81edo: Difference between revisions
m Notation system and decscription |
No edit summary |
||
| Line 2: | Line 2: | ||
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). | 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). | ||
[[File:81 Notation and Colour Notation.jpg|thumb|Colour notation and general structure of 81 EDO utilizing the accidentals displayed below. Black font indicates the '6 deep' non enharmonic accidental notation, whilst white text continues through to full enharmonic notation.]] | |||
[[File:81 EDO Accidentals.png|thumb| | [[File:81 EDO Accidentals.png|thumb| | ||
81 EDO Accidentals created and used by Tom Winspear. | 81 EDO Accidentals created and used by Tom Winspear. | ||
Based on those provided in Scala though with a logic correction. | Based on those provided in Scala though with a logic correction. | ||
The innermost accidentals represent the 15 cent EDOstep, followed by two, then the bracket representing three. Conventional sharp/doublesharp/flat/doubleflat accidentals are reached in steps of five. | The innermost accidentals represent the 15 cent EDOstep, followed by two, then the bracket representing three. Conventional sharp/doublesharp/flat/doubleflat accidentals are reached in steps of five. | ||
The chromatic scale can be notated utilizing only six accidentals in either direction - the rest are for enharmonics. | The chromatic scale can be notated utilizing only six accidentals in either direction - the rest are for enharmonics. | ||
]] | ]] | ||
Revision as of 23:52, 10 March 2020
81edo divides the octave into 81 steps of 14.815 cents each. It is notable as a tuning for meantone and related temperaments and is the 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 erato. The electronic music pioneer 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>
7-limit commas: 81/80, 126/125, |-24 1 0 8>
11-limit commas: 81/80, 126/125, 385/384, 12005/11979
13-limit commas: 81/80, 105/104, 144/143, 196/195, 6655/6591