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29edo/Unque's compositional approach: Difference between revisions

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Major rearrangement of interval table
 
Line 8: Line 8:
!Degree
!Degree
!Cents
!Cents
!Native Fifths
!Interval
!Additional Categories
!Notation
!Notation
!JI*
!Notes
!Notes
|-
|-
Line 16: Line 16:
|0.000
|0.000
|P1
|P1
|
|C
|C
|1/1
|
|
|-
|-
|1
|1
|41.379
|41.379
|A7
|A7 ([[Diesis (interval region)|Diesis]])
|[[Diesis (interval region)|Diesis]]
|B♯
|B♯
|[[45/44]], [[50/49]], [[37/36]]
|Distinct from the octave.  Three major thirds reach this augmented seventh.
|Distinct from the octave.  Three major thirds reach this augmented seventh.
|-
|-
Line 30: Line 30:
|82.759
|82.759
|m2
|m2
|
|D♭
|D♭
|[[256/243]], [[22/21]]
|
|
|-
|-
Line 37: Line 37:
|124.138
|124.138
|[[Chroma]] (A1)
|[[Chroma]] (A1)
|Supraminor 2nd
|C♯
|C♯
|[[15/14]], [[14/13]], [[29/27]]
|Distinct from the minor second, nullifying the familiar enharmonic equivalences.
|Distinct from the minor second, nullifying the familiar enharmonic equivalences.
|-
|-
|4
|4
|165.517
|165.517
|d3
|[[Porcupine|Quill]] (d3)
|Submajor 2nd
|B𝄪, E𝄫
|B𝄪, E𝄫
|[[11/10]], [[32/29]]
|
|
|-
|-
Line 51: Line 51:
|206.897
|206.897
|M2
|M2
|
|D
|D
|[[9/8]]
|
|
|-
|-
|6
|6
|248.276
|248.276
|[[Chthonic]]
|[[Chthonic]] ([[Extraclassical tonality|r3]])
|[[Extraclassical tonality|Arto]] 3rd
|C𝄪, F𝄫
|C𝄪, F𝄫
|[[37/32]]
|New region in between M2 and m3; two of them make a perfect fourth.
|New region in between M2 and m3; two of them make a perfect fourth.
|-
|-
Line 65: Line 65:
|289.655
|289.655
|m3
|m3
|
|E♭
|E♭
|[[32/27]], [[13/11]]
|
|
|-
|-
Line 72: Line 72:
|331.034
|331.034
|A2
|A2
|Supraminor 3rd
|D♯
|D♯
|[[29/24]]
|Distinct from the minor third, as can be seen in the Harmonic Minor modes.
|Distinct from the minor third, as can be seen in the Harmonic Minor modes.
|-
|-
Line 79: Line 79:
|372.414
|372.414
|d4
|d4
|Submajor 3rd
|F♭
|F♭
|[[36/29]]
|May be used as a neutral third, but does not bisect the perfect fifth.
|May be used as a neutral third, but does not bisect the perfect fifth.
|-
|-
Line 86: Line 86:
|413.793
|413.793
|M3
|M3
|
|E
|E
|[[81/64]], [[14/11]]
|
|
|-
|-
|11
|11
|455.172
|455.172
|[[Naiadic]]
|[[Naiadic]] ([[Extraclassical tonality|T3]])
|[[Extraclassical tonality|Tendo]] 3rd
|D𝄪, G𝄫
|D𝄪, G𝄫
|[[13/10]], [[48/37]]
|New region in between M3 and P4; two of them make a major sixth.
|New region in between M3 and P4; two of them make a major sixth.
|-
|-
Line 100: Line 100:
|496.552
|496.552
|P4
|P4
|
|F
|F
|[[4/3]]
|Just barely flatter than the fourth of 12edo, and closer to justly-tuned 4/3.
|Just barely flatter than the fourth of 12edo, and closer to justly-tuned 4/3.
|-
|-
Line 107: Line 107:
|537.931
|537.931
|A3
|A3
|Wolf 4th
|E♯
|E♯
|[[37/27]]
|
|
|-
|-
Line 114: Line 114:
|579.310
|579.310
|d5
|d5
|Minor tritone
|G♭
|G♭
|[[7/5]]
|Distinct from the augmented fourth.  Two minor thirds reach this diminished fifth.
|Distinct from the augmented fourth.  Two minor thirds reach this diminished fifth.
|-
|-
Line 121: Line 121:
|620.690
|620.690
|A4
|A4
|Major tritone
|F♯
|F♯
|[[10/7]]
|Distinct from the diminished fifth.  Three whole tones reach this augmented fourth.
|Distinct from the diminished fifth.  Three whole tones reach this augmented fourth.
|-
|-
Line 128: Line 128:
|662.069
|662.069
|d6
|d6
|Wolf 5th
|E𝄪, A𝄫
|E𝄪, A𝄫
|[[54/37]]
|
|
|-
|-
Line 135: Line 135:
|703.448
|703.448
|P5
|P5
|
|G
|G
|[[3/2]]
|Just barely sharper than the fifth of 12edo, and closer to justly-tuned 3/2.
|Just barely sharper than the fifth of 12edo, and closer to justly-tuned 3/2.
|-
|-
|18
|18
|744.828
|744.828
|[[Cocytic]]
|[[Cocytic]] ([[Extraclassical tonality|r6]])
|Arto 6th
|F𝄪
|F𝄪
|[[20/13]], [[37/24]]
|New region between P5 and m6; two of them reduce to a minor third.
|New region between P5 and m6; two of them reduce to a minor third.
|-
|-
Line 149: Line 149:
|786.207
|786.207
|m6
|m6
|
|A♭
|A♭
|[[128/81]], [[11/7]]
|
|
|-
|-
Line 156: Line 156:
|827.586
|827.586
|A5
|A5
|Supraminor 6th
|G♯
|G♯
|[[29/18]]
|Distinct from the minor sixth.  Two major thirds reach this augmented fifth.
|Distinct from the minor sixth.  Two major thirds reach this augmented fifth.
|-
|-
Line 163: Line 163:
|868.966
|868.966
|d7
|d7
|Submajor 6th
|B𝄫
|B𝄫
|[[48/29]]
|Distinct from the major sixth.  Three minor thirds reach this diminished seventh.
|Distinct from the major sixth.  Three minor thirds reach this diminished seventh.
|-
|-
Line 170: Line 170:
|910.345
|910.345
|M6
|M6
|
|A
|A
|[[27/16]], [[22/13]]
|
|
|-
|-
|23
|23
|951.724
|951.724
|[[Ouranic]]
|[[Ouranic]] ([[Extraclassical tonality|T6/r7]])
|Tendo 6th/arto 7th
|G𝄪, C𝄫
|G𝄪, C𝄫
|[[64/37]]
|New region between M6 and m7; two of them reduce to a perfect fifth.
|New region between M6 and m7; two of them reduce to a perfect fifth.
|-
|-
Line 184: Line 184:
|993.103
|993.103
|m7
|m7
|
|B♭
|B♭
|[[16/9]]
|
|
|-
|-
Line 191: Line 191:
|1034.483
|1034.483
|A6
|A6
|Supraminor 7th
|A♯
|A♯
|[[20/11]], [[29/16]]
|[[wikipedia:Augmented_sixth_chord|Augmented Sixth chords]] use this interval, not the typical minor seventh.
|[[wikipedia:Augmented_sixth_chord|Augmented Sixth chords]] use this interval, not the typical minor seventh.
|-
|-
Line 198: Line 198:
|1075.862
|1075.862
|d8
|d8
|Submajor 7th
|C♭
|C♭
|[[13/7]], [[54/29]]
|
|
|-
|-
Line 205: Line 205:
|1117.241
|1117.241
|M7
|M7
|
|B
|B
|[[243/128]], [[21/11]]
|
|
|-
|-
|28
|28
|1158.621
|1158.621
|d2
|d2 ([[Extraclassical tonality|T7]])
|Tendo 7th
|A𝄪, D𝄫
|A𝄪, D𝄫
|[[88/45]], [[72/37]]
|Distinct from the octave.  Four minor thirds reach this diminished ninth.
|Distinct from the octave.  Four minor thirds reach this diminished ninth.
|-
|-
Line 219: Line 219:
|1200.000
|1200.000
|P8
|P8
|
|C
|C
|[[2/1]]
|
|
|}
|}
<small>*Assuming the 2.3.7/5.11/5.13/5.29.37 subgroup; see Harmonic Approximations for details.</small>
As can be seen here, the familiar diatonic categories allow composers to root themselves in established structures, permitting them to fall back onto comprehensible harmony while still allowing for the interordinals and other new colors to be utilized alongside them.
As can be seen here, the familiar diatonic categories allow composers to root themselves in established structures, permitting them to fall back onto comprehensible harmony while still allowing for the interordinals and other new colors to be utilized alongside them.


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