159edo/Interval names and harmonies: Difference between revisions
No edit summary |
Revised and Added Melodic and Harmonic Ratings |
||
| Line 61: | Line 61: | ||
| D↑ | | D↑ | ||
| -5 | | -5 | ||
| - | | -2 | ||
| This interval… | | This interval… | ||
* Approximates the [[syntonic comma]], and as such… | * Approximates the [[syntonic comma]], and as such… | ||
| Line 78: | Line 78: | ||
| Greater Superprime, Narrow Inframinor Second | | Greater Superprime, Narrow Inframinor Second | ||
| Edb<, Dt<↓ | | Edb<, Dt<↓ | ||
| - | | -5 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Approximates the [[septimal comma|Archytas comma]], and thus… | * Approximates the [[septimal comma|Archytas comma]], and thus… | ||
| Line 100: | Line 100: | ||
| Inframinor Second, Wide Superprime | | Inframinor Second, Wide Superprime | ||
| Edb>, Dt>↓ | | Edb>, Dt>↓ | ||
| - | | -5 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 121: | Line 121: | ||
| Wide Inframinor Second, Narrow Ultraprime | | Wide Inframinor Second, Narrow Ultraprime | ||
| Eb↓↓, Dt<\ | | Eb↓↓, Dt<\ | ||
| - | | -5 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 140: | Line 140: | ||
| Ultraprime, Narrow Subminor Second | | Ultraprime, Narrow Subminor Second | ||
| Dt<, Edb<↑ | | Dt<, Edb<↑ | ||
| - | | -4 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 161: | Line 161: | ||
| Lesser Subminor Second, Wide Ultraprime, Infra-Augmented Prime | | Lesser Subminor Second, Wide Ultraprime, Infra-Augmented Prime | ||
| Dt>, Eb↓\ | | Dt>, Eb↓\ | ||
| - | | -4 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 179: | Line 179: | ||
| Greater Subminor Second, Diptolemaic Augmented Prime | | Greater Subminor Second, Diptolemaic Augmented Prime | ||
| Eb↓, D#↓↓ | | Eb↓, D#↓↓ | ||
| - | | -4 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 194: | Line 194: | ||
| Wide Subminor Second, Lesser Sub-Augmented Prime | | Wide Subminor Second, Lesser Sub-Augmented Prime | ||
| Eb↓/, Dt<↑ | | Eb↓/, Dt<↑ | ||
| - | | -4 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 209: | Line 209: | ||
| Narrow Minor Second, Greater Sub-Augmented Prime | | Narrow Minor Second, Greater Sub-Augmented Prime | ||
| Eb\, Dt>↑ | | Eb\, Dt>↑ | ||
| - | | -3 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 223: | Line 223: | ||
| Pythagorean Minor Second, Ptolemaic Augmented Prime | | Pythagorean Minor Second, Ptolemaic Augmented Prime | ||
| Eb, D#↓ | | Eb, D#↓ | ||
| | | -3 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 244: | Line 244: | ||
| Artomean Minor Second, Artomean Augmented Prime | | Artomean Minor Second, Artomean Augmented Prime | ||
| Eb/, D#↓/ | | Eb/, D#↓/ | ||
| | | -3 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 260: | Line 260: | ||
| Tendomean Minor Second, Tendomean Augmented Prime | | Tendomean Minor Second, Tendomean Augmented Prime | ||
| D#\, Eb↑\ | | D#\, Eb↑\ | ||
| | | -2 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 276: | Line 276: | ||
| Ptolemaic Minor Second, Pythagorean Augmented Prime | | Ptolemaic Minor Second, Pythagorean Augmented Prime | ||
| D#, Eb↑ | | D#, Eb↑ | ||
| | | -2 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 297: | Line 297: | ||
| Wide Minor Second, Artoretromean Augmented Prime | | Wide Minor Second, Artoretromean Augmented Prime | ||
| Ed<↓, Eb↑/, D#/ | | Ed<↓, Eb↑/, D#/ | ||
| | | -3 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 311: | Line 311: | ||
| Lesser Supraminor Second, Tendoretromean Augmented Prime | | Lesser Supraminor Second, Tendoretromean Augmented Prime | ||
| Ed>↓, D#↑\ | | Ed>↓, D#↑\ | ||
| | | -3 | ||
| 4 | | 4 | ||
| This interval… | | This interval… | ||
| Line 327: | Line 327: | ||
| Greater Supraminor Second, Diptolemaic Limma, Retroptolemaic Augmented Prime | | Greater Supraminor Second, Diptolemaic Limma, Retroptolemaic Augmented Prime | ||
| Ed<\, Eb↑↑, D#↑ | | Ed<\, Eb↑↑, D#↑ | ||
| | | -4 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[27/25|Large Limma]], and thus… | * Approximates the [[27/25|Large Limma]], and thus… | ||
| Line 342: | Line 342: | ||
| Artoneutral Second, Lesser Super-Augmented Prime | | Artoneutral Second, Lesser Super-Augmented Prime | ||
| Ed<, Dt#<↓ | | Ed<, Dt#<↓ | ||
| | | -4 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Approximates the [[88/81|Alpharabian Artoneutral Second]] or 2nd Undecimal Neutral Second, and as such… | * Approximates the [[88/81|Alpharabian Artoneutral Second]] or 2nd Undecimal Neutral Second, and as such… | ||
| Line 361: | Line 361: | ||
| Tendoneutral Second, Greater Super-Augmented Prime | | Tendoneutral Second, Greater Super-Augmented Prime | ||
| Ed>, Dt#>↓ | | Ed>, Dt#>↓ | ||
| | | -4 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Approximates the [[12/11|Alpharabian Tendoneutral Second]], which is the traditional, [[low-complexity JI|low complexity]] Undecimal Neutral Second, and as such… | * Approximates the [[12/11|Alpharabian Tendoneutral Second]], which is the traditional, [[low-complexity JI|low complexity]] Undecimal Neutral Second, and as such… | ||
| Line 380: | Line 380: | ||
| Lesser Submajor Second, Retrodiptolemaic Augmented Prime | | Lesser Submajor Second, Retrodiptolemaic Augmented Prime | ||
| Ed>/, E↓↓, Dt#>↓/, D#↑↑ | | Ed>/, E↓↓, Dt#>↓/, D#↑↑ | ||
| | | -4 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Is one half of this system's approximation of the Classic Minor Third | * Is one half of this system's approximation of the Classic Minor Third | ||
| Line 393: | Line 393: | ||
| Greater Submajor Second, Ultra-Augmented Prime | | Greater Submajor Second, Ultra-Augmented Prime | ||
| Ed<↑, Dt#<, Fb↓/ | | Ed<↑, Dt#<, Fb↓/ | ||
| | | -3 | ||
| | | 4 | ||
| This interval… | | This interval… | ||
* Approximates the [[11/10|Undecimal Submajor Second]] and a similar 13-limit interval that acts as the Submajor counterpart to the Tridecimal Supraminor Second, and thus… | * Approximates the [[11/10|Undecimal Submajor Second]] and a similar 13-limit interval that acts as the Submajor counterpart to the Tridecimal Supraminor Second, and thus… | ||
| Line 409: | Line 409: | ||
| Narrow Major Second | | Narrow Major Second | ||
| Ed>↑, E↓\, Dt#>, Fb\ | | Ed>↑, E↓\, Dt#>, Fb\ | ||
| | | -3 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Is one half of the approximation of the traditional, [[low-complexity JI|low complexity]] Undecimal Neutral Third in this system | * Is one half of the approximation of the traditional, [[low-complexity JI|low complexity]] Undecimal Neutral Third in this system | ||
| Line 422: | Line 422: | ||
| Ptolemaic Major Second | | Ptolemaic Major Second | ||
| E↓, Fb | | E↓, Fb | ||
| | | -2 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[10/9|Classic Major Second]] or Ptolemaic Major Second, and as such… | * Approximates the [[10/9|Classic Major Second]] or Ptolemaic Major Second, and as such… | ||
| Line 441: | Line 441: | ||
| Artomean Major Second | | Artomean Major Second | ||
| E↓/, Fb/ | | E↓/, Fb/ | ||
| | | -2 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[143/128|Grossmic Whole Tone]], and thus… | * Approximates the [[143/128|Grossmic Whole Tone]], and thus… | ||
| Line 455: | Line 455: | ||
| Tendomean Major Second | | Tendomean Major Second | ||
| E\, Fb↑\ | | E\, Fb↑\ | ||
| | | -2 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[28/25|Middle Major Second]] | * Approximates the [[28/25|Middle Major Second]] | ||
| Line 469: | Line 469: | ||
| Pythagorean Major Second | | Pythagorean Major Second | ||
| E, Fb↑ | | E, Fb↑ | ||
| | | -1 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[9/8|Pythagorean Major Second]], and as such… | * Approximates the [[9/8|Pythagorean Major Second]], and as such… | ||
| Line 489: | Line 489: | ||
| Wide Major Second | | Wide Major Second | ||
| E/, Fd<↓ | | E/, Fd<↓ | ||
| | | -1 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[44/39|Tridecimal Major Second]], and thus… | * Approximates the [[44/39|Tridecimal Major Second]], and thus… | ||
| Line 503: | Line 503: | ||
| Narrow Supermajor Second | | Narrow Supermajor Second | ||
| E↑\, Fd>↓ | | E↑\, Fd>↓ | ||
| | | -1 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[17/15|Septendecimal Whole Tone]], and thus… | * Approximates the [[17/15|Septendecimal Whole Tone]], and thus… | ||
| Line 520: | Line 520: | ||
| Lesser Supermajor Second | | Lesser Supermajor Second | ||
| E↑, Fd<\, Fb↑↑, Dx | | E↑, Fd<\, Fb↑↑, Dx | ||
| | | -1 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[256/225|Neapolitan Diminished Third]], and thus… | * Approximates the [[256/225|Neapolitan Diminished Third]], and thus… | ||
| Line 536: | Line 536: | ||
| Greater Supermajor Second, Narrow Inframinor Third | | Greater Supermajor Second, Narrow Inframinor Third | ||
| Fd<, Et<↓, E↑/ | | Fd<, Et<↓, E↑/ | ||
| | | 0 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[8/7|Septimal Supermajor Second]] or Octave-Reduced Seventh Subharmonic, and as such… | * Approximates the [[8/7|Septimal Supermajor Second]] or Octave-Reduced Seventh Subharmonic, and as such… | ||
| Line 554: | Line 554: | ||
| Inframinor Third, Wide Supermajor Second | | Inframinor Third, Wide Supermajor Second | ||
| Fd>, Et>↓ | | Fd>, Et>↓ | ||
| | | 0 | ||
| | | 4 | ||
| This interval… | | This interval… | ||
* Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic third that sounds more like a second, and as such… | * Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic third that sounds more like a second, and as such… | ||
| Line 569: | Line 569: | ||
| Wide Inframinor Third, Narrow Ultramajor Second, Semifourth | | Wide Inframinor Third, Narrow Ultramajor Second, Semifourth | ||
| Fd>/, Et<\, F↓↓, E↑↑ | | Fd>/, Et<\, F↓↓, E↑↑ | ||
| | | 0 | ||
| | | 4 | ||
| This interval… | | This interval… | ||
* Approximates the [[15/13|Tridecimal Semifourth]], and thus… | * Approximates the [[15/13|Tridecimal Semifourth]], and thus… | ||
| Line 585: | Line 585: | ||
| Ultramajor Second, Narrow Subminor Third | | Ultramajor Second, Narrow Subminor Third | ||
| Et<, Fd<↑ | | Et<, Fd<↑ | ||
| | | 0 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic second that sounds more like a third, and as such… | * Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic second that sounds more like a third, and as such… | ||
| Line 599: | Line 599: | ||
| Lesser Subminor Third, Wide Ultramajor Second | | Lesser Subminor Third, Wide Ultramajor Second | ||
| Et>, Fd>↑, F↓\ | | Et>, Fd>↑, F↓\ | ||
| | | 0 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[7/6|Septimal Subminor Third]], and as such… | * Approximates the [[7/6|Septimal Subminor Third]], and as such… | ||
| Line 616: | Line 616: | ||
| Greater Subminor Third | | Greater Subminor Third | ||
| F↓, Et>/, E#↓↓, Gbb | | F↓, Et>/, E#↓↓, Gbb | ||
| | | -1 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[75/64|Classic Augmented Second]], and as such… | * Approximates the [[75/64|Classic Augmented Second]], and as such… | ||
| Line 633: | Line 633: | ||
| Wide Subminor Third | | Wide Subminor Third | ||
| F↓/, Et<↑ | | F↓/, Et<↑ | ||
| | | -1 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[20/17|Septendecimal Minor Third]] | * Approximates the [[20/17|Septendecimal Minor Third]] | ||
| Line 647: | Line 647: | ||
| Narrow Minor Third | | Narrow Minor Third | ||
| F\, Et>↑ | | F\, Et>↑ | ||
| | | 0 | ||
| | | 4 | ||
| This interval… | | This interval… | ||
* Approximates the [[13/11|Neo-Gothic Minor Third]], and thus… | * Approximates the [[13/11|Neo-Gothic Minor Third]], and thus… | ||
| Line 662: | Line 662: | ||
| Pythagorean Minor Third | | Pythagorean Minor Third | ||
| F | | F | ||
| | | -1 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[32/27|Pythagorean Minor Third]], and as such… | * Approximates the [[32/27|Pythagorean Minor Third]], and as such… | ||
| Line 679: | Line 679: | ||
| Artomean Minor Third | | Artomean Minor Third | ||
| F/ | | F/ | ||
| | | 0 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[25/21|Quasi-Tempered Minor Third]], and as such… | * Approximates the [[25/21|Quasi-Tempered Minor Third]], and as such… | ||
| Line 693: | Line 693: | ||
| Tendomean Minor Third | | Tendomean Minor Third | ||
| F↑\ | | F↑\ | ||
| | | 1 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[153/128|Septendecimal Tendomean Minor Third]] | * Approximates the [[153/128|Septendecimal Tendomean Minor Third]] | ||
| Line 709: | Line 709: | ||
| Ptolemaic Minor Third | | Ptolemaic Minor Third | ||
| F↑, E# | | F↑, E# | ||
| | | 2 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[6/5|Classic Minor Third]], and as such… | * Approximates the [[6/5|Classic Minor Third]], and as such… | ||
| Line 727: | Line 727: | ||
| Wide Minor Third | | Wide Minor Third | ||
| Ft<↓, F↑/, Gdb< | | Ft<↓, F↑/, Gdb< | ||
| | | 1 | ||
| | | 4 | ||
| This interval… | | This interval… | ||
* Approximates the [[135/112|Marvelous Minor Third]], and as such… | * Approximates the [[135/112|Marvelous Minor Third]], and as such… | ||
| Line 742: | Line 742: | ||
| Lesser Supraminor Third, Infra-Diminished Fourth | | Lesser Supraminor Third, Infra-Diminished Fourth | ||
| Ft>↓, Gdb> | | Ft>↓, Gdb> | ||
| | | 0 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[40/33|Undecimal Supraminor Third]], and thus… | * Approximates the [[40/33|Undecimal Supraminor Third]], and thus… | ||
| Line 755: | Line 755: | ||
| Greater Supraminor Third, Retrodiptolemaic Diminished Fourth | | Greater Supraminor Third, Retrodiptolemaic Diminished Fourth | ||
| Ft<\, F↑↑, Gdb<↑\, Gb↓↓ | | Ft<\, F↑↑, Gdb<↑\, Gb↓↓ | ||
| | | -1 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[39/32|Lesser Tridecimal Neutral Third]], and thus… | * Approximates the [[39/32|Lesser Tridecimal Neutral Third]], and thus… | ||
| Line 772: | Line 772: | ||
| Artoneutral Third, Lesser Sub-Diminished Fourth | | Artoneutral Third, Lesser Sub-Diminished Fourth | ||
| Ft<, Gdb<↑ | | Ft<, Gdb<↑ | ||
| | | 0 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[11/9|Alpharabian Artoneutral Third]], which is the traditional, low complexity Undecimal Neutral Third, and as such… | * Approximates the [[11/9|Alpharabian Artoneutral Third]], which is the traditional, low complexity Undecimal Neutral Third, and as such… | ||
| Line 792: | Line 792: | ||
| Tendoneutral Third, Greater Sub-Diminished Fourth | | Tendoneutral Third, Greater Sub-Diminished Fourth | ||
| Ft>, Gdb>↑ | | Ft>, Gdb>↑ | ||
| | | -1 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[27/22|Alpharabian Tendoneutral Third]] or 2nd Undecimal Neutral Third, and as such… | * Approximates the [[27/22|Alpharabian Tendoneutral Third]] or 2nd Undecimal Neutral Third, and as such… | ||
| Line 809: | Line 809: | ||
| Lesser Submajor Third, Retroptolemaic Diminished Fourth | | Lesser Submajor Third, Retroptolemaic Diminished Fourth | ||
| Ft>/, F#↓↓, Gb↓ | | Ft>/, F#↓↓, Gb↓ | ||
| | | 0 | ||
| | | 3 | ||
| This interval | | This interval | ||
* Approximates the [[16/13|Greater Tridecimal Neutral Third]] or Octave-Reduced Thirteenth Subharmonic, and as such… | * Approximates the [[16/13|Greater Tridecimal Neutral Third]] or Octave-Reduced Thirteenth Subharmonic, and as such… | ||
| Line 824: | Line 824: | ||
| Greater Submajor Third, Artoretromean Diminished Fourth | | Greater Submajor Third, Artoretromean Diminished Fourth | ||
| Ft<↑, Gb↓/ | | Ft<↑, Gb↓/ | ||
| | | 1 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[26/21|Tridecimal Submajor Third]] and a similar 11-limit interval that acts as the Submajor counterpart to the Undecimal Supraminor Third, and thus… | * Approximates the [[26/21|Tridecimal Submajor Third]] and a similar 11-limit interval that acts as the Submajor counterpart to the Undecimal Supraminor Third, and thus… | ||
| Line 838: | Line 838: | ||
| Narrow Major Third, Tendoretromean Diminished Fourth | | Narrow Major Third, Tendoretromean Diminished Fourth | ||
| Ft>↑, F#↓\, Gb\ | | Ft>↑, F#↓\, Gb\ | ||
| | | 2 | ||
| | | 4 | ||
| This interval… | | This interval… | ||
* Approximates the [[56/45|Marvelous Major Third]], and as such… | * Approximates the [[56/45|Marvelous Major Third]], and as such… | ||
| Line 854: | Line 854: | ||
| Ptolemaic Major Third, Pythagorean Diminished Fourth | | Ptolemaic Major Third, Pythagorean Diminished Fourth | ||
| Gb, F#↓ | | Gb, F#↓ | ||
| | | 3 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[5/4|Classic Major Third]] or Octave-Reduced Fifth Harmonic, and as such… | * Approximates the [[5/4|Classic Major Third]] or Octave-Reduced Fifth Harmonic, and as such… | ||
| Line 875: | Line 875: | ||
| Artomean Major Third, Artomean Diminished Fourth | | Artomean Major Third, Artomean Diminished Fourth | ||
| Gb/, F#↓/ | | Gb/, F#↓/ | ||
| | | 2 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[64/51|Septendecimal Artomean Major Third]] | * Approximates the [[64/51|Septendecimal Artomean Major Third]] | ||
| Line 887: | Line 887: | ||
| Tendomean Major Third, Tendomean Diminished Fourth | | Tendomean Major Third, Tendomean Diminished Fourth | ||
| F#\, Gb↑\ | | F#\, Gb↑\ | ||
| | | 0 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[63/50|Quasi-Tempered Major Third]] | * Approximates the [[63/50|Quasi-Tempered Major Third]] | ||
| Line 903: | Line 903: | ||
| Pythagorean Major Third, Ptolemaic Diminished Fourth | | Pythagorean Major Third, Ptolemaic Diminished Fourth | ||
| F#, Gb↑ | | F#, Gb↑ | ||
| | | -1 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[81/64|Pythagorean Major Third]], and as such… | * Approximates the [[81/64|Pythagorean Major Third]], and as such… | ||
| Line 922: | Line 922: | ||
| Wide Major Third, Lesser Super-Diminished Fourth | | Wide Major Third, Lesser Super-Diminished Fourth | ||
| F#/, Gd<↓, Gb↑/ | | F#/, Gd<↓, Gb↑/ | ||
| | | 0 | ||
| | | 4 | ||
| This interval… | | This interval… | ||
* Approximates the [[14/11|Neo-Gothic Major Third]], and thus… | * Approximates the [[14/11|Neo-Gothic Major Third]], and thus… | ||
| Line 938: | Line 938: | ||
| Narrow Supermajor Third, Greater Super-Diminished Fourth | | Narrow Supermajor Third, Greater Super-Diminished Fourth | ||
| F#↑\, Gd>↓ | | F#↑\, Gd>↓ | ||
| | | -1 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[51/40|Septendecimal Major Third]] | * Approximates the [[51/40|Septendecimal Major Third]] | ||
| Line 952: | Line 952: | ||
| Lesser Supermajor Third, Diptolemaic Diminished Fourth | | Lesser Supermajor Third, Diptolemaic Diminished Fourth | ||
| F#↑, Gd<\, Gb↑↑ | | F#↑, Gd<\, Gb↑↑ | ||
| | | -1 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Approximates the [[32/25|Classic Diminished Fourth]] or Diptolemaic Diminished Fourth, and thus… | * Approximates the [[32/25|Classic Diminished Fourth]] or Diptolemaic Diminished Fourth, and thus… | ||
| Line 966: | Line 966: | ||
| Greater Supermajor Third, Ultra-Diminished Fourth | | Greater Supermajor Third, Ultra-Diminished Fourth | ||
| Gd<, F#↑/ | | Gd<, F#↑/ | ||
| | | 0 | ||
| | | 1 | ||
| This interval… | | This interval… | ||
* Approximates the [[9/7|Septimal Supermajor Third]], and as such… | * Approximates the [[9/7|Septimal Supermajor Third]], and as such… | ||
| Line 981: | Line 981: | ||
| Paraminor Fourth, Wide Supermajor Third | | Paraminor Fourth, Wide Supermajor Third | ||
| Gd>, Ft#>↓ | | Gd>, Ft#>↓ | ||
| | | -1 | ||
| | | 0 | ||
| This interval… | | This interval… | ||
* Approximates the [[128/99|Just Paraminor Fourth]], and as such… | * Approximates the [[128/99|Just Paraminor Fourth]], and as such… | ||
| Line 999: | Line 999: | ||
| Wide Paraminor Fourth, Narrow Ultramajor Third | | Wide Paraminor Fourth, Narrow Ultramajor Third | ||
| Gd>/, F#↑↑, G↓↓ | | Gd>/, F#↑↑, G↓↓ | ||
| | | -1 | ||
| | | -1 | ||
| This interval… | | This interval… | ||
* Approximates the [[13/10|Tridecimal Semisixth]] | * Approximates the [[13/10|Tridecimal Semisixth]] | ||
| Line 1,012: | Line 1,012: | ||
| Ultramajor Third, Narrow Grave Fourth | | Ultramajor Third, Narrow Grave Fourth | ||
| Gd<↑, Ft#< | | Gd<↑, Ft#< | ||
| | | -2 | ||
| | | -2 | ||
| This interval… | | This interval… | ||
* Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic third that sounds more like a fourth, and as such… | * Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic third that sounds more like a fourth, and as such… | ||
| Line 1,027: | Line 1,027: | ||
| Lesser Grave Fourth, Wide Ultramajor Third | | Lesser Grave Fourth, Wide Ultramajor Third | ||
| Gd>↑, G↓\ | | Gd>↑, G↓\ | ||
| | | -3 | ||
| | | -1 | ||
| This Interval… | | This Interval… | ||
* Approximates the [[21/16|Septimal Subfourth]], and thus… | * Approximates the [[21/16|Septimal Subfourth]], and thus… | ||
| Line 1,041: | Line 1,041: | ||
| Greater Grave Fourth | | Greater Grave Fourth | ||
| G↓ | | G↓ | ||
| | | -2 | ||
| | | 0 | ||
| This interval… | | This interval… | ||
* Approximates a complex 5-limit interval formed by subtracting a syntonic comma from a Perfect Fourth | * Approximates a complex 5-limit interval formed by subtracting a syntonic comma from a Perfect Fourth | ||
| Line 1,053: | Line 1,053: | ||
| Wide Grave Fourth | | Wide Grave Fourth | ||
| G↓/ | | G↓/ | ||
| | | -1 | ||
| | | 1 | ||
| This interval… | | This interval… | ||
* Is one half of this system's approximation of the Octave-Reduced Seventh Harmonic | * Is one half of this system's approximation of the Octave-Reduced Seventh Harmonic | ||
| Line 1,066: | Line 1,066: | ||
| Narrow Fourth | | Narrow Fourth | ||
| G\ | | G\ | ||
| | | 1 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[85/64|Septendecimal Fourth]], and thus… | * Approximates the [[85/64|Septendecimal Fourth]], and thus… | ||
| Line 1,081: | Line 1,081: | ||
| Perfect Fourth | | Perfect Fourth | ||
| G | | G | ||
| | | 4 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[4/3|Perfect Fourth]] or Octave-Reduced Third Subharmonic, and as such… | * Approximates the [[4/3|Perfect Fourth]] or Octave-Reduced Third Subharmonic, and as such… | ||
| Line 1,107: | Line 1,107: | ||
| Wide Fourth | | Wide Fourth | ||
| G/ | | G/ | ||
| | | 1 | ||
| | | 4 | ||
| This interval… | | This interval… | ||
* Approximates the [[75/56|Marvelous Fourth]], and thus… | * Approximates the [[75/56|Marvelous Fourth]], and thus… | ||
| Line 1,122: | Line 1,122: | ||
| Narrow Acute Fourth | | Narrow Acute Fourth | ||
| G↑\ | | G↑\ | ||
| | | -1 | ||
| | | 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 1,136: | Line 1,136: | ||
| Lesser Acute Fourth | | Lesser Acute Fourth | ||
| G↑ | | G↑ | ||
| | | -2 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[27/20|Classic Acute Fourth]], and as such… | * Approximates the [[27/20|Classic Acute Fourth]], and as such… | ||
| Line 1,152: | Line 1,152: | ||
| Greater Acute Fourth | | Greater Acute Fourth | ||
| Gt<↓, G↑/, Adb< | | Gt<↓, G↑/, Adb< | ||
| | | -2 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Is reachable through stacking two of this system's approximation of the Septimal Subminor Third | * Is reachable through stacking two of this system's approximation of the Septimal Subminor Third | ||
| Line 1,165: | Line 1,165: | ||
| Wide Acute Fourth, Infra-Diminished Fifth | | Wide Acute Fourth, Infra-Diminished Fifth | ||
| Gt>↓, Adb> | | Gt>↓, Adb> | ||
| | | -1 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Approximates the [[15/11|Undecimal Grave Infra-Augmented Fourth]], and thus… | * Approximates the [[15/11|Undecimal Grave Infra-Augmented Fourth]], and thus… | ||
| Line 1,180: | Line 1,180: | ||
| Narrow Paramajor Fourth, Retrodiptolemaic Diminished Fifth | | Narrow Paramajor Fourth, Retrodiptolemaic Diminished Fifth | ||
| Gt<\, G↑↑, Ab↓↓ | | Gt<\, G↑↑, Ab↓↓ | ||
| | | -1 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Is reachable through stacking three of this system's approximation of the Classic Major Second……. | * Is reachable through stacking three of this system's approximation of the Classic Major Second……. | ||
| Line 1,194: | Line 1,194: | ||
| Paramajor Fourth, Lesser Sub-Diminished Fifth | | Paramajor Fourth, Lesser Sub-Diminished Fifth | ||
| Gt<, Adb<↑ | | Gt<, Adb<↑ | ||
| | | 0 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[11/8|Just Paramajor Fourth]], and as such… | * Approximates the [[11/8|Just Paramajor Fourth]], and as such… | ||
| Line 1,216: | Line 1,216: | ||
| Infra-Augmented Fourth, Greater Sub-Diminished Fifth | | Infra-Augmented Fourth, Greater Sub-Diminished Fifth | ||
| Gt>, Adb>↑ | | Gt>, Adb>↑ | ||
| | | -1 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Approximates the [[112/81|Septimal Subdiminished Fifth]], and thus… | * Approximates the [[112/81|Septimal Subdiminished Fifth]], and thus… | ||
| Line 1,231: | Line 1,231: | ||
| Diptolemaic Augmented Fourth, Retroptolemaic Diminished Fifth | | Diptolemaic Augmented Fourth, Retroptolemaic Diminished Fifth | ||
| G#↓↓, Ab↓ | | G#↓↓, Ab↓ | ||
| | | -2 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Approximates the [[25/18|Classic Augmented Fourth]], and thus… | * Approximates the [[25/18|Classic Augmented Fourth]], and thus… | ||
| Line 1,248: | Line 1,248: | ||
| Lesser Sub-Augmented Fourth, Artoretromean Diminished Fifth | | Lesser Sub-Augmented Fourth, Artoretromean Diminished Fifth | ||
| Gt<↑, Ab↓/ | | Gt<↑, Ab↓/ | ||
| | | -1 | ||
| | | 2 | ||
| This interval… | | This interval… | ||
* Approximates a complex 11-limit interval formed by stacking a Syntonic Comma on top of a Paramajor Fourth, and thus… | * Approximates a complex 11-limit interval formed by stacking a Syntonic Comma on top of a Paramajor Fourth, and thus… | ||
| Line 1,261: | Line 1,261: | ||
| Greater Sub-Augmented Fourth, Tendoretromean Diminished Fifth | | Greater Sub-Augmented Fourth, Tendoretromean Diminished Fifth | ||
| Gt>↑, Ab\ | | Gt>↑, Ab\ | ||
| | | 0 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[7/5|Lesser Septimal Tritone]] and thus… | * Approximates the [[7/5|Lesser Septimal Tritone]] and thus… | ||
| Line 1,275: | Line 1,275: | ||
| Ptolemaic Augmented Fourth, Pythagorean Diminished Fifth | | Ptolemaic Augmented Fourth, Pythagorean Diminished Fifth | ||
| Ab, G#↓ | | Ab, G#↓ | ||
| | | -3 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[45/32|Smaller Diatonic Tritone]], and as such… | * Approximates the [[45/32|Smaller Diatonic Tritone]], and as such… | ||
| Line 1,290: | Line 1,290: | ||
| Artomean Augmented Fourth, Artomean Diminished Fifth | | Artomean Augmented Fourth, Artomean Diminished Fifth | ||
| G#↓/, Ab/ | | G#↓/, Ab/ | ||
| | | -5 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[24/17|Smaller Septendecimal Tritone]], and thus… | * Approximates the [[24/17|Smaller Septendecimal Tritone]], and thus… | ||
| Line 1,305: | Line 1,305: | ||
| Tendomean Diminished Fifth, Tendomean Augmented Fourth | | Tendomean Diminished Fifth, Tendomean Augmented Fourth | ||
| Ab↑\, G#\ | | Ab↑\, G#\ | ||
| | | -5 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[17/12|Larger Septendecimal Tritone]], and thus… | * Approximates the [[17/12|Larger Septendecimal Tritone]], and thus… | ||
| Line 1,320: | Line 1,320: | ||
| Ptolemaic Diminished Fifth, Pythagorean Augmented Fourth | | Ptolemaic Diminished Fifth, Pythagorean Augmented Fourth | ||
| Ab↑, G# | | Ab↑, G# | ||
| | | -3 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[64/45|Larger Diatonic Tritone]], and as such… | * Approximates the [[64/45|Larger Diatonic Tritone]], and as such… | ||
| Line 1,335: | Line 1,335: | ||
| Lesser Super-Diminished Fifth, Artoretromean Augmented Fourth | | Lesser Super-Diminished Fifth, Artoretromean Augmented Fourth | ||
| Ad<↓, G#/ | | Ad<↓, G#/ | ||
| | | 0 | ||
| | | | ||
| This interval… | | This interval… | ||
| Line 1,501: | Line 1,501: | ||
| Perfect Fifth | | Perfect Fifth | ||
| A | | A | ||
| | | 4 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[3/2|Perfect Fifth]] or Octave-Reduced Third Harmonic, and as such… | * Approximates the [[3/2|Perfect Fifth]] or Octave-Reduced Third Harmonic, and as such… | ||