13edo: Difference between revisions

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This is a heptatonic notation generated by 5ths. Alternative notations include pentatonic 5th-generated, octotonic 5th-generated, and heptatonic 2nd-generated.

This is a heptatonic notation generated by 5ths (5th meaning 3/2). Alternative notations include pentatonic 5th-generated, octotonic 5th-generated, and heptatonic 2nd-generated.

'''Pentatonic 5th-generated:''' ~~(generator = 8\13 = perfect 5thoid)~~ D * * E * G * * A * C * * D

'''Pentatonic 5th-generated:''' '''D * * E * G * * A * C * * D''' (generator = wide 3/2 = 8\13 = perfect 5thoid)

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

P1 - A1/ds3 - ms3 - Ms3 - As3/d4d - P4d - A4d - d5d - P5d - A5d/ds7 - ms7 - Ms7 - As7/d8d - P8d

P1 - A1/ds3 - ms3 - Ms3 - As3/d4d - P4d - A4d - d5d - P5d - A5d/ds7 - ms7 - Ms7 - As7/d8d - P8d (s = sub-, d = -oid)

~~'''Octatonic 5th~~-~~generated:''' (wide 3/2 maps to 8\13 = perfect 6th)~~

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

~~octotonic~~ genchain of ~~sixths~~: M3 - M8 - M5 - M2 - M7 - P4 - P1 - P6 - m3 - m8 - m5 - m2 - m7

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)

'''Octatonic 5th-generated:''' '''A * B C * D * E F * G H * A''' (generator = wide 3/2 = 8\13 = perfect 6th)

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

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

'''Heptatonic 2nd-generated:''' ~~(generator = 2\13 = perfect 2nd)~~ D * E * F * G A * B * C * D

octotonic genchain of sixths: ..D# - A# - F# - C# - H# - E - B - G - D - A - F - C - H - Eb - Bb - Gb - Db - Ab...

octotonic genchain of sixths: ...M3 - M8 - M5 - M2 - M7 - P4 - P1 - P6 - m3 - m8 - m5 - m2 - m7...

'''Heptatonic 2nd-generated:''' '''D * E * F * G A * B * C * D''' (generator = 2\13 = perfect 2nd)

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

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P1 - A1/d2 - P2 - m3 - M3 - m4 - M4 - m5 - M5 - m6 - M6 - P7 - A7/d8 - P8

genchain of seconds: d2 - m3 - m4 - m5 - m6 - P7 - P1 - P2 - M3 - M4 - M5 - M6 - ~~A7 etc~~.

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

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

genchain of seconds: ...d6 - d7 - d8 - d2 - m3 - m4 - m5 - m6 - P7 - P1 - P2 - M3 - M4 - M5 - M6 - A7 - A1 - A2 - A3...

[[:File:13edo-chromatic-scale.mid|13 edo chromatic ascending and descending scale on C (MIDI)]]

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-This is a heptatonic notation generated by 5ths. Alternative notations include pentatonic 5th-generated, octotonic 5th-generated, and heptatonic 2nd-generated.
+This is a heptatonic notation generated by 5ths (5th meaning 3/2). Alternative notations include pentatonic 5th-generated, octotonic 5th-generated, and heptatonic 2nd-generated.
-'''<u>Pentatonic 5th-generated</u>:''' (generator = 8\13 = perfect 5thoid) D * * E * G * * A * C * * D
+'''<u>Pentatonic 5th-generated</u>:''' '''D * * E * G * * A * C * * D''' (generator = wide 3/2 = 8\13 = perfect 5thoid)
 D - D# - Eb - E - E#/Gb - G - G# - Ab - A - A#/Cb - C - C# - Db - D
-P1 - A1/ds3 - ms3 - Ms3 - As3/d4d - P4d - A4d - d5d - P5d - A5d/ds7 - ms7 - Ms7 - As7/d8d - P8d
+P1 - A1/ds3 - ms3 - Ms3 - As3/d4d - P4d - A4d - d5d - P5d - A5d/ds7 - ms7 - Ms7 - As7/d8d - P8d (s = sub-, d = -oid)
-'''<u>Octatonic 5th-generated</u>:''' (wide 3/2 maps to 8\13 = perfect 6th)
+pentatonic genchain of fifths: ...Ebb - Cb - Gb - Db - Ab - Eb - C - G - D - A - E - C# - G# - D# - A# - E# - Cx...
-octotonic genchain of sixths: M3 - M8 - M5 - M2 - M7 - P4 - P1 - P6 - m3 - m8 - m5 - m2 - m7
+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>Octatonic 5th-generated</u>:''' '''A * B C * D * E F * G H * A''' (generator = wide 3/2 = 8\13 = perfect 6th)
+A - A#/Bb - B - C - C#/Db - D - D#/Eb - E - F - F#/Gb - G - H - H#/Ab - A
 P1 - m2 - M2 - m3 - M3 - P4 - m5 - M5 - P6 - m7 - M7 - m8 - M8 - P9
-'''<u>Heptatonic 2nd-generated</u>:''' (generator = 2\13 = perfect 2nd) D * E * F * G A * B * C * D
+octotonic genchain of sixths: ..D# - A# - F# - C# - H# - E - B - G - D - A - F - C - H - Eb - Bb - Gb - Db - Ab...
+octotonic genchain of sixths: ...M3 - M8 - M5 - M2 - M7 - P4 - P1 - P6 - m3 - m8 - m5 - m2 - m7...
+'''<u>Heptatonic 2nd-generated</u>:''' '''D * E * F * G A * B * C * D''' (generator = 2\13 = perfect 2nd)
 D - D#/Eb - E - E#/Fb - F - F#/Gb - G - A - A#/Bb - B - B#/Cb - C - C#/Db - D
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 P1 - A1/d2 - P2 - m3 - M3 - m4 - M4 - m5 - M5 - m6 - M6 - P7 - A7/d8 - P8
-genchain of seconds: d2 - m3 - m4 - m5 - m6 - P7 - P1 - P2 - M3 - M4 - M5 - M6 - A7 etc.
+genchain of seconds: ...Ab - Bb - Cb - Db - Eb - Fb - Gb - A - B - C - D - E - F - G - A# - B# - C# - D# - E# - F# - G#...
-genchain of seconds: Ab - Bb - Cb - Db - Eb - Fb - Gb - A - B - C - D - E - F - G - A# - B# - C# - D# - E# - F# - G#
+genchain of seconds: ...d6 - d7 - d8 - d2 - m3 - m4 - m5 - m6 - P7 - P1 - P2 - M3 - M4 - M5 - M6 - A7 - A1 - A2 - A3...
 [[:File:13edo-chromatic-scale.mid|13 edo chromatic ascending and descending scale on C (MIDI)]]