1/3-comma meantone: Difference between revisions

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[[de:Drittelkomma-mitteltönig]]
{{interwiki
In '''1/3-comma [[Meantone|meantone]]''' temperament, each perfect fifth is tempered by a third of a [[Syntonic_Comma|syntonic comma]] from its just value of [[3/2|3/2]]. This results in minor thirds being exactly [[6/5|6/5]] (and major sixths being exactly [[5/3|5/3]]).
| de = Drittelkomma-mitteltönig
| en = 1/3 syntonic comma meantone
| es =
| ja =
}}
'''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|19edo]] (although technically there is a slight difference).
[[Tuning map]]: {{val| 1200 1894.7862 2779.1450 3347.8624 }}


=External links=
[[Error map]]: {{val| 0 -7.1688 -7.1688 -20.9635 }}
[http://www.lehrklaenge.de/html/mitteltonige_stimmung_iii.html Die mitteltönige Stimmung mit reinen kleinen Terzen] (explanation of 1/3 comma meantone, in german)
 
[[Category:definition]]
== External links ==
[[Category:meantone]]
* [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

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

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