User:Lhearne/15edo: Difference between revisions
m Text replacement - "Ups and Downs Notation" to "Ups and downs notation" |
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inverse of tetrachordal major, "just"/tetrachordal minor - 3123123 | inverse of tetrachordal major, "just"/tetrachordal minor - 3123123 | ||
Porcupine | Porcupine bright major #7 - Porcupine[7] 6|0 #7 - 3222231 | ||
Porcupine | Porcupine bright major #6 #7 - Porcupine[7] 6|0 #7 - 3222321 | ||
Porcupine bright minor #2 - Porcupine[7] 4|2 #2 3132222 (mode of bright major #7) | |||
Porcupine dark minor #2 - Porcupine[7] 3|3 #2 3123222 (inverse of bright major #6 #7) | |||
Porcupine bright harmonic 11th mode - Porcupine[7] 6|0 b7 3222213 | |||
"just" harmonic minor - 3123141 | "just" harmonic minor - 3123141 | ||
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=Notation= | =Notation= | ||
Because 15edo's best fifth is the same as that of [[5edo]], the circle of fifths fully closes with only five notes, meaning the [[256/243|Pythagorean limma]] is tempered out. This slightly breaks traditional fifth-based notation, because E and F, as well as B and C, will merge into singular pitches. This also has the effect of making the [[2187/2048|Pythagorean apotome]] equal to the [[9/8|Pythagorean whole-tone]], such that the sharp and flat accidentals will indicate raising or lowering by one step of 5edo, or 240 cents. There are two main approaches to dealing with this issue: the use of ups and downs in conjunction with the traditional A through G nominals based on the 5edo circle of fifths, and the use of Porcupine temperament instead of the circle of fifths as a notational basis. | Because 15edo's best fifth is the same as that of [[5edo]], the circle of fifths fully closes with only five notes, meaning the [[256/243|Pythagorean limma]] is tempered out. This slightly breaks traditional fifth-based notation, because E and F, as well as B and C, will merge into singular pitches. This also has the effect of making the [[2187/2048|Pythagorean apotome]] equal to the [[9/8|Pythagorean whole-tone]], such that the sharp and flat accidentals will indicate raising or lowering by one step of 5edo, or 240 cents. There are two main approaches to dealing with this issue: the use of ups and downs in conjunction with the traditional A through G nominals based on the 5edo circle of fifths, and the use of Porcupine temperament instead of the circle of fifths as a notational basis. | ||
==Ups and | ==Ups and downs notation== | ||
In [[Ups and | In [[Ups and downs notation#Summary of EDO notation-.22Pentatonic.22 EDOs|ups and downs notation]], which is fifth-generated, every 15edo note has at least three names. | ||
{| class="wikitable" | {| class="wikitable" | ||
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0-4-9-13 = D F^ A C^ = D.^m7 = "D dot up minor-seven", or D F^ A B^ = D.^m6 = "D dot up minor-six" | 0-4-9-13 = D F^ A C^ = D.^m7 = "D dot up minor-seven", or D F^ A B^ = D.^m6 = "D dot up minor-six" | ||
For a more complete list, see [[Ups and | For a more complete list, see [[Ups and downs notation#Chord names in other EDOs|Ups and downs notation - Chord names in other EDOs]]. | ||
==Porcupine[7] Notation== | ==Porcupine[7] Notation== | ||
''See the main [[Porcupine Notation|porcupine notation]] page.'' | ''See the main [[Porcupine Notation|porcupine notation]] page.'' | ||
15edo can also be notated using the [[Ups and | 15edo can also be notated using the [[Ups and downs notation#Natural Generators|natural generator]], which is not the 9\15 5th but the 2\15 2nd. For 15edo, this is also known as porcupine notation. The 15edo porcupine genchain in both relative and absolute notation: | ||
...A3 - A4 - A5 - A6 - A7 - A1 - A2 - M3 - M4 - M5 - M6 - P7 - P1 - P2 - m3 - m4 - m5 - m6 - d7 -- d8 - d2 - d3 -- d4 - d5 -- d6... | ...A3 - A4 - A5 - A6 - A7 - A1 - A2 - M3 - M4 - M5 - M6 - P7 - P1 - P2 - m3 - m4 - m5 - m6 - d7 -- d8 - d2 - d3 -- d4 - d5 -- d6... | ||