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13edo: Difference between revisions

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autopatrolled, Sysops
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updated the ups/down format, added a bit about alternative notations
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| style="text-align:center;" | up unison, minor 2nd
| style="text-align:center;" | up unison, minor 2nd
| style="text-align:center;" | ^1, m2
| style="text-align:center;" | ^1, m2
| style="text-align:center;" | D^, E
| style="text-align:center;" | ^D, E
| style="text-align:center;" | up unison, major 2nd
| style="text-align:center;" | up unison, major 2nd
| style="text-align:center;" | ^1, M2
| style="text-align:center;" | ^1, M2
| style="text-align:center;" | D^, E
| style="text-align:center;" | ^D, E
|-
|-
| style="text-align:center;" | 2
| style="text-align:center;" | 2
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| style="text-align:center;" | upminor 2nd, minor 3rd
| style="text-align:center;" | upminor 2nd, minor 3rd
| style="text-align:center;" | ^m2, m3
| style="text-align:center;" | ^m2, m3
| style="text-align:center;" | E^, Fb
| style="text-align:center;" | ^E, Fb
| style="text-align:center;" | upmajor 2nd, major 3rd
| style="text-align:center;" | upmajor 2nd, major 3rd
| style="text-align:center;" | ^M2, M3
| style="text-align:center;" | ^M2, M3
| style="text-align:center;" | E^, F#
| style="text-align:center;" | ^E, F#
|-
|-
| style="text-align:center;" | 3
| style="text-align:center;" | 3
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| style="text-align:center;" | downmajor 2nd, upminor 3rd
| style="text-align:center;" | downmajor 2nd, upminor 3rd
| style="text-align:center;" | vM2, ^m3
| style="text-align:center;" | vM2, ^m3
| style="text-align:center;" | E#v, Fb^
| style="text-align:center;" | vE#, ^Fb
| style="text-align:center;" | downminor 2nd, upmajor 3rd
| style="text-align:center;" | downminor 2nd, upmajor 3rd
| style="text-align:center;" | vm2, ^M3
| style="text-align:center;" | vm2, ^M3
| style="text-align:center;" | Ebv, F#^
| style="text-align:center;" | vEb, ^F#
|-
|-
| style="text-align:center;" | 4
| style="text-align:center;" | 4
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| style="text-align:center;" | major 2nd, downmajor 3rd
| style="text-align:center;" | major 2nd, downmajor 3rd
| style="text-align:center;" | M2, vM3
| style="text-align:center;" | M2, vM3
| style="text-align:center;" | E#, Fv
| style="text-align:center;" | E#, vF
| style="text-align:center;" | minor 2nd, downminor 3rd
| style="text-align:center;" | minor 2nd, downminor 3rd
| style="text-align:center;" | m2, vm3
| style="text-align:center;" | m2, vm3
| style="text-align:center;" | Eb, Fv
| style="text-align:center;" | Eb, vF
|-
|-
| style="text-align:center;" | 5
| style="text-align:center;" | 5
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| style="text-align:center;" | major 3rd, down 4th
| style="text-align:center;" | major 3rd, down 4th
| style="text-align:center;" | M3, v4
| style="text-align:center;" | M3, v4
| style="text-align:center;" | F, Gv
| style="text-align:center;" | F, vG
| style="text-align:center;" | minor 3rd, down 4th
| style="text-align:center;" | minor 3rd, down 4th
| style="text-align:center;" | m3, v4
| style="text-align:center;" | m3, v4
| style="text-align:center;" | F, Gv
| style="text-align:center;" | F, vG
|-
|-
| style="text-align:center;" | 6
| style="text-align:center;" | 6
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| style="text-align:center;" | perfect 4th, down 5th
| style="text-align:center;" | perfect 4th, down 5th
| style="text-align:center;" | P4, v5
| style="text-align:center;" | P4, v5
| style="text-align:center;" | G, Av
| style="text-align:center;" | G, vA
| style="text-align:center;" | perfect 4th, down 5th
| style="text-align:center;" | perfect 4th, down 5th
| style="text-align:center;" | P4, v5
| style="text-align:center;" | P4, v5
| style="text-align:center;" | G, Av
| style="text-align:center;" | G, vA
|-
|-
| style="text-align:center;" | 7
| style="text-align:center;" | 7
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| style="text-align:center;" | up 4th, perfect 5th
| style="text-align:center;" | up 4th, perfect 5th
| style="text-align:center;" | ^4, P5
| style="text-align:center;" | ^4, P5
| style="text-align:center;" | G^, A
| style="text-align:center;" | ^G, A
| style="text-align:center;" | up 4th, perfect 5th
| style="text-align:center;" | up 4th, perfect 5th
| style="text-align:center;" | ^4, P5
| style="text-align:center;" | ^4, P5
| style="text-align:center;" | G^, A
| style="text-align:center;" | ^G, A
|-
|-
| style="text-align:center;" | 8
| style="text-align:center;" | 8
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| style="text-align:center;" | up 5th, minor 6th
| style="text-align:center;" | up 5th, minor 6th
| style="text-align:center;" | ^5, m6
| style="text-align:center;" | ^5, m6
| style="text-align:center;" | A^, B
| style="text-align:center;" | ^A, B
| style="text-align:center;" | up 5th, major 6th
| style="text-align:center;" | up 5th, major 6th
| style="text-align:center;" | ^5, M6
| style="text-align:center;" | ^5, M6
| style="text-align:center;" | A^, B
| style="text-align:center;" | ^A, B
|-
|-
| style="text-align:center;" | 9
| style="text-align:center;" | 9
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| style="text-align:center;" | upminor 6th, minor 7th
| style="text-align:center;" | upminor 6th, minor 7th
| style="text-align:center;" | ^m6, m7
| style="text-align:center;" | ^m6, m7
| style="text-align:center;" | B^, Cb
| style="text-align:center;" | ^B, Cb
| style="text-align:center;" | upmajor 6th, major 7th
| style="text-align:center;" | upmajor 6th, major 7th
| style="text-align:center;" | ^M6, M7
| style="text-align:center;" | ^M6, M7
| style="text-align:center;" | B^, C#
| style="text-align:center;" | ^B, C#
|-
|-
| style="text-align:center;" | 10
| style="text-align:center;" | 10
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| style="text-align:center;" | downmajor 6th, upminor 7th
| style="text-align:center;" | downmajor 6th, upminor 7th
| style="text-align:center;" | vM6, ^m7
| style="text-align:center;" | vM6, ^m7
| style="text-align:center;" | B#v, Cb^
| style="text-align:center;" | vB#, ^Cb
| style="text-align:center;" | downminor 6th, upmajor 7th
| style="text-align:center;" | downminor 6th, upmajor 7th
| style="text-align:center;" | vm6, ^M7
| style="text-align:center;" | vm6, ^M7
| style="text-align:center;" | Bbv, C#^
| style="text-align:center;" | vBb, ^C#
|-
|-
| style="text-align:center;" | 11
| style="text-align:center;" | 11
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| style="text-align:center;" | major 6th, downmajor 7th
| style="text-align:center;" | major 6th, downmajor 7th
| style="text-align:center;" | M6, vM7
| style="text-align:center;" | M6, vM7
| style="text-align:center;" | B#, Cv
| style="text-align:center;" | B#, vC
| style="text-align:center;" | minor 6th, downminor 7th
| style="text-align:center;" | minor 6th, downminor 7th
| style="text-align:center;" | m6, vm7
| style="text-align:center;" | m6, vm7
| style="text-align:center;" | Bb, Cv
| style="text-align:center;" | Bb, vC
|-
|-
| style="text-align:center;" | 12
| style="text-align:center;" | 12
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| style="text-align:center;" | major 7th, down 8ve
| style="text-align:center;" | major 7th, down 8ve
| style="text-align:center;" | M7, v8
| style="text-align:center;" | M7, v8
| style="text-align:center;" | C, Dv
| style="text-align:center;" | C, vD
| style="text-align:center;" | minor 7th, down 8ve
| style="text-align:center;" | minor 7th, down 8ve
| style="text-align:center;" | m7, v8
| style="text-align:center;" | m7, v8
| style="text-align:center;" | C, Dv
| style="text-align:center;" | C, vD
|-
|-
| style="text-align:center;" | 13
| style="text-align:center;" | 13
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|}
|}


For alternative notations, see [[Ups_and_Downs_Notation#Summary of EDO notation-"Supersharp" EDOs|Ups and Downs Notation -"Supersharp" EDOs]] (pentatonic and octotonic fifth-based) and [[Ups_and_Downs_Notation#Natural Generators|Ups and Downs Notation - Natural Generators]] (heptatonic second-based).
This is a heptatonic notation generated by 5ths. 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
 
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
 
'''<u>Octatonic 5th-generated</u>:''' (wide 3/2 maps to 8\13 = perfect 6th)
 
octotonic genchain of sixths: M3 - M8 - M5 - M2 - M7 - P4 - P1 - P6 - m3 - m8 - m5 - m2 - m7
 
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
 
D - D#/Eb - E - E#/Fb - F - F#/Gb - G - A - A#/Bb - B - B#/Cb - C - C#/Db - D
 
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#


[[:File:13edo-chromatic-scale.mid|13 edo chromatic ascending and descending scale on C (MIDI)]]
[[:File:13edo-chromatic-scale.mid|13 edo chromatic ascending and descending scale on C (MIDI)]]
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<ul><li>[[13EDO_Scales_and_Chords_for_Guitar|13EDO Scales and Chords for Guitar]]</li></ul>
<ul><li>[[13EDO_Scales_and_Chords_for_Guitar|13EDO Scales and Chords for Guitar]]</li></ul>


='''Compositions'''=
=Compositions=
<span style="">[http://www.microtonalmusic.net/audio/slowdance13edo.mp3 Slow Dance]</span> by [http://danielthompson.blogspot.com/ Daniel Thompson]
<span style="">[http://www.microtonalmusic.net/audio/slowdance13edo.mp3 Slow Dance]</span> by [http://danielthompson.blogspot.com/ Daniel Thompson]


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