Maximal evenness: Difference between revisions

Wikispaces>FREEZE
No edit summary
Xenwolf (talk | contribs)
todo
Line 1: Line 1:
Within every [[EDO|edo]] one can specify a "maximally even" (ME) scale for every smaller edo. The maximally even scale is the closest the parent edo can get to representing the smaller edo. Mathematically, ME scales of n notes in m edo are any [[mode|mode]] of the sequence ME(n, m) = [floor(i*m/n) | i=1..n], where the [https://en.wikipedia.org/wiki/Floor_and_ceiling_functions "floor"] function rounds down to the nearest integer.
Within every [[EDO|edo]] one can specify a '''maximally even''' (ME) scale for every smaller edo. The maximally even scale is the closest the parent edo can get to representing the smaller edo. Mathematically, ME scales of n notes in m edo are any [[mode|mode]] of the sequence ME(n, m) = [floor(i*m/n) | i=1..n], where the [https://en.wikipedia.org/wiki/Floor_and_ceiling_functions "floor"] function rounds down to the nearest integer.


The maximally even scale will be one:
The maximally even scale will be one:
Line 104: Line 104:


Note that "maximally even" is equivalent to "quasi-equal-interval-symmetrical" in [[Joel_Mandelbaum|Joel Mandelbaum]]'s 1961 thesis [http://www.anaphoria.com/mandelbaum.html Multiple Divisions of the Octave and the Tonal Resources of 19-Tone Temperament]. Previous versions of this article have conflated "quasi-equal" with "quasi-equal-interval symmetrical". In fact, "quasi-equal" scales, according to Mandelbaum, meet the first criterion listed above, but not necessarily the second.
Note that "maximally even" is equivalent to "quasi-equal-interval-symmetrical" in [[Joel_Mandelbaum|Joel Mandelbaum]]'s 1961 thesis [http://www.anaphoria.com/mandelbaum.html Multiple Divisions of the Octave and the Tonal Resources of 19-Tone Temperament]. Previous versions of this article have conflated "quasi-equal" with "quasi-equal-interval symmetrical". In fact, "quasi-equal" scales, according to Mandelbaum, meet the first criterion listed above, but not necessarily the second.
[[Category:Todo:cleanup]]