Xenharmonic Wiki

1/3-comma meantone: Difference between revisions

← Older edit
VisualWikitext
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
m Xenwolf moved page 1-3 Syntonic Comma Meantone to 1/3 syntonic comma meantone: changed into intended lemma (that was not possible in Wikispaces), changed into Sentence case
clarify in “practically identical”
 
(12 intermediate revisions by 7 users not shown)
Line 1: Line 1:
[[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, which is about 7 cents flatter than in [[Quarter-comma_meantone|1/4-comma meantone]].
{| 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]]
Retrieved from "https://en.xen.wiki/w/1/3-comma_meantone"