8edo: Difference between revisions

Line 94:

! [[Cent]]s

! colspan="2" | 24edo subset notation

([[Enharmonic unisons in ups and downs notation|EUs:]] vvA1 and d2)

! colspan="2" | 16edo subset notation (major narrower than minor)

! colspan="2" | 16edo subset notation (major wider than minor)

Line 205:

Line 206:

D - D#/Eb - E - G - G#/Ab - A - C - C#/Db - D

P1 - A1/ms3 - Ms3 - P4d - A4d/d5d - P5d - ms7 - Ms7/d8d - P8d (s = sub-, d = -oid)

P1 - A1/ms3 - Ms3 - P4d - A4d/d5d - P5d - ms7 - Ms7/d8d - P8d (s = sub-, d = -oid, see [[5edo#Alternative notations|5edo]] notation)

pentatonic genchain of 5ths: ...Cb - Gb - Db - Ab - Eb - C - G - D - A - E - C# - G# - D# - A# - E#...

pentatonic genchain of 5ths: ...d8d - d5d - ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d - A1... (s = sub-, d = -oid)

[[Enharmonic unison]]: ds3

'''Octatonic:''' '''A B C D E F G H A''' (every interval is a generator)

P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 - P9

Enharmonic unison: none

'''Heptatonic 2nd-generated: D E F G * A B C D''' (generator = 1\8 = perfect 2nd = 150¢)

Line 224:

Line 229:

genchain of 2nds: ...A1 - A2 - M3 - M4 - M5 - M6 - P7 - P1 - P2 - m3 - m4 - m5 - m6 - d7 - d8...

Enharmonic unison: d2

=== Chord names ===

[[Ups and Downs Notation #Chords and Chord Progressions|Ups and downs]] can name any 8edo chord. Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13).

8edo chords are very ambiguous, with many chord homonyms. Even the major and minor triads are homonyms. Chord components usually default to M2, M3, P4, P5, M6, m7, M9, P11 and M13. Thus D7 has a M3, P5 and m7. 8-edo chord names using 24edo subset names are greatly simplified by using different defaults: ~2, ^M3, v4, ^5, M6, ~7, ~9, v11 and M13. Thus D7 becomes ^M3, ^5 and ~7.

8edo chords are very ambiguous, with many chord homonyms. Even the major and minor triads are [[Chord homonym|homonyms]]. Chord components usually default to M2, M3, P4, P5, M6, m7, M9, P11 and M13. Thus D7 has a M3, P5 and m7. 8-edo chord names using 24edo subset names are greatly simplified by using different defaults: instead of the conventional M2, M3, P4, P5, M6, m7, M9, P11 and M13, we have ~2, ^M3, v4, ^5, M6, ~7, ~9, v11 and M13. Thus D7 becomes ^M3, ^5 and ~7.

{| class="wikitable"

@@ Line 94: / Line 94: @@
 ! [[Cent]]s
 ! colspan="2" | 24edo subset notation
+([[Enharmonic unisons in ups and downs notation|EUs:]] vvA1 and d2)
 ! colspan="2" | 16edo subset notation<br>(major narrower than minor)
 ! colspan="2" | 16edo subset notation<br>(major wider than minor)
@@ Line 205: / Line 206: @@
 D - D#/Eb - E - G - G#/Ab - A - C - C#/Db - D
-P1 - A1/ms3 - Ms3 - P4d - A4d/d5d - P5d - ms7 - Ms7/d8d - P8d  (s = sub-, d = -oid)
+P1 - A1/ms3 - Ms3 - P4d - A4d/d5d - P5d - ms7 - Ms7/d8d - P8d  (s = sub-, d = -oid, see [[5edo#Alternative notations|5edo]] notation)
 pentatonic genchain of 5ths: ...Cb - Gb - Db - Ab - Eb - C - G - D - A - E - C# - G# - D# - A# - E#...
 pentatonic genchain of 5ths: ...d8d - d5d - ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d - A1... (s = sub-, d = -oid)
+[[Enharmonic unison]]: ds3
 '''<u>Octatonic:</u>''' '''A B C D E F G H A'''  (every interval is a generator)
 P1 - P2 - P3 - P4 - P5 - P6 - P7 - P8 - P9
+Enharmonic unison: none
 '''<u>Heptatonic 2nd-generated</u>: D E F G * A B C D'''  (generator = 1\8 = perfect 2nd = 150¢)
@@ Line 224: / Line 229: @@
 genchain of 2nds: ...A1 - A2 - M3 - M4 - M5 - M6 - P7 - P1 - P2 - m3 - m4 - m5 - m6 - d7 - d8...
+Enharmonic unison: d2
 === Chord names ===
 [[Ups and Downs Notation #Chords and Chord Progressions|Ups and downs]] can name any 8edo chord. Alterations are always enclosed in parentheses, additions never are. An up, down or mid immediately after the chord root affects the 3rd, 6th, 7th, and/or the 11th (every other note of a stacked-3rds chord 6-1-3-5-7-9-11-13).
-edo chords are very ambiguous, with many chord homonyms. Even the major and minor triads are homonyms. Chord components usually default to M2, M3, P4, P5, M6, m7, M9, P11 and M13. Thus D7 has a M3, P5 and m7. 8-edo chord names using 24edo subset names are greatly simplified by using different defaults: ~2, ^M3, v4, ^5, M6, ~7, ~9, v11 and M13. Thus D7 becomes ^M3, ^5 and ~7.
+edo chords are very ambiguous, with many chord homonyms. Even the major and minor triads are [[Chord homonym|homonyms]]. Chord components usually default to M2, M3, P4, P5, M6, m7, M9, P11 and M13. Thus D7 has a M3, P5 and m7. 8-edo chord names using 24edo subset names are greatly simplified by using different defaults: instead of the conventional M2, M3, P4, P5, M6, m7, M9, P11 and M13, we have  ~2, ^M3, v4, ^5, M6, ~7, ~9, v11 and M13. Thus D7 becomes ^M3, ^5 and ~7.
 {| class="wikitable"