159edo/Interval names and harmonies: Difference between revisions
ArrowHead294 (talk | contribs) m Em dashes |
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 |
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[[159edo]] contains all the intervals of [[53edo]], however, as some of the interpretations differ due 159edo having different mappings for certain primes, those differences show up in how harmonies are constructed. It should be noted that since 159edo does a better job of representing the 2.3.11 subgroup than [[24edo]], some of the chords listed on the page for [[24edo interval names and harmonies]] carry over to this page, even though the exact sets of enharmonics differ between the two systems. Furthermore, just as with 24edo can be thought of as essentially having two fields of 12edo separated by a quartertone, 159edo can be thought of as having three fields of 53edo, each separated from the others by a third of a 53edo step on either side. This even lends to 159edo having its own variation on the [[Dinner Party Rules]]—represented here by the Harmonic Compatibility Rating and Melodic Compatibility Rating columns where | [[159edo]] contains all the intervals of [[53edo]], however, as some of the interpretations differ due 159edo having different mappings for certain primes, those differences show up in how harmonies are constructed. It should be noted that since 159edo does a better job of representing the 2.3.11 subgroup than [[24edo]], some of the chords listed on the page for [[24edo interval names and harmonies]] carry over to this page, even though the exact sets of enharmonics differ between the two systems. Furthermore, just as with 24edo can be thought of as essentially having two fields of 12edo separated by a quartertone, 159edo can be thought of as having three fields of 53edo, each separated from the others by a third of a 53edo step on either side. This even lends to 159edo having its own variation on the [[Dinner Party Rules]]—represented here by the Harmonic Compatibility Rating and Melodic Compatibility Rating columns where 10 is a full-blown friend relative to the root and −10 if a full-blown enemy relative to the root. Note that the Harmonic Compatibility and Melodic Compatibility ratings are based on octave-equivalence, and that some of the ratings are still speculative. | ||
== Interval chart == | == Interval chart == | ||
| Line 20: | Line 20: | ||
| Perfect Unison | | Perfect Unison | ||
| D | | D | ||
| | | 10 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Is the [[1/1|perfect unison]], and thus… | * Is the [[1/1|perfect unison]], and thus… | ||
| Line 50: | Line 50: | ||
| Narrow Superprime | | Narrow Superprime | ||
| D↑\ | | D↑\ | ||
| | | -10 | ||
| | | -10 | ||
| This interval… | | This interval… | ||
* Approximates the [[ptolemisma]] and the [[biyatisma]] | * Approximates the [[ptolemisma]] and the [[biyatisma]] | ||
| Line 62: | Line 62: | ||
| Lesser Superprime | | Lesser Superprime | ||
| D↑ | | D↑ | ||
| | | -10 | ||
| | | -3 | ||
| This interval… | | This interval… | ||
* Approximates the [[syntonic comma]], and as such… | * Approximates the [[syntonic comma]], and as such… | ||
| Line 80: | Line 80: | ||
| Greater Superprime, Narrow Inframinor Second | | Greater Superprime, Narrow Inframinor Second | ||
| Edb<, Dt<↓ | | Edb<, Dt<↓ | ||
| | | -10 | ||
| | | 3 | ||
| This interval… | | This interval… | ||
* Approximates the [[septimal comma|Archytas comma]], and thus… | * Approximates the [[septimal comma|Archytas comma]], and thus… | ||
| Line 102: | Line 102: | ||
| Inframinor Second, Wide Superprime | | Inframinor Second, Wide Superprime | ||
| Edb>, Dt>↓ | | Edb>, Dt>↓ | ||
| | | -9 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[45/44|Undecimal Fifth-Tone]] | * Approximates the [[45/44|Undecimal Fifth-Tone]] | ||
| Line 123: | Line 123: | ||
| Wide Inframinor Second, Narrow Ultraprime | | Wide Inframinor Second, Narrow Ultraprime | ||
| Eb↓↓, Dt<\ | | Eb↓↓, Dt<\ | ||
| | | -9 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[40/39|Tridecimal Minor Diesis]] | * Approximates the [[40/39|Tridecimal Minor Diesis]] | ||
| Line 142: | Line 142: | ||
| Ultraprime, Narrow Subminor Second | | Ultraprime, Narrow Subminor Second | ||
| Dt<, Edb<↑ | | Dt<, Edb<↑ | ||
| | | -9 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[33/32|Al-Farabi Quartertone]], and as such… | * Approximates the [[33/32|Al-Farabi Quartertone]], and as such… | ||
| Line 163: | Line 163: | ||
| Lesser Subminor Second, Wide Ultraprime, Infra-Augmented Prime | | Lesser Subminor Second, Wide Ultraprime, Infra-Augmented Prime | ||
| Dt>, Eb↓\ | | Dt>, Eb↓\ | ||
| | | -8 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[28/27|Septimal Subminor Second]], and thus… | * Approximates the [[28/27|Septimal Subminor Second]], and thus… | ||
| Line 181: | Line 181: | ||
| Greater Subminor Second, Diptolemaic Augmented Prime | | Greater Subminor Second, Diptolemaic Augmented Prime | ||
| Eb↓, D#↓↓ | | Eb↓, D#↓↓ | ||
| | | -8 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[25/24|Classic Chroma]] or Diptolemaic Chroma, and thus… | * Approximates the [[25/24|Classic Chroma]] or Diptolemaic Chroma, and thus… | ||
| Line 196: | Line 196: | ||
| Wide Subminor Second, Lesser Sub-Augmented Prime | | Wide Subminor Second, Lesser Sub-Augmented Prime | ||
| Eb↓/, Dt<↑ | | Eb↓/, Dt<↑ | ||
| | | -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 211: | Line 211: | ||
| Narrow Minor Second, Greater Sub-Augmented Prime | | Narrow Minor Second, Greater Sub-Augmented Prime | ||
| Eb\, Dt>↑ | | Eb\, Dt>↑ | ||
| | | -7 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[21/20|Septimal Minor Semitone]], and thus… | * Approximates the [[21/20|Septimal Minor Semitone]], and thus… | ||
| Line 225: | Line 225: | ||
| Pythagorean Minor Second, Ptolemaic Augmented Prime | | Pythagorean Minor Second, Ptolemaic Augmented Prime | ||
| Eb, D#↓ | | Eb, D#↓ | ||
| | | -6 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[256/243|Pythagorean Limma]] or Pythagorean Minor Second, and as such… | * Approximates the [[256/243|Pythagorean Limma]] or Pythagorean Minor Second, and as such… | ||
| Line 246: | Line 246: | ||
| Artomean Minor Second, Artomean Augmented Prime | | Artomean Minor Second, Artomean Augmented Prime | ||
| Eb/, D#↓/ | | Eb/, D#↓/ | ||
| | | -6 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[18/17|Small Septendecimal Semitone]], and thus… | * Approximates the [[18/17|Small Septendecimal Semitone]], and thus… | ||
| Line 262: | Line 262: | ||
| Tendomean Minor Second, Tendomean Augmented Prime | | Tendomean Minor Second, Tendomean Augmented Prime | ||
| D#\, Eb↑\ | | D#\, Eb↑\ | ||
| | | -5 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[17/16|Large Septendecimal Semitone]] or [[octave reduction|Octave-Reduced]] Seventeenth Harmonic, and thus… | * Approximates the [[17/16|Large Septendecimal Semitone]] or [[octave reduction|Octave-Reduced]] Seventeenth Harmonic, and thus… | ||
| Line 278: | Line 278: | ||
| Ptolemaic Minor Second, Pythagorean Augmented Prime | | Ptolemaic Minor Second, Pythagorean Augmented Prime | ||
| D#, Eb↑ | | D#, Eb↑ | ||
| | | -5 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[16/15|Classic Minor Second]] or Ptolemaic Minor Second, and as such… | * Approximates the [[16/15|Classic Minor Second]] or Ptolemaic Minor Second, and as such… | ||
| Line 299: | Line 299: | ||
| Wide Minor Second, Artoretromean Augmented Prime | | Wide Minor Second, Artoretromean Augmented Prime | ||
| Ed<↓, Eb↑/, D#/ | | Ed<↓, Eb↑/, D#/ | ||
| | | -5 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[15/14|Septimal Major Semitone]], and thus… | * Approximates the [[15/14|Septimal Major Semitone]], and thus… | ||
| Line 313: | Line 313: | ||
| Lesser Supraminor Second, Tendoretromean Augmented Prime | | Lesser Supraminor Second, Tendoretromean Augmented Prime | ||
| Ed>↓, D#↑\ | | Ed>↓, D#↑\ | ||
| | | -6 | ||
| | | 8 | ||
| This interval… | | This interval… | ||
* Approximates the [[14/13|Tridecimal Supraminor Second]] and a similar 11-limit interval that acts as the Supraminor counterpart to the Undecimal Submajor Second, and thus… | * Approximates the [[14/13|Tridecimal Supraminor Second]] and a similar 11-limit interval that acts as the Supraminor counterpart to the Undecimal Submajor Second, and thus… | ||
| Line 329: | Line 329: | ||
| Greater Supraminor Second, Diptolemaic Limma, Retroptolemaic Augmented Prime | | Greater Supraminor Second, Diptolemaic Limma, Retroptolemaic Augmented Prime | ||
| Ed<\, Eb↑↑, D#↑ | | Ed<\, Eb↑↑, D#↑ | ||
| | | -7 | ||
| | | 6 | ||
| This interval… | | This interval… | ||
* Approximates the [[27/25|Large Limma]], and thus… | * Approximates the [[27/25|Large Limma]], and thus… | ||
| Line 344: | Line 344: | ||
| Artoneutral Second, Lesser Super-Augmented Prime | | Artoneutral Second, Lesser Super-Augmented Prime | ||
| Ed<, Dt#<↓ | | Ed<, Dt#<↓ | ||
| | | -8 | ||
| | | 5 | ||
| 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 363: | Line 363: | ||
| Tendoneutral Second, Greater Super-Augmented Prime | | Tendoneutral Second, Greater Super-Augmented Prime | ||
| Ed>, Dt#>↓ | | Ed>, Dt#>↓ | ||
| | | -7 | ||
| | | 6 | ||
| 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 382: | Line 382: | ||
| Lesser Submajor Second, Retrodiptolemaic Augmented Prime | | Lesser Submajor Second, Retrodiptolemaic Augmented Prime | ||
| Ed>/, E↓↓, Dt#>↓/, D#↑↑ | | Ed>/, E↓↓, Dt#>↓/, D#↑↑ | ||
| | | -6 | ||
| | | 8 | ||
| 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 395: | Line 395: | ||
| Greater Submajor Second, Ultra-Augmented Prime | | Greater Submajor Second, Ultra-Augmented Prime | ||
| Ed<↑, Dt#<, Fb↓/ | | Ed<↑, Dt#<, Fb↓/ | ||
| | | -5 | ||
| | | 9 | ||
| 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 411: | Line 411: | ||
| Narrow Major Second | | Narrow Major Second | ||
| Ed>↑, E↓\, Dt#>, Fb\ | | Ed>↑, E↓\, Dt#>, Fb\ | ||
| | | -4 | ||
| | | 10 | ||
| 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 424: | Line 424: | ||
| Ptolemaic Major Second | | Ptolemaic Major Second | ||
| E↓, Fb | | E↓, Fb | ||
| | | -3 | ||
| | | 10 | ||
| 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 443: | Line 443: | ||
| Artomean Major Second | | Artomean Major Second | ||
| E↓/, Fb/ | | E↓/, Fb/ | ||
| | | -3 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[143/128|Grossmic Whole Tone]], and thus… | * Approximates the [[143/128|Grossmic Whole Tone]], and thus… | ||
| Line 457: | Line 457: | ||
| Tendomean Major Second | | Tendomean Major Second | ||
| E\, Fb↑\ | | E\, Fb↑\ | ||
| | | -2 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[28/25|Middle Major Second]] | * Approximates the [[28/25|Middle Major Second]] | ||
| Line 471: | Line 471: | ||
| Pythagorean Major Second | | Pythagorean Major Second | ||
| E, Fb↑ | | E, Fb↑ | ||
| | | -2 | ||
| | | 10 | ||
| 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 491: | Line 491: | ||
| Wide Major Second | | Wide Major Second | ||
| E/, Fd<↓ | | E/, Fd<↓ | ||
| | | -1 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[44/39|Tridecimal Major Second]], and thus… | * Approximates the [[44/39|Tridecimal Major Second]], and thus… | ||
| Line 505: | Line 505: | ||
| Narrow Supermajor Second | | Narrow Supermajor Second | ||
| E↑\, Fd>↓ | | E↑\, Fd>↓ | ||
| | | -1 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[17/15|Septendecimal Whole Tone]], and thus… | * Approximates the [[17/15|Septendecimal Whole Tone]], and thus… | ||
| Line 522: | Line 522: | ||
| Lesser Supermajor Second | | Lesser Supermajor Second | ||
| E↑, Fd<\, Fb↑↑, Dx | | E↑, Fd<\, Fb↑↑, Dx | ||
| | | -1 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[256/225|Neapolitan Diminished Third]], and thus… | * Approximates the [[256/225|Neapolitan Diminished Third]], and thus… | ||
| Line 538: | Line 538: | ||
| Fd<, Et<↓, E↑/ | | Fd<, Et<↓, E↑/ | ||
| 0 | | 0 | ||
| | | 9 | ||
| 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 555: | Line 555: | ||
| Inframinor Third, Wide Supermajor Second | | Inframinor Third, Wide Supermajor Second | ||
| Fd>, Et>↓ | | Fd>, Et>↓ | ||
| | | -1 | ||
| | | 8 | ||
| 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 571: | Line 571: | ||
| Fd>/, Et<\, F↓↓, E↑↑ | | Fd>/, Et<\, F↓↓, E↑↑ | ||
| 0 | | 0 | ||
| | | 8 | ||
| This interval… | | This interval… | ||
* Approximates the [[15/13|Tridecimal Semifourth]], and thus… | * Approximates the [[15/13|Tridecimal Semifourth]], and thus… | ||
| Line 586: | Line 586: | ||
| Ultramajor Second, Narrow Subminor Third | | Ultramajor Second, Narrow Subminor Third | ||
| Et<, Fd<↑ | | Et<, Fd<↑ | ||
| | | -1 | ||
| | | 7 | ||
| 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 601: | Line 601: | ||
| Et>, Fd>↑, F↓\ | | Et>, Fd>↑, F↓\ | ||
| 0 | | 0 | ||
| | | 7 | ||
| 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 617: | Line 617: | ||
| Greater Subminor Third | | Greater Subminor Third | ||
| F↓, Et>/, E#↓↓, Gbb | | F↓, Et>/, E#↓↓, Gbb | ||
| | | -1 | ||
| | | 7 | ||
| 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 634: | Line 634: | ||
| Wide Subminor Third | | Wide Subminor Third | ||
| F↓/, Et<↑ | | F↓/, Et<↑ | ||
| | | -1 | ||
| | | 8 | ||
| This interval… | | This interval… | ||
* Approximates the [[20/17|Septendecimal Minor Third]] | * Approximates the [[20/17|Septendecimal Minor Third]] | ||
| Line 649: | Line 649: | ||
| F\, Et>↑ | | F\, Et>↑ | ||
| 0 | | 0 | ||
| | | 8 | ||
| 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 663: | Line 663: | ||
| Pythagorean Minor Third | | Pythagorean Minor Third | ||
| F | | F | ||
| | | -1 | ||
| | | 9 | ||
| 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 680: | Line 680: | ||
| Artomean Minor Third | | Artomean Minor Third | ||
| F/ | | F/ | ||
| | | 1 | ||
| | | 9 | ||
| 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 694: | Line 694: | ||
| Tendomean Minor Third | | Tendomean Minor Third | ||
| F↑\ | | F↑\ | ||
| | | 4 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[153/128|Septendecimal Tendomean Minor Third]] | * Approximates the [[153/128|Septendecimal Tendomean Minor Third]] | ||
| Line 710: | Line 710: | ||
| Ptolemaic Minor Third | | Ptolemaic Minor Third | ||
| F↑, E# | | F↑, E# | ||
| | | 7 | ||
| | | 10 | ||
| 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 728: | Line 728: | ||
| Wide Minor Third | | Wide Minor Third | ||
| Ft<↓, F↑/, Gdb< | | Ft<↓, F↑/, Gdb< | ||
| 4 | | 4 | ||
| 9 | |||
| 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 743: | Line 743: | ||
| Lesser Supraminor Third, Infra-Diminished Fourth | | Lesser Supraminor Third, Infra-Diminished Fourth | ||
| Ft>↓, Gdb> | | Ft>↓, Gdb> | ||
| | | 1 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[40/33|Undecimal Supraminor Third]], and thus… | * Approximates the [[40/33|Undecimal Supraminor Third]], and thus… | ||
| Line 756: | Line 756: | ||
| Greater Supraminor Third, Retrodiptolemaic Diminished Fourth | | Greater Supraminor Third, Retrodiptolemaic Diminished Fourth | ||
| Ft<\, F↑↑, Gdb<↑\, Gb↓↓ | | Ft<\, F↑↑, Gdb<↑\, Gb↓↓ | ||
| | | -1 | ||
| | | 8 | ||
| 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 774: | Line 774: | ||
| Ft<, Gdb<↑ | | Ft<, Gdb<↑ | ||
| 0 | | 0 | ||
| | | 7 | ||
| 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 793: | Line 793: | ||
| Tendoneutral Third, Greater Sub-Diminished Fourth | | Tendoneutral Third, Greater Sub-Diminished Fourth | ||
| Ft>, Gdb>↑ | | Ft>, Gdb>↑ | ||
| | | -1 | ||
| | | 7 | ||
| 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 811: | Line 811: | ||
| Ft>/, F#↓↓, Gb↓ | | Ft>/, F#↓↓, Gb↓ | ||
| 0 | | 0 | ||
| | | 8 | ||
| 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 825: | Line 825: | ||
| Greater Submajor Third, Artoretromean Diminished Fourth | | Greater Submajor Third, Artoretromean Diminished Fourth | ||
| Ft<↑, Gb↓/ | | Ft<↑, Gb↓/ | ||
| 1 | | -1 | ||
| | | 9 | ||
| 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 839: | Line 839: | ||
| Narrow Major Third, Tendoretromean Diminished Fourth | | Narrow Major Third, Tendoretromean Diminished Fourth | ||
| Ft>↑, F#↓\, Gb\ | | Ft>↑, F#↓\, Gb\ | ||
| | | 3 | ||
| | | 9 | ||
| 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 855: | Line 855: | ||
| Ptolemaic Major Third, Pythagorean Diminished Fourth | | Ptolemaic Major Third, Pythagorean Diminished Fourth | ||
| Gb, F#↓ | | Gb, F#↓ | ||
| | | 8 | ||
| | | 10 | ||
| 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 876: | Line 876: | ||
| Artomean Major Third, Artomean Diminished Fourth | | Artomean Major Third, Artomean Diminished Fourth | ||
| Gb/, F#↓/ | | Gb/, F#↓/ | ||
| | | 4 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[64/51|Septendecimal Artomean Major Third]] | * Approximates the [[64/51|Septendecimal Artomean Major Third]] | ||
| Line 888: | Line 888: | ||
| Tendomean Major Third, Tendomean Diminished Fourth | | Tendomean Major Third, Tendomean Diminished Fourth | ||
| F#\, Gb↑\ | | F#\, Gb↑\ | ||
| | | 1 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[63/50|Quasi-Tempered Major Third]] | * Approximates the [[63/50|Quasi-Tempered Major Third]] | ||
| Line 904: | Line 904: | ||
| Pythagorean Major Third, Ptolemaic Diminished Fourth | | Pythagorean Major Third, Ptolemaic Diminished Fourth | ||
| F#, Gb↑ | | F#, Gb↑ | ||
| | | -1 | ||
| | | 9 | ||
| 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 924: | Line 924: | ||
| F#/, Gd<↓, Gb↑/ | | F#/, Gd<↓, Gb↑/ | ||
| 0 | | 0 | ||
| | | 8 | ||
| 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 939: | Line 939: | ||
| Narrow Supermajor Third, Greater Super-Diminished Fourth | | Narrow Supermajor Third, Greater Super-Diminished Fourth | ||
| F#↑\, Gd>↓ | | F#↑\, Gd>↓ | ||
| | | -1 | ||
| | | 7 | ||
| This interval… | | This interval… | ||
* Approximates the [[51/40|Septendecimal Major Third]] | * Approximates the [[51/40|Septendecimal Major Third]] | ||
| Line 953: | Line 953: | ||
| Lesser Supermajor Third, Diptolemaic Diminished Fourth | | Lesser Supermajor Third, Diptolemaic Diminished Fourth | ||
| F#↑, Gd<\, Gb↑↑ | | F#↑, Gd<\, Gb↑↑ | ||
| | | -1 | ||
| | | 6 | ||
| 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 968: | Line 968: | ||
| Gd<, F#↑/ | | Gd<, F#↑/ | ||
| 0 | | 0 | ||
| | | 5 | ||
| 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 982: | Line 982: | ||
| Paraminor Fourth, Wide Supermajor Third | | Paraminor Fourth, Wide Supermajor Third | ||
| Gd>, Ft#>↓ | | Gd>, Ft#>↓ | ||
| | | -1 | ||
| | | 3 | ||
| 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 1,000: | Line 1,000: | ||
| Wide Paraminor Fourth, Narrow Ultramajor Third | | Wide Paraminor Fourth, Narrow Ultramajor Third | ||
| Gd>/, F#↑↑, G↓↓ | | Gd>/, F#↑↑, G↓↓ | ||
| | | -2 | ||
| | | 1 | ||
| This interval… | | This interval… | ||
* Approximates the [[13/10|Tridecimal Semisixth]] | * Approximates the [[13/10|Tridecimal Semisixth]] | ||
| Line 1,013: | Line 1,013: | ||
| Ultramajor Third, Narrow Grave Fourth | | Ultramajor Third, Narrow Grave Fourth | ||
| Gd<↑, Ft#< | | Gd<↑, Ft#< | ||
| | | -4 | ||
| | | -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 1,028: | Line 1,028: | ||
| Lesser Grave Fourth, Wide Ultramajor Third | | Lesser Grave Fourth, Wide Ultramajor Third | ||
| Gd>↑, G↓\ | | Gd>↑, G↓\ | ||
| | | -7 | ||
| | | -4 | ||
| This Interval… | | This Interval… | ||
* Approximates the [[21/16|Septimal Subfourth]], and thus… | * Approximates the [[21/16|Septimal Subfourth]], and thus… | ||
| Line 1,042: | Line 1,042: | ||
| Greater Grave Fourth | | Greater Grave Fourth | ||
| G↓ | | G↓ | ||
| | | -6 | ||
| | | -5 | ||
| 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 1,054: | Line 1,054: | ||
| Wide Grave Fourth | | Wide Grave Fourth | ||
| G↓/ | | G↓/ | ||
| | | -4 | ||
| | | 0 | ||
| 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 1,068: | Line 1,068: | ||
| G\ | | G\ | ||
| 1 | | 1 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[85/64|Septendecimal Fourth]], and thus… | * Approximates the [[85/64|Septendecimal Fourth]], and thus… | ||
| Line 1,082: | Line 1,082: | ||
| Perfect Fourth | | Perfect Fourth | ||
| G | | G | ||
| | | 9 | ||
| | | 10 | ||
| 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 1,109: | Line 1,109: | ||
| G/ | | G/ | ||
| 1 | | 1 | ||
| | | 8 | ||
| This interval… | | This interval… | ||
* Approximates the [[75/56|Marvelous Fourth]], and thus… | * Approximates the [[75/56|Marvelous Fourth]], and thus… | ||
| Line 1,123: | Line 1,123: | ||
| Narrow Acute Fourth | | Narrow Acute Fourth | ||
| G↑\ | | G↑\ | ||
| | | -3 | ||
| | | 6 | ||
| 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 1,137: | Line 1,137: | ||
| Lesser Acute Fourth | | Lesser Acute Fourth | ||
| G↑ | | G↑ | ||
| | | -5 | ||
| | | 5 | ||
| 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 1,153: | Line 1,153: | ||
| Greater Acute Fourth | | Greater Acute Fourth | ||
| Gt<↓, G↑/, Adb< | | Gt<↓, G↑/, Adb< | ||
| | | -3 | ||
| | | 5 | ||
| 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 1,166: | Line 1,166: | ||
| Wide Acute Fourth, Infra-Diminished Fifth | | Wide Acute Fourth, Infra-Diminished Fifth | ||
| Gt>↓, Adb> | | Gt>↓, Adb> | ||
| | | -2 | ||
| | | 5 | ||
| 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 1,181: | Line 1,181: | ||
| Narrow Paramajor Fourth, Retrodiptolemaic Diminished Fifth | | Narrow Paramajor Fourth, Retrodiptolemaic Diminished Fifth | ||
| Gt<\, G↑↑, Ab↓↓ | | Gt<\, G↑↑, Ab↓↓ | ||
| | | -1 | ||
| | | 6 | ||
| 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 1,196: | Line 1,196: | ||
| Gt<, Adb<↑ | | Gt<, Adb<↑ | ||
| 0 | | 0 | ||
| | | 7 | ||
| 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 1,217: | Line 1,217: | ||
| Infra-Augmented Fourth, Greater Sub-Diminished Fifth | | Infra-Augmented Fourth, Greater Sub-Diminished Fifth | ||
| Gt>, Adb>↑ | | Gt>, Adb>↑ | ||
| | | -2 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[112/81|Septimal Subdiminished Fifth]], and thus… | * Approximates the [[112/81|Septimal Subdiminished Fifth]], and thus… | ||
| Line 1,232: | Line 1,232: | ||
| Diptolemaic Augmented Fourth, Retroptolemaic Diminished Fifth | | Diptolemaic Augmented Fourth, Retroptolemaic Diminished Fifth | ||
| G#↓↓, Ab↓ | | G#↓↓, Ab↓ | ||
| | | -3 | ||
| | | 4 | ||
| This interval… | | This interval… | ||
* Approximates the [[25/18|Classic Augmented Fourth]], and thus… | * Approximates the [[25/18|Classic Augmented Fourth]], and thus… | ||
| Line 1,249: | Line 1,249: | ||
| Lesser Sub-Augmented Fourth, Artoretromean Diminished Fifth | | Lesser Sub-Augmented Fourth, Artoretromean Diminished Fifth | ||
| Gt<↑, Ab↓/ | | Gt<↑, Ab↓/ | ||
| | | -2 | ||
| | | 4 | ||
| 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 1,263: | Line 1,263: | ||
| Gt>↑, Ab\ | | Gt>↑, Ab\ | ||
| 0 | | 0 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[7/5|Lesser Septimal Tritone]] and thus… | * Approximates the [[7/5|Lesser Septimal Tritone]] and thus… | ||
| Line 1,276: | Line 1,276: | ||
| Ptolemaic Augmented Fourth, Pythagorean Diminished Fifth | | Ptolemaic Augmented Fourth, Pythagorean Diminished Fifth | ||
| Ab, G#↓ | | Ab, G#↓ | ||
| | | -5 | ||
| | | 6 | ||
| 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 1,291: | Line 1,291: | ||
| Artomean Augmented Fourth, Artomean Diminished Fifth | | Artomean Augmented Fourth, Artomean Diminished Fifth | ||
| G#↓/, Ab/ | | G#↓/, Ab/ | ||
| | | -9 | ||
| | | 7 | ||
| This interval… | | This interval… | ||
* Approximates the [[24/17|Smaller Septendecimal Tritone]], and thus… | * Approximates the [[24/17|Smaller Septendecimal Tritone]], and thus… | ||
| Line 1,306: | Line 1,306: | ||
| Tendomean Diminished Fifth, Tendomean Augmented Fourth | | Tendomean Diminished Fifth, Tendomean Augmented Fourth | ||
| Ab↑\, G#\ | | Ab↑\, G#\ | ||
| | | -9 | ||
| | | 7 | ||
| This interval… | | This interval… | ||
* Approximates the [[17/12|Larger Septendecimal Tritone]], and thus… | * Approximates the [[17/12|Larger Septendecimal Tritone]], and thus… | ||
| Line 1,321: | Line 1,321: | ||
| Ptolemaic Diminished Fifth, Pythagorean Augmented Fourth | | Ptolemaic Diminished Fifth, Pythagorean Augmented Fourth | ||
| Ab↑, G# | | Ab↑, G# | ||
| | | -5 | ||
| | | 6 | ||
| 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 1,337: | Line 1,337: | ||
| Ad<↓, G#/ | | Ad<↓, G#/ | ||
| 0 | | 0 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[10/7|Greater Septimal Tritone]] and thus… | * Approximates the [[10/7|Greater Septimal Tritone]] and thus… | ||
| Line 1,350: | Line 1,350: | ||
| Greater Super-Diminished Fifth, Tendoretromean Augmented Fourth | | Greater Super-Diminished Fifth, Tendoretromean Augmented Fourth | ||
| Ad>↓, G#↑\ | | Ad>↓, G#↑\ | ||
| | | -2 | ||
| | | 4 | ||
| 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 1,363: | Line 1,363: | ||
| Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth | | Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth | ||
| Ab↑↑, G#↑ | | Ab↑↑, G#↑ | ||
| | | -3 | ||
| | | 4 | ||
| This interval… | | This interval… | ||
* Approximates the [[36/25|Classic Diminished Fifth]], and thus… | * Approximates the [[36/25|Classic Diminished Fifth]], and thus… | ||
| Line 1,380: | Line 1,380: | ||
| Ultra-Diminished Fifth, Lesser Super-Augmented Fourth | | Ultra-Diminished Fifth, Lesser Super-Augmented Fourth | ||
| Ad<, Gt#<↓ | | Ad<, Gt#<↓ | ||
| | | -2 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[81/56|Septimal Superaugmented Fourth]], and thus… | * Approximates the [[81/56|Septimal Superaugmented Fourth]], and thus… | ||
| Line 1,395: | Line 1,395: | ||
| Ad>, Gt#>↓ | | Ad>, Gt#>↓ | ||
| 0 | | 0 | ||
| | | 7 | ||
| 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 1,415: | Line 1,415: | ||
| Wide Paraminor Fifth, Retrodiptolemaic Augmented Fourth | | Wide Paraminor Fifth, Retrodiptolemaic Augmented Fourth | ||
| Ad<\, G#↑, Ab↑↑ | | Ad<\, G#↑, Ab↑↑ | ||
| | | -1 | ||
| | | 6 | ||
| 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 1,429: | Line 1,429: | ||
| Narrow Grave Fifth, Ultra-Augmented Fourth | | Narrow Grave Fifth, Ultra-Augmented Fourth | ||
| Ad<↑, Gt#< | | Ad<↑, Gt#< | ||
| | | -2 | ||
| | | 5 | ||
| 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 1,444: | Line 1,444: | ||
| Lesser Grave Fifth | | Lesser Grave Fifth | ||
| Ad>↑, A↓\, Gt#> | | Ad>↑, A↓\, Gt#> | ||
| | | -3 | ||
| | | 5 | ||
| 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 1,456: | Line 1,456: | ||
| Greater Grave Fifth | | Greater Grave Fifth | ||
| A↓ | | A↓ | ||
| | | -5 | ||
| | | 5 | ||
| 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 1,472: | Line 1,472: | ||
| Wide Grave Fifth | | Wide Grave Fifth | ||
| A↓/ | | A↓/ | ||
| | | -3 | ||
| | | 6 | ||
| 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 1,487: | Line 1,487: | ||
| A\ | | A\ | ||
| 1 | | 1 | ||
| | | 8 | ||
| This interval… | | This interval… | ||
* Approximates the [[112/75|Marvelous Fifth]], and thus… | * Approximates the [[112/75|Marvelous Fifth]], and thus… | ||
| Line 1,502: | Line 1,502: | ||
| Perfect Fifth | | Perfect Fifth | ||
| A | | A | ||
| | | 9 | ||
| | | 10 | ||
| 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… | ||
| Line 1,529: | Line 1,529: | ||
| A/ | | A/ | ||
| 1 | | 1 | ||
| | | 5 | ||
| This interval… | | This interval… | ||
* Approximates the [[128/85|Septendecimal Fifth]], and thus… | * Approximates the [[128/85|Septendecimal Fifth]], and thus… | ||
| Line 1,544: | Line 1,544: | ||
| Narrow Acute Fifth | | Narrow Acute Fifth | ||
| A↑\ | | A↑\ | ||
| | | -4 | ||
| | | 0 | ||
| 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 1,557: | Line 1,557: | ||
| Lesser Acute Fifth | | Lesser Acute Fifth | ||
| A↑ | | A↑ | ||
| | | -6 | ||
| | | -5 | ||
| 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 1,569: | Line 1,569: | ||
| Greater Acute Fifth, Narrow Inframinor Sixth | | Greater Acute Fifth, Narrow Inframinor Sixth | ||
| At<↓, A↑/ | | At<↓, A↑/ | ||
| | | -7 | ||
| | | -4 | ||
| This Interval… | | This Interval… | ||
* Approximates the [[32/21|Septimal Superfifth]], and thus… | * Approximates the [[32/21|Septimal Superfifth]], and thus… | ||
| Line 1,582: | Line 1,582: | ||
| Inframinor Sixth, Wide Acute Fifth | | Inframinor Sixth, Wide Acute Fifth | ||
| At>↓, Bdb> | | At>↓, Bdb> | ||
| | | -4 | ||
| | | -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 1,597: | Line 1,597: | ||
| Narrow Paramajor Fifth, Wide Inframinor Sixth | | Narrow Paramajor Fifth, Wide Inframinor Sixth | ||
| At<\, Bb↓↓, A↑↑ | | At<\, Bb↓↓, A↑↑ | ||
| | | -2 | ||
| | | 1 | ||
| This interval… | | This interval… | ||
* Approximates the [[20/13|Tridecimal Semitenth]] | * Approximates the [[20/13|Tridecimal Semitenth]] | ||
| Line 1,610: | Line 1,610: | ||
| Paramajor Fifth, Narrow Subminor Sixth | | Paramajor Fifth, Narrow Subminor Sixth | ||
| At<, Bdb<↑ | | At<, Bdb<↑ | ||
| | | -1 | ||
| | | 3 | ||
| 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 1,629: | Line 1,629: | ||
| At>, Bb↓\ | | At>, Bb↓\ | ||
| 0 | | 0 | ||
| | | 5 | ||
| 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 1,642: | Line 1,642: | ||
| Greater Subminor Sixth, Diptolemaic Augmented Fifth | | Greater Subminor Sixth, Diptolemaic Augmented Fifth | ||
| Bb↓, At>/, A#↓↓ | | Bb↓, At>/, A#↓↓ | ||
| | | -1 | ||
| | | 6 | ||
| 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 1,659: | Line 1,659: | ||
| Wide Subminor Sixth, Lesser Sub-Augmented Fifth | | Wide Subminor Sixth, Lesser Sub-Augmented Fifth | ||
| Bb↓/, At<↑ | | Bb↓/, At<↑ | ||
| | | -1 | ||
| | | 7 | ||
| This interval… | | This interval… | ||
* Approximates the [[80/51|Septendecimal Minor Sixth]] | * Approximates the [[80/51|Septendecimal Minor Sixth]] | ||
| Line 1,674: | Line 1,674: | ||
| Bb\, At>↑, A#↓\ | | Bb\, At>↑, A#↓\ | ||
| 0 | | 0 | ||
| | | 8 | ||
| This interval… | | This interval… | ||
* Approximates the [[11/7|Neo-Gothic Minor Sixth]], and thus… | * Approximates the [[11/7|Neo-Gothic Minor Sixth]], and thus… | ||
| Line 1,688: | Line 1,688: | ||
| Pythagorean Minor Sixth, Ptolemaic Augmented Fifth | | Pythagorean Minor Sixth, Ptolemaic Augmented Fifth | ||
| Bb, A#↓ | | Bb, A#↓ | ||
| | | -1 | ||
| | | 9 | ||
| 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 1,705: | Line 1,705: | ||
| Artomean Minor Sixth, Artomean Augmented Fifth | | Artomean Minor Sixth, Artomean Augmented Fifth | ||
| Bb/, A#↓/ | | Bb/, A#↓/ | ||
| | | 1 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[100/63|Quasi-Tempered Minor Sixth]] | * Approximates the [[100/63|Quasi-Tempered Minor Sixth]] | ||
| Line 1,719: | Line 1,719: | ||
| Tendomean Minor Sixth, Tendomean Augmented Fifth | | Tendomean Minor Sixth, Tendomean Augmented Fifth | ||
| A#\, Bb↑\ | | A#\, Bb↑\ | ||
| | | 4 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[51/32|Septendecimal Tendomean Minor Sixth]] | * Approximates the [[51/32|Septendecimal Tendomean Minor Sixth]] | ||
| Line 1,730: | Line 1,730: | ||
| Ptolemaic Minor Sixth, Pythagorean Augmented Fifth | | Ptolemaic Minor Sixth, Pythagorean Augmented Fifth | ||
| A#, Bb↑ | | A#, Bb↑ | ||
| | | 8 | ||
| | | 10 | ||
| 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 1,751: | Line 1,751: | ||
|Wide Minor Sixth, Artoretromean Augmented Fifth | |Wide Minor Sixth, Artoretromean Augmented Fifth | ||
| Bd<↓, Bb↑/, A#/ | | Bd<↓, Bb↑/, A#/ | ||
| | | 3 | ||
| | | 9 | ||
| 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 1,766: | Line 1,766: | ||
| Lesser Supraminor Sixth, Tendoretromean Augmented Fifth | | Lesser Supraminor Sixth, Tendoretromean Augmented Fifth | ||
| Bd>↓, A#↑\ | | Bd>↓, A#↑\ | ||
| 1 | | -1 | ||
| | | 9 | ||
| 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 1,780: | Line 1,780: | ||
| Bd<\, Bb↑↑, A#↑ | | Bd<\, Bb↑↑, A#↑ | ||
| 0 | | 0 | ||
| | | 8 | ||
| 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 1,794: | Line 1,794: | ||
| Artoneutral Sixth, Lesser Super-Augmented Fifth | | Artoneutral Sixth, Lesser Super-Augmented Fifth | ||
| Bd<, At#<↓ | | Bd<, At#<↓ | ||
| | | -1 | ||
| | | 7 | ||
| 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 1,811: | Line 1,811: | ||
| Bd>, At#>↓ | | Bd>, At#>↓ | ||
| 0 | | 0 | ||
| | | 7 | ||
| 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 1,830: | Line 1,830: | ||
| Lesser Submajor Sixth, Retrodiptolemaic Augmented Fifth | | Lesser Submajor Sixth, Retrodiptolemaic Augmented Fifth | ||
| Bd>/, B↓↓, At#>↓/, A#↑↑ | | Bd>/, B↓↓, At#>↓/, A#↑↑ | ||
| | | -1 | ||
| | | 8 | ||
| This interval… | | This interval… | ||
* Approximates the [[64/39|Greater Tridecimal Neutral Sixth]] | * Approximates the [[64/39|Greater Tridecimal Neutral Sixth]] | ||
| Line 1,846: | Line 1,846: | ||
| Greater Submajor Sixth, Ultra-Augmented Fifth | | Greater Submajor Sixth, Ultra-Augmented Fifth | ||
| Bd<↑, At#< | | Bd<↑, At#< | ||
| | | 1 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[33/20|Undecimal Submajor Sixth]] | * Approximates the [[33/20|Undecimal Submajor Sixth]] | ||
| Line 1,857: | Line 1,857: | ||
| Narrow Major Sixth | | Narrow Major Sixth | ||
| Bd>↑, B↓\, At#> | | Bd>↑, B↓\, At#> | ||
| 4 | | 4 | ||
| 9 | |||
| 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 1,870: | Line 1,870: | ||
| Ptolemaic Major Sixth | | Ptolemaic Major Sixth | ||
| B↓, Cb | | B↓, Cb | ||
| | | 7 | ||
| | | 10 | ||
| 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 1,889: | Line 1,889: | ||
| Artomean Major Sixth | | Artomean Major Sixth | ||
| B↓/ | | B↓/ | ||
| | | 4 | ||
| | | 10 | ||
| This interval… | | This interval… | ||
* Approximates the [[256/153|Septendecimal Artomean Major Sixth]] | * Approximates the [[256/153|Septendecimal Artomean Major Sixth]] | ||
| Line 1,902: | Line 1,902: | ||
| Tendomean Major Sixth | | Tendomean Major Sixth | ||
| B\ | | B\ | ||
| | | 1 | ||
| | | 9 | ||
| 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… | ||
| Line 1,915: | Line 1,915: | ||
| Pythagorean Major Sixth | | Pythagorean Major Sixth | ||
| B | | B | ||
| | | -1 | ||
| | | 9 | ||
| This interval… | | This interval… | ||
* Approximates the [[27/16|Pythagorean Major Sixth]], and as such… | * Approximates the [[27/16|Pythagorean Major Sixth]], and as such… | ||
| Line 1,934: | Line 1,934: | ||
| B/, Cd<↓ | | B/, Cd<↓ | ||
| 0 | | 0 | ||
| | | 8 | ||
| This interval… | | This interval… | ||
* Approximates the [[22/13|Neo-Gothic Major Sixth]], and thus… | * Approximates the [[22/13|Neo-Gothic Major Sixth]], and thus… | ||