1/3-comma meantone: Difference between revisions
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Wikispaces>hstraub **Imported revision 237681909 - Original comment: ** |
Hotcrystal0 (talk | contribs) clarify in “practically identical” |
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| de = Drittelkomma-mitteltönig | |||
| en = 1/3 syntonic comma meantone | |||
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'''1/3-comma meantone''' is the tuning of [[meantone]] temperament in which each perfect fifth is tempered by a third of a [[syntonic comma]] from its just value of [[3/2]]. This results in minor thirds being exactly [[6/5]] (and major sixths being exactly [[5/3]]). In other words, 1/3-comma meantone is the specific tuning of [[meantone]] temperament with an [[Eigenmonzo|eigenmonzo (unchanged interval)]] of 6/5. The fifth is 694.786 cents in size, and the major third 379.145 cents. Both are flat by 1/3 syntonic comma (''c''. 7.2 cents) than that in the JI. 1/3-comma meantone is practically identical to the closed system of [[19edo]] (although technically there is a slight difference as 19edo's fifth is 0.05 cents flatter). | |||
[ | == Tuning profile == | ||
[[Projection map]]: | |||
{| class="right-all" | |||
|- | |||
| [⟨ || 1 || 4/3 || 4/3 || 1/3 || ] | |||
|- | |||
| ⟨ || 0 || -1/3 || -4/3 || -10/3 || ] | |||
|- | |||
| ⟨ || 0 || 1/3 || 4/3 || 10/3 || ] | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 0 || ]] | |||
|} | |||
[[Tuning map]]: {{val| 1200 1894.7862 2779.1450 3347.8624 }} | |||
[[Error map]]: {{val| 0 -7.1688 -7.1688 -20.9635 }} | |||
== External links == | |||
* [http://www.lehrklaenge.de/PHP/Tonsystem/MitteltoenigeStimmung3.php Lehrklaenge.de | ''Die mitteltönige Stimmung mit reinen kleinen Terzen''] (explanation of 1/3 comma meantone, German) | |||
* [http://tonalsoft.com/enc/number/19edo.aspx 19-tone equal-temperament and 1/3-comma meantone / 19-edo / 19-ed2] on [[Tonalsoft Encyclopedia]] | |||
[[Category:Meantone]] | |||
[[Category:Historical]] | |||
Latest revision as of 18:43, 23 January 2026
1/3-comma meantone is the tuning of meantone temperament in which each perfect fifth is tempered by a third of a syntonic comma from its just value of 3/2. This results in minor thirds being exactly 6/5 (and major sixths being exactly 5/3). In other words, 1/3-comma meantone is the specific tuning of meantone temperament with an eigenmonzo (unchanged interval) of 6/5. The fifth is 694.786 cents in size, and the major third 379.145 cents. Both are flat by 1/3 syntonic comma (c. 7.2 cents) than that in the JI. 1/3-comma meantone is practically identical to the closed system of 19edo (although technically there is a slight difference as 19edo's fifth is 0.05 cents flatter).
Tuning profile
| [⟨ | 1 | 4/3 | 4/3 | 1/3 | ] |
| ⟨ | 0 | -1/3 | -4/3 | -10/3 | ] |
| ⟨ | 0 | 1/3 | 4/3 | 10/3 | ] |
| ⟨ | 0 | 0 | 0 | 0 | ]] |
Tuning map: ⟨1200 1894.7862 2779.1450 3347.8624]
Error map: ⟨0 -7.1688 -7.1688 -20.9635]
External links
- Lehrklaenge.de | Die mitteltönige Stimmung mit reinen kleinen Terzen (explanation of 1/3 comma meantone, German)
- 19-tone equal-temperament and 1/3-comma meantone / 19-edo / 19-ed2 on Tonalsoft Encyclopedia