159edo/Interval names and harmonies: Difference between revisions
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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 5 is a full-blown friend relative to the root and | [[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 5 is a full-blown friend relative to the root and −5 if a full-blown enemy relative to the root. Note that the Harmonic Compatibility and Melodic Compatibility ratings are based on octave-equivalence, and many of the ratings are speculative at this point, adjustments are to be expected in the future. | ||
== Interval chart == | == Interval chart == | ||
| Line 50: | Line 50: | ||
| Narrow Superprime | | Narrow Superprime | ||
| D↑\ | | D↑\ | ||
| | | −5 | ||
| | | −5 | ||
| 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↑ | ||
| | | −5 | ||
| | | −2 | ||
| 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<↓ | ||
| | | −5 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 102: | Line 102: | ||
| Inframinor Second, Wide Superprime | | Inframinor Second, Wide Superprime | ||
| Edb>, Dt>↓ | | Edb>, Dt>↓ | ||
| | | −5 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 123: | Line 123: | ||
| Wide Inframinor Second, Narrow Ultraprime | | Wide Inframinor Second, Narrow Ultraprime | ||
| Eb↓↓, Dt<\ | | Eb↓↓, Dt<\ | ||
| | | −5 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 142: | Line 142: | ||
| Ultraprime, Narrow Subminor Second | | Ultraprime, Narrow Subminor Second | ||
| Dt<, Edb<↑ | | Dt<, Edb<↑ | ||
| | | −5 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 163: | Line 163: | ||
| 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 181: | Line 181: | ||
| Greater Subminor Second, Diptolemaic Augmented Prime | | Greater Subminor Second, Diptolemaic Augmented Prime | ||
| Eb↓, D#↓↓ | | Eb↓, D#↓↓ | ||
| | | −4 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 196: | Line 196: | ||
| 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 211: | Line 211: | ||
| 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 225: | Line 225: | ||
| Pythagorean Minor Second, Ptolemaic Augmented Prime | | Pythagorean Minor Second, Ptolemaic Augmented Prime | ||
| Eb, D#↓ | | Eb, D#↓ | ||
| | | −3 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 246: | Line 246: | ||
| Artomean Minor Second, Artomean Augmented Prime | | Artomean Minor Second, Artomean Augmented Prime | ||
| Eb/, D#↓/ | | Eb/, D#↓/ | ||
| | | −3 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 262: | Line 262: | ||
| Tendomean Minor Second, Tendomean Augmented Prime | | Tendomean Minor Second, Tendomean Augmented Prime | ||
| D#\, Eb↑\ | | D#\, Eb↑\ | ||
| | | −2 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 278: | Line 278: | ||
| Ptolemaic Minor Second, Pythagorean Augmented Prime | | Ptolemaic Minor Second, Pythagorean Augmented Prime | ||
| D#, Eb↑ | | D#, Eb↑ | ||
| | | −2 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 299: | Line 299: | ||
| Wide Minor Second, Artoretromean Augmented Prime | | Wide Minor Second, Artoretromean Augmented Prime | ||
| Ed<↓, Eb↑/, D#/ | | Ed<↓, Eb↑/, D#/ | ||
| | | −2 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 313: | Line 313: | ||
| Lesser Supraminor Second, Tendoretromean Augmented Prime | | Lesser Supraminor Second, Tendoretromean Augmented Prime | ||
| Ed>↓, D#↑\ | | Ed>↓, D#↑\ | ||
| | | −3 | ||
| 4 | | 4 | ||
| This interval… | | This interval… | ||
| 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#↑ | ||
| | | −4 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 344: | Line 344: | ||
| Artoneutral Second, Lesser Super-Augmented Prime | | Artoneutral Second, Lesser Super-Augmented Prime | ||
| Ed<, Dt#<↓ | | Ed<, Dt#<↓ | ||
| | | −4 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 363: | Line 363: | ||
| Tendoneutral Second, Greater Super-Augmented Prime | | Tendoneutral Second, Greater Super-Augmented Prime | ||
| Ed>, Dt#>↓ | | Ed>, Dt#>↓ | ||
| | | −4 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 382: | Line 382: | ||
| Lesser Submajor Second, Retrodiptolemaic Augmented Prime | | Lesser Submajor Second, Retrodiptolemaic Augmented Prime | ||
| Ed>/, E↓↓, Dt#>↓/, D#↑↑ | | Ed>/, E↓↓, Dt#>↓/, D#↑↑ | ||
| | | −4 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 395: | Line 395: | ||
| Greater Submajor Second, Ultra-Augmented Prime | | Greater Submajor Second, Ultra-Augmented Prime | ||
| Ed<↑, Dt#<, Fb↓/ | | Ed<↑, Dt#<, Fb↓/ | ||
| | | −3 | ||
| 4 | | 4 | ||
| This interval… | | This interval… | ||
| Line 411: | Line 411: | ||
| Narrow Major Second | | Narrow Major Second | ||
| Ed>↑, E↓\, Dt#>, Fb\ | | Ed>↑, E↓\, Dt#>, Fb\ | ||
| | | −3 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 424: | Line 424: | ||
| Ptolemaic Major Second | | Ptolemaic Major Second | ||
| E↓, Fb | | E↓, Fb | ||
| | | −2 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 443: | Line 443: | ||
| Artomean Major Second | | Artomean Major Second | ||
| E↓/, Fb/ | | E↓/, Fb/ | ||
| | | −2 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 457: | Line 457: | ||
| Tendomean Major Second | | Tendomean Major Second | ||
| E\, Fb↑\ | | E\, Fb↑\ | ||
| | | −2 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 471: | Line 471: | ||
| Pythagorean Major Second | | Pythagorean Major Second | ||
| E, Fb↑ | | E, Fb↑ | ||
| | | −1 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 491: | Line 491: | ||
| Wide Major Second | | Wide Major Second | ||
| E/, Fd<↓ | | E/, Fd<↓ | ||
| | | −1 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 505: | Line 505: | ||
| Narrow Supermajor Second | | Narrow Supermajor Second | ||
| E↑\, Fd>↓ | | E↑\, Fd>↓ | ||
| | | −1 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 522: | Line 522: | ||
| Lesser Supermajor Second | | Lesser Supermajor Second | ||
| E↑, Fd<\, Fb↑↑, Dx | | E↑, Fd<\, Fb↑↑, Dx | ||
| | | −1 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 617: | Line 617: | ||
| Greater Subminor Third | | Greater Subminor Third | ||
| F↓, Et>/, E#↓↓, Gbb | | F↓, Et>/, E#↓↓, Gbb | ||
| | | −1 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 634: | Line 634: | ||
| Wide Subminor Third | | Wide Subminor Third | ||
| F↓/, Et<↑ | | F↓/, Et<↑ | ||
| | | −1 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 663: | Line 663: | ||
| Pythagorean Minor Third | | Pythagorean Minor Third | ||
| F | | F | ||
| | | −1 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| 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 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 793: | Line 793: | ||
| Tendoneutral Third, Greater Sub-Diminished Fourth | | Tendoneutral Third, Greater Sub-Diminished Fourth | ||
| Ft>, Gdb>↑ | | Ft>, Gdb>↑ | ||
| | | −1 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 904: | Line 904: | ||
| Pythagorean Major Third, Ptolemaic Diminished Fourth | | Pythagorean Major Third, Ptolemaic Diminished Fourth | ||
| F#, Gb↑ | | F#, Gb↑ | ||
| | | −1 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 939: | Line 939: | ||
| Narrow Supermajor Third, Greater Super-Diminished Fourth | | Narrow Supermajor Third, Greater Super-Diminished Fourth | ||
| F#↑\, Gd>↓ | | F#↑\, Gd>↓ | ||
| | | −1 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 953: | Line 953: | ||
| Lesser Supermajor Third, Diptolemaic Diminished Fourth | | Lesser Supermajor Third, Diptolemaic Diminished Fourth | ||
| F#↑, Gd<\, Gb↑↑ | | F#↑, Gd<\, Gb↑↑ | ||
| | | −1 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 982: | Line 982: | ||
| Paraminor Fourth, Wide Supermajor Third | | Paraminor Fourth, Wide Supermajor Third | ||
| Gd>, Ft#>↓ | | Gd>, Ft#>↓ | ||
| | | −1 | ||
| 0 | | 0 | ||
| This interval… | | This interval… | ||
| Line 1,000: | Line 1,000: | ||
| 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 1,013: | Line 1,013: | ||
| 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 1,028: | Line 1,028: | ||
| 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 1,042: | Line 1,042: | ||
| Greater Grave Fourth | | Greater Grave Fourth | ||
| G↓ | | G↓ | ||
| | | −2 | ||
| 0 | | 0 | ||
| This interval… | | This interval… | ||
| Line 1,054: | Line 1,054: | ||
| Wide Grave Fourth | | Wide Grave Fourth | ||
| G↓/ | | G↓/ | ||
| | | −1 | ||
| 1 | | 1 | ||
| This interval… | | This interval… | ||
| Line 1,123: | Line 1,123: | ||
| Narrow Acute Fourth | | Narrow Acute Fourth | ||
| G↑\ | | G↑\ | ||
| | | −2 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 1,137: | Line 1,137: | ||
| Lesser Acute Fourth | | Lesser Acute Fourth | ||
| G↑ | | G↑ | ||
| | | −3 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 1,153: | Line 1,153: | ||
| Greater Acute Fourth | | Greater Acute Fourth | ||
| Gt<↓, G↑/, Adb< | | Gt<↓, G↑/, Adb< | ||
| | | −2 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 1,166: | Line 1,166: | ||
| Wide Acute Fourth, Infra-Diminished Fifth | | Wide Acute Fourth, Infra-Diminished Fifth | ||
| Gt>↓, Adb> | | Gt>↓, Adb> | ||
| | | −1 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| 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 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 1,217: | Line 1,217: | ||
| Infra-Augmented Fourth, Greater Sub-Diminished Fifth | | Infra-Augmented Fourth, Greater Sub-Diminished Fifth | ||
| Gt>, Adb>↑ | | Gt>, Adb>↑ | ||
| | | −1 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 1,232: | Line 1,232: | ||
| Diptolemaic Augmented Fourth, Retroptolemaic Diminished Fifth | | Diptolemaic Augmented Fourth, Retroptolemaic Diminished Fifth | ||
| G#↓↓, Ab↓ | | G#↓↓, Ab↓ | ||
| | | −2 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 1,249: | Line 1,249: | ||
| Lesser Sub-Augmented Fourth, Artoretromean Diminished Fifth | | Lesser Sub-Augmented Fourth, Artoretromean Diminished Fifth | ||
| Gt<↑, Ab↓/ | | Gt<↑, Ab↓/ | ||
| | | −1 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 1,276: | Line 1,276: | ||
| Ptolemaic Augmented Fourth, Pythagorean Diminished Fifth | | Ptolemaic Augmented Fourth, Pythagorean Diminished Fifth | ||
| Ab, G#↓ | | Ab, G#↓ | ||
| | | −3 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 1,291: | Line 1,291: | ||
| Artomean Augmented Fourth, Artomean Diminished Fifth | | Artomean Augmented Fourth, Artomean Diminished Fifth | ||
| G#↓/, Ab/ | | G#↓/, Ab/ | ||
| | | −5 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 1,306: | Line 1,306: | ||
| Tendomean Diminished Fifth, Tendomean Augmented Fourth | | Tendomean Diminished Fifth, Tendomean Augmented Fourth | ||
| Ab↑\, G#\ | | Ab↑\, G#\ | ||
| | | −5 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 1,321: | Line 1,321: | ||
| Ptolemaic Diminished Fifth, Pythagorean Augmented Fourth | | Ptolemaic Diminished Fifth, Pythagorean Augmented Fourth | ||
| Ab↑, G# | | Ab↑, G# | ||
| | | −3 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 1,350: | Line 1,350: | ||
| Greater Super-Diminished Fifth, Tendoretromean Augmented Fourth | | Greater Super-Diminished Fifth, Tendoretromean Augmented Fourth | ||
| Ad>↓, G#↑\ | | Ad>↓, G#↑\ | ||
| | | −1 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 1,363: | Line 1,363: | ||
| Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth | | Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth | ||
| Ab↑↑, G#↑ | | Ab↑↑, G#↑ | ||
| | | −2 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 1,380: | Line 1,380: | ||
| Ultra-Diminished Fifth, Lesser Super-Augmented Fourth | | Ultra-Diminished Fifth, Lesser Super-Augmented Fourth | ||
| Ad<, Gt#<↓ | | Ad<, Gt#<↓ | ||
| | | −1 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| 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 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 1,429: | Line 1,429: | ||
| Narrow Grave Fifth, Ultra-Augmented Fourth | | Narrow Grave Fifth, Ultra-Augmented Fourth | ||
| Ad<↑, Gt#< | | Ad<↑, Gt#< | ||
| | | −1 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 1,444: | Line 1,444: | ||
| Lesser Grave Fifth | | Lesser Grave Fifth | ||
| Ad>↑, A↓\, Gt#> | | Ad>↑, A↓\, Gt#> | ||
| | | −2 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 1,456: | Line 1,456: | ||
| Greater Grave Fifth | | Greater Grave Fifth | ||
| A↓ | | A↓ | ||
| | | −3 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 1,472: | Line 1,472: | ||
| Wide Grave Fifth | | Wide Grave Fifth | ||
| A↓/ | | A↓/ | ||
| | | −2 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 1,544: | Line 1,544: | ||
| Narrow Acute Fifth | | Narrow Acute Fifth | ||
| A↑\ | | A↑\ | ||
| | | −1 | ||
| 1 | | 1 | ||
| This interval… | | This interval… | ||
| Line 1,557: | Line 1,557: | ||
| Lesser Acute Fifth | | Lesser Acute Fifth | ||
| A↑ | | A↑ | ||
| | | −2 | ||
| 0 | | 0 | ||
| This interval… | | This interval… | ||
| Line 1,569: | Line 1,569: | ||
| 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 1,582: | Line 1,582: | ||
| 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 1,597: | Line 1,597: | ||
| 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 1,610: | Line 1,610: | ||
| Paramajor Fifth, Narrow Subminor Sixth | | Paramajor Fifth, Narrow Subminor Sixth | ||
| At<, Bdb<↑ | | At<, Bdb<↑ | ||
| | | −1 | ||
| 0 | | 0 | ||
| This interval… | | This interval… | ||
| 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 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| 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 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 1,688: | Line 1,688: | ||
| Pythagorean Minor Sixth, Ptolemaic Augmented Fifth | | Pythagorean Minor Sixth, Ptolemaic Augmented Fifth | ||
| Bb, A#↓ | | Bb, A#↓ | ||
| | | −1 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 1,794: | Line 1,794: | ||
| Artoneutral Sixth, Lesser Super-Augmented Fifth | | Artoneutral Sixth, Lesser Super-Augmented Fifth | ||
| Bd<, At#<↓ | | Bd<, At#<↓ | ||
| | | −1 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| 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 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 1,915: | Line 1,915: | ||
| Pythagorean Major Sixth | | Pythagorean Major Sixth | ||
| B | | B | ||
| | | −1 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 1,947: | Line 1,947: | ||
| Narrow Supermajor Sixth | | Narrow Supermajor Sixth | ||
| B↑\, Cd>↓ | | B↑\, Cd>↓ | ||
| | | −1 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 1,961: | Line 1,961: | ||
| Lesser Supermajor Sixth | | Lesser Supermajor Sixth | ||
| B↑, Cd<\, Cb↑↑, A## | | B↑, Cd<\, Cb↑↑, A## | ||
| | | −1 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 2,054: | Line 2,054: | ||
| Greater Subminor Seventh | | Greater Subminor Seventh | ||
| C↓, Bt>/, B#↓↓, Dbb | | C↓, Bt>/, B#↓↓, Dbb | ||
| | | −1 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,069: | Line 2,069: | ||
| Wide Subminor Seventh | | Wide Subminor Seventh | ||
| C↓/, Bt<↑ | | C↓/, Bt<↑ | ||
| | | −1 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,085: | Line 2,085: | ||
| Narrow Minor Seventh | | Narrow Minor Seventh | ||
| C\, Bt>↑ | | C\, Bt>↑ | ||
| | | −1 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,098: | Line 2,098: | ||
| Pythagorean Minor Seventh | | Pythagorean Minor Seventh | ||
| C, B#↓ | | C, B#↓ | ||
| | | −1 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,115: | Line 2,115: | ||
| Artomean Minor Seventh | | Artomean Minor Seventh | ||
| C/, B#↓/ | | C/, B#↓/ | ||
| | | −2 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 2,129: | Line 2,129: | ||
| Tendomean Minor Seventh | | Tendomean Minor Seventh | ||
| C↑\, B#\ | | C↑\, B#\ | ||
| | | −2 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,142: | Line 2,142: | ||
| Ptolemaic Minor Seventh | | Ptolemaic Minor Seventh | ||
| C↑, B# | | C↑, B# | ||
| | | −2 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,159: | Line 2,159: | ||
| Wide Minor Seventh | | Wide Minor Seventh | ||
| Ct<↓, C↑/, Ddb<, B#/ | | Ct<↓, C↑/, Ddb<, B#/ | ||
| | | −3 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,171: | Line 2,171: | ||
| Lesser Supraminor Seventh, Infra-Diminished Octave | | Lesser Supraminor Seventh, Infra-Diminished Octave | ||
| Ct>↓, Ddb>, B#↑\ | | Ct>↓, Ddb>, B#↑\ | ||
| | | −3 | ||
| 4 | | 4 | ||
| This interval… | | This interval… | ||
| Line 2,186: | Line 2,186: | ||
| Greater Supraminor Seventh, Retrodiptolemaic Diminished Octave | | Greater Supraminor Seventh, Retrodiptolemaic Diminished Octave | ||
| Ct<\, C↑↑, Ddb<↑\, Db↓↓ | | Ct<\, C↑↑, Ddb<↑\, Db↓↓ | ||
| | | −4 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 2,198: | Line 2,198: | ||
| Artoneutral Seventh, Lesser Sub-Diminished Octave | | Artoneutral Seventh, Lesser Sub-Diminished Octave | ||
| Ct<, Ddb<↑ | | Ct<, Ddb<↑ | ||
| | | −4 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 2,215: | Line 2,215: | ||
| Tendoneutral Seventh, Greater Sub-Diminished Octave | | Tendoneutral Seventh, Greater Sub-Diminished Octave | ||
| Ct>, Ddb>↑ | | Ct>, Ddb>↑ | ||
| | | −4 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 2,231: | Line 2,231: | ||
| Lesser Submajor Seventh, Diptolemaic Major Seventh, Retroptolemaic Diminished Octave | | Lesser Submajor Seventh, Diptolemaic Major Seventh, Retroptolemaic Diminished Octave | ||
| Ct>/, C#↓↓, Db↓ | | Ct>/, C#↓↓, Db↓ | ||
| | | −4 | ||
| 3 | | 3 | ||
| This interval… | | This interval… | ||
| Line 2,244: | Line 2,244: | ||
| Greater Submajor Seventh, Artoretromean Diminished Octave | | Greater Submajor Seventh, Artoretromean Diminished Octave | ||
| Ct<↑, Db↓/ | | Ct<↑, Db↓/ | ||
| | | −3 | ||
| 4 | | 4 | ||
| This interval… | | This interval… | ||
| Line 2,259: | Line 2,259: | ||
| Narrow Major Seventh, Tendoretromean Diminished Octave | | Narrow Major Seventh, Tendoretromean Diminished Octave | ||
| Ct>↑, C#↓\, Db\ | | Ct>↑, C#↓\, Db\ | ||
| | | −2 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,272: | Line 2,272: | ||
| Ptolemaic Major Seventh, Pythagorean Diminished Octave | | Ptolemaic Major Seventh, Pythagorean Diminished Octave | ||
| Db, C#↓ | | Db, C#↓ | ||
| | | −2 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,290: | Line 2,290: | ||
| Artomean Major Seventh, Artomean Diminished Octave | | Artomean Major Seventh, Artomean Diminished Octave | ||
| Db/, C#↓/ | | Db/, C#↓/ | ||
| | | −2 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,306: | Line 2,306: | ||
| Tendomean Major Seventh, Tendomean Diminished Octave | | Tendomean Major Seventh, Tendomean Diminished Octave | ||
| C#\, Db↑\ | | C#\, Db↑\ | ||
| | | −3 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,321: | Line 2,321: | ||
| Pythagorean Major Seventh, Ptolemaic Diminished Octave | | Pythagorean Major Seventh, Ptolemaic Diminished Octave | ||
| C#, Db↑ | | C#, Db↑ | ||
| | | −3 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,339: | Line 2,339: | ||
| Wide Major Seventh, Lesser Super-Diminished Octave | | Wide Major Seventh, Lesser Super-Diminished Octave | ||
| C#/, Dd<↓ | | C#/, Dd<↓ | ||
| | | −3 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,352: | Line 2,352: | ||
| Narrow Supermajor Seventh, Greater Super-Diminished Octave | | Narrow Supermajor Seventh, Greater Super-Diminished Octave | ||
| C#↑\, Dd>↓ | | C#↑\, Dd>↓ | ||
| | | −4 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,367: | Line 2,367: | ||
| Lesser Supermajor Seventh, Diptolemaic Diminished Octave | | Lesser Supermajor Seventh, Diptolemaic Diminished Octave | ||
| C#↑, Db↑↑ | | C#↑, Db↑↑ | ||
| | | −4 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,381: | Line 2,381: | ||
| Greater Supermajor Seventh, Narrow Infraoctave, Ultra-Diminished Octave | | Greater Supermajor Seventh, Narrow Infraoctave, Ultra-Diminished Octave | ||
| Dd<, C#↑/ | | Dd<, C#↑/ | ||
| | | −4 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,397: | Line 2,397: | ||
| Infraoctave, Wide Supermajor Seventh | | Infraoctave, Wide Supermajor Seventh | ||
| Dd>, Ct#>↓ | | Dd>, Ct#>↓ | ||
| | | −5 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,417: | Line 2,417: | ||
| Narrow Ultramajor Seventh, Wide Infraoctave | | Narrow Ultramajor Seventh, Wide Infraoctave | ||
| C#↑↑, Dd>/ | | C#↑↑, Dd>/ | ||
| | | −5 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,435: | Line 2,435: | ||
| Ultramajor Seventh, Wide Superprime | | Ultramajor Seventh, Wide Superprime | ||
| Ct#<, Dd<↑ | | Ct#<, Dd<↑ | ||
| | | −5 | ||
| 5 | | 5 | ||
| This interval… | | This interval… | ||
| Line 2,455: | Line 2,455: | ||
| Lesser Suboctave, Wide Ultramajor Seventh | | Lesser Suboctave, Wide Ultramajor Seventh | ||
| Ct#>, Dd>↑ | | Ct#>, Dd>↑ | ||
| | | −5 | ||
| 2 | | 2 | ||
| This interval… | | This interval… | ||
| Line 2,476: | Line 2,476: | ||
| Greater Suboctave | | Greater Suboctave | ||
| D↓ | | D↓ | ||
| | | −5 | ||
| | | −2 | ||
| This interval… | | This interval… | ||
* Approximates the [[syntonic suboctave]] | * Approximates the [[syntonic suboctave]] | ||
| Line 2,492: | Line 2,492: | ||
| Wide Suboctave | | Wide Suboctave | ||
| D↓/ | | D↓/ | ||
| | | −5 | ||
| | | −5 | ||
| This interval… | | This interval… | ||
* Approximates the [[ptolemismic suboctave]] and the [[biyatismic suboctave]] | * Approximates the [[ptolemismic suboctave]] and the [[biyatismic suboctave]] | ||