Meantone: Difference between revisions
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== Scales == | == Scales == | ||
; EDO tunings | ; EDO tunings | ||
* [[Meantone5]] | * [[Meantone5]] – pentic scale in 31edo | ||
* [[Meantone7]] | * [[Meantone7]] – diatonic scale in 19edo and 31edo | ||
* [[Meantone12]] | * [[Meantone12]] – chromatic scale in 31edo | ||
; Eigenmonzo (unchanged-interval) tunings | ; Eigenmonzo (unchanged-interval) tunings | ||
* [[Meanwoo12]] | * [[Meanwoo12]] – chromatic scale in 5/4.7-eigenmonzo tuning | ||
* [[Meanwoo19]] | * [[Meanwoo19]] – enharmonic scale in 5/4.7-eigenmonzo tuning | ||
* [[Ratwolf]] | * [[Ratwolf]] – chromatic scale with 20/13 wolf fifth | ||
; Others | ; Others | ||
* [[Meaneb471a]] | * [[Meaneb471a]] – chromatic scale in one equal beating tuning of ~3/1 and ~5/1 | ||
* [[Meaneb471]] | * [[Meaneb471]] – chromatic scale in the other equal beating tuning of ~3/1 and ~5/1, also called "metameantone" | ||
== Tunings == | == Tunings == | ||
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{| class="wikitable mw-collapsible mw-collapsed" | {| class="wikitable mw-collapsible mw-collapsed" | ||
|+style="font-size: 105%; white-space: nowrap;" | 7-limit Prime-Optimized Tunings | |+ style="font-size: 105%; white-space: nowrap;" | 7-limit Prime-Optimized Tunings | ||
|- | |- | ||
! Weight-skew\Order !! Euclidean | ! Weight-skew\Order !! Euclidean | ||
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{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
|- | |||
! Edo<br />Generator | ! Edo<br />Generator | ||
! [[Eigenmonzo|Eigenmonzo<br />(Unchanged-interval)]] | ! [[Eigenmonzo|Eigenmonzo<br />(Unchanged-interval)]]* | ||
! Generator<br />(¢) | ! Generator<br />(¢) | ||
! Comments | ! Comments | ||
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| '''Upper bound of 5-odd-limit diamond monotone''' | | '''Upper bound of 5-odd-limit diamond monotone''' | ||
|} | |} | ||
<nowiki />* Besides the octave | |||
=== Formula for ''n''-comma meantone === | === Formula for ''n''-comma meantone === | ||
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<math>\displaystyle g = g_J - ng_c</math> | <math>\displaystyle g = g_J - ng_c</math> | ||
where ''g''<sub>''J''</sub> = 701.955001 cents is the size of the just perfect fifth, and ''g''<sub>c</sub> = 21.506290 cents is the size of the syntonic comma. | where {{nowrap|''g''<sub>''J''</sub> {{=}} 701.955001}} cents is the size of the just perfect fifth, and ''g''<sub>c</sub> = 21.506290 cents is the size of the syntonic comma. | ||
Conversely, ''n'' can be found by | Conversely, ''n'' can be found by | ||
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== See also == | == See also == | ||
* [[Angel]] | * [[Angel]] – fifth-equivalent or 5/1-equivalent meantone | ||
== External links == | == External links == | ||
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[[Category:Temperaments]] | [[Category:Temperaments]] | ||
[[Category:Meantone| ]] <!-- | [[Category:Meantone| ]] <!-- Main article --> | ||
[[Category:Meantone family]] | [[Category:Meantone family]] | ||
[[Category:Starling temperaments]] | [[Category:Starling temperaments]] | ||
[[Category:Marvel temperaments]] | [[Category:Marvel temperaments]] | ||
[[Category:Historical]] | [[Category:Historical]] | ||