159edo/Interval names and harmonies: Difference between revisions
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Almost done with Major Sevenths... |
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| Rm2, RkA1 | | Rm2, RkA1 | ||
| Artomean Minor Second, Artomean Augmented Prime | | Artomean Minor Second, Artomean Augmented Prime | ||
| Eb/, D# | | Eb/, D#ɔ/ | ||
| This interval... | | This interval... | ||
* Approximates the [[18/17|Small Septendecimal Semitone]], and thus... | * Approximates the [[18/17|Small Septendecimal Semitone]], and thus... | ||
| Line 386: | Line 386: | ||
* Approximates the [[27/25|Large Limma]], and thus... | * Approximates the [[27/25|Large Limma]], and thus... | ||
:* It frequently acts as a Diatonic semitone in Western-Classical-based harmony | :* It frequently acts as a Diatonic semitone in Western-Classical-based harmony | ||
* | * Approximates the [[13/12|Tridecimal Neutral Second]], and thus... | ||
:* It demonstrates two-third-tone functionality- especially in relation to this system's approximation of the Pythagorean Major Second- due to the combination of commas tempered out in this system | :* It demonstrates two-third-tone functionality- especially in relation to this system's approximation of the Pythagorean Major Second- due to the combination of commas tempered out in this system | ||
:* It demonstrates trienthird functionality- namely in relation to this system's approximation of the Pythagorean Major Third- due to the combination of commas tempered out in this system | :* It demonstrates trienthird functionality- namely in relation to this system's approximation of the Pythagorean Major Third- due to the combination of commas tempered out in this system | ||
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| ? | | ? | ||
| ? | | ? | ||
| n2, | | n2, SA1 | ||
| Artoneutral Second, Lesser Super-Augmented Prime | | Artoneutral Second, Lesser Super-Augmented Prime | ||
| Ed<, Dt#<ɔ | | Ed<, Dt#<ɔ | ||
| Line 2,596: | Line 2,596: | ||
| KKm7, rn7, Rud8 | | KKm7, rn7, Rud8 | ||
| Greater Supraminor Seventh, Diretroptolemaic Diminished Octave | | Greater Supraminor Seventh, Diretroptolemaic Diminished Octave | ||
| Ct<\, C++, Ddb<+ | | Ct<\, C++, Ddb<+\, Dbɔɔ | ||
| 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 2,609: | Line 2,609: | ||
| ? | | ? | ||
| ? | | ? | ||
| | | n7, rKud8 | ||
| | | Artoneutral Seventh, Lesser Sub-Diminished Octave | ||
| | | Ct<, Ddb<+ | ||
| | | This interval... | ||
* Approximates the [[11/6|Alpharabian Artoneutral Seventh]], which is the traditional, [[low-complexity JI|low complexity]] Undecimal Neutral Seventh, and as such... | |||
:* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this crowds the octave, and is thus prone to decomposition | |||
:* It serves as the smaller and more consonant of two Neutral Sevenths in Western-Classical-based Paradiatonic functional harmony, and thus... | |||
::* Has the potential to move to the Pythagorean Major Sixth through a Paradiatonic "wide semitone" motion | |||
::* Has the potential to move to the Greater Supermajor Seventh through a type of Chromatic semitone motion | |||
* Is the closest approximation of 24edo's own Neutral Seventh in this system, and thus... | |||
:* Follows similar interval arithmetic logic in relation to Pythagorean intervals, albeit with caveats, since the rastma is not tempered out | |||
:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system | |||
|- | |- | ||
| 140 | | 140 | ||
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| ? | | ? | ||
| ? | | ? | ||
| | | N7, sd8 | ||
| | | Tendoneutral Seventh, Greater Sub-Diminished Octave | ||
| | | Ct>, Ddb>+ | ||
| | | This interval... | ||
* Approximates the [[81/44|Alpharabian Tendoneutral Seventh]] or 2nd Undecimal Neutral Seventh, and as such... | |||
:* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this causes dissonance, and thus requires resolution | |||
:* It serves as the larger and more dissonant of two Neutral Sevenths in Western-Classical-based Paradiatonic functional harmony, and thus... | |||
::* Has the potential to move to the Pythagorean Major Sixth through a Paradiatonic "narrow whole tone" motion | |||
::* Has the potential to move to the Greater Supermajor Seventh through a type of Chromatic semitone motion | |||
* Is the closest approximation of 17edo's Neutral Seventh found in this system, and thus... | |||
:* Is capable of being used for similar modulatory moves, albeit with caveats, albeit with caveats, since such moves on their own don't work the exact same way in this system | |||
|- | |- | ||
| 141 | | 141 | ||
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| [[24/13]] | | [[24/13]] | ||
| ? | | ? | ||
| | | kkM7, RN7, kd8 | ||
| | | Lesser Submajor Seventh, Diptolemaic Major Seventh, Retroptolemaic Diminished Octave | ||
| | | Ct>/, C#ɔɔ, Dbɔ | ||
| | | This interval... | ||
* Approximates the [[50/27|Grave Major Seventh]], and thus... | |||
:* It frequently acts as the inverse of a diatonic semitone in Western-Classical-based harmony | |||
* Approximates the [[24/13|Tridecimal Neutral Seventh]] | |||
* Is found in 53edo as that system's Submajor Seventh, and can thus be used to create identical-sounding melodic and harmonic gestures in this system | |||
|- | |- | ||
| 142 | | 142 | ||
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| [[13/7]] | | [[13/7]] | ||
| 119/64 | | 119/64 | ||
| | | Kn7, Rkd8 | ||
| | | Greater Submajor Seventh, Artoretromean Diminished Octave | ||
| | | Ct<+, Dbɔ/ | ||
| | | 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... | |||
:* It demonstrates leading-tone functionality | |||
* Approximates a complex yet rooted 17-limit interval relative to the Tonic and can be used... | |||
:* As an unexpected option for a Diatonic Major Seventh in Western-Classical-based harmony | |||
* Is the closest approximation of 19edo's Major Seventh found in this system, and thus... | |||
:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, since such moves on their own don't work the exact same way in this system | |||
|- | |- | ||
| 143 | | 143 | ||
| Line 2,657: | Line 2,682: | ||
| ? | | ? | ||
| ? | | ? | ||
| | | rkM7, KN7, rd8 | ||
| | | Narrow Major Seventh, Tendoretromean Diminished Octave | ||
| | | Ct>+, C#ɔ\, Db\ | ||
| | | This interval... | ||
* Approximates the [[28/15|Septimal Grave Major Seventh]], and thus... | |||
:* It functions as both a type of Diminished Oetave and a type of Major Seventh in septimal harmony | |||
* Is the closest approximation of [[10edo]]'s Major Seventh found in this system, and thus... | |||
:* Can be used in Warped Diatonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system | |||
|- | |- | ||
| 144 | | 144 | ||
| Line 2,669: | Line 2,698: | ||
| ? | | ? | ||
| ? | | ? | ||
| | | kM7, d8 | ||
| | | Ptolemaic Major Seventh, Pythagorean Diminished Octave | ||
| | | Db, C#ɔ | ||
| | | This interval... | ||
* Approximates the [[15/8|Classic Major Seventh]] or Ptolemaic Major Seventh, and as such... | |||
:* Is one of the staples of both melodic and harmonic voice-leading | |||
:* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this crowds the octave, and is thus prone to decomposition | |||
:* It readily serves as the traditional Major Seventh in 5-limit Western-Classical-based functional harmony and thus... | |||
::* Has the potential to move directly up to the Tonic as a Lead, though in non-meantone systems like this one, such a gesture using this interval has a slightly more lax and natural feel | |||
::* Has close affinities with the Dominant due to being located at roughly a Ptolemaic Major Third away from it | |||
* Approximates the [[4096/2187|Pythagorean Diminished Octave]] | |||
* Is the closest approximation of 31edo's own Major Seventh found in this system, and thus... | |||
:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system | |||
|- | |- | ||
| 145 | | 145 | ||
| Line 2,681: | Line 2,719: | ||
| ? | | ? | ||
| '''[[32/17]]''' | | '''[[32/17]]''' | ||
| | | RkM7, Rd8 | ||
| | | Artomean Major Seventh, Artomean Diminished Octave | ||
| | | Db/, C#ɔ/ | ||
| | | This interval... | ||
* Approximates the [[32/17|Small Septendecimal Major Seventh]] or Octave-Reduced Seventeenth Subharmonic, and thus... | |||
:* Can be used as an unexpected option for a Major Seventh in Western-Classical-based harmony | |||
* Approximates the [[2048/1089|Alpharabian Diminished Octave]] and thus... | |||
:* Can be used as a type of Diminished Octave in undecimal harmony | |||
* Is the closest approximation of 22edo's Lesser Major Seventh in this system, and thus... | |||
:* Can be used in Faux-Classical-based melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since the biyatisma is not tempered out | |||
:* Can be used in Warped Diatonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system | |||
|- | |- | ||
| 146 | | 146 | ||
| Line 2,693: | Line 2,738: | ||
| [[104/55]] | | [[104/55]] | ||
| [[17/9]] | | [[17/9]] | ||
| | | rM7, rKd8 | ||
| | | Tendomean Major Seventh, Tendomean Diminished Octave | ||
| | | C#\, Db+\ | ||
| | | This interval... | ||
* Approximates the [[17/9|Large Septendecimal Major Seventh]], and thus... | |||
:* Can be used as an unexpected option for a Diminished Octave in Western-Classical-based harmony | |||
* Approximates the [[128/121|Axirabian Major Seventh]], and thus... | |||
:* Can be used as a type of Major Seventh in undecimal harmony | |||
* Is the closest approximation of the [[12edo]] Major Seventh found in this system, and thus... | |||
:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system | |||
|- | |- | ||
| 147 | | 147 | ||
| Line 2,705: | Line 2,756: | ||
| ? | | ? | ||
| ? | | ? | ||
| | | M7, Kd8 | ||
| | | Pythagorean Major Seventh, Ptolemaic Diminished Octave | ||
| | | Eb, D#ɔ | ||
| | | This interval... | ||
* Approximates the [[243/128|Pythagorean Major Seventh]], and as such... | |||
:* Can be used readily in both melodic and harmonic voice-leading in general | |||
:* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this causes dissonance, and thus requires resolution | |||
:* It serves as a Diatonic Major Seventh in both Western-Classical-based functional harmony and Neo-Medieval harmony in general, and thus... | |||
::* Has the potential to move directly up to the Tonic as a Lead, though in non-meantone systems like this one, such a gesture using this interval has a slightly more tense feel | |||
* Approximates the [[256/135|Ptolemaic Diminished Octave]], and as such... | |||
:* It serves as a Diminished Octave in the 5-limit Diatonic settings that are common to Western-Classical-based harmony | |||
* Is the closest approximation of [[13edo]]'s own Major Seventh in this system, and thus... | |||
:* Can be used in [[Warped diatonic|Warped Diatonic]] gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system | |||
|- | |- | ||
| 148 | | 148 | ||
| Line 2,717: | Line 2,777: | ||
| ? | | ? | ||
| ? | | ? | ||
| | | RM7, kUd8 | ||
| | | Wide Major Seventh, Lesser Super-Diminished Octave | ||
| | | Eb\, Dt>+ | ||
| | | This interval... | ||
* Approximates the [[21/20|Septimal Minor Semitone]], and thus... | |||
:* It serves as a type of leading tone when resolving septimal harmony constructions to classic harmony constructions | |||
* Approximates the [[22/21|Small Undecimal Semitone]], and thus... | |||
:* It serves as a type of small chromatic semitone in undecimal harmony constructions | |||
* Is one sixth of this system's approximation of the Perfect Fourth | |||
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| 149 | | 149 | ||