43edo: Difference between revisions

43edo is strongly associated with [[meantone]], particularly [[1/5-comma meantone]], being a good tuning system in the 5, 7, 11, and 13-limit. The version of 11-limit meantone is the one tempering out [[99/98]], [[176/175]] and [[441/440]] sometimes called Huygens. 43-equal has the first good 13-limit meantone available as an equal division of the octave. The baroque, French, ironically hearing and speech impaired acoustician [[wikipedia: Joseph Sauveur|Joseph Sauveur]] based his system on 43 equal tones to the octave, calling them "merides". Further information: [http://tonalsoft.com/enc/m/meride.aspx Tonalsoft encyclopedia entry of meride].  

Although not [[consistent]], it performs quite decently in very high limits. It has unambiguous mappings for all prime harmonics up to ''109'', with the sole exceptions of 23, 71 and 89, making a great [[#Ringer 43|Ringer scale]]. The mappings for composite harmonics can then be derived from those for the primes, giving an almost-complete version of mode 32 of the harmonic series, although the aforementioned lack of consistency will give some unusual results. Indeed, the step size of 43edo is very close to the [[64/63|septimal comma (64/63)]], while two steps is close to [[32/31]], and four steps to [[16/15]].