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]]. | [[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. | ||
== Interval chart == | == Interval chart == | ||
| Line 9: | Line 9: | ||
! Cents | ! Cents | ||
! colspan="3"| Interval Names | ! colspan="3"| Interval Names | ||
! Harmonic Compatibility Rating | |||
! Melodic Compatibility Rating | |||
! Notes | ! Notes | ||
|- | |- | ||
| Line 16: | Line 18: | ||
| Perfect Unison | | Perfect Unison | ||
| D | | D | ||
| 5 | |||
| 5 | |||
| This interval… | | This interval… | ||
* Is the [[1/1|Perfect Unison]], and thus… | * Is the [[1/1|Perfect Unison]], and thus… | ||
| Line 28: | Line 32: | ||
| Wide Prime | | Wide Prime | ||
| D/ | | D/ | ||
| -5 | |||
| 0 | |||
| This interval… | | This interval… | ||
* Approximates the [[rastma]], and thus… | * Approximates the [[rastma]], and thus… | ||
| Line 42: | Line 48: | ||
| Narrow Superprime | | Narrow Superprime | ||
| D↑\ | | D↑\ | ||
| -5 | |||
| 0 | |||
| This interval… | | This interval… | ||
* Approximates the [[ptolemisma]] and the [[biyatisma]] | * Approximates the [[ptolemisma]] and the [[biyatisma]] | ||
| Line 52: | Line 60: | ||
| Lesser Superprime | | Lesser Superprime | ||
| D↑ | | D↑ | ||
| -5 | |||
| 0 | |||
| This interval… | | This interval… | ||
* Approximates the [[syntonic comma]], and as such… | * Approximates the [[syntonic comma]], and as such… | ||
| Line 68: | Line 78: | ||
| Greater Superprime, Narrow Inframinor Second | | Greater Superprime, Narrow Inframinor Second | ||
| Edb<, Dt<↓ | | Edb<, Dt<↓ | ||
| -5 | |||
| 1 | |||
| This interval… | | This interval… | ||
* Approximates the [[septimal comma|Archytas comma]], and thus… | * Approximates the [[septimal comma|Archytas comma]], and thus… | ||
| Line 88: | Line 100: | ||
| Inframinor Second, Wide Superprime | | Inframinor Second, Wide Superprime | ||
| Edb>, Dt>↓ | | Edb>, Dt>↓ | ||
| -5 | |||
| 3 | |||
| This interval… | | This interval… | ||
* Approximates the [[45/44|Undecimal Fifth-Tone]] | * Approximates the [[45/44|Undecimal Fifth-Tone]] | ||
| Line 107: | Line 121: | ||
| Wide Inframinor Second, Narrow Ultraprime | | Wide Inframinor Second, Narrow Ultraprime | ||
| Eb↓↓, Dt<\ | | Eb↓↓, Dt<\ | ||
| -5 | |||
| 5 | |||
| This interval… | | This interval… | ||
* Approximates the [[40/39|Tridecimal Minor Diesis]] | * Approximates the [[40/39|Tridecimal Minor Diesis]] | ||
| Line 124: | Line 140: | ||
| Ultraprime, Narrow Subminor Second | | Ultraprime, Narrow Subminor Second | ||
| Dt<, Edb<↑ | | Dt<, Edb<↑ | ||
| -5 | |||
| 5 | |||
| 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 143: | Line 161: | ||
| Lesser Subminor Second, Wide Ultraprime, Infra-Augmented Prime | | Lesser Subminor Second, Wide Ultraprime, Infra-Augmented Prime | ||
| Dt>, Eb↓\ | | Dt>, Eb↓\ | ||
| -4 | |||
| 5 | |||
| This interval… | | This interval… | ||
* Approximates the [[28/27|Septimal Subminor Second]], and thus… | * Approximates the [[28/27|Septimal Subminor Second]], and thus… | ||
| Line 159: | Line 179: | ||
| Greater Subminor Second, Diptolemaic Augmented Prime | | Greater Subminor Second, Diptolemaic Augmented Prime | ||
| Eb↓, D#↓↓ | | Eb↓, D#↓↓ | ||
| -3 | |||
| 5 | |||
| 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 172: | Line 194: | ||
| Wide Subminor Second, Lesser Sub-Augmented Prime | | Wide Subminor Second, Lesser Sub-Augmented Prime | ||
| Eb↓/, Dt<↑ | | Eb↓/, Dt<↑ | ||
| -3 | |||
| 5 | |||
| 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 185: | Line 209: | ||
| Narrow Minor Second, Greater Sub-Augmented Prime | | Narrow Minor Second, Greater Sub-Augmented Prime | ||
| Eb\, Dt>↑ | | Eb\, Dt>↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[21/20|Septimal Minor Semitone]], and thus… | * Approximates the [[21/20|Septimal Minor Semitone]], and thus… | ||
| Line 197: | Line 223: | ||
| Pythagorean Minor Second, Ptolemaic Augmented Prime | | Pythagorean Minor Second, Ptolemaic Augmented Prime | ||
| Eb, D#↓ | | Eb, D#↓ | ||
| | |||
| | |||
| 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 216: | Line 244: | ||
| Artomean Minor Second, Artomean Augmented Prime | | Artomean Minor Second, Artomean Augmented Prime | ||
| Eb/, D#↓/ | | Eb/, D#↓/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[18/17|Small Septendecimal Semitone]], and thus… | * Approximates the [[18/17|Small Septendecimal Semitone]], and thus… | ||
| Line 230: | Line 260: | ||
| Tendomean Minor Second, Tendomean Augmented Prime | | Tendomean Minor Second, Tendomean Augmented Prime | ||
| D#\, Eb↑\ | | D#\, Eb↑\ | ||
| | |||
| | |||
| 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 244: | Line 276: | ||
| Ptolemaic Minor Second, Pythagorean Augmented Prime | | Ptolemaic Minor Second, Pythagorean Augmented Prime | ||
| D#, Eb↑ | | D#, Eb↑ | ||
| | |||
| | |||
| 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 263: | Line 297: | ||
| Wide Minor Second, Artoretromean Augmented Prime | | Wide Minor Second, Artoretromean Augmented Prime | ||
| Ed<↓, Eb↑/, D#/ | | Ed<↓, Eb↑/, D#/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[15/14|Septimal Major Semitone]], and thus… | * Approximates the [[15/14|Septimal Major Semitone]], and thus… | ||
| Line 275: | Line 311: | ||
| Lesser Supraminor Second, Tendoretromean Augmented Prime | | Lesser Supraminor Second, Tendoretromean Augmented Prime | ||
| Ed>↓, D#↑\ | | Ed>↓, D#↑\ | ||
| | |||
| | |||
| 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 288: | Line 326: | ||
| KKm2, rn2, KA1 | | KKm2, rn2, KA1 | ||
| Greater Supraminor Second, Diptolemaic Limma, Retroptolemaic Augmented Prime | | Greater Supraminor Second, Diptolemaic Limma, Retroptolemaic Augmented Prime | ||
| Ed<\, Eb↑↑, D#↑ | | Ed<\, Eb↑↑, D#↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[27/25|Large Limma]], and thus… | * Approximates the [[27/25|Large Limma]], and thus… | ||
| Line 302: | Line 342: | ||
| Artoneutral Second, Lesser Super-Augmented Prime | | Artoneutral Second, Lesser Super-Augmented Prime | ||
| Ed<, Dt#<↓ | | Ed<, Dt#<↓ | ||
| | |||
| | |||
| 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 319: | Line 361: | ||
| Tendoneutral Second, Greater Super-Augmented Prime | | Tendoneutral Second, Greater Super-Augmented Prime | ||
| Ed>, Dt#>↓ | | Ed>, Dt#>↓ | ||
| | |||
| | |||
| 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 336: | Line 380: | ||
| Lesser Submajor Second, Retrodiptolemaic Augmented Prime | | Lesser Submajor Second, Retrodiptolemaic Augmented Prime | ||
| Ed>/, E↓↓, Dt#>↓/, D#↑↑ | | Ed>/, E↓↓, Dt#>↓/, D#↑↑ | ||
| | |||
| | |||
| 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 347: | Line 393: | ||
| Greater Submajor Second, Ultra-Augmented Prime | | Greater Submajor Second, Ultra-Augmented Prime | ||
| Ed<↑, Dt#<, Fb↓/ | | Ed<↑, Dt#<, Fb↓/ | ||
| | |||
| | |||
| 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 361: | Line 409: | ||
| Narrow Major Second | | Narrow Major Second | ||
| Ed>↑, E↓\, Dt#>, Fb\ | | Ed>↑, E↓\, Dt#>, Fb\ | ||
| | |||
| | |||
| 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 372: | Line 422: | ||
| Ptolemaic Major Second | | Ptolemaic Major Second | ||
| E↓, Fb | | E↓, Fb | ||
| | |||
| | |||
| 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 389: | Line 441: | ||
| Artomean Major Second | | Artomean Major Second | ||
| E↓/, Fb/ | | E↓/, Fb/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[143/128|Grossmic Whole Tone]], and thus… | * Approximates the [[143/128|Grossmic Whole Tone]], and thus… | ||
| Line 401: | Line 455: | ||
| Tendomean Major Second | | Tendomean Major Second | ||
| E\, Fb↑\ | | E\, Fb↑\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[28/25|Middle Major Second]] | * Approximates the [[28/25|Middle Major Second]] | ||
| Line 413: | Line 469: | ||
| Pythagorean Major Second | | Pythagorean Major Second | ||
| E, Fb↑ | | E, Fb↑ | ||
| | |||
| | |||
| 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 431: | Line 489: | ||
| Wide Major Second | | Wide Major Second | ||
| E/, Fd<↓ | | E/, Fd<↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[44/39|Tridecimal Major Second]], and thus… | * Approximates the [[44/39|Tridecimal Major Second]], and thus… | ||
| Line 443: | Line 503: | ||
| Narrow Supermajor Second | | Narrow Supermajor Second | ||
| E↑\, Fd>↓ | | E↑\, Fd>↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[17/15|Septendecimal Whole Tone]], and thus… | * Approximates the [[17/15|Septendecimal Whole Tone]], and thus… | ||
| Line 458: | Line 520: | ||
| Lesser Supermajor Second | | Lesser Supermajor Second | ||
| E↑, Fd<\, Fb↑↑, Dx | | E↑, Fd<\, Fb↑↑, Dx | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[256/225|Neapolitan Diminished Third]], and thus… | * Approximates the [[256/225|Neapolitan Diminished Third]], and thus… | ||
| Line 472: | Line 536: | ||
| Greater Supermajor Second, Narrow Inframinor Third | | Greater Supermajor Second, Narrow Inframinor Third | ||
| Fd<, Et<↓, E↑/ | | Fd<, Et<↓, E↑/ | ||
| | |||
| | |||
| 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 488: | Line 554: | ||
| Inframinor Third, Wide Supermajor Second | | Inframinor Third, Wide Supermajor Second | ||
| Fd>, Et>↓ | | Fd>, Et>↓ | ||
| | |||
| | |||
| 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 501: | Line 569: | ||
| Wide Inframinor Third, Narrow Ultramajor Second, Semifourth | | Wide Inframinor Third, Narrow Ultramajor Second, Semifourth | ||
| Fd>/, Et<\, F↓↓, E↑↑ | | Fd>/, Et<\, F↓↓, E↑↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[15/13|Tridecimal Semifourth]], and thus… | * Approximates the [[15/13|Tridecimal Semifourth]], and thus… | ||
| Line 515: | Line 585: | ||
| Ultramajor Second, Narrow Subminor Third | | Ultramajor Second, Narrow Subminor Third | ||
| Et<, Fd<↑ | | Et<, Fd<↑ | ||
| | |||
| | |||
| 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 527: | Line 599: | ||
| Lesser Subminor Third, Wide Ultramajor Second | | Lesser Subminor Third, Wide Ultramajor Second | ||
| Et>, Fd>↑, F↓\ | | Et>, Fd>↑, F↓\ | ||
| | |||
| | |||
| 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 542: | Line 616: | ||
| Greater Subminor Third | | Greater Subminor Third | ||
| F↓, Et>/, E#↓↓, Gbb | | F↓, Et>/, E#↓↓, Gbb | ||
| | |||
| | |||
| 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 557: | Line 633: | ||
| Wide Subminor Third | | Wide Subminor Third | ||
| F↓/, Et<↑ | | F↓/, Et<↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[20/17|Septendecimal Minor Third]] | * Approximates the [[20/17|Septendecimal Minor Third]] | ||
| Line 569: | Line 647: | ||
| Narrow Minor Third | | Narrow Minor Third | ||
| F\, Et>↑ | | F\, Et>↑ | ||
| | |||
| | |||
| 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 582: | Line 662: | ||
| Pythagorean Minor Third | | Pythagorean Minor Third | ||
| F | | F | ||
| | |||
| | |||
| 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 597: | Line 679: | ||
| Artomean Minor Third | | Artomean Minor Third | ||
| F/ | | F/ | ||
| | |||
| | |||
| 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 609: | Line 693: | ||
| Tendomean Minor Third | | Tendomean Minor Third | ||
| F↑\ | | F↑\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[153/128|Septendecimal Tendomean Minor Third]] | * Approximates the [[153/128|Septendecimal Tendomean Minor Third]] | ||
| Line 623: | Line 709: | ||
| Ptolemaic Minor Third | | Ptolemaic Minor Third | ||
| F↑, E# | | F↑, E# | ||
| | |||
| | |||
| 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 639: | Line 727: | ||
| Wide Minor Third | | Wide Minor Third | ||
| Ft<↓, F↑/, Gdb< | | Ft<↓, F↑/, Gdb< | ||
| | |||
| | |||
| 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 652: | Line 742: | ||
| Lesser Supraminor Third, Infra-Diminished Fourth | | Lesser Supraminor Third, Infra-Diminished Fourth | ||
| Ft>↓, Gdb> | | Ft>↓, Gdb> | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[40/33|Undecimal Supraminor Third]], and thus… | * Approximates the [[40/33|Undecimal Supraminor Third]], and thus… | ||
| Line 663: | Line 755: | ||
| Greater Supraminor Third, Retrodiptolemaic Diminished Fourth | | Greater Supraminor Third, Retrodiptolemaic Diminished Fourth | ||
| Ft<\, F↑↑, Gdb<↑\, Gb↓↓ | | Ft<\, F↑↑, Gdb<↑\, Gb↓↓ | ||
| | |||
| | |||
| 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 678: | Line 772: | ||
| Artoneutral Third, Lesser Sub-Diminished Fourth | | Artoneutral Third, Lesser Sub-Diminished Fourth | ||
| Ft<, Gdb<↑ | | Ft<, Gdb<↑ | ||
| | |||
| | |||
| 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 696: | Line 792: | ||
| Tendoneutral Third, Greater Sub-Diminished Fourth | | Tendoneutral Third, Greater Sub-Diminished Fourth | ||
| Ft>, Gdb>↑ | | Ft>, Gdb>↑ | ||
| | |||
| | |||
| 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 711: | Line 809: | ||
| Lesser Submajor Third, Retroptolemaic Diminished Fourth | | Lesser Submajor Third, Retroptolemaic Diminished Fourth | ||
| Ft>/, F#↓↓, Gb↓ | | Ft>/, F#↓↓, Gb↓ | ||
| | |||
| | |||
| 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 724: | Line 824: | ||
| Greater Submajor Third, Artoretromean Diminished Fourth | | Greater Submajor Third, Artoretromean Diminished Fourth | ||
| Ft<↑, Gb↓/ | | Ft<↑, Gb↓/ | ||
| | |||
| | |||
| 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 736: | Line 838: | ||
| Narrow Major Third, Tendoretromean Diminished Fourth | | Narrow Major Third, Tendoretromean Diminished Fourth | ||
| Ft>↑, F#↓\, Gb\ | | Ft>↑, F#↓\, Gb\ | ||
| | |||
| | |||
| 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 750: | Line 854: | ||
| Ptolemaic Major Third, Pythagorean Diminished Fourth | | Ptolemaic Major Third, Pythagorean Diminished Fourth | ||
| Gb, F#↓ | | Gb, F#↓ | ||
| | |||
| | |||
| 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 769: | Line 875: | ||
| Artomean Major Third, Artomean Diminished Fourth | | Artomean Major Third, Artomean Diminished Fourth | ||
| Gb/, F#↓/ | | Gb/, F#↓/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[64/51|Septendecimal Artomean Major Third]] | * Approximates the [[64/51|Septendecimal Artomean Major Third]] | ||
| Line 779: | Line 887: | ||
| Tendomean Major Third, Tendomean Diminished Fourth | | Tendomean Major Third, Tendomean Diminished Fourth | ||
| F#\, Gb↑\ | | F#\, Gb↑\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[63/50|Quasi-Tempered Major Third]] | * Approximates the [[63/50|Quasi-Tempered Major Third]] | ||
| Line 793: | Line 903: | ||
| Pythagorean Major Third, Ptolemaic Diminished Fourth | | Pythagorean Major Third, Ptolemaic Diminished Fourth | ||
| F#, Gb↑ | | F#, Gb↑ | ||
| | |||
| | |||
| 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 810: | Line 922: | ||
| Wide Major Third, Lesser Super-Diminished Fourth | | Wide Major Third, Lesser Super-Diminished Fourth | ||
| F#/, Gd<↓, Gb↑/ | | F#/, Gd<↓, Gb↑/ | ||
| | |||
| | |||
| 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 824: | Line 938: | ||
| Narrow Supermajor Third, Greater Super-Diminished Fourth | | Narrow Supermajor Third, Greater Super-Diminished Fourth | ||
| F#↑\, Gd>↓ | | F#↑\, Gd>↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[51/40|Septendecimal Major Third]] | * Approximates the [[51/40|Septendecimal Major Third]] | ||
| Line 836: | Line 952: | ||
| Lesser Supermajor Third, Diptolemaic Diminished Fourth | | Lesser Supermajor Third, Diptolemaic Diminished Fourth | ||
| F#↑, Gd<\, Gb↑↑ | | F#↑, Gd<\, Gb↑↑ | ||
| | |||
| | |||
| 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 848: | Line 966: | ||
| Greater Supermajor Third, Ultra-Diminished Fourth | | Greater Supermajor Third, Ultra-Diminished Fourth | ||
| Gd<, F#↑/ | | Gd<, F#↑/ | ||
| | |||
| | |||
| 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 861: | Line 981: | ||
| Paraminor Fourth, Wide Supermajor Third | | Paraminor Fourth, Wide Supermajor Third | ||
| Gd>, Ft#>↓ | | Gd>, Ft#>↓ | ||
| | |||
| | |||
| 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 877: | Line 999: | ||
| Wide Paraminor Fourth, Narrow Ultramajor Third | | Wide Paraminor Fourth, Narrow Ultramajor Third | ||
| Gd>/, F#↑↑, G↓↓ | | Gd>/, F#↑↑, G↓↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[13/10|Tridecimal Semisixth]] | * Approximates the [[13/10|Tridecimal Semisixth]] | ||
| Line 888: | Line 1,012: | ||
| Ultramajor Third, Narrow Grave Fourth | | Ultramajor Third, Narrow Grave Fourth | ||
| Gd<↑, Ft#< | | Gd<↑, Ft#< | ||
| | |||
| | |||
| 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 901: | Line 1,027: | ||
| Lesser Grave Fourth, Wide Ultramajor Third | | Lesser Grave Fourth, Wide Ultramajor Third | ||
| Gd>↑, G↓\ | | Gd>↑, G↓\ | ||
| | |||
| | |||
| This Interval… | | This Interval… | ||
* Approximates the [[21/16|Septimal Subfourth]], and thus… | * Approximates the [[21/16|Septimal Subfourth]], and thus… | ||
| Line 913: | Line 1,041: | ||
| Greater Grave Fourth | | Greater Grave Fourth | ||
| G↓ | | G↓ | ||
| | |||
| | |||
| 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 923: | Line 1,053: | ||
| Wide Grave Fourth | | Wide Grave Fourth | ||
| G↓/ | | G↓/ | ||
| | |||
| | |||
| 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 934: | Line 1,066: | ||
| Narrow Fourth | | Narrow Fourth | ||
| G\ | | G\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[85/64|Septendecimal Fourth]], and thus… | * Approximates the [[85/64|Septendecimal Fourth]], and thus… | ||
| Line 947: | Line 1,081: | ||
| Perfect Fourth | | Perfect Fourth | ||
| G | | G | ||
| | |||
| | |||
| 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 971: | Line 1,107: | ||
| Wide Fourth | | Wide Fourth | ||
| G/ | | G/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[75/56|Marvelous Fourth]], and thus… | * Approximates the [[75/56|Marvelous Fourth]], and thus… | ||
| Line 984: | Line 1,122: | ||
| Narrow Acute Fourth | | Narrow Acute Fourth | ||
| G↑\ | | G↑\ | ||
| | |||
| | |||
| 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 996: | Line 1,136: | ||
| Lesser Acute Fourth | | Lesser Acute Fourth | ||
| G↑ | | G↑ | ||
| | |||
| | |||
| 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 1,010: | Line 1,152: | ||
| Greater Acute Fourth | | Greater Acute Fourth | ||
| Gt<↓, G↑/, Adb< | | Gt<↓, G↑/, Adb< | ||
| | |||
| | |||
| 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 1,021: | Line 1,165: | ||
| Wide Acute Fourth, Infra-Diminished Fifth | | Wide Acute Fourth, Infra-Diminished Fifth | ||
| Gt>↓, Adb> | | Gt>↓, Adb> | ||
| | |||
| | |||
| 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 1,034: | Line 1,180: | ||
| Narrow Paramajor Fourth, Retrodiptolemaic Diminished Fifth | | Narrow Paramajor Fourth, Retrodiptolemaic Diminished Fifth | ||
| Gt<\, G↑↑, Ab↓↓ | | Gt<\, G↑↑, Ab↓↓ | ||
| | |||
| | |||
| 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 1,046: | Line 1,194: | ||
| Paramajor Fourth, Lesser Sub-Diminished Fifth | | Paramajor Fourth, Lesser Sub-Diminished Fifth | ||
| Gt<, Adb<↑ | | Gt<, Adb<↑ | ||
| | |||
| | |||
| 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 1,066: | Line 1,216: | ||
| Infra-Augmented Fourth, Greater Sub-Diminished Fifth | | Infra-Augmented Fourth, Greater Sub-Diminished Fifth | ||
| Gt>, Adb>↑ | | Gt>, Adb>↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[112/81|Septimal Subdiminished Fifth]], and thus… | * Approximates the [[112/81|Septimal Subdiminished Fifth]], and thus… | ||
| Line 1,079: | Line 1,231: | ||
| Diptolemaic Augmented Fourth, Retroptolemaic Diminished Fifth | | Diptolemaic Augmented Fourth, Retroptolemaic Diminished Fifth | ||
| G#↓↓, Ab↓ | | G#↓↓, Ab↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[25/18|Classic Augmented Fourth]], and thus… | * Approximates the [[25/18|Classic Augmented Fourth]], and thus… | ||
| Line 1,094: | Line 1,248: | ||
| Lesser Sub-Augmented Fourth, Artoretromean Diminished Fifth | | Lesser Sub-Augmented Fourth, Artoretromean Diminished Fifth | ||
| Gt<↑, Ab↓/ | | Gt<↑, Ab↓/ | ||
| | |||
| | |||
| 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 1,105: | Line 1,261: | ||
| Greater Sub-Augmented Fourth, Tendoretromean Diminished Fifth | | Greater Sub-Augmented Fourth, Tendoretromean Diminished Fifth | ||
| Gt>↑, Ab\ | | Gt>↑, Ab\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[7/5|Lesser Septimal Tritone]] and thus… | * Approximates the [[7/5|Lesser Septimal Tritone]] and thus… | ||
| Line 1,117: | Line 1,275: | ||
| Ptolemaic Augmented Fourth, Pythagorean Diminished Fifth | | Ptolemaic Augmented Fourth, Pythagorean Diminished Fifth | ||
| Ab, G#↓ | | Ab, G#↓ | ||
| | |||
| | |||
| 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 1,130: | Line 1,290: | ||
| Artomean Augmented Fourth, Artomean Diminished Fifth | | Artomean Augmented Fourth, Artomean Diminished Fifth | ||
| G#↓/, Ab/ | | G#↓/, Ab/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[24/17|Smaller Septendecimal Tritone]], and thus… | * Approximates the [[24/17|Smaller Septendecimal Tritone]], and thus… | ||
| Line 1,143: | Line 1,305: | ||
| Tendomean Diminished Fifth, Tendomean Augmented Fourth | | Tendomean Diminished Fifth, Tendomean Augmented Fourth | ||
| Ab↑\, G#\ | | Ab↑\, G#\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[17/12|Larger Septendecimal Tritone]], and thus… | * Approximates the [[17/12|Larger Septendecimal Tritone]], and thus… | ||
| Line 1,156: | Line 1,320: | ||
| Ptolemaic Diminished Fifth, Pythagorean Augmented Fourth | | Ptolemaic Diminished Fifth, Pythagorean Augmented Fourth | ||
| Ab↑, G# | | Ab↑, G# | ||
| | |||
| | |||
| 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 1,168: | Line 1,334: | ||
| kUd5, RA4 | | kUd5, RA4 | ||
| Lesser Super-Diminished Fifth, Artoretromean Augmented Fourth | | Lesser Super-Diminished Fifth, Artoretromean Augmented Fourth | ||
| Ad<↓, G#/ | | Ad<↓, G#/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[10/7|Greater Septimal Tritone]] and thus… | * Approximates the [[10/7|Greater Septimal Tritone]] and thus… | ||
| Line 1,181: | Line 1,349: | ||
| Greater Super-Diminished Fifth, Tendoretromean Augmented Fourth | | Greater Super-Diminished Fifth, Tendoretromean Augmented Fourth | ||
| Ad>↓, G#↑\ | | Ad>↓, G#↑\ | ||
| | |||
| | |||
| 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 1,192: | Line 1,362: | ||
| Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth | | Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth | ||
| Ab↑↑, G#↑ | | Ab↑↑, G#↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[36/25|Classic Diminished Fifth]], and thus… | * Approximates the [[36/25|Classic Diminished Fifth]], and thus… | ||
| Line 1,207: | Line 1,379: | ||
| Ultra-Diminished Fifth, Lesser Super-Augmented Fourth | | Ultra-Diminished Fifth, Lesser Super-Augmented Fourth | ||
| Ad<, Gt#<↓ | | Ad<, Gt#<↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[81/56|Septimal Superaugmented Fourth]], and thus… | * Approximates the [[81/56|Septimal Superaugmented Fourth]], and thus… | ||
| Line 1,219: | Line 1,393: | ||
| Paraminor Fifth, Greater Super-Augmented Fourth | | Paraminor Fifth, Greater Super-Augmented Fourth | ||
| Ad>, Gt#>↓ | | Ad>, Gt#>↓ | ||
| | |||
| | |||
| 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 1,238: | Line 1,414: | ||
| Wide Paraminor Fifth, Retrodiptolemaic Augmented Fourth | | Wide Paraminor Fifth, Retrodiptolemaic Augmented Fourth | ||
| Ad<\, G#↑, Ab↑↑ | | Ad<\, G#↑, Ab↑↑ | ||
| | |||
| | |||
| 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 1,250: | Line 1,428: | ||
| Narrow Grave Fifth, Ultra-Augmented Fourth | | Narrow Grave Fifth, Ultra-Augmented Fourth | ||
| Ad<↑, Gt#< | | Ad<↑, Gt#< | ||
| | |||
| | |||
| 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 1,263: | Line 1,443: | ||
| Lesser Grave Fifth | | Lesser Grave Fifth | ||
| Ad>↑, A↓\, Gt#> | | Ad>↑, A↓\, Gt#> | ||
| | |||
| | |||
| 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 1,273: | Line 1,455: | ||
| Greater Grave Fifth | | Greater Grave Fifth | ||
| A↓ | | A↓ | ||
| | |||
| | |||
| 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 1,287: | Line 1,471: | ||
| Wide Grave Fifth | | Wide Grave Fifth | ||
| A↓/ | | A↓/ | ||
| | |||
| | |||
| 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 1,299: | Line 1,485: | ||
| Narrow Fifth | | Narrow Fifth | ||
| A\ | | A\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[112/75|Marvelous Fifth]], and thus… | * Approximates the [[112/75|Marvelous Fifth]], and thus… | ||
| Line 1,313: | Line 1,501: | ||
| Perfect Fifth | | Perfect Fifth | ||
| A | | A | ||
| | |||
| | |||
| 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 1,337: | Line 1,527: | ||
| Wide Fifth | | Wide Fifth | ||
| A/ | | A/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[128/85|Septendecimal Fifth]], and thus… | * Approximates the [[128/85|Septendecimal Fifth]], and thus… | ||
| Line 1,351: | Line 1,543: | ||
| Narrow Acute Fifth | | Narrow Acute Fifth | ||
| A↑\ | | A↑\ | ||
| | |||
| | |||
| 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 1,362: | Line 1,556: | ||
| Lesser Acute Fifth | | Lesser Acute Fifth | ||
| A↑ | | A↑ | ||
| | |||
| | |||
| 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 1,372: | Line 1,568: | ||
| Greater Acute Fifth, Narrow Inframinor Sixth | | Greater Acute Fifth, Narrow Inframinor Sixth | ||
| At<↓, A↑/ | | At<↓, A↑/ | ||
| | |||
| | |||
| This Interval… | | This Interval… | ||
* Approximates the [[32/21|Septimal Superfifth]], and thus… | * Approximates the [[32/21|Septimal Superfifth]], and thus… | ||
| Line 1,383: | Line 1,581: | ||
| Inframinor Sixth, Wide Acute Fifth | | Inframinor Sixth, Wide Acute Fifth | ||
| At>↓, Bdb> | | At>↓, Bdb> | ||
| | |||
| | |||
| 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 1,396: | Line 1,596: | ||
| Narrow Paramajor Fifth, Wide Inframinor Sixth | | Narrow Paramajor Fifth, Wide Inframinor Sixth | ||
| At<\, Bb↓↓, A↑↑ | | At<\, Bb↓↓, A↑↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[20/13|Tridecimal Semitenth]] | * Approximates the [[20/13|Tridecimal Semitenth]] | ||
| Line 1,407: | Line 1,609: | ||
| Paramajor Fifth, Narrow Subminor Sixth | | Paramajor Fifth, Narrow Subminor Sixth | ||
| At<, Bdb<↑ | | At<, Bdb<↑ | ||
| | |||
| | |||
| 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 1,423: | Line 1,627: | ||
| Lesser Subminor Sixth, Infra-Augmented Fifth | | Lesser Subminor Sixth, Infra-Augmented Fifth | ||
| At>, Bb↓\ | | At>, Bb↓\ | ||
| | |||
| | |||
| 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 1,435: | Line 1,641: | ||
| Greater Subminor Sixth, Diptolemaic Augmented Fifth | | Greater Subminor Sixth, Diptolemaic Augmented Fifth | ||
| Bb↓, At>/, A#↓↓ | | Bb↓, At>/, A#↓↓ | ||
| | |||
| | |||
| 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 1,450: | Line 1,658: | ||
| Wide Subminor Sixth, Lesser Sub-Augmented Fifth | | Wide Subminor Sixth, Lesser Sub-Augmented Fifth | ||
| Bb↓/, At<↑ | | Bb↓/, At<↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[80/51|Septendecimal Minor Sixth]] | * Approximates the [[80/51|Septendecimal Minor Sixth]] | ||
| Line 1,462: | Line 1,672: | ||
| Narrow Minor Sixth, Greater Sub-Augmented Fifth | | Narrow Minor Sixth, Greater Sub-Augmented Fifth | ||
| Bb\, At>↑, A#↓\ | | Bb\, At>↑, A#↓\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[14/11|Neo-Gothic Minor Sixth]], and thus… | * Approximates the [[14/11|Neo-Gothic Minor Sixth]], and thus… | ||
| Line 1,475: | Line 1,687: | ||
| Pythagorean Minor Sixth, Ptolemaic Augmented Fifth | | Pythagorean Minor Sixth, Ptolemaic Augmented Fifth | ||
| Bb, A#↓ | | Bb, A#↓ | ||
| | |||
| | |||
| 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 1,490: | Line 1,704: | ||
| Artomean Minor Sixth, Artomean Augmented Fifth | | Artomean Minor Sixth, Artomean Augmented Fifth | ||
| Bb/, A#↓/ | | Bb/, A#↓/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[100/63|Quasi-Tempered Minor Sixth]] | * Approximates the [[100/63|Quasi-Tempered Minor Sixth]] | ||
| Line 1,502: | Line 1,718: | ||
| Tendomean Minor Sixth, Tendomean Augmented Fifth | | Tendomean Minor Sixth, Tendomean Augmented Fifth | ||
| A#\, Bb↑\ | | A#\, Bb↑\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[51/32|Septendecimal Tendomean Minor Sixth]] | * Approximates the [[51/32|Septendecimal Tendomean Minor Sixth]] | ||
| Line 1,511: | Line 1,729: | ||
| Ptolemaic Minor Sixth, Pythagorean Augmented Fifth | | Ptolemaic Minor Sixth, Pythagorean Augmented Fifth | ||
| A#, Bb↑ | | A#, Bb↑ | ||
| | |||
| | |||
| 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 1,530: | Line 1,750: | ||
|Wide Minor Sixth, Artoretromean Augmented Fifth | |Wide Minor Sixth, Artoretromean Augmented Fifth | ||
| Bd<↓, Bb↑/, A#/ | | Bd<↓, Bb↑/, A#/ | ||
| | |||
| | |||
| 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 1,543: | Line 1,765: | ||
| Lesser Supraminor Sixth, Tendoretromean Augmented Fifth | | Lesser Supraminor Sixth, Tendoretromean Augmented Fifth | ||
| Bd>↓, A#↑\ | | Bd>↓, A#↑\ | ||
| | |||
| | |||
| 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 1,554: | Line 1,778: | ||
| Greater Supraminor Sixth, Retroptolemaic Augmented Fifth | | Greater Supraminor Sixth, Retroptolemaic Augmented Fifth | ||
| Bd<\, Bb↑↑, A#↑ | | Bd<\, Bb↑↑, A#↑ | ||
| | |||
| | |||
| 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 1,567: | Line 1,793: | ||
| Artoneutral Sixth, Lesser Super-Augmented Fifth | | Artoneutral Sixth, Lesser Super-Augmented Fifth | ||
| Bd<, At#<↓ | | Bd<, At#<↓ | ||
| | |||
| | |||
| 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 1,581: | Line 1,809: | ||
| Tendoneutral Sixth, Greater Super-Augmented Fifth | | Tendoneutral Sixth, Greater Super-Augmented Fifth | ||
| Bd>, At#>↓ | | Bd>, At#>↓ | ||
| | |||
| | |||
| 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 1,599: | Line 1,829: | ||
| Lesser Submajor Sixth, Retrodiptolemaic Augmented Fifth | | Lesser Submajor Sixth, Retrodiptolemaic Augmented Fifth | ||
| Bd>/, B↓↓, At#>↓/, A#↑↑ | | Bd>/, B↓↓, At#>↓/, A#↑↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[64/39|Greater Tridecimal Neutral Sixth]] | * Approximates the [[64/39|Greater Tridecimal Neutral Sixth]] | ||
| Line 1,613: | Line 1,845: | ||
| Greater Submajor Sixth, Ultra-Augmented Fifth | | Greater Submajor Sixth, Ultra-Augmented Fifth | ||
| Bd<↑, At#< | | Bd<↑, At#< | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[33/20|Undecimal Submajor Sixth]] | * Approximates the [[33/20|Undecimal Submajor Sixth]] | ||
| Line 1,622: | Line 1,856: | ||
| Narrow Major Sixth | | Narrow Major Sixth | ||
| Bd>↑, B↓\, At#> | | Bd>↑, B↓\, At#> | ||
| | |||
| | |||
| 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 1,633: | Line 1,869: | ||
| Ptolemaic Major Sixth | | Ptolemaic Major Sixth | ||
| B↓, Cb | | B↓, Cb | ||
| | |||
| | |||
| 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 1,650: | Line 1,888: | ||
| Artomean Major Sixth | | Artomean Major Sixth | ||
| B↓/ | | B↓/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[256/153|Septendecimal Artomean Major Sixth]] | * Approximates the [[256/153|Septendecimal Artomean Major Sixth]] | ||
| Line 1,661: | Line 1,901: | ||
| Tendomean Major Sixth | | Tendomean Major Sixth | ||
| B\ | | B\ | ||
| | |||
| | |||
| 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 1,672: | Line 1,914: | ||
| Pythagorean Major Sixth | | Pythagorean Major Sixth | ||
| B | | B | ||
| | |||
| | |||
| 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 1,688: | Line 1,932: | ||
| Wide Major Sixth | | Wide Major Sixth | ||
| B/, Cd<↓ | | B/, Cd<↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[22/13|Neo-Gothic Major Sixth]], and thus… | * Approximates the [[22/13|Neo-Gothic Major Sixth]], and thus… | ||
| Line 1,700: | Line 1,946: | ||
| Narrow Supermajor Sixth | | Narrow Supermajor Sixth | ||
| B↑\, Cd>↓ | | B↑\, Cd>↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[17/10|Septendecimal Major Sixth]] | * Approximates the [[17/10|Septendecimal Major Sixth]] | ||
| Line 1,712: | Line 1,960: | ||
| Lesser Supermajor Sixth | | Lesser Supermajor Sixth | ||
| B↑, Cd<\, Cb↑↑, A## | | B↑, Cd<\, Cb↑↑, A## | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[128/75|Classic Diminished Seventh]], and as such… | * Approximates the [[128/75|Classic Diminished Seventh]], and as such… | ||
| Line 1,727: | Line 1,977: | ||
| Greater Supermajor Second, Narrow Inframinor Seventh | | Greater Supermajor Second, Narrow Inframinor Seventh | ||
| Cb<, Bt<↓, B↑/ | | Cb<, Bt<↓, B↑/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[12/7|Septimal Supermajor Sixth]], and as such… | * Approximates the [[12/7|Septimal Supermajor Sixth]], and as such… | ||
| Line 1,741: | Line 1,993: | ||
| Inframinor Seventh, Wide Supermajor Sixth | | Inframinor Seventh, Wide Supermajor Sixth | ||
| Cd>, Bt>↓ | | Cd>, Bt>↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic seventh that sounds more like a sixth, and as such… | * Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic seventh that sounds more like a sixth, and as such… | ||
| Line 1,752: | Line 2,006: | ||
| Narrow Ultramajor Sixth, Wide Inframinor Seventh, Semitwelfth | | Narrow Ultramajor Sixth, Wide Inframinor Seventh, Semitwelfth | ||
| Bt<\, Cd>/, B↑↑, C↓↓ | | Bt<\, Cd>/, B↑↑, C↓↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[26/15|Tridecimal Semitwelfth]], and thus… | * Approximates the [[26/15|Tridecimal Semitwelfth]], and thus… | ||
| Line 1,766: | Line 2,022: | ||
| Ultramajor Sixth, Narrow Subminor Seventh | | Ultramajor Sixth, Narrow Subminor Seventh | ||
| Bt<, Cd<↑ | | Bt<, Cd<↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic sixth that sounds more like a seventh, and as such… | * Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic sixth that sounds more like a seventh, and as such… | ||
| Line 1,778: | Line 2,036: | ||
| Lesser Subminor Seventh, Wide Ultramajor Sixth | | Lesser Subminor Seventh, Wide Ultramajor Sixth | ||
| Bt>, Cd>↑, C↓\ | | Bt>, Cd>↑, C↓\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[7/4|Septimal Subminor Seventh]] or Octave-Reduced Seventh Harmonic, and as such… | * Approximates the [[7/4|Septimal Subminor Seventh]] or Octave-Reduced Seventh Harmonic, and as such… | ||
| Line 1,793: | Line 2,053: | ||
| Greater Subminor Seventh | | Greater Subminor Seventh | ||
| C↓, Bt>/, B#↓↓, Dbb | | C↓, Bt>/, B#↓↓, Dbb | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[225/128|Neapolitan Augmented Sixth]], and thus… | * Approximates the [[225/128|Neapolitan Augmented Sixth]], and thus… | ||
| Line 1,807: | Line 2,069: | ||
| Wide Subminor Seventh | | Wide Subminor Seventh | ||
| C↓/, Bt<↑ | | C↓/, Bt<↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[30/17|Septendecimal Minor Seventh]], and thus… | * Approximates the [[30/17|Septendecimal Minor Seventh]], and thus… | ||
| Line 1,821: | Line 2,085: | ||
| Narrow Minor Seventh | | Narrow Minor Seventh | ||
| C\, Bt>↑ | | C\, Bt>↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[39/22|Tridecimal Minor Seventh]], and thus… | * Approximates the [[39/22|Tridecimal Minor Seventh]], and thus… | ||
| Line 1,832: | Line 2,098: | ||
| Pythagorean Minor Seventh | | Pythagorean Minor Seventh | ||
| C, B#↓ | | C, B#↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[16/9|Pythagorean Minor Seventh]], and as such… | * Approximates the [[16/9|Pythagorean Minor Seventh]], and as such… | ||
| Line 1,847: | Line 2,115: | ||
| Artomean Minor Seventh | | Artomean Minor Seventh | ||
| C/, B#↓/ | | C/, B#↓/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[25/14|Middle Minor Seventh]] | * Approximates the [[25/14|Middle Minor Seventh]] | ||
| Line 1,859: | Line 2,129: | ||
| Tendomean Minor Seventh | | Tendomean Minor Seventh | ||
| C↑\, B#\ | | C↑\, B#\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[256/143|Grossmic Minor Seventh]], and thus… | * Approximates the [[256/143|Grossmic Minor Seventh]], and thus… | ||
| Line 1,870: | Line 2,142: | ||
| Ptolemaic Minor Seventh | | Ptolemaic Minor Seventh | ||
| C↑, B# | | C↑, B# | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[9/5|Classic Minor Seventh]] or Ptolemaic Minor Seventh, and as such… | * Approximates the [[9/5|Classic Minor Seventh]] or Ptolemaic Minor Seventh, and as such… | ||
| Line 1,885: | Line 2,159: | ||
| Wide Minor Seventh | | Wide Minor Seventh | ||
| Ct<↓, C↑/, Ddb<, B#/ | | Ct<↓, C↑/, Ddb<, B#/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Is reachable through stacking eight of this system's approximation of the Tridecimal Supraminor Second | * Is reachable through stacking eight of this system's approximation of the Tridecimal Supraminor Second | ||
| Line 1,895: | Line 2,171: | ||
| Lesser Supraminor Seventh, Infra-Diminished Octave | | Lesser Supraminor Seventh, Infra-Diminished Octave | ||
| Ct>↓, Ddb>, B#↑\ | | Ct>↓, Ddb>, B#↑\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[20/11|Undecimal Supraminor Seventh]] and a similar 13-limit interval that acts as the Supraminor counterpart to the Tridecimal Submajor Seventh | * Approximates the [[20/11|Undecimal Supraminor Seventh]] and a similar 13-limit interval that acts as the Supraminor counterpart to the Tridecimal Submajor Seventh | ||
| Line 1,908: | Line 2,186: | ||
| Greater Supraminor Seventh, Retrodiptolemaic Diminished Octave | | Greater Supraminor Seventh, Retrodiptolemaic Diminished Octave | ||
| Ct<\, C↑↑, Ddb<↑\, Db↓↓ | | Ct<\, C↑↑, Ddb<↑\, Db↓↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Is the closest approximation of 31edo's own Middle Seventh found in this system, and thus… | * Is the closest approximation of 31edo's own Middle Seventh found in this system, and thus… | ||
| Line 1,918: | Line 2,198: | ||
| Artoneutral Seventh, Lesser Sub-Diminished Octave | | Artoneutral Seventh, Lesser Sub-Diminished Octave | ||
| Ct<, Ddb<↑ | | Ct<, Ddb<↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[11/6|Alpharabian Artoneutral Seventh]], which is the traditional, [[low-complexity JI|low complexity]] Undecimal Neutral Seventh, and as such… | * Approximates the [[11/6|Alpharabian Artoneutral Seventh]], which is the traditional, [[low-complexity JI|low complexity]] Undecimal Neutral Seventh, and as such… | ||
| Line 1,933: | Line 2,215: | ||
| Tendoneutral Seventh, Greater Sub-Diminished Octave | | Tendoneutral Seventh, Greater Sub-Diminished Octave | ||
| Ct>, Ddb>↑ | | Ct>, Ddb>↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[81/44|Alpharabian Tendoneutral Seventh]] or 2nd Undecimal Neutral Seventh, and as such… | * Approximates the [[81/44|Alpharabian Tendoneutral Seventh]] or 2nd Undecimal Neutral Seventh, and as such… | ||
| Line 1,946: | Line 2,230: | ||
| kkM7, RN7, kd8 | | kkM7, RN7, kd8 | ||
| Lesser Submajor Seventh, Diptolemaic Major Seventh, Retroptolemaic Diminished Octave | | Lesser Submajor Seventh, Diptolemaic Major Seventh, Retroptolemaic Diminished Octave | ||
| Ct>/, C#↓↓, Db↓ | | Ct>/, C#↓↓, Db↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[50/27|Grave Major Seventh]], and thus… | * Approximates the [[50/27|Grave Major Seventh]], and thus… | ||
| Line 1,958: | Line 2,244: | ||
| Greater Submajor Seventh, Artoretromean Diminished Octave | | Greater Submajor Seventh, Artoretromean Diminished Octave | ||
| Ct<↑, Db↓/ | | Ct<↑, Db↓/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[13/7|Tridecimal Submajor Seventh]] and a similar 11-limit interval that acts as the Submajor counterpart to the Undecimal Supraminor Seventh, and thus… | * Approximates the [[13/7|Tridecimal Submajor Seventh]] and a similar 11-limit interval that acts as the Submajor counterpart to the Undecimal Supraminor Seventh, and thus… | ||
| Line 1,971: | Line 2,259: | ||
| Narrow Major Seventh, Tendoretromean Diminished Octave | | Narrow Major Seventh, Tendoretromean Diminished Octave | ||
| Ct>↑, C#↓\, Db\ | | Ct>↑, C#↓\, Db\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[28/15|Septimal Grave Major Seventh]], and thus… | * Approximates the [[28/15|Septimal Grave Major Seventh]], and thus… | ||
| Line 1,982: | Line 2,272: | ||
| Ptolemaic Major Seventh, Pythagorean Diminished Octave | | Ptolemaic Major Seventh, Pythagorean Diminished Octave | ||
| Db, C#↓ | | Db, C#↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[15/8|Classic Major Seventh]] or Ptolemaic Major Seventh, and as such… | * Approximates the [[15/8|Classic Major Seventh]] or Ptolemaic Major Seventh, and as such… | ||
| Line 1,998: | Line 2,290: | ||
| Artomean Major Seventh, Artomean Diminished Octave | | Artomean Major Seventh, Artomean Diminished Octave | ||
| Db/, C#↓/ | | Db/, C#↓/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[32/17|Small Septendecimal Major Seventh]] or Octave-Reduced Seventeenth Subharmonic, and thus… | * Approximates the [[32/17|Small Septendecimal Major Seventh]] or Octave-Reduced Seventeenth Subharmonic, and thus… | ||
| Line 2,012: | Line 2,306: | ||
| Tendomean Major Seventh, Tendomean Diminished Octave | | Tendomean Major Seventh, Tendomean Diminished Octave | ||
| C#\, Db↑\ | | C#\, Db↑\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[17/9|Large Septendecimal Major Seventh]], and thus… | * Approximates the [[17/9|Large Septendecimal Major Seventh]], and thus… | ||
| Line 2,025: | Line 2,321: | ||
| Pythagorean Major Seventh, Ptolemaic Diminished Octave | | Pythagorean Major Seventh, Ptolemaic Diminished Octave | ||
| C#, Db↑ | | C#, Db↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[243/128|Pythagorean Major Seventh]], and as such… | * Approximates the [[243/128|Pythagorean Major Seventh]], and as such… | ||
| Line 2,041: | Line 2,339: | ||
| Wide Major Seventh, Lesser Super-Diminished Octave | | Wide Major Seventh, Lesser Super-Diminished Octave | ||
| C#/, Dd<↓ | | C#/, Dd<↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[40/21|Septimal Acute Major Seventh]], and thus… | * Approximates the [[40/21|Septimal Acute Major Seventh]], and thus… | ||
| Line 2,052: | Line 2,352: | ||
| Narrow Supermajor Seventh, Greater Super-Diminished Octave | | Narrow Supermajor Seventh, Greater Super-Diminished Octave | ||
| C#↑\, Dd>↓ | | C#↑\, Dd>↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates multiple complex [[17-limit]] intervals relative to the Tonic and can be used… | * Approximates multiple complex [[17-limit]] intervals relative to the Tonic and can be used… | ||
| Line 2,065: | Line 2,367: | ||
| Lesser Supermajor Seventh, Diptolemaic Diminished Octave | | Lesser Supermajor Seventh, Diptolemaic Diminished Octave | ||
| C#↑, Db↑↑ | | C#↑, Db↑↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[48/25|Classic Diminished Octave]] or Diptolemaic Diminished Octave, and thus… | * Approximates the [[48/25|Classic Diminished Octave]] or Diptolemaic Diminished Octave, and thus… | ||
| Line 2,077: | Line 2,381: | ||
| Greater Supermajor Seventh, Narrow Infraoctave, Ultra-Diminished Octave | | Greater Supermajor Seventh, Narrow Infraoctave, Ultra-Diminished Octave | ||
| Dd<, C#↑/ | | Dd<, C#↑/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[27/14|Septimal Supermajor Seventh]], and thus… | * Approximates the [[27/14|Septimal Supermajor Seventh]], and thus… | ||
| Line 2,091: | Line 2,397: | ||
| Infraoctave, Wide Supermajor Seventh | | Infraoctave, Wide Supermajor Seventh | ||
| Dd>, Ct#>↓ | | Dd>, Ct#>↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[64/33|Alpharabian Infraoctave]], and as such… | * Approximates the [[64/33|Alpharabian Infraoctave]], and as such… | ||
| Line 2,109: | Line 2,417: | ||
| Narrow Ultramajor Seventh, Wide Infraoctave | | Narrow Ultramajor Seventh, Wide Infraoctave | ||
| C#↑↑, Dd>/ | | C#↑↑, Dd>/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[39/20|Tridecimal Ultramajor Seventh]] | * Approximates the [[39/20|Tridecimal Ultramajor Seventh]] | ||
| Line 2,125: | Line 2,435: | ||
| Ultramajor Seventh, Wide Superprime | | Ultramajor Seventh, Wide Superprime | ||
| Ct#<, Dd<↑ | | Ct#<, Dd<↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[88/45|Undecimal Suboctave]] | * Approximates the [[88/45|Undecimal Suboctave]] | ||
| Line 2,143: | Line 2,455: | ||
| Lesser Suboctave, Wide Ultramajor Seventh | | Lesser Suboctave, Wide Ultramajor Seventh | ||
| Ct#>, Dd>↑ | | Ct#>, Dd>↑ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[septimal suboctave|Archytas suboctave]], and thus… | * Approximates the [[septimal suboctave|Archytas suboctave]], and thus… | ||
| Line 2,162: | Line 2,476: | ||
| Greater Suboctave | | Greater Suboctave | ||
| D↓ | | D↓ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[syntonic suboctave]] | * Approximates the [[syntonic suboctave]] | ||
| Line 2,176: | Line 2,492: | ||
| Wide Suboctave | | Wide Suboctave | ||
| D↓/ | | D↓/ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[ptolemismic suboctave]] and the [[biyatismic suboctave]] | * Approximates the [[ptolemismic suboctave]] and the [[biyatismic suboctave]] | ||
| Line 2,186: | Line 2,504: | ||
| Narrow Octave | | Narrow Octave | ||
| D\ | | D\ | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Approximates the [[rastmic narrow octave]] | * Approximates the [[rastmic narrow octave]] | ||
| Line 2,198: | Line 2,518: | ||
| Perfect Octave | | Perfect Octave | ||
| D | | D | ||
| | |||
| | |||
| This interval… | | This interval… | ||
* Is the [[2/1|Perfect Octave]], and thus… | * Is the [[2/1|Perfect Octave]], and thus… | ||