Xenharmonic Wiki

Huygens vs meanpop: Difference between revisions

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== Tuning spectra ==
== Tuning spectra ==
=== Undecimal meantone ===
=== Undecimal meantone ===
 
{| class="wikitable center-all left-3"
{| class="wikitable center-all"
|-
|-
! | [[eigenmonzo|eigenmonzo<br>(unchanged-interval]])
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! | fifth<br>(¢)
! Generator (¢)
! | 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
| | 696.578
| 696.578
| | 5, 7, 9-odd-limit minimax
| 5, 7, 9-odd-limit minimax
|-
|-
| | 11/9
| 11/9
| | 696.713
| 696.713
| | 11-odd-limit minimax
| 11-odd-limit minimax
|-
|-
| | 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
| |
|  
|}
|}


==== Fokkertone ====
==== Fokkertone ====
{| class="wikitable center-all"
{| class="wikitable center-all left-3"
|-
|-
! | eigenmonzo<br>(unchanged interval)
! Eigenmonzo<br>(unchanged-interval)
! | fifth<br>(¢)
! Generator (¢)
! | 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
| | 696.578
| 696.578
| | 5, 7, 9-odd-limit minimax
| 5, 7, 9-odd-limit minimax
|-
|-
| | 11/9
| 11/9
| | 696.713
| 696.713
| | 11, 13, 15-odd-limit minimax
| 11, 13, 15-odd-limit minimax
|-
|-
| | 4/3
| 4/3
| | 701.955
| 701.955
| |
|  
|-
|-
| | 33/26
| 33/26
| | 703.186
| 703.186
| |
|  
|-
|-
| | 13/11
| 13/11
| | 703.597
| 703.597
| |
|  
|}
|}


==== Grosstone ====
==== Grosstone ====
{| class="wikitable center-all"
{| class="wikitable center-all left-3"
|-
|-
! | eigenmonzo<br>(unchanged interval)
! Eigenmonzo<br>(unchanged-interval)
! | fifth<br>(¢)
! Generator (¢)
! | comments
! Comments
|-
|-
| | 10/9
| 10/9
| | 691.202
| 691.202
| |
|  
|-
|-
| | 33/26
| 33/26
| | 693.178
| 693.178
| |
|  
|-
|-
| | 5/4
| 5/4
| | 696.578
| 696.578
| | 5, 7, 9-odd-limit minimax
| 5, 7, 9-odd-limit minimax
|-
|-
| | 11/9
| 11/9
| | 696.713
| 696.713
| | 11-odd-limit minimax
| 11-odd-limit minimax
|-
|-
| | 39/32
| 39/32
| | 697.168
| 697.168
| |
|  
|-
|-
| | 14/13
| 14/13
| | 697.242
| 697.242
| | 13, 15-odd-limit minimax
| 13, 15-odd-limit minimax
|-
|-
| | 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
| |
|  
|}
|}


==== Meridetone ====
==== Meridetone ====
{| class="wikitable center-all"
{| class="wikitable center-all left-3"
|-
|-
! | eigenmonzo<br>(unchanged interval)
! Eigenmonzo<br>(unchanged-interval)
! | fifth<br>(¢)
! Generator (¢)
! | comments
! Comments
|-
|-
| | 10/9
| 10/9
| | 691.202
| 691.202
| |
|  
|-
|-
| | 5/4
| 5/4
| | 696.578
| 696.578
| | 5, 7, 9-odd-limit minimax
| 5, 7, 9-odd-limit minimax
|-
|-
| | 11/9
| 11/9
| | 696.713
| 696.713
| | 11-odd-limit minimax
| 11-odd-limit minimax
|-
|-
| | 18/13
| 18/13
| | 697.465
| 697.465
| | 13, 15-odd-limit minimax
| 13, 15-odd-limit minimax
|-
|-
| | 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
| |
|  
|}
|}


=== Meanpop ===
=== Meanpop ===
{| class="wikitable center-all"
{| class="wikitable center-all left-3"
|-
|-
! | eigenmonzo<br>(unchanged interval)
! Eigenmonzo<br>(unchanged-interval)
! | fifth<br>(¢)
! Generator (¢)
! | 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
| | 696.578
| 696.578
| | 5, 7, 9, 11-odd-limit minimax
| 5, 7, 9, 11-odd-limit minimax
|-
|-
| | 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
| |
|  
|}
|}


==== Tridecimal meanpop ====
==== Tridecimal meanpop ====
{| class="wikitable center-all"
{| class="wikitable center-all left-3"
|-
|-
! | eigenmonzo<br>(unchanged interval)
! Eigenmonzo<br>(unchanged-interval)
! | fifth<br>(¢)
! Generator (¢)
! | 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
| | 696.043
| 696.043
| | 13 and 15-odd-limit minimax
| 13 and 15-odd-limit minimax
|-
|-
| | 39/32
| 39/32
| | 696.405
| 696.405
| |
|  
|-
|-
| | 5/4
| 5/4
| | 696.578
| 696.578
| | 5, 7, 9 and 11-odd-limit minimax
| 5, 7, 9 and 11-odd-limit minimax
|-
|-
| | 4/3
| 4/3
| | 701.955
| 701.955
| |
|  
|}
|}


<!-- formerly known as meanplop
<!-- formerly known as meanplop
==== Meanpop variant ====
==== Meanpop variant ====
{| class="wikitable center-all"
{| class="wikitable center-all left-3"
|-
|-
! | eigenmonzo<br>(unchanged interval)
! Eigenmonzo<br>(unchanged-interval)
! | fifth<br>(¢)
! Generator (¢)
! | comments
! Comments
|-
|-
| | 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
| | 696.052
| 696.052
| | 13 and 15-odd-limit minimax
| 13 and 15-odd-limit minimax
|-
|-
| | 5/4
| 5/4
| | 696.578
| 696.578
| | 5, 7, 9 and 11-odd-limit minimax
| 5, 7, 9 and 11-odd-limit minimax
|-
|-
| | 33/26
| 33/26
| | 698.407
| 698.407
| |
|  
|-
|-
| | 13/11
| 13/11
| | 698.801
| 698.801
| |
|  
|-
|-
| | 4/3
| 4/3
| | 701.955
| 701.955
| |
|  
|}
|}
-->
-->
Retrieved from "https://en.xen.wiki/w/Huygens_vs_meanpop"