26edo: Difference between revisions

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{{~~interwiki~~

{{Interwiki

| en = 26edo

| de = 26-EDO

~~| en = 26edo~~

| es =

| ja =

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26edo has a [[3/2|perfect fifth]] of about 692 cents and [[tempering out|tempers out]] [[81/80]] in the [[5-limit]], making it a very flat [[meantone]] tuning (0.088957{{c}} flat of the [[4/9-comma meantone]] fifth) with a very soft [[5L 2s|diatonic scale]].

In the [[7-limit]], it tempers out [[50/49]], [[525/512]], [[875/864~~]], and [[Fynn's comma~~]], and [[support]]s temperaments like [[injera]], [[flattone]], [[lemba]], and [[doublewide]]. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-odd-limit]] [[consistent]]ly. 26edo has a very good approximation of the harmonic seventh ([[7/4]]), as it is the denominator of a convergent to log<sub>2</sub>7.

In the [[7-limit]], it tempers out [[50/49]], [[525/512]], and [[875/864]], and [[support]]s temperaments like [[injera]], [[flattone]], [[lemba]], and [[doublewide]]. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-odd-limit]] [[consistent]]ly. 26edo has a very good approximation of the harmonic seventh ([[7/4]]), as it is the denominator of a convergent to log<sub>2</sub>7.

26edo's minor sixth (1.6158) is very close to {{nowrap|''φ'' ≈ 1.6180}} (i.e. the golden ratio).

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=== Subsets and supersets ===

26edo has [[2edo]] and [[13edo]] as subsets, of which 13edo is non-trivial, sharing the 2.9.5.21.11.13.17.19-subgroup with 26edo. Multiplying 26edo by 3 yields [[78edo]], which corrects several harmonics. [[104edo]] is a notable dual-5s system. [[130edo]], [[364edo]], [[494edo]], and [[624edo]] do well in approximating JI, though they are more complex.

26edo has [[2edo]] and [[13edo]] as subsets, of which 13edo is non-trivial, sharing the 2.9.5.21.11.13.17.19-subgroup with 26edo.

26edo tempers out [[Fynn's comma]], which sets ~7/4 to 21\26. This is shared by several notable superset edos. Multiplying 26edo by 3 yields [[78edo]], which corrects several harmonics. [[104edo]] is a notable dual-5's system. [[130edo]], [[364edo]], [[494edo]], and [[624edo]] do well in approximating JI, though they are more complex.

== Intervals ==

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* [[Lumatone mapping for 26edo]]

* [https://www.youtube.com/watch?v=HrZ-PoUXGTg ''A rough introduction to 26edo on the Lumatone''] by [[YoVariable]] (2026)

== Literature ==

[http://www.ronsword.com Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.]

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* [https://www.youtube.com/shorts/1aCl6tuVS0c ''Happy Together - The Turtles (microtonal cover in 26edo)''] (2026)

* ''My Violet - 26edo'' (2026)

** [https://www.youtube.com/shorts/m76bQWxg_CA <nowiki>[short 1]</nowiki>'']

** [https://www.youtube.com/shorts/m76bQWxg_CA <nowiki>[short 1]</nowiki>] (Lumatone view)

** [https://www.youtube.com/shorts/L2JzCNj6jak <nowiki>[short 2]</nowiki>'']

** [https://www.youtube.com/shorts/L2JzCNj6jak <nowiki>[short 2]</nowiki>] (Lumatone view)

** [https://www.youtube.com/watch?v=XplpKE_Tc38 <nowiki>[full version[</nowiki>] (with animation by WIRED0006)

* [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026)

* ''Caprice in 26edo'' (2026)

** [https://www.youtube.com/shorts/WvnJb5VNGj4 <nowiki>[short clip]</nowiki>] (Lumatone view)

** [https://www.youtube.com/watch?v=mMQADmxJkFc <nowiki>[full version]</nowiki>]

; [[User:Eboone|Ebooone]]

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-{{interwiki
+{{Interwiki
+| en = 26edo
 | de = 26-EDO
-| en = 26edo
 | es =
 | ja =
@@ Line 11: / Line 11: @@
 edo has a [[3/2|perfect fifth]] of about 692 cents and [[tempering out|tempers out]] [[81/80]] in the [[5-limit]], making it a very flat [[meantone]] tuning (0.088957{{c}} flat of the [[4/9-comma meantone]] fifth) with a very soft [[5L 2s|diatonic scale]].
-In the [[7-limit]], it tempers out [[50/49]], [[525/512]], [[875/864]], and [[Fynn's comma]], and [[support]]s temperaments like [[injera]], [[flattone]], [[lemba]], and [[doublewide]]. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-odd-limit]] [[consistent]]ly. 26edo has a very good approximation of the harmonic seventh ([[7/4]]), as it is the denominator of a convergent to log<sub>2</sub>7.
+In the [[7-limit]], it tempers out [[50/49]], [[525/512]], and [[875/864]], and [[support]]s temperaments like [[injera]], [[flattone]], [[lemba]], and [[doublewide]]. It really comes into its own as a higher-limit temperament, being the smallest equal division which represents the [[13-odd-limit]] [[consistent]]ly. 26edo has a very good approximation of the harmonic seventh ([[7/4]]), as it is the denominator of a convergent to log<sub>2</sub>7.
 edo's minor sixth (1.6158) is very close to {{nowrap|''φ'' ≈ 1.6180}} (i.e. the golden ratio).
@@ Line 33: / Line 33: @@
 === Subsets and supersets ===
-edo has [[2edo]] and [[13edo]] as subsets, of which 13edo is non-trivial, sharing the 2.9.5.21.11.13.17.19-subgroup with 26edo. Multiplying 26edo by 3 yields [[78edo]], which corrects several harmonics. [[104edo]] is a notable dual-5s system. [[130edo]], [[364edo]], [[494edo]], and [[624edo]] do well in approximating JI, though they are more complex.
+edo has [[2edo]] and [[13edo]] as subsets, of which 13edo is non-trivial, sharing the 2.9.5.21.11.13.17.19-subgroup with 26edo.
+edo tempers out [[Fynn's comma]], which sets ~7/4 to 21\26. This is shared by several notable superset edos. Multiplying 26edo by 3 yields [[78edo]], which corrects several harmonics. [[104edo]] is a notable dual-5's system. [[130edo]], [[364edo]], [[494edo]], and [[624edo]] do well in approximating JI, though they are more complex.
 == Intervals ==
@@ Line 796: / Line 798: @@
 * [[Lumatone mapping for 26edo]]
+* [https://www.youtube.com/watch?v=HrZ-PoUXGTg ''A rough introduction to 26edo on the Lumatone''] by [[YoVariable]] (2026)
 == Literature ==
 [http://www.ronsword.com Sword, Ron. **Icosihexaphonic Scales for Guitar**. IAAA Press. 2010 - A Guitar-scale thesaurus for 26-EDO.]
@@ Line 851: / Line 856: @@
 * [https://www.youtube.com/shorts/1aCl6tuVS0c ''Happy Together - The Turtles (microtonal cover in 26edo)''] (2026)
 * ''My Violet - 26edo'' (2026)
-** [https://www.youtube.com/shorts/m76bQWxg_CA <nowiki>[short 1]</nowiki>'']
+** [https://www.youtube.com/shorts/m76bQWxg_CA <nowiki>[short 1]</nowiki>] (Lumatone view)
-** [https://www.youtube.com/shorts/L2JzCNj6jak <nowiki>[short 2]</nowiki>'']
+** [https://www.youtube.com/shorts/L2JzCNj6jak <nowiki>[short 2]</nowiki>] (Lumatone view)
+** [https://www.youtube.com/watch?v=XplpKE_Tc38 <nowiki>[full version[</nowiki>] (with animation by WIRED0006)
 * [https://www.youtube.com/shorts/wHGLOaeAkt8 ''26edo groove''] (2026)
+* ''Caprice in 26edo'' (2026)
+** [https://www.youtube.com/shorts/WvnJb5VNGj4 <nowiki>[short clip]</nowiki>] (Lumatone view)
+** [https://www.youtube.com/watch?v=mMQADmxJkFc <nowiki>[full version]</nowiki>]
 ; [[User:Eboone|Ebooone]]