11edo: Difference between revisions

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[[File:Sagittal11EDO.jpg|alt=Sagittal11EDO.jpg|Sagittal11EDO.jpg]]

~~For alternative~~ notations, ~~see [[Ups_and_Downs_Notation~~#~~Summary~~ of ~~EDO notation~~-~~"Supersharp" EDOs|Ups and Downs Notation~~ -~~"Supersharp" EDOs]]~~ (~~pentatonic~~, ~~octotonic and nonatonic fifth~~-generated) ~~and [[Ups_and_Downs_Notation~~#~~Natural Generators|Ups and Downs Notation~~ - ~~Natural Generators]]~~ (~~heptatonic third~~-generated).

These are heptatonic notations generated by 5ths (5th meaning 3/2). Alternative notations include pentatonic 5th-generated, octotonic 5th-generated, nonatonic 5th-generated, and heptatonic 3rd-generated.

'''Pentatonic 5th-generated:''' '''D * * E G * * A C * * D''' (generator = wide 3/2 = 7\11 = perfect 5thoid)

D - ^D/Eb - D#/vE - E - G - ^G/Ab - G#/vA - A - C - ^C/Db - C#/vD - D

P1 - ^1/ms3 - A1/~s3 - Ms3 - P4d - ^4d/d5d - A4d/v5d - P5d - ms7 - ~s7/d8d - Ms7/v8d - P8d (s = sub-, d = -oid)

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

pentatonic genchain of fifths: ...ds3 - ds7 - d4d - d8d - d5d - ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d - A1 - A5d - As3 - As7... (s = sub-, d = -oid)

'''Octotonic 5th-generated:''' '''A B * C D E * F G * H A''' (generator = wide 3/2 = 7\11 = perfect 6th)

A - B - B#/Cb - C - D - E - E#/Fb - F - G - G#/Hb - H - A

P1 - m2 - M2/m3 - M3 - P4 - m5 - M5 - P6 - m7 - M7/m8 - M8 - P9

octatonic genchain of sixths: ...Db - Ab - Fb - Cb - Hb - E - B - G - D - A - F - C - H - E# - B# - G# - D# - A#...

octatonic genchain of sixths: ...d7 - d4 - d9 - d6 - m3 - m8 - m5 - m2 - m7 - P4 - P1 - P6 - M3 - M8 - M5 - M2 - M7 - A4 - A1 - A6 - A3...

'''Nonatonic 5th-generated: A B * C D E F G * H J A''' (generator = narrow 3/2 = 6\11 = perfect 6th)

A - B - B#/Cb - C - D - E - F - G - G#/Hb - H - J - A

P1 - m2 - M2/m3 - M3/m4 - M4 - P5 - P6 - m7 - M7/m8 - M8/m9 - M9 - P10

nonotonic genchain of sixths: ...E# - A# - F# - B# - G# - C - H - D - J - E - A - F - B - G - Cb - Hb - Db - Jb - Eb...

nonotonic genchain of sixths: ...M2 - M7 - M3 - M8 - M4 - M9 - P5 - P1 - P6 - m2 - m7 - m3 - m8 - m4 - m9...

'''Heptatonic 3rd-generated: D * E F * G A * B C * D''' (generator = 3\11 = perfect 3rd)

D - D#/Eb - E - F - F#/Gb - G - A - A#/Bb - B - C - C#/Db - D

P1 - m2 - M2 - P3 - m4 - M4 - m5 - M5 - P6 - m7 - M7 - P8

genchain of thirds: ...E# - G# - B# - D# - F# - A# - C# - E - G - B - D - F - A - C - Eb - Gb - Bb - Db - Fb - Ab - Cb...

genchain of thirds: ...M5 - M7 - M2 - M4 - P6 - P1 - P3 - m5 - m7 - m2 - m4 - d6...

==Commas==

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 [[File:Sagittal11EDO.jpg|alt=Sagittal11EDO.jpg|Sagittal11EDO.jpg]]
-For alternative notations, see [[Ups_and_Downs_Notation#Summary of EDO notation-"Supersharp" EDOs|Ups and Downs Notation -"Supersharp" EDOs]] (pentatonic, octotonic and nonatonic fifth-generated) and [[Ups_and_Downs_Notation#Natural Generators|Ups and Downs Notation - Natural Generators]] (heptatonic third-generated).
+These are heptatonic notations generated by 5ths (5th meaning 3/2). Alternative notations include pentatonic 5th-generated, octotonic 5th-generated, nonatonic 5th-generated, and heptatonic 3rd-generated.
+'''<u>Pentatonic 5th-generated:</u>''' '''D * * E G * * A C * * D'''  (generator = wide 3/2 = 7\11 = perfect 5thoid)
+D - ^D/Eb - D#/vE - E - G - ^G/Ab - G#/vA - A - C - ^C/Db - C#/vD - D
+P1 - ^1/ms3 - A1/~s3 - Ms3 - P4d - ^4d/d5d - A4d/v5d - P5d - ms7 - ~s7/d8d - Ms7/v8d - P8d (s = sub-, d = -oid)
+pentatonic genchain of fifths: ...Cb - Gb - Db - Ab - Eb - C - G - D - A - E - C# - G# - D# - A# - E#...
+pentatonic genchain of fifths: ...ds3 - ds7 - d4d - d8d - d5d - ms3 - ms7 - P4d - P1 - P5d - Ms3 - Ms7 - A4d - A1 - A5d - As3 - As7... (s = sub-, d = -oid)
+'''<u>Octotonic 5th-generated:</u>''' '''A B * C D E * F G * H A''' (generator = wide 3/2 = 7\11 = perfect 6th)
+A - B - B#/Cb - C - D - E - E#/Fb - F - G - G#/Hb - H - A
+P1 - m2 - M2/m3 - M3 - P4 - m5 - M5 - P6 - m7 - M7/m8 - M8 - P9
+octatonic genchain of sixths: ...Db - Ab - Fb - Cb - Hb - E - B - G - D - A - F - C - H - E# - B# - G# - D# - A#...
+octatonic genchain of sixths: ...d7 - d4 - d9 - d6 - m3 - m8 - m5 - m2 - m7 - P4 - P1 - P6 - M3 - M8 - M5 - M2 - M7 - A4 - A1 - A6 - A3...
+'''<u>Nonatonic 5th-generated:</u> A B * C D E F G * H J A''' (generator = narrow 3/2 = 6\11 = perfect 6th)
+A - B - B#/Cb - C - D - E - F - G - G#/Hb - H - J - A
+P1 - m2 - M2/m3 - M3/m4 - M4 - P5 - P6 - m7 - M7/m8 - M8/m9 - M9 - P10
+nonotonic genchain of sixths: ...E# - A# - F# - B# - G# - C - H - D - J - E - A - F - B - G - Cb - Hb - Db - Jb - Eb...
+nonotonic genchain of sixths: ...M2 - M7 - M3 - M8 - M4 - M9 - P5 - P1 - P6 - m2 - m7 - m3 - m8 - m4 - m9...
+'''<u>Heptatonic 3rd-generated:</u> D * E F * G A * B C * D''' (generator = 3\11 = perfect 3rd)
+D - D#/Eb - E - F - F#/Gb - G - A - A#/Bb - B - C - C#/Db - D
+P1 - m2 - M2 - P3 - m4 - M4 - m5 - M5 - P6 - m7 - M7 - P8
+genchain of thirds: ...E# - G# - B# - D# - F# - A# - C# - E - G - B - D - F - A - C - Eb - Gb - Bb - Db - Fb - Ab - Cb...
+genchain of thirds: ...M5 - M7 - M2 - M4 - P6 - P1 - P3 - m5 - m7 - m2 - m4 - d6...
 ==Commas==