1/3-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 (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).
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