Macrotonal EDO: Difference between revisions
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A '''macrotonal EDO''' is any EDO smaller than [[12edo|12]], which has as its smallest interval a step larger than a 12edo semitone. Confusingly, "macrotonal" is a subset of "microtonal," according to the loose definition of microtonal meaning "tuning systems other than 12-tone equal temperament". | A '''macrotonal EDO''' is any EDO smaller than [[12edo|12]], which has as its smallest interval a step larger than a 12edo semitone. Confusingly, "macrotonal" is a subset of "microtonal," according to the loose definition of microtonal meaning "tuning systems other than 12-tone equal temperament". | ||
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Note that "macrotonal edos" is a finite set containing 11 members. "Xenharmonic macrotonal edos" would exclude those which are subsets of 12edo (1-4 & 6), & would thus contain 6 members (5, 7, 8, 9, 10, 11). | Note that "macrotonal edos" is a finite set containing 11 members. "Xenharmonic macrotonal edos" would exclude those which are subsets of 12edo (1-4 & 6), & would thus contain 6 members (5, 7, 8, 9, 10, 11). | ||
==EDO Families== | == Archetypal use == | ||
Many macrotonal edos, especially 5edo through 10edo, provide an underlying structure in many temperaments, while erasing many of their distinctions. Nonetheless, melody and to an extent harmony can be imitated in them, and many characteristics are still similar. | |||
{| class="wikitable" | |||
! EDO | |||
! Example subgroup | |||
! Temperaments | |||
! Comments | |||
|- | |||
| [[4edo]] | |||
| 2.5/3.7/3.17/3 | |||
| [[Starlingtet]], [[kleismic]], … | |||
| | |||
|- | |||
| [[5edo]] | |||
| 2.3.7 | |||
| [[Semaphore]], [[superpyth]], [[slendric]], [[meantone]],… | |||
| See also [[Archytas–diatonic equivalence continuum]]<br>and [[Syntonic–diatonic equivalence continuum]]. | |||
|- | |||
| [[6edo]] | |||
| 2.9.5.7.11 | |||
| [[Didacus]], [[Baldy]], [[Machine]],… | |||
| See also [[Jubilismic–augmented equivalence continuum]]. | |||
|- | |||
| [[7edo]] | |||
| 2.3.5.11.13 | |||
| [[Meantone]], [[neutral]], [[porcupine]], [[tetracot]], … | |||
| See also [[Syntonic–chromatic equivalence continuum]]. | |||
|- | |||
| [[8edo]] | |||
| 2.5/3.7/3.11/3.13/3.17/3 | |||
| [[Sensi]], [[Tridec]], [[Ammonite]], … | |||
| | |||
|- | |||
| [[9edo]] | |||
| 2.5.7/3.11 | |||
| [[Orwell]], [[Mavila]], [[Semaphore]], [[Negri]], … | |||
| | |||
|- | |||
| [[10edo]] | |||
| 2.3.5.7.13 | |||
| [[Pajara]], [[Negri]], … | |||
| | |||
|} | |||
== EDO Families == | |||
Macrotonal edos (or any edo really) are available in larger edos which are multiples of them; the edos which are multiples of the same smaller edo can be thought of as being "related," perhaps even "in the same family" as one another. This becomes especially significant with linear temperaments such as [[blackwood]] which use some division of the octave (in the case of Blackwood, a fifth of an octave) as the period. It also suggests a family of superscales that one could use to expand upon the potential of a simpler scale: for instance, [[14edo]] as a superscale containing two [[7edo]]s. Here are some edo families: | Macrotonal edos (or any edo really) are available in larger edos which are multiples of them; the edos which are multiples of the same smaller edo can be thought of as being "related," perhaps even "in the same family" as one another. This becomes especially significant with linear temperaments such as [[blackwood]] which use some division of the octave (in the case of Blackwood, a fifth of an octave) as the period. It also suggests a family of superscales that one could use to expand upon the potential of a simpler scale: for instance, [[14edo]] as a superscale containing two [[7edo]]s. Here are some edo families: | ||