21edo: Difference between revisions

(3 intermediate revisions by 3 users not shown)

Line 18:

In terms of interval regions, 21edo possesses four types of 2nd (subminor, minor, submajor, and supermajor), three types of 3rd (subminor, neutral, and major), a "third-fourth" (an interval that can function as either a supermajor 3rd or a narrow 4th), a wide (or acute) 4th, and a narrow tritone, as well as the octave-inversions of all of these intervals.

Because 21edo is a Fibonacci edo, it contains an approximation to the [[logarithmic phi]] superfifth, which generates golden MOS scales 8L 5s, 5L 3s, and 3L 2s.

Thanks to its sevenths, 21edo is an ideal tuning for its size for [[metallic harmony]].

Line 366:

Line 368:

| C (sus) down-four up-five

|}

~~== Approximation to JI ==~~

~~=== Zeta peak index ===~~

~~{{ZPI~~

~~| zpi = 75~~

~~| steps = 21.0279383259393~~

~~| step size = 57.0669354931351~~

~~| tempered height = 4.107322~~

~~| pure height = 3.877024~~

~~| integral = 0.716469~~

~~| gap = 12.853639~~

~~| octave = 1198.40564535584~~

~~| consistent = 4~~

~~| distinct = 4~~

}}

== Scales ==

Line 690:

Line 677:

; [[Francium]]

* [https://www.youtube.com/watch?v=pOJhks06uLI ''~~Gordon Guide~~''] (~~2024~~) ~~– gorgo[11] in 21edo tuning~~

* "Gordon Guide" from ''XenRhythms'' (2024) – [https://open.spotify.com/track/3O8rX7wHSYFV2AXj6yVc5u Spotify] | [https://francium223.bandcamp.com/track/gordon-guide Bandcamp] | [https://www.youtube.com/watch?v=pOJhks06uLI YouTube] – in Gorgo[11], 21edo tuning

* [https://www.youtube.com/watch?v=llr_vws6alY ''Gumballs & Party Dancing''] (2025)

; [[Frédéric Gagné]]

Line 741:

Line 729:

* [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/15%20-%2015.%2021%20octave.mp3 Comets Over Flatland 15]

* [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/18%20-%2018.%2021%20octave.mp3 Comets Over Flatland 18]

; [[User:Fitzgerald_Lee|Fitzgerald Lee]]

* [https://youtu.be/Nxn2FJWORIg Teetering Rag] (2025)

== See also ==

@@ Line 18: / Line 18: @@
 In terms of interval regions, 21edo possesses four types of 2nd (subminor, minor, submajor, and supermajor), three types of 3rd (subminor, neutral, and major), a "third-fourth" (an interval that can function as either a supermajor 3rd or a narrow 4th), a wide (or acute) 4th, and a narrow tritone, as well as the octave-inversions of all of these intervals.
+Because 21edo is a Fibonacci edo, it contains an approximation to the [[logarithmic phi]] superfifth, which generates golden MOS scales 8L 5s, 5L 3s, and 3L 2s.
 Thanks to its sevenths, 21edo is an ideal tuning for its size for [[metallic harmony]].
@@ Line 366: / Line 368: @@
 | C (sus) down-four up-five
 |}
-== Approximation to JI ==
-=== Zeta peak index ===
-{{ZPI
-| zpi = 75
-| steps = 21.0279383259393
-| step size = 57.0669354931351
-| tempered height = 4.107322
-| pure height = 3.877024
-| integral = 0.716469
-| gap = 12.853639
-| octave = 1198.40564535584
-| consistent = 4
-| distinct = 4
-}}
 == Scales ==
@@ Line 690: / Line 677: @@
 ; [[Francium]]
-* [https://www.youtube.com/watch?v=pOJhks06uLI ''Gordon Guide''] (2024) – gorgo[11] in 21edo tuning
+* "Gordon Guide" from ''XenRhythms'' (2024) – [https://open.spotify.com/track/3O8rX7wHSYFV2AXj6yVc5u Spotify] | [https://francium223.bandcamp.com/track/gordon-guide Bandcamp] | [https://www.youtube.com/watch?v=pOJhks06uLI YouTube] – in Gorgo[11], 21edo tuning
+* [https://www.youtube.com/watch?v=llr_vws6alY ''Gumballs & Party Dancing''] (2025)
 ; [[Frédéric Gagné]]
@@ Line 741: / Line 729: @@
 * [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/15%20-%2015.%2021%20octave.mp3 Comets Over Flatland 15]
 * [http://micro.soonlabel.com/gene_ward_smith/Others/Winchester/18%20-%2018.%2021%20octave.mp3 Comets Over Flatland 18]
+; [[User:Fitzgerald_Lee|Fitzgerald Lee]]
+* [https://youtu.be/Nxn2FJWORIg Teetering Rag] (2025)
 == See also ==