1/3-comma meantone: Difference between revisions

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In '''1/3-comma meantone''' temperament, 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]]).
'''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).


In other words, 1/3-comma meantone is the specific tuning of [[meantone]] temperament with an [[Fractional_monzos|eigenmonzo]] of 6/5.
== Tuning profile ==
[[Projection map]]:


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.
{| 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 || ]]
|}


1/3-comma meantone is practically identical to the closed system of [[19edo]] (although technically there is a slight difference).
[[Tuning map]]: {{val| 1200 1894.7862 2779.1450 3347.8624 }}
 
[[Error map]]: {{val| 0 -7.1688 -7.1688 -20.9635 }}


== External links ==
== 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]]


* [http://www.lehrklaenge.de/PHP/Tonsystem/MitteltoenigeStimmung3.php Die mitteltönige Stimmung mit reinen kleinen Terzen] (explanation of 1/3 comma meantone, German)
[[Category:Definition]]
[[Category:Meantone]]
[[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

Projection map:

[⟨ 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