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TES: The largest network of teachers in the world

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Macrotonal: literally, "(noticeably) larger than a half step". A "macrotonal" scale would be one where all step sizes exceed 100 cents (in theory) or at least equal 103.5 cents (in practice). Paradoxically, "macrotonal" is a subset of "microtonal," according to the loose definition of microtonal meaning "tuning systems other than 12-tone equal temperament". Just as paradoxically, macrotones will become incisive steps relative to hyperoctaves larger than 1300 cents (13edt being the canonical example of this paradox), and also "emphatic" approaches to a scale degree (meantone temperament being the canonical example of this paradox).

"Macrotonal Edo," then, refers to a tuning system which cuts the octave into fewer than 12 equal parts.

Macrotonal edos offer as one possible starting point for exploring non-12 tunings. Each offers its own set of unique constraints. Some seem to offer less variety than 12edo does (so are, in a way, simple -- eg. 5edo, 7edo), and some seem to offer more variety (eg. 11edo). As a set, they offer abundant variety and could keep a student happily confused for a good while, perhaps a lifetime.

If what you're after is very close approximations to low-number frequency ratios, you will find only one example here: 9edo has a very close approximation to 7/6 and 12/7. You will, however, find something else.

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

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 Temperament 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 7edos. Here are some edo families: