1/5-comma meantone: Difference between revisions
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{{Interwiki | |||
| en = 1/5-comma meantone | |||
| de = Fünftelkomma-mitteltönig | |||
}} | |||
'''1/5-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a fifth of a [[syntonic comma]] from its just value of [[3/2]]. This results in major sevenths being exactly [[15/8]] (and minor seconds being exactly [[16/15]]), and in fact this defines 1/5-comma; it is the regular tuning which tempers out [[81/80]] and tunes [[2/1|2]] and [[16/15]] purely. | |||
The major third ([[5/4]]) and the fifth are equally off from JI by 1/5 syntonic comma (''c''. 4.3 [[cent]]s), with the major third sharp and the fifth flat. The augmented sixth is exactly [[225/128]], and for septimal meantone, this means the [[7/4]] is sharp by a [[225/224|septimal kleisma (225/224)]]. | |||
1/5-comma meantone is practically identical to the closed system of [[43edo]] (although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.) | |||
== Tuning profile == | |||
[[Projection map]]: | |||
{| class="right-all" | |||
|- | |||
| [⟨ || 1 || 4/5 || -4/5 || -5 || ] | |||
|- | |||
| ⟨ || 0 || 1/5 || 4/5 || 2 || ] | |||
|- | |||
| ⟨ || 0 || 1/5 || 4/5 || 2 || ] | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 0 || ]] | |||
|} | |||
[[Tuning map]]: {{val| 1200 1897.6537 2790.6150 3376.5374 }} | |||
[[Error map]]: {{val| 0 -4.3013 +4.3013 +7.7115 }} | |||
== Music == | |||
; [[septimal lemon]] | |||
* [https://youtu.be/jlbpQqahZh0 ''Bubbles''] (2025) | |||
[[Category:Meantone]] | |||
[[Category:Historical]] | |||
Latest revision as of 08:30, 3 May 2026
1/5-comma meantone is the tuning of meantone temperament in which each perfect fifth is tempered by a fifth of a syntonic comma from its just value of 3/2. This results in major sevenths being exactly 15/8 (and minor seconds being exactly 16/15), and in fact this defines 1/5-comma; it is the regular tuning which tempers out 81/80 and tunes 2 and 16/15 purely.
The major third (5/4) and the fifth are equally off from JI by 1/5 syntonic comma (c. 4.3 cents), with the major third sharp and the fifth flat. The augmented sixth is exactly 225/128, and for septimal meantone, this means the 7/4 is sharp by a septimal kleisma (225/224).
1/5-comma meantone is practically identical to the closed system of 43edo (although technically there is a slight difference, as the fifth of 43 is 0.0207 cents sharper.)
Tuning profile
| [⟨ | 1 | 4/5 | -4/5 | -5 | ] |
| ⟨ | 0 | 1/5 | 4/5 | 2 | ] |
| ⟨ | 0 | 1/5 | 4/5 | 2 | ] |
| ⟨ | 0 | 0 | 0 | 0 | ]] |
Tuning map: ⟨1200 1897.6537 2790.6150 3376.5374]
Error map: ⟨0 -4.3013 +4.3013 +7.7115]
Music
- Bubbles (2025)