94edo: Difference between revisions
→Scales: removing these mmtmisms because clarifications never happened until he was banned |
m →Intervals: Changed from “main article” to “see also” |
||
| Line 15: | Line 15: | ||
== Intervals == | == Intervals == | ||
''See also: [[Table of 94edo intervals]]'' | |||
Assuming [[23-limit]] [[patent val]] <94 149 218 264 325 348 384 399 425|, here is a table of intervals as approximated by [[94edo]] steps, and their corresponding 13-limit well-ordered extended diatonic interval names. 'S' indicates alteration by the septimal comma, [[64/63]]; 'K' indicates alteration by the syntonic comma, [[81/80]]; 'U' by the undecimal quatertone, [[33/32]]; 'L' by pentacircle comma, [[896/891]]; 'O' by [[45/44]]; 'R' by the rastma, [[243/242]]; 'T' by the tridecimal quartertone, [[1053/1024]]; and finally, 'H', by [[40/39]]. Capital letters alter downward, lowercase alter upwards. Important 13-limit intervals approximated that are not associated with the extended diatonic interval names are added in brackets. Multiple alterations by 'K' down from augmented and major, or up from diminished and minor intervals are also added in brackets, along with their associated (5-limit) intervals. | Assuming [[23-limit]] [[patent val]] <94 149 218 264 325 348 384 399 425|, here is a table of intervals as approximated by [[94edo]] steps, and their corresponding 13-limit well-ordered extended diatonic interval names. 'S' indicates alteration by the septimal comma, [[64/63]]; 'K' indicates alteration by the syntonic comma, [[81/80]]; 'U' by the undecimal quatertone, [[33/32]]; 'L' by pentacircle comma, [[896/891]]; 'O' by [[45/44]]; 'R' by the rastma, [[243/242]]; 'T' by the tridecimal quartertone, [[1053/1024]]; and finally, 'H', by [[40/39]]. Capital letters alter downward, lowercase alter upwards. Important 13-limit intervals approximated that are not associated with the extended diatonic interval names are added in brackets. Multiple alterations by 'K' down from augmented and major, or up from diminished and minor intervals are also added in brackets, along with their associated (5-limit) intervals. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 789: | Line 790: | ||
The regular major second divisible into 16 equal parts can be helpful for realising some of the subtle tunings of Ancient Greek [[tetrachord]]al theory, [[Indian]] raga and Turkish [[maqam]], though it has not been used historically as a division in those musical cultures. | The regular major second divisible into 16 equal parts can be helpful for realising some of the subtle tunings of Ancient Greek [[tetrachord]]al theory, [[Indian]] raga and Turkish [[maqam]], though it has not been used historically as a division in those musical cultures. | ||
While having the whole gamut of 94 intervals available on a keyboard or other instrument would be quite a feat, one can get a lot out of a 41-tone chain of fifths (with the odd fifth one degree wide) or a 53-tone chain of fifths (with the odd fifth one degree narrow), where the subset behaves much like a well-temperament, arguably usable in all keys but with some interval size variation between closer and more distant keys. | While having the whole gamut of 94 intervals available on a keyboard or other instrument would be quite a feat, one can get a lot out of a 41-tone chain of fifths (with the odd fifth one degree wide) or a 53-tone chain of fifths (with the odd fifth one degree narrow), where the subset behaves much like a well-temperament, arguably usable in all keys but with some interval size variation between closer and more distant keys. | ||
== Regular temperament properties == | == Regular temperament properties == | ||