159edo/Interval names and harmonies: Difference between revisions
No edit summary |
No edit summary |
||
| Line 1,349: | Line 1,349: | ||
| Greater Super-Diminished Fifth, Tendoretromean Augmented Fourth | | Greater Super-Diminished Fifth, Tendoretromean Augmented Fourth | ||
| Ad>↓, G#↑\ | | Ad>↓, G#↑\ | ||
| | | -1 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Approximates a complex 11-limit interval formed by subtracting a Syntonic Comma from a Paraminor Fifth, and thus… | * Approximates a complex 11-limit interval formed by subtracting a Syntonic Comma from a Paraminor Fifth, and thus… | ||
| Line 1,362: | Line 1,362: | ||
| Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth | | Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth | ||
| Ab↑↑, G#↑ | | Ab↑↑, G#↑ | ||
| | | -2 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Approximates the [[36/25|Classic Diminished Fifth]], and thus… | * Approximates the [[36/25|Classic Diminished Fifth]], and thus… | ||
| Line 1,379: | Line 1,379: | ||
| Ultra-Diminished Fifth, Lesser Super-Augmented Fourth | | Ultra-Diminished Fifth, Lesser Super-Augmented Fourth | ||
| Ad<, Gt#<↓ | | Ad<, Gt#<↓ | ||
| | | -1 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Approximates the [[81/56|Septimal Superaugmented Fourth]], and thus… | * Approximates the [[81/56|Septimal Superaugmented Fourth]], and thus… | ||
| Line 1,393: | Line 1,393: | ||
| Paraminor Fifth, Greater Super-Augmented Fourth | | Paraminor Fifth, Greater Super-Augmented Fourth | ||
| Ad>, Gt#>↓ | | Ad>, Gt#>↓ | ||
| | | 0 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[16/11|Just Paraminor Fifth]], and as such… | * Approximates the [[16/11|Just Paraminor Fifth]], and as such… | ||
| Line 1,414: | Line 1,414: | ||
| Wide Paraminor Fifth, Retrodiptolemaic Augmented Fourth | | Wide Paraminor Fifth, Retrodiptolemaic Augmented Fourth | ||
| Ad<\, G#↑, Ab↑↑ | | Ad<\, G#↑, Ab↑↑ | ||
| | | -1 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Is reachable through stacking three of this system's approximation of the Septendecimal Whole Tone | * Is reachable through stacking three of this system's approximation of the Septendecimal Whole Tone | ||
| Line 1,428: | Line 1,428: | ||
| Narrow Grave Fifth, Ultra-Augmented Fourth | | Narrow Grave Fifth, Ultra-Augmented Fourth | ||
| Ad<↑, Gt#< | | Ad<↑, Gt#< | ||
| | | -1 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Approximates the [[22/15|Undecimal Acute Ultra-Diminished Fifth]], and thus… | * Approximates the [[22/15|Undecimal Acute Ultra-Diminished Fifth]], and thus… | ||
| Line 1,443: | Line 1,443: | ||
| Lesser Grave Fifth | | Lesser Grave Fifth | ||
| Ad>↑, A↓\, Gt#> | | Ad>↑, A↓\, Gt#> | ||
| | | -2 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Is reachable through stacking four of this system's approximation of the Werckismic Subfourth and octave-reducing | * Is reachable through stacking four of this system's approximation of the Werckismic Subfourth and octave-reducing | ||
| Line 1,455: | Line 1,455: | ||
| Greater Grave Fifth | | Greater Grave Fifth | ||
| A↓ | | A↓ | ||
| | | -3 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[40/27|Classic Grave Fifth]], and as such… | * Approximates the [[40/27|Classic Grave Fifth]], and as such… | ||
| Line 1,471: | Line 1,471: | ||
| Wide Grave Fifth | | Wide Grave Fifth | ||
| A↓/ | | A↓/ | ||
| | | -2 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates a complex 11-limit interval, which, in this system… | * Approximates a complex 11-limit interval, which, in this system… | ||
| Line 1,485: | Line 1,485: | ||
| Narrow Fifth | | Narrow Fifth | ||
| A\ | | A\ | ||
| | | 1 | ||
| | | 4 | ||
| This interval… | | This interval… | ||
* Approximates the [[112/75|Marvelous Fifth]], and thus… | * Approximates the [[112/75|Marvelous Fifth]], and thus… | ||
| Line 1,501: | Line 1,501: | ||
| Perfect Fifth | | Perfect Fifth | ||
| A | | A | ||
| | | 5 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 1,527: | Line 1,527: | ||
| Wide Fifth | | Wide Fifth | ||
| A/ | | A/ | ||
| | | 1 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[128/85|Septendecimal Fifth]], and thus… | * Approximates the [[128/85|Septendecimal Fifth]], and thus… | ||
| Line 1,543: | Line 1,543: | ||
| Narrow Acute Fifth | | Narrow Acute Fifth | ||
| A↑\ | | A↑\ | ||
| | | -1 | ||
| | | 1 | ||
| This interval… | | This interval… | ||
* Is reachable through stacking five of this system's approximation of the 2nd Undecimal Neutral Second | * Is reachable through stacking five of this system's approximation of the 2nd Undecimal Neutral Second | ||
| Line 1,556: | Line 1,556: | ||
| Lesser Acute Fifth | | Lesser Acute Fifth | ||
| A↑ | | A↑ | ||
| | | -2 | ||
| | | 0 | ||
| This interval… | | This interval… | ||
* Approximates a complex 5-limit interval formed by stacking a syntonic comma on top of a Perfect Fifth | * Approximates a complex 5-limit interval formed by stacking a syntonic comma on top of a Perfect Fifth | ||
| Line 1,568: | Line 1,568: | ||
| Greater Acute Fifth, Narrow Inframinor Sixth | | Greater Acute Fifth, Narrow Inframinor Sixth | ||
| At<↓, A↑/ | | At<↓, A↑/ | ||
| | | -3 | ||
| | | -1 | ||
| This Interval… | | This Interval… | ||
* Approximates the [[32/21|Septimal Superfifth]], and thus… | * Approximates the [[32/21|Septimal Superfifth]], and thus… | ||
| Line 1,581: | Line 1,581: | ||
| Inframinor Sixth, Wide Acute Fifth | | Inframinor Sixth, Wide Acute Fifth | ||
| At>↓, Bdb> | | At>↓, Bdb> | ||
| | | -2 | ||
| | | -2 | ||
| This interval… | | This interval… | ||
* Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic sixth that sounds more like a fifth, and as such… | * Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic sixth that sounds more like a fifth, and as such… | ||
| Line 1,596: | Line 1,596: | ||
| Narrow Paramajor Fifth, Wide Inframinor Sixth | | Narrow Paramajor Fifth, Wide Inframinor Sixth | ||
| At<\, Bb↓↓, A↑↑ | | At<\, Bb↓↓, A↑↑ | ||
| | | -1 | ||
| | | -1 | ||
| This interval… | | This interval… | ||
* Approximates the [[20/13|Tridecimal Semitenth]] | * Approximates the [[20/13|Tridecimal Semitenth]] | ||
| Line 1,609: | Line 1,609: | ||
| Paramajor Fifth, Narrow Subminor Sixth | | Paramajor Fifth, Narrow Subminor Sixth | ||
| At<, Bdb<↑ | | At<, Bdb<↑ | ||
| | | -1 | ||
| | | 0 | ||
| This interval… | | This interval… | ||
* Approximates the [[99/64|Just Paramajor Fifth]], and as such… | * Approximates the [[99/64|Just Paramajor Fifth]], and as such… | ||
| Line 1,627: | Line 1,627: | ||
| Lesser Subminor Sixth, Infra-Augmented Fifth | | Lesser Subminor Sixth, Infra-Augmented Fifth | ||
| At>, Bb↓\ | | At>, Bb↓\ | ||
| | | 0 | ||
| | | 1 | ||
| This interval… | | This interval… | ||
* Approximates the [[14/9|Septimal Subminor Sixth]], and as such… | * Approximates the [[14/9|Septimal Subminor Sixth]], and as such… | ||
| Line 1,641: | Line 1,641: | ||
| Greater Subminor Sixth, Diptolemaic Augmented Fifth | | Greater Subminor Sixth, Diptolemaic Augmented Fifth | ||
| Bb↓, At>/, A#↓↓ | | Bb↓, At>/, A#↓↓ | ||
| | | -1 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Approximates the [[25/16|Classic Augmented Fifth]] or Diptolemaic Augmented Fifth, and thus… | * Approximates the [[25/16|Classic Augmented Fifth]] or Diptolemaic Augmented Fifth, and thus… | ||
| Line 1,658: | Line 1,658: | ||
| Wide Subminor Sixth, Lesser Sub-Augmented Fifth | | Wide Subminor Sixth, Lesser Sub-Augmented Fifth | ||
| Bb↓/, At<↑ | | Bb↓/, At<↑ | ||
| | | -1 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[80/51|Septendecimal Minor Sixth]] | * Approximates the [[80/51|Septendecimal Minor Sixth]] | ||
| Line 1,672: | Line 1,672: | ||
| Narrow Minor Sixth, Greater Sub-Augmented Fifth | | Narrow Minor Sixth, Greater Sub-Augmented Fifth | ||
| Bb\, At>↑, A#↓\ | | Bb\, At>↑, A#↓\ | ||
| | | 0 | ||
| | | 4 | ||
| This interval… | | This interval… | ||
* Approximates the [[ | * Approximates the [[11/7|Neo-Gothic Minor Sixth]], and thus… | ||
:* Can be used in Western-Classical-based harmony and Neo-Medieval harmony very easily | :* Can be used in Western-Classical-based harmony and Neo-Medieval harmony very easily | ||
:* Has additional applications in Paradiatonic harmony, particularly… | :* Has additional applications in Paradiatonic harmony, particularly… | ||
| Line 1,687: | Line 1,687: | ||
| Pythagorean Minor Sixth, Ptolemaic Augmented Fifth | | Pythagorean Minor Sixth, Ptolemaic Augmented Fifth | ||
| Bb, A#↓ | | Bb, A#↓ | ||
| | | -1 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[128/81|Pythagorean Minor Sixth]], and as such… | * Approximates the [[128/81|Pythagorean Minor Sixth]], and as such… | ||
| Line 1,704: | Line 1,704: | ||
| Artomean Minor Sixth, Artomean Augmented Fifth | | Artomean Minor Sixth, Artomean Augmented Fifth | ||
| Bb/, A#↓/ | | Bb/, A#↓/ | ||
| | | 0 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[100/63|Quasi-Tempered Minor Sixth]] | * Approximates the [[100/63|Quasi-Tempered Minor Sixth]] | ||
| Line 1,718: | Line 1,718: | ||
| Tendomean Minor Sixth, Tendomean Augmented Fifth | | Tendomean Minor Sixth, Tendomean Augmented Fifth | ||
| A#\, Bb↑\ | | A#\, Bb↑\ | ||
| | | 2 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[51/32|Septendecimal Tendomean Minor Sixth]] | * Approximates the [[51/32|Septendecimal Tendomean Minor Sixth]] | ||
| Line 1,729: | Line 1,729: | ||
| Ptolemaic Minor Sixth, Pythagorean Augmented Fifth | | Ptolemaic Minor Sixth, Pythagorean Augmented Fifth | ||
| A#, Bb↑ | | A#, Bb↑ | ||
| | | 4 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[8/5|Classic Minor Sixth]] or Octave-Reduced Fifth Subharmonic, and as such… | * Approximates the [[8/5|Classic Minor Sixth]] or Octave-Reduced Fifth Subharmonic, and as such… | ||
| Line 1,750: | Line 1,750: | ||
|Wide Minor Sixth, Artoretromean Augmented Fifth | |Wide Minor Sixth, Artoretromean Augmented Fifth | ||
| Bd<↓, Bb↑/, A#/ | | Bd<↓, Bb↑/, A#/ | ||
| | | 2 | ||
| | | 4 | ||
| This interval… | | This interval… | ||
* Approximates the [[45/28|Marvelous Minor Sixth]], and as such… | * Approximates the [[45/28|Marvelous Minor Sixth]], and as such… | ||
| Line 1,765: | Line 1,765: | ||
| Lesser Supraminor Sixth, Tendoretromean Augmented Fifth | | Lesser Supraminor Sixth, Tendoretromean Augmented Fifth | ||
| Bd>↓, A#↑\ | | Bd>↓, A#↑\ | ||
| | | 1 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[21/13|Tridecimal Supraminor Sixth]] and a similar 11-limit interval that acts as the Supraminor counterpart to the Undecimal Submajor Sixth | * Approximates the [[21/13|Tridecimal Supraminor Sixth]] and a similar 11-limit interval that acts as the Supraminor counterpart to the Undecimal Submajor Sixth | ||
| Line 1,778: | Line 1,778: | ||
| Greater Supraminor Sixth, Retroptolemaic Augmented Fifth | | Greater Supraminor Sixth, Retroptolemaic Augmented Fifth | ||
| Bd<\, Bb↑↑, A#↑ | | Bd<\, Bb↑↑, A#↑ | ||
| | | 0 | ||
| | | 3 | ||
| This interval | | This interval | ||
* Approximates the [[13/8|Lesser Tridecimal Neutral Sixth]] or Octave-Reduced Thirteenth Harmonic, and as such… | * Approximates the [[13/8|Lesser Tridecimal Neutral Sixth]] or Octave-Reduced Thirteenth Harmonic, and as such… | ||
| Line 1,793: | Line 1,793: | ||
| Artoneutral Sixth, Lesser Super-Augmented Fifth | | Artoneutral Sixth, Lesser Super-Augmented Fifth | ||
| Bd<, At#<↓ | | Bd<, At#<↓ | ||
| | | -1 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[44/27|Alpharabian Artoneutral Sixth]] or 2nd Undecimal Neutral Sixth, and as such… | * Approximates the [[44/27|Alpharabian Artoneutral Sixth]] or 2nd Undecimal Neutral Sixth, and as such… | ||
| Line 1,809: | Line 1,809: | ||
| Tendoneutral Sixth, Greater Super-Augmented Fifth | | Tendoneutral Sixth, Greater Super-Augmented Fifth | ||
| Bd>, At#>↓ | | Bd>, At#>↓ | ||
| | | 0 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[18/11|Alpharabian Tendoneutral Sixth]], which is the traditional, low complexity Undecimal Neutral Sixth, and as such… | * Approximates the [[18/11|Alpharabian Tendoneutral Sixth]], which is the traditional, low complexity Undecimal Neutral Sixth, and as such… | ||
| Line 1,829: | Line 1,829: | ||
| Lesser Submajor Sixth, Retrodiptolemaic Augmented Fifth | | Lesser Submajor Sixth, Retrodiptolemaic Augmented Fifth | ||
| Bd>/, B↓↓, At#>↓/, A#↑↑ | | Bd>/, B↓↓, At#>↓/, A#↑↑ | ||
| | | -1 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[64/39|Greater Tridecimal Neutral Sixth]] | * Approximates the [[64/39|Greater Tridecimal Neutral Sixth]] | ||
| Line 1,845: | Line 1,845: | ||
| Greater Submajor Sixth, Ultra-Augmented Fifth | | Greater Submajor Sixth, Ultra-Augmented Fifth | ||
| Bd<↑, At#< | | Bd<↑, At#< | ||
| | | 0 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[33/20|Undecimal Submajor Sixth]] | * Approximates the [[33/20|Undecimal Submajor Sixth]] | ||
| Line 1,856: | Line 1,856: | ||
| Narrow Major Sixth | | Narrow Major Sixth | ||
| Bd>↑, B↓\, At#> | | Bd>↑, B↓\, At#> | ||
| | | 1 | ||
| | | 4 | ||
| This interval… | | This interval… | ||
* Approximates the [[224/135|Marvelous Major Sixth]], and as such… | * Approximates the [[224/135|Marvelous Major Sixth]], and as such… | ||
| Line 1,869: | Line 1,869: | ||
| Ptolemaic Major Sixth | | Ptolemaic Major Sixth | ||
| B↓, Cb | | B↓, Cb | ||
| | | 3 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[5/3|Classic Major Sixth]], and as such… | * Approximates the [[5/3|Classic Major Sixth]], and as such… | ||
| Line 1,888: | Line 1,888: | ||
| Artomean Major Sixth | | Artomean Major Sixth | ||
| B↓/ | | B↓/ | ||
| | | 1 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[256/153|Septendecimal Artomean Major Sixth]] | * Approximates the [[256/153|Septendecimal Artomean Major Sixth]] | ||
| Line 1,901: | Line 1,901: | ||
| Tendomean Major Sixth | | Tendomean Major Sixth | ||
| B\ | | B\ | ||
| | | 0 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[42/25|Quasi-Tempered Major Sixth]], and as such… | * Approximates the [[42/25|Quasi-Tempered Major Sixth]], and as such… | ||