81edo: Difference between revisions

By Tom Winspear, utilizing the Accidents shown below. Left: Chain of 4ths/5ths , Right: Chromatic view. Black font represents the '6 accidentals deep' notation that covers the chromatic scale with enharmonics only across EF & BC. White text displays deep enharmonics in the ambiguous infrared & ultraviolet area of the colour notation.  

''81edo'' divides the octave into 81 steps of 14.815 cents each. It is notable as a tuning for [[Meantone_family|meantone]] and related temperaments and is the [[Optimal_patent_val|optimal patent val]] for a number of them. In particular it is the optimal patent val for 5-limit meantone, 7-limit meantone, 11-limit meanpop, 13-limit meanpop, and the rank three temperament [[Didymus_rank_three_family|erato]]. The electronic music pioneer [http://daphneoram.org/2012/01/13/letter-from-yehudi-menuhin/ Daphne Oram] was interested in 81edo.

As a step in the [[Golden Meantone]] series of EDOs, 81 EDO marks the point at which the series ceases to display audible changes to meantone temperament, and is also the EDO with the lowest average and most evenly spread Just-error across the scale (though 31 EDO does have the best harmonic 7th).  

=Commas=

5-limit commas: 81/80, |-48 1 20>

 

 

[[leantone6|leantone6]]

 

 

[[leantone13|leantone13]]    

[[Category:edo]]

[[Category:erato]]

[[Category:meanpop]]

[[Category:meantone]]

[[Category:theory]]