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Huygens vs meanpop: Difference between revisions

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→Tuning spectra: improve and standardize tuning spectra tables
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= Tuning spectra =
== Tuning spectra ==
== Spectrum of undecimal meantone tunings by eigenmonzos ==
=== Undecimal meantone ===
Gencom: [2 4/3; 81/80 99/98 126/125]
Gencom: [2 4/3; 81/80 99/98 126/125]


Gencom map: [{{val|1 2 4 7 11}}, {{val|0 -1 -4 -10 -18}}]
Gencom map: [{{val|1 2 4 7 11}}, {{val|0 -1 -4 -10 -18}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
! | Fifth
! | fifth<br>(¢)
! | Comments
! | comments
|-
|-
| | 10/9
| | 10/9
| | 691.202
| | 691.202
| |  
| |
|-
|-
| | 6/5
| | 6/5
| | 694.786
| | 694.786
| |  
| |
|-
|-
| | 9/7
| | 9/7
| | 695.614
| | 695.614
| |  
| |
|-
|-
| | 15/14
| | 15/14
| | 696.111
| | 696.111
| |  
| |
|-
|-
| | 7/6
| | 7/6
| | 696.319
| | 696.319
| |  
| |
|-
|-
| | 5/4
| | 5/4
Line 196: Line 196:
| | 8/7
| | 8/7
| | 696.883
| | 696.883
| |  
| |
|-
|-
| | 12/11
| | 12/11
| | 697.021
| | 697.021
| |  
| |
|-
|-
| | 7/5
| | 7/5
| | 697.085
| | 697.085
| |  
| |
|-
|-
| | 15/11
| | 15/11
| | 697.158
| | 697.158
| |  
| |
|-
|-
| | 27/22
| | 27/22
| | 697.159
| | 697.159
| |  
| |
|-
|-
| | 22/21
| | 22/21
| | 697.22
| | 697.22
| |  
| |
|-
|-
| | 11/8
| | 11/8
| | 697.295
| | 697.295
| |  
| |
|-
|-
| | 21/16
| | 21/16
| | 697.344
| | 697.344
| |  
| |
|-
|-
| | 11/10
| | 11/10
| | 697.5
| | 697.5
| |  
| |
|-
|-
| | 16/15
| | 16/15
| | 697.654
| | 697.654
| |  
| |
|-
|-
| | 40/33
| | 40/33
| | 697.797
| | 697.797
| |  
| |
|-
|-
| | 14/11
| | 14/11
| | 697.812
| | 697.812
| |  
| |
|-
|-
| | 33/28
| | 33/28
| | 698.272
| | 698.272
| |  
| |
|-
|-
| | 112/99
| | 112/99
| | 698.640
| | 698.640
| |  
| |
|-
|-
| | 4/3
| | 4/3
| | 701.955
| | 701.955
| |  
| |
|}
|}


Line 260: Line 260:
Gencom map: [{{val|1 2 4 7 11 10}}, {{val|0 -1 -4 -10 -18 -15}}]
Gencom map: [{{val|1 2 4 7 11 10}}, {{val|0 -1 -4 -10 -18 -15}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | eigenmonzo<br>(unchanged interval)
! | Fifth
! | fifth<br>(¢)
! | Comments
! | comments
|-
|-
| | 10/9
| | 10/9
| | 691.202
| | 691.202
| |  
| |
|-
|-
| | 14/13
| | 14/13
| | 694.340
| | 694.340
| |  
| |
|-
|-
| | 18/13
| | 18/13
| | 695.124
| | 695.124
| |  
| |
|-
|-
| | 15/13
| | 15/13
| | 695.226
| | 695.226
| |  
| |
|-
|-
| | 39/28
| | 39/28
| | 695.609
| | 695.609
| |  
| |
|-
|-
| | 13/12
| | 13/12
| | 695.612
| | 695.612
| |  
| |
|-
|-
| | 13/10
| | 13/10
| | 695.838
| | 695.838
| |  
| |
|-
|-
| | 16/13
| | 16/13
| | 696.035
| | 696.035
| |  
| |
|-
|-
| | 39/32
| | 39/32
| | 696.405
| | 696.405
| |  
| |
|-
|-
| | 5/4
| | 5/4
Line 312: Line 312:
| | 4/3
| | 4/3
| | 701.955
| | 701.955
| |  
| |
|-
|-
| | 33/26
| | 33/26
| | 703.186
| | 703.186
| |  
| |
|-
|-
| | 13/11
| | 13/11
| | 703.597
| | 703.597
| |  
| |
|}
|}


Line 328: Line 328:
Gencom map: [{{val|1 2 4 7 11 -3}}, {{val|0 -1 -4 -10 -18 16}}]
Gencom map: [{{val|1 2 4 7 11 -3}}, {{val|0 -1 -4 -10 -18 16}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | eigenmonzo<br>(unchanged interval)
! | Fifth
! | fifth<br>(¢)
! | Comments
! | comments
|-
|-
| | 10/9
| | 10/9
| | 691.202
| | 691.202
| |  
| |
|-
|-
| | 33/26
| | 33/26
| | 693.178
| | 693.178
| |  
| |
|-
|-
| | 5/4
| | 5/4
Line 352: Line 352:
| | 39/32
| | 39/32
| | 697.168
| | 697.168
| |  
| |
|-
|-
| | 14/13
| | 14/13
Line 360: Line 360:
| | 13/10
| | 13/10
| | 697.289
| | 697.289
| |  
| |
|-
|-
| | 13/11
| | 13/11
| | 697.376
| | 697.376
| |  
| |
|-
|-
| | 16/13
| | 16/13
| | 697.467
| | 697.467
| |  
| |
|-
|-
| | 15/13
| | 15/13
| | 697.511
| | 697.511
| |  
| |
|-
|-
| | 13/12
| | 13/12
| | 697.731
| | 697.731
| |  
| |
|-
|-
| | 18/13
| | 18/13
| | 697.966
| | 697.966
| |  
| |
|-
|-
| | 4/3
| | 4/3
| | 701.955
| | 701.955
| |  
| |
|}
|}


Line 392: Line 392:
Gencom map: [{{val|1 2 4 7 11 15}}, {{val|0 -1 -4 -10 -18 -27}}]
Gencom map: [{{val|1 2 4 7 11 15}}, {{val|0 -1 -4 -10 -18 -27}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | eigenmonzo<br>(unchanged interval)
! | Fifth
! | fifth<br>(¢)
! | Comments
! | comments
|-
|-
| | 10/9
| | 10/9
| | 691.202
| | 691.202
| |  
| |
|-
|-
| | 5/4
| | 5/4
Line 416: Line 416:
| | 13/12
| | 13/12
| | 697.637
| | 697.637
| |  
| |
|-
|-
| | 16/13
| | 16/13
| | 697.797
| | 697.797
| |  
| |
|-
|-
| | 15/13
| | 15/13
| | 697.83
| | 697.83
| |  
| |
|-
|-
| | 39/32
| | 39/32
| | 697.946
| | 697.946
| |  
| |
|-
|-
| | 13/10
| | 13/10
| | 698.009
| | 698.009
| |  
| |
|-
|-
| | 14/13
| | 14/13
| | 698.335
| | 698.335
| |  
| |
|-
|-
| | 33/26
| | 33/26
| | 698.407
| | 698.407
| |  
| |
|-
|-
| | 13/11
| | 13/11
| | 698.801
| | 698.801
| |  
| |
|-
|-
| | 4/3
| | 4/3
| | 701.955
| | 701.955
| |  
| |
|}
|}


== Spectrum of meanpop tunings by eigenmonzos ==
=== Meanpop ===
Gencom: [2 4/3; 81/80 126/125 385/384]
Gencom: [2 4/3; 81/80 126/125 385/384]


Gencom map: [{{val|1 2 4 7 -2}}, {{val|0 -1 -4 -10 13}}]
Gencom map: [{{val|1 2 4 7 -2}}, {{val|0 -1 -4 -10 13}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | eigenmonzo<br>(unchanged interval)
! | Fifth
! | fifth<br>(¢)
! | Comments
! | comments
|-
|-
| | 10/9
| | 10/9
| | 691.202
| | 691.202
| |  
| |
|-
|-
| | 6/5
| | 6/5
| | 694.786
| | 694.786
| |  
| |
|-
|-
| | 9/7
| | 9/7
| | 695.614
| | 695.614
| |  
| |
|-
|-
| | 40/33
| | 40/33
| | 695.815
| | 695.815
| |  
| |
|-
|-
| | 112/99
| | 112/99
| | 695.886
| | 695.886
| |  
| |
|-
|-
| | 11/8
| | 11/8
| | 696.052
| | 696.052
| |  
| |
|-
|-
| | 15/14
| | 15/14
| | 696.111
| | 696.111
| |  
| |
|-
|-
| | 11/10
| | 11/10
| | 696.176
| | 696.176
| |  
| |
|-
|-
| | 7/6
| | 7/6
| | 696.319
| | 696.319
| |  
| |
|-
|-
| | 27/22
| | 27/22
| | 696.3635
| | 696.3635
| |  
| |
|-
|-
| | 14/11
| | 14/11
| | 696.413
| | 696.413
| |  
| |
|-
|-
| | 12/11
| | 12/11
| | 696.474
| | 696.474
| |  
| |
|-
|-
| | 15/11
| | 15/11
| | 696.497
| | 696.497
| |  
| |
|-
|-
| | 5/4
| | 5/4
Line 520: Line 520:
| | 11/9
| | 11/9
| | 696.839
| | 696.839
| |  
| |
|-
|-
| | 8/7
| | 8/7
| | 696.883
| | 696.883
| |  
| |
|-
|-
| | 7/5
| | 7/5
| | 697.085
| | 697.085
| |  
| |
|-
|-
| | 16/15
| | 16/15
| | 697.654
| | 697.654
| |  
| |
|-
|-
| | 4/3
| | 4/3
| | 701.955
| | 701.955
| |  
| |
|-
|-
| | ''22/21''
| | ''22/21''
| | ''703.356''
| | ''703.356''
| |  
| |
|-
|-
| | ''88/81''
| | ''88/81''
| | ''707.946''
| | ''707.946''
| |  
| |
|}
|}


Line 552: Line 552:
Gencom map: [{{val|1 2 4 7 -2 10}}, {{val|0 -1 -4 -10 13 -15}}]
Gencom map: [{{val|1 2 4 7 -2 10}}, {{val|0 -1 -4 -10 13 -15}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | eigenmonzo<br>(unchanged interval)
! | Fifth
! | fifth<br>(¢)
! | Comments
! | comments
|-
|-
| | 10/9
| | 10/9
| | 691.202
| | 691.202
| |  
| |
|-
|-
| | 14/13
| | 14/13
| | 694.340
| | 694.340
| |  
| |
|-
|-
| | 18/13
| | 18/13
| | 695.124
| | 695.124
| |  
| |
|-
|-
| | 15/13
| | 15/13
| | 695.226
| | 695.226
| |  
| |
|-
|-
| | 39/28
| | 39/28
| | 695.609
| | 695.609
| |  
| |
|-
|-
| | 13/12
| | 13/12
| | 695.612
| | 695.612
| |  
| |
|-
|-
| | 33/26
| | 33/26
| | 695.824
| | 695.824
| |  
| |
|-
|-
| | 13/10
| | 13/10
| | 695.838
| | 695.838
| |  
| |
|-
|-
| | 16/13
| | 16/13
| | 696.035
| | 696.035
| |  
| |
|-
|-
| | 13/11
| | 13/11
Line 608: Line 608:
| | 4/3
| | 4/3
| | 701.955
| | 701.955
| |  
| |
|}
|}


Line 616: Line 616:
Gencom map: [{{val|1 2 4 7 -2 2}}, {{val|0 -1 -4 -10 13 4}}]
Gencom map: [{{val|1 2 4 7 -2 2}}, {{val|0 -1 -4 -10 13 4}}]


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! | Eigenmonzo
! | eigenmonzo<br>(unchanged interval)
! | Fifth
! | fifth<br>(¢)
! | Comments
! | comments
|-
|-
| | ''39/32''
| | ''39/32''
| | ''685.839''
| | ''685.839''
| |  
| |
|-
|-
| | 16/13
| | 16/13
| | 689.868
| | 689.868
| |  
| |
|-
|-
| | 10/9
| | 10/9
| | 691.202
| | 691.202
| |  
| |
|-
|-
| | 13/12
| | 13/12
| | 692.285
| | 692.285
| |  
| |
|-
|-
| | 13/10
| | 13/10
| | 693.223
| | 693.223
| |  
| |
|-
|-
| | 18/13
| | 18/13
| | 693.897
| | 693.897
| |  
| |
|-
|-
| | 15/13
| | 15/13
| | 694.193
| | 694.193
| |  
| |
|-
|-
| | 14/13
| | 14/13
| | 694.878
| | 694.878
| |  
| |
|-
|-
| | 11/8
| | 11/8
Line 664: Line 664:
| | 33/26
| | 33/26
| | 698.407
| | 698.407
| |  
| |
|-
|-
| | 13/11
| | 13/11
| | 698.801
| | 698.801
| |  
| |
|-
|-
| | 4/3
| | 4/3
| | 701.955
| | 701.955
| |  
| |
|}
|}


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