23rd-octave temperaments: Difference between revisions

Although 23edo itself is not particularly accurate for low-complexity harmonics, some temperaments which are multiples of 23 are.  

However, if we want to guarantee we can find ''all'' primes relative to the same root note, we require a 5*23=115-note [[MOS]], corresponding to [[46L 69s]], that is, to [[2L 3s]] (pentic) with a [[23edo|1\23 period]], a fascinating "microtonal minification" of the familiar pentatonic scale, using the small step for very subtle commatic variations on notes of 46edo, though few dare to use scales this elaborate, and the [[23L 46s]] scale is likely sufficient for exploring most of the harmony offered (and likely more interesting to play with), so that it might also serve in some strange way as a [[well temperament]] of [[69edo]] (not just 46edo), which is a flat tuning of [[meantone]] supporting many but not all of the equivalences of icositritonic.