Xenharmonic Wiki

Huygens vs meanpop: Difference between revisions

← Older editNewer edit →
VisualWikitext
Xenllium (talk | contribs)
autopatrolled, emailconfirmed
4,516 edits
No edit summary
Cleanup and some really important corrections
Line 11: Line 11:
Can meantone and meanpop be combined into a single temperament? Yes! It works wonderfully and that temperament is [[31edo|31EDO]]. In 31EDO the circle of fifths closes perfectly after 31 fifths, so Ex and Gbb are the same note. (In other words, the interval of the ''quadruply diminished third'' is tuned to 0 cents, if that makes any sense to you.) This makes everything much simpler and results in 121/120 and 243/242 being tempered out, so that 12/11~11/10 is a "neutral second" (exactly half of a minor third), and 11/9 is a "neutral third" (exactly half of a perfect fifth). Keep in mind that neither of these things are true in either meantone or meanpop.
Can meantone and meanpop be combined into a single temperament? Yes! It works wonderfully and that temperament is [[31edo|31EDO]]. In 31EDO the circle of fifths closes perfectly after 31 fifths, so Ex and Gbb are the same note. (In other words, the interval of the ''quadruply diminished third'' is tuned to 0 cents, if that makes any sense to you.) This makes everything much simpler and results in 121/120 and 243/242 being tempered out, so that 12/11~11/10 is a "neutral second" (exactly half of a minor third), and 11/9 is a "neutral third" (exactly half of a perfect fifth). Keep in mind that neither of these things are true in either meantone or meanpop.


{| class="wikitable"
{| class="wikitable center-3 center-5"
! rowspan="2" | JI Interval
! colspan="2" | Meantone mapping
! colspan="2" | Meanpop mapping
|-
|-
! | JI interval
! Nominals
! | meantone mapping
! Fifth Steps
! | meantone fifths
! Nominals
! | meanpop mapping
! Fifth Steps
! | meanpop fifths
|-
|-
| | 22/21
| 22/21
| | Augmented prime (C-C#)
| Augmented unison (C-C#), same as 25/24
| | +7
| +7
| | Triply diminished third (C-Ebbbb)
| Triply diminished third (C-Ebbbb)
| | -24
| -24
|-
|-
| | 12/11, 88/81
| 12/11
| | Doubly diminished third (C-Ebbb)
| Doubly diminished third (C-Ebbb)
| | -17
| -17
| | Doubly augmented prime (C-Cx)
| Doubly augmented unison (C-Cx)
| | +14
| +14
|-
|-
| | 11/10
| 11/10, 88/81
| | Doubly augmented prime (C-Cx)
| Doubly augmented unison (C-Cx)
| | +14
| +14
| | Doubly diminished third (C-Ebbb)
| Doubly diminished third (C-Ebbb)
| | -17
| -17
|-
|-
| | 112/99
| 112/99
| | Diminished third (C-Ebb), same as 8/7
| Diminished third (C-Ebb), same as 8/7
| | -10
| -10
| | Triply augmented prime (C-C*)
| Triply augmented unison (C-C#x)
| | +21
| +21
|-
|-
| | 33/28
| 33/28
| | Augmented second (C-D#), same as 7/6
| Augmented second (C-D#), same as 7/6
| | +9
| +9
| | Triply diminished fourth (C-Fbbb)
| Triply diminished fourth (C-Fbbb)
| | -22
| -22
|-
|-
| | 40/33
| 27/22, 40/33
| | Doubly diminished fourth (C-Fbb)
| Doubly diminished fourth (C-Fbb)
| | -15
| -15
| | Doubly augmented second (C-Dx)
| Doubly augmented second (C-Dx)
| | +16
| +16
|-
|-
| | 11/9, 27/22
| 11/9, 99/80
| | Doubly augmented second (C-Dx)
| Doubly augmented second (C-Dx)
| | +16
| +16
| | Doubly diminished fourth (C-Fbb)
| Doubly diminished fourth (C-Fbb)
| | -15
| -15
|-
|-
| | 14/11
| 14/11
| | Diminished fourth (C-Fb), same as 9/7
| Diminished fourth (C-Fb), same as 9/7
| | -8
| -8
| | Triply augmented second (C-D*)
| Triply augmented second (C-D#x)
| | +23
| +23
|-
|-
| | 15/11
| 15/11
| | Triply diminished sixth (C-Abbbb)
| Doubly diminished fifth (C-Gbb)
| | -25
| -13
| | Augmented fourth (C-F#), same as 7/5
| Doubly augmented third (C-Ex)
| | +6
| +18
|-
|-
| | 11/8
| 11/8
| | Doubly augmented third (C-Ex)
| Doubly augmented third (C-Ex)
| | +18
| +18
| | Doubly diminished fifth (C-Gbb)
| Doubly diminished fifth (C-Gbb)
| | -13
| -13
|-
|-
| | 16/11
| 16/11
| | Doubly diminished sixth (C-Abbb)
| Doubly diminished sixth (C-Abbb)
| | -18
| -18
| | Doubly augmented fourth (C-Fx)
| Doubly augmented fourth (C-Fx)
| | +13
| +13
|-
|-
|22/15
| 22/15
|Triply augmented third (C-E*)
| Doubly augmented fourth (C-Fx)
| +25
| +13
|Diminished fifth (C-Gb), same as 10/7
| Doubly diminished sixth (C-Abbb)
| -6
| -18
|-
|-
| | 11/7
| 11/7
| | Augmented fifth (C-G#), same as 14/9
| Augmented fifth (C-G#), same as 14/9
| | +8
| +8
| | Triply diminished seventh (C-Bbbbb)
| Triply diminished seventh (C-Bbbbb)
| | -23
| -23
|-
|-
| | 18/11, 44/27
| 18/11, 160/99
| | Doubly diminished seventh (C-Bbbb)
| Doubly diminished seventh (C-Bbbb)
| | -16
| -16
| | Doubly augmented fifth (C-Gx)
| Doubly augmented fifth (C-Gx)
| | +15
| +15
|-
|-
| | 33/20
| 33/20, 44/27
| | Doubly augmented fifth (C-Gx)
| Doubly augmented fifth (C-Gx)
| | +15
| +15
| | Doubly diminished seventh (C-Bbbb)
| Doubly diminished seventh (C-Bbbb)
| | -16
| -16
|-
|-
| | 56/33
| 56/33
| | Diminished seventh (C-Bbb), same as 12/7
| Diminished seventh (C-Bbb), same as 12/7
| | -9
| -9
| | Triply augmented fifth (C-G*)
| Triply augmented fifth (C-G#x)
| | +16
| +16
|-
|-
| | 99/56
| 99/56
| | Augmented sixth (C-A#), same as 7/4
| Augmented sixth (C-A#), same as 7/4
| | +10
| +10
| | Triply diminished octave (C-Cbbb)
| Triply diminished octave (C-Cbbb)
| | -21
| -21
|-
|-
| | 20/11
| 20/11, 81/44
| | Doubly diminished octave (C-Cbb)
| Doubly diminished octave (C-Cbb)
| | -14
| -14
| | Doubly augmented sixth (C-Ax)
| Doubly augmented sixth (C-Ax)
| | +17
| +17
|-
|-
| | 11/6, 81/44
| 11/6
| | Doubly augmented sixth (C-Ax)
| Doubly augmented sixth (C-Ax)
| | +17
| +17
| | Doubly diminished octave (C-Cbb)
| Doubly diminished octave (C-Cbb)
| | -14
| -14
|-
|-
| | 21/11
| 21/11
| | Diminished octave (C-Cb)
| Diminished octave (C-Cb), same as 48/25
| | -7
| -7
| | Triply augmented sixth (C-A*)
| Triply augmented sixth (C-A#x)
| | +24
| +24
|}
|}


Retrieved from "https://en.xen.wiki/w/Huygens_vs_meanpop"