | 696.474
|-
| | 15/11
| | 696.497
|-
|-
| | 5/4
| | 5/4
| | 696.578 (minimax tuning)
| | 696.578 (5, 7, 9, 11 limit minimax)
|-
|-
| | 11/9
| | 11/9
Line 171: Line 436:
| | 7/5
| | 7/5
| | 697.085
| | 697.085
|-
| | 16/15
| | 697.654
|-
|-
| | 4/3
| | 4/3
| | 701.955
| | 701.955
|}
|}
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