21edo: Difference between revisions

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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.
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]].
Thanks to its sevenths, 21edo is an ideal tuning for its size for [[metallic harmony]].
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| C (sus) down-four up-five
| 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 ==
== Scales ==
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* [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/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]
* [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 ==
== See also ==