Map of rank-2 temperaments: Difference between revisions

<ul><li>[[Blackwood|Blackwood]]/[[blacksmith|blacksmith]] - The prime 3, and in blacksmith also 7, is represented using [[5edo|5edo]]. The generator gets you to all intervals of 5.</li><li>Elderthing - generator of phi. Two generators up to 3, two down to 7, other primes are more complex. (One generator up or one down are ambiguous 13.)</li></ul>

==Six periods per octave==

<ul><li>[[Hexe|Hexe]] - The 2.5.7 subgroup is represented using [[6edo|6edo]], and the generator gets you to 4/3 and 3/2. Makes little sense not to additionally temper down to [[12edo|12edo]].</li></ul>

<ul><li>[[Whitewood|Whitewood]] - Analogue of blackwood. The prime 3 is represented using 7edo, the generator is used for 5.</li><li>[[Jamesbond|Jamesbond]]/[[septimal|septimal]] - The 5-limit (and in septimal the prime 11) is represented using [[7edo|7edo]], and the generator is only used for intervals of 7.</li><li>[[Sevond|Sevond]] - 10/9 is tempered to be exactly 1\7 of an octave. Therefore 3/2 is 1 generator sharp of a 7edo step and 5/4 is 2 generators sharp.</li><li>[[Absurdity|Absurdity]] - A complex temperament (perhaps "absurdly" so).</li></ul>

<ul><li>[[Octoid|Octoid]] - 16-cent generator, sub-cent accuracy.</li></ul>

<ul><li>[[Ennealimmal|Ennealimmal]] - The generator is 49.02 cents, and don't forget the ".02" because it really is that accurate.</li></ul>

See also: [[Pythagorean_family|Pythagorean family]]

Temperaments in this family are interesting because they can be thought of as [[12edo|12edo]] with microtonal alterations.

<ul><li>[[Compton|Compton]] - 3-limit as in 12edo; intervals of 5 are off by one generator. In the 7-limit (sometimes called [[waage|waage]]), intervals of 7 are off by two generators. In the 11-limit, intervals of 11 are off by 3 generators. Thinking of [[72edo|72edo]] might make this more concrete.</li><li>[[Catler|Catler]] - 5-limit as in 12edo; intervals of 7 are off by one generator.</li><li>[[Atomic|Atomic]] - Does not temper out the schisma, so 3/2 is one schisma sharp of its 12edo value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the Pythagorean comma is twelve schismas, and hence 81/80, the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate.</li></ul>

== See also ==

* [[Fractional-octave temperaments]]