159edo/Interval names and harmonies: Difference between revisions
Starting to redo the harmonic and melodic compatibility ratings based on more data, as well as taking another guess at certain other intervals' ratings in a new system |
Fixed another notation error in chart |
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:* It readily serves as a Diatonic whole tone in both Western-Classical-based functional harmony and Neo-Medieval harmony in general, since… | :* It readily serves as a Diatonic whole tone in both Western-Classical-based functional harmony and Neo-Medieval harmony in general, since… | ||
::* It functions as a Double Dominant due to being the result of stacking two Perfect Fifths and octave-reducing | ::* It functions as a Double Dominant due to being the result of stacking two Perfect Fifths and octave-reducing | ||
:* Is the whole tone that is used as a reference interval in [[ | :* Is the whole tone that is used as a reference interval in [[diatonic, chromatic, enharmonic, subchromatic|diatonic-and-chromatic-style]] interval logic in this system as it pertains to both semitones and quartertones, and thus… | ||
::* It sees usage in Paradiatonic and Parachromatic harmonies in addition to the more obvious Diatonic-related uses | ::* It sees usage in Paradiatonic and Parachromatic harmonies in addition to the more obvious Diatonic-related uses | ||
* Is one fourth of this system's approximation of the Classic Minor Sixth as a consequence of the schisma being tempered out in this system | * Is one fourth of this system's approximation of the Classic Minor Sixth as a consequence of the schisma being tempered out in this system | ||
| Line 1,100: | Line 1,100: | ||
:* Virtually all of its functionality in the realm of Western-Classical-based Diatonic scales and Diatonic functional harmony | :* Virtually all of its functionality in the realm of Western-Classical-based Diatonic scales and Diatonic functional harmony | ||
* New elements to its functionality include… | * New elements to its functionality include… | ||
:* New approaches enabled by this system supporting temperaments such as [[ | :* New approaches enabled by this system supporting temperaments such as [[sextilifourths]] | ||
:* A sizable chunk of its functionality in the realm of Western-Classical-based Paradiatonic functional harmony | :* A sizable chunk of its functionality in the realm of Western-Classical-based Paradiatonic functional harmony | ||
|- | |- | ||
| Line 1,414: | Line 1,414: | ||
| Rm5, rUA4 | | Rm5, rUA4 | ||
| Wide Paraminor Fifth, Retrodiptolemaic Augmented Fourth | | Wide Paraminor Fifth, Retrodiptolemaic Augmented Fourth | ||
| Ad | | Ad>/, G#↑, Ab↑↑ | ||
| -1 | | -1 | ||
| 6 | | 6 | ||
| Line 1,593: | Line 1,593: | ||
| 99 | | 99 | ||
| 747.1698113 | | 747.1698113 | ||
| Rm4, KKM3, rUM3 | | Rm4, KKM3, rUM3 | ||
| Narrow Paramajor Fifth, Wide Inframinor Sixth | | Narrow Paramajor Fifth, Wide Inframinor Sixth | ||
| Line 1,947: | Line 1,946: | ||
| Narrow Supermajor Sixth | | Narrow Supermajor Sixth | ||
| B↑\, Cd>↓ | | B↑\, Cd>↓ | ||
| | | -1 | ||
| | | 8 | ||
| This interval… | | This interval… | ||
* Approximates the [[17/10|Septendecimal Major Sixth]] | * Approximates the [[17/10|Septendecimal Major Sixth]] | ||
| Line 1,961: | Line 1,960: | ||
| Lesser Supermajor Sixth | | Lesser Supermajor Sixth | ||
| B↑, Cd<\, Cb↑↑, A## | | B↑, Cd<\, Cb↑↑, A## | ||
| | | -1 | ||
| | | 7 | ||
| This interval… | | This interval… | ||
* Approximates the [[128/75|Classic Diminished Seventh]], and as such… | * Approximates the [[128/75|Classic Diminished Seventh]], and as such… | ||
| Line 1,977: | Line 1,976: | ||
| SM6, kUM6 | | SM6, kUM6 | ||
| Greater Supermajor Second, Narrow Inframinor Seventh | | Greater Supermajor Second, Narrow Inframinor Seventh | ||
| | | Cd<, Bt<↓, B↑/ | ||
| 0 | | 0 | ||
| | | 7 | ||
| This interval… | | This interval… | ||
* Approximates the [[12/7|Septimal Supermajor Sixth]], and as such… | * Approximates the [[12/7|Septimal Supermajor Sixth]], and as such… | ||
| Line 1,994: | Line 1,993: | ||
| Inframinor Seventh, Wide Supermajor Sixth | | Inframinor Seventh, Wide Supermajor Sixth | ||
| Cd>, Bt>↓ | | Cd>, Bt>↓ | ||
| | | -1 | ||
| | | 7 | ||
| This interval… | | This interval… | ||
* Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic seventh that sounds more like a sixth, and as such… | * Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic seventh that sounds more like a sixth, and as such… | ||
| Line 2,008: | Line 2,007: | ||
| Bt<\, Cd>/, B↑↑, C↓↓ | | Bt<\, Cd>/, B↑↑, C↓↓ | ||
| 0 | | 0 | ||
| | | 8 | ||
| This interval… | | This interval… | ||
* Approximates the [[26/15|Tridecimal Semitwelfth]], and thus… | * Approximates the [[26/15|Tridecimal Semitwelfth]], and thus… | ||
| Line 2,023: | Line 2,022: | ||
| Ultramajor Sixth, Narrow Subminor Seventh | | Ultramajor Sixth, Narrow Subminor Seventh | ||
| Bt<, Cd<↑ | | Bt<, Cd<↑ | ||
| | | -1 | ||
| | | 8 | ||
| This interval… | | This interval… | ||
* Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic sixth that sounds more like a seventh, and as such… | * Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic sixth that sounds more like a seventh, and as such… | ||
| Line 2,038: | Line 2,037: | ||
| Bt>, Cd>↑, C↓\ | | Bt>, Cd>↑, C↓\ | ||
| 0 | | 0 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[7/4|Septimal Subminor Seventh]] or Octave-Reduced Seventh Harmonic, and as such… | * Approximates the [[7/4|Septimal Subminor Seventh]] or Octave-Reduced Seventh Harmonic, and as such… | ||
| Line 2,054: | Line 2,053: | ||
| Greater Subminor Seventh | | Greater Subminor Seventh | ||
| C↓, Bt>/, B#↓↓, Dbb | | C↓, Bt>/, B#↓↓, Dbb | ||
| | | -1 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[225/128|Neapolitan Augmented Sixth]], and thus… | * Approximates the [[225/128|Neapolitan Augmented Sixth]], and thus… | ||
| Line 2,069: | Line 2,068: | ||
| Wide Subminor Seventh | | Wide Subminor Seventh | ||
| C↓/, Bt<↑ | | C↓/, Bt<↑ | ||
| | | -1 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[30/17|Septendecimal Minor Seventh]], and thus… | * Approximates the [[30/17|Septendecimal Minor Seventh]], and thus… | ||
| Line 2,079: | Line 2,078: | ||
* Is the closest approximation of 22edo's Lesser Minor Seventh in this system, and thus… | * Is the closest approximation of 22edo's Lesser Minor Seventh in this system, and thus… | ||
:* Can be used in Superpyth-based melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system | :* Can be used in Superpyth-based melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system | ||
| | |- | ||
| 131 | | 131 | ||
| 988.6792458 | | 988.6792458 | ||
| Line 2,085: | Line 2,084: | ||
| Narrow Minor Seventh | | Narrow Minor Seventh | ||
| C\, Bt>↑ | | C\, Bt>↑ | ||
| | | -1 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[39/22|Tridecimal Minor Seventh]], and thus… | * Approximates the [[39/22|Tridecimal Minor Seventh]], and thus… | ||
| Line 2,098: | Line 2,097: | ||
| Pythagorean Minor Seventh | | Pythagorean Minor Seventh | ||
| C, B#↓ | | C, B#↓ | ||
| | | -2 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[16/9|Pythagorean Minor Seventh]], and as such… | * Approximates the [[16/9|Pythagorean Minor Seventh]], and as such… | ||
| Line 2,115: | Line 2,114: | ||
| Artomean Minor Seventh | | Artomean Minor Seventh | ||
| C/, B#↓/ | | C/, B#↓/ | ||
| | | -2 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[25/14|Middle Minor Seventh]] | * Approximates the [[25/14|Middle Minor Seventh]] | ||
| Line 2,129: | Line 2,128: | ||
| Tendomean Minor Seventh | | Tendomean Minor Seventh | ||
| C↑\, B#\ | | C↑\, B#\ | ||
| | | -3 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[256/143|Grossmic Minor Seventh]], and thus… | * Approximates the [[256/143|Grossmic Minor Seventh]], and thus… | ||
| Line 2,142: | Line 2,141: | ||
| Ptolemaic Minor Seventh | | Ptolemaic Minor Seventh | ||
| C↑, B# | | C↑, B# | ||
| | | -3 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[9/5|Classic Minor Seventh]] or Ptolemaic Minor Seventh, and as such… | * Approximates the [[9/5|Classic Minor Seventh]] or Ptolemaic Minor Seventh, and as such… | ||
| Line 2,159: | Line 2,158: | ||
| Wide Minor Seventh | | Wide Minor Seventh | ||
| Ct<↓, C↑/, Ddb<, B#/ | | Ct<↓, C↑/, Ddb<, B#/ | ||
| | | -4 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Is reachable through stacking eight of this system's approximation of the Tridecimal Supraminor Second | * Is reachable through stacking eight of this system's approximation of the Tridecimal Supraminor Second | ||
| Line 2,171: | Line 2,170: | ||
| Lesser Supraminor Seventh, Infra-Diminished Octave | | Lesser Supraminor Seventh, Infra-Diminished Octave | ||
| Ct>↓, Ddb>, B#↑\ | | Ct>↓, Ddb>, B#↑\ | ||
| | | -5 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[20/11|Undecimal Supraminor Seventh]] and a similar 13-limit interval that acts as the Supraminor counterpart to the Tridecimal Submajor Seventh | * Approximates the [[20/11|Undecimal Supraminor Seventh]] and a similar 13-limit interval that acts as the Supraminor counterpart to the Tridecimal Submajor Seventh | ||
| Line 2,186: | Line 2,185: | ||
| Greater Supraminor Seventh, Retrodiptolemaic Diminished Octave | | Greater Supraminor Seventh, Retrodiptolemaic Diminished Octave | ||
| Ct<\, C↑↑, Ddb<↑\, Db↓↓ | | Ct<\, C↑↑, Ddb<↑\, Db↓↓ | ||
| | | -6 | ||
| | | 8 | ||
| This interval… | | This interval… | ||
* Is the closest approximation of 31edo's own Middle Seventh found in this system, and thus… | * Is the closest approximation of 31edo's own Middle Seventh found in this system, and thus… | ||
| Line 2,198: | Line 2,197: | ||
| Artoneutral Seventh, Lesser Sub-Diminished Octave | | Artoneutral Seventh, Lesser Sub-Diminished Octave | ||
| Ct<, Ddb<↑ | | Ct<, Ddb<↑ | ||
| | | -7 | ||
| | | 6 | ||
| This interval… | | This interval… | ||
* Approximates the [[11/6|Alpharabian Artoneutral Seventh]], which is the traditional, [[low-complexity JI|low complexity]] Undecimal Neutral Seventh, and as such… | * Approximates the [[11/6|Alpharabian Artoneutral Seventh]], which is the traditional, [[low-complexity JI|low complexity]] Undecimal Neutral Seventh, and as such… | ||
| Line 2,215: | Line 2,214: | ||
| Tendoneutral Seventh, Greater Sub-Diminished Octave | | Tendoneutral Seventh, Greater Sub-Diminished Octave | ||
| Ct>, Ddb>↑ | | Ct>, Ddb>↑ | ||
| | | -8 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[81/44|Alpharabian Tendoneutral Seventh]] or 2nd Undecimal Neutral Seventh, and as such… | * Approximates the [[81/44|Alpharabian Tendoneutral Seventh]] or 2nd Undecimal Neutral Seventh, and as such… | ||
| Line 2,231: | Line 2,230: | ||
| Lesser Submajor Seventh, Diptolemaic Major Seventh, Retroptolemaic Diminished Octave | | Lesser Submajor Seventh, Diptolemaic Major Seventh, Retroptolemaic Diminished Octave | ||
| Ct>/, C#↓↓, Db↓ | | Ct>/, C#↓↓, Db↓ | ||
| | | -7 | ||
| | | 6 | ||
| This interval… | | This interval… | ||
* Approximates the [[50/27|Grave Major Seventh]], and thus… | * Approximates the [[50/27|Grave Major Seventh]], and thus… | ||
| Line 2,244: | Line 2,243: | ||
| Greater Submajor Seventh, Artoretromean Diminished Octave | | Greater Submajor Seventh, Artoretromean Diminished Octave | ||
| Ct<↑, Db↓/ | | Ct<↑, Db↓/ | ||
| | | -6 | ||
| | | 8 | ||
| This interval… | | This interval… | ||
* Approximates the [[13/7|Tridecimal Submajor Seventh]] and a similar 11-limit interval that acts as the Submajor counterpart to the Undecimal Supraminor Seventh, and thus… | * Approximates the [[13/7|Tridecimal Submajor Seventh]] and a similar 11-limit interval that acts as the Submajor counterpart to the Undecimal Supraminor Seventh, and thus… | ||
| Line 2,259: | Line 2,258: | ||
| Narrow Major Seventh, Tendoretromean Diminished Octave | | Narrow Major Seventh, Tendoretromean Diminished Octave | ||
| Ct>↑, C#↓\, Db\ | | Ct>↑, C#↓\, Db\ | ||
| | | -5 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[28/15|Septimal Grave Major Seventh]], and thus… | * Approximates the [[28/15|Septimal Grave Major Seventh]], and thus… | ||
| Line 2,272: | Line 2,271: | ||
| Ptolemaic Major Seventh, Pythagorean Diminished Octave | | Ptolemaic Major Seventh, Pythagorean Diminished Octave | ||
| Db, C#↓ | | Db, C#↓ | ||
| | | -5 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[15/8|Classic Major Seventh]] or Ptolemaic Major Seventh, and as such… | * Approximates the [[15/8|Classic Major Seventh]] or Ptolemaic Major Seventh, and as such… | ||
| Line 2,290: | Line 2,289: | ||
| Artomean Major Seventh, Artomean Diminished Octave | | Artomean Major Seventh, Artomean Diminished Octave | ||
| Db/, C#↓/ | | Db/, C#↓/ | ||
| | | -5 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[32/17|Small Septendecimal Major Seventh]] or Octave-Reduced Seventeenth Subharmonic, and thus… | * Approximates the [[32/17|Small Septendecimal Major Seventh]] or Octave-Reduced Seventeenth Subharmonic, and thus… | ||
| Line 2,306: | Line 2,305: | ||
| Tendomean Major Seventh, Tendomean Diminished Octave | | Tendomean Major Seventh, Tendomean Diminished Octave | ||
| C#\, Db↑\ | | C#\, Db↑\ | ||
| | | -6 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[17/9|Large Septendecimal Major Seventh]], and thus… | * Approximates the [[17/9|Large Septendecimal Major Seventh]], and thus… | ||
| Line 2,321: | Line 2,320: | ||
| Pythagorean Major Seventh, Ptolemaic Diminished Octave | | Pythagorean Major Seventh, Ptolemaic Diminished Octave | ||
| C#, Db↑ | | C#, Db↑ | ||
| | | -6 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[243/128|Pythagorean Major Seventh]], and as such… | * Approximates the [[243/128|Pythagorean Major Seventh]], and as such… | ||
| Line 2,339: | Line 2,338: | ||
| Wide Major Seventh, Lesser Super-Diminished Octave | | Wide Major Seventh, Lesser Super-Diminished Octave | ||
| C#/, Dd<↓ | | C#/, Dd<↓ | ||
| | | -7 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[40/21|Septimal Acute Major Seventh]], and thus… | * Approximates the [[40/21|Septimal Acute Major Seventh]], and thus… | ||
| Line 2,352: | Line 2,351: | ||
| Narrow Supermajor Seventh, Greater Super-Diminished Octave | | Narrow Supermajor Seventh, Greater Super-Diminished Octave | ||
| C#↑\, Dd>↓ | | C#↑\, Dd>↓ | ||
| | | -7 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates multiple complex [[17-limit]] intervals relative to the Tonic and can be used… | * Approximates multiple complex [[17-limit]] intervals relative to the Tonic and can be used… | ||
| Line 2,367: | Line 2,366: | ||
| Lesser Supermajor Seventh, Diptolemaic Diminished Octave | | Lesser Supermajor Seventh, Diptolemaic Diminished Octave | ||
| C#↑, Db↑↑ | | C#↑, Db↑↑ | ||
| | | -8 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[48/25|Classic Diminished Octave]] or Diptolemaic Diminished Octave, and thus… | * Approximates the [[48/25|Classic Diminished Octave]] or Diptolemaic Diminished Octave, and thus… | ||
| Line 2,381: | Line 2,380: | ||
| Greater Supermajor Seventh, Narrow Infraoctave, Ultra-Diminished Octave | | Greater Supermajor Seventh, Narrow Infraoctave, Ultra-Diminished Octave | ||
| Dd<, C#↑/ | | Dd<, C#↑/ | ||
| | | -8 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[27/14|Septimal Supermajor Seventh]], and thus… | * Approximates the [[27/14|Septimal Supermajor Seventh]], and thus… | ||
| Line 2,397: | Line 2,396: | ||
| Infraoctave, Wide Supermajor Seventh | | Infraoctave, Wide Supermajor Seventh | ||
| Dd>, Ct#>↓ | | Dd>, Ct#>↓ | ||
| | | -9 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[64/33|Alpharabian Infraoctave]], and as such… | * Approximates the [[64/33|Alpharabian Infraoctave]], and as such… | ||
| Line 2,417: | Line 2,416: | ||
| Narrow Ultramajor Seventh, Wide Infraoctave | | Narrow Ultramajor Seventh, Wide Infraoctave | ||
| C#↑↑, Dd>/ | | C#↑↑, Dd>/ | ||
| | | -9 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[39/20|Tridecimal Ultramajor Seventh]] | * Approximates the [[39/20|Tridecimal Ultramajor Seventh]] | ||
| Line 2,435: | Line 2,434: | ||
| Ultramajor Seventh, Wide Superprime | | Ultramajor Seventh, Wide Superprime | ||
| Ct#<, Dd<↑ | | Ct#<, Dd<↑ | ||
| | | -9 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[88/45|Undecimal Suboctave]] | * Approximates the [[88/45|Undecimal Suboctave]] | ||
| Line 2,455: | Line 2,454: | ||
| Lesser Suboctave, Wide Ultramajor Seventh | | Lesser Suboctave, Wide Ultramajor Seventh | ||
| Ct#>, Dd>↑ | | Ct#>, Dd>↑ | ||
| | | -10 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[septimal suboctave|Archytas suboctave]], and thus… | * Approximates the [[septimal suboctave|Archytas suboctave]], and thus… | ||
| Line 2,476: | Line 2,475: | ||
| Greater Suboctave | | Greater Suboctave | ||
| D↓ | | D↓ | ||
| | | -10 | ||
| | | -3 | ||
| This interval… | | This interval… | ||
* Approximates the [[syntonic suboctave]] | * Approximates the [[syntonic suboctave]] | ||
| Line 2,492: | Line 2,491: | ||
| Wide Suboctave | | Wide Suboctave | ||
| D↓/ | | D↓/ | ||
| | | -10 | ||
| | | -10 | ||
| This interval… | | This interval… | ||
* Approximates the [[ptolemismic suboctave]] and the [[biyatismic suboctave]] | * Approximates the [[ptolemismic suboctave]] and the [[biyatismic suboctave]] | ||
| Line 2,518: | Line 2,517: | ||
| Perfect Octave | | Perfect Octave | ||
| D | | D | ||
| | | 10 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Is the [[2/1|Perfect Octave]], and thus… | * Is the [[2/1|Perfect Octave]], and thus… | ||