This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A116474 #8 Oct 02 2013 16:16:05 %S A116474 1,3,4,5,22,26,29,58,80,94,282,311,17461 %N A116474 Equal divisions of the octave with progressively increasing consistency levels. %C A116474 An equal temperament is consistent at level N (odd integer) if all the intervals in the N-limit tonality diamond (set of ratios with odd factors of numerator and denominator not exceeding N) are approximated consistently, i.e. the composition of the approximations is the closest approximation of the composition. %C A116474 These EDOs are not necessarily any good for musical purposes. Even though 4-EDO is consistent through the 7 limit, no one would seriously consider using it for 7-limit music because the approximations are so bad. %C A116474 While for the smallest values these EDOs are not directly usable, their consistency is even so a valuable feature. For example, 4-EDO is consistent through the 7 limit, but is not usable directly for 7-limit music. However, indirectly, by means of subsequently adjusting the harmony, it can be and has been useful as a compositional tool for composing music in the 7-limit. The same comment applies to 3 in the 5-limit and 5 in the 9-limit. Any of the values above 5 are usable directly as equal temperament approximations to the corresponding limit. - _Gene Ward Smith_, Mar 29 2006 %H A116474 <a href="http://library.wustl.edu/~manynote/music.html">Tables of consistency levels.</a> %H A116474 <a href="http://www.tonalsoft.com/enc/c/consistent.aspx">Entry in Tonalsoft encyclopedia of microtonal music theory.</a> %e A116474 3-EDO is consistent through the 5 limit because 6/5, 5/4 and 4/3 map to 1 step and 3/2, 8/5 and 5/3 map to 2 steps and all the compositions work out, for example 6/5 * 5/4 = 3/2 and 1 step + 1 step = 2 steps. It is not consistent through the 7 limit because 8/7 and 7/6 both map to 1 step, but 8/7 * 7/6 = 4/3 also maps to 1 step. %Y A116474 Cf. A116475, A117577, A117578. %K A116474 nonn,more %O A116474 3,2 %A A116474 _Keenan Pepper_, Mar 17 2006 %E A116474 More terms from _Gene Ward Smith_, Mar 29 2006