7edo: Difference between revisions
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It has often been stated that 7edo approximates tunings used in [[Thai]] classical music, though this is a myth unsupported by [[empirical]] studies of the instruments.<ref>Garzoli, John. [http://iftawm.org/journal/oldsite/articles/2015b/Garzoli_AAWM_Vol_4_2.pdf ''The Myth of Equidistance in Thai Tuning.'']</ref> | It has often been stated that 7edo approximates tunings used in [[Thai]] classical music, though this is a myth unsupported by [[empirical]] studies of the instruments.<ref>Garzoli, John. [http://iftawm.org/journal/oldsite/articles/2015b/Garzoli_AAWM_Vol_4_2.pdf ''The Myth of Equidistance in Thai Tuning.'']</ref> | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
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== Approximation to JI == | == Approximation to JI == | ||
[[File:7ed2-001.svg | [[File:7ed2-001.svg]] | ||
== Regular temperament properties == | == Regular temperament properties == | ||
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3/7 is on the intersection of [[meantone]] and [[mavila]], and has MOS's of 331 and 21211, making 7edo the first edo with a non-equalized, non-1L''n''s [[pentatonic]] mos. This is in part because 7edo is close to low-complexity JI for its size, and is the second edo with a good fifth for its size (after [[5edo]]), the fifth serving as a generator for the edo's meantone and mavila interpertations. | 3/7 is on the intersection of [[meantone]] and [[mavila]], and has MOS's of 331 and 21211, making 7edo the first edo with a non-equalized, non-1L''n''s [[pentatonic]] mos. This is in part because 7edo is close to low-complexity JI for its size, and is the second edo with a good fifth for its size (after [[5edo]]), the fifth serving as a generator for the edo's meantone and mavila interpertations. | ||
== Octave stretch or compression == | |||
[[Stretched and compressed tuning|Stretched-octaves]] tunings such as [[11edt]], [[18ed6]] or [[zpi|15zpi]] greatly improves 7edo's approximation of harmonics 3, 5 and 11, at the cost of slightly worsening 2 and 7, and greatly worsening 13. If one is hoping to use 7edo for full [[11-limit]] harmonies, then these are good choices to make that easier. | |||
== Instruments == | == Instruments == | ||
* [[Lumatone mapping for 7edo]] | * [[Lumatone mapping for 7edo]] | ||
In addition, various fretted string instruments have been built to play in 7edo (an example is linked in the [[#see also]] section below). | |||
== Music == | == Music == | ||
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== Ear training == | == Ear training == | ||
7edo ear-training exercises by Alex Ness available [https://drive.google.com/folderview?id=0BwsXD8q2VCYUT3VEZUVmeVZUcmc&usp=drive_web#list here]. | 7edo ear-training exercises by Alex Ness available [https://drive.google.com/folderview?id=0BwsXD8q2VCYUT3VEZUVmeVZUcmc&usp=drive_web#list here]. | ||
== See also == | |||
* [[Alpha, beta, and gamma family of equal divisions]] | |||
; [[Noah Jordan]] | |||
* [https://www.youtube.com/watch?v=6MDUxUEnQT4 ''7 tone equal temperament (7edo) microtonal tuning talk and demonstration''] (2024) — Here, Noah Jordan uses variations in the tuning of a {{W|jarana jarocha}} fretted for 7edo to demonstrate the concept of modifying a 7edo tuning to get non-neutral pitches. | |||
== Notes == | == Notes == | ||