159edo/Interval names and harmonies: Difference between revisions

Aura (talk | contribs)
Finally covered the Classic Major Third...
Aura (talk | contribs)
Need to come up with more xen uses for none other than 12edo's major third...
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| This interval...
| This interval...
* Approximates the [[28/25|Middle Major Second]]
* Approximates the [[28/25|Middle Major Second]]
* Is one of two intervals that serve as the closest approximation of the 12edo Major Second 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
* Is the closest approximation of 31edo's Major Second found in this system, and thus...
* Is the closest approximation of 31edo's Major Second 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
:* 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
* Is one of two intervals that serve as the closest approximation of the 12edo Major Second 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
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| ?
| ?
| 512/429
| 512/429
| 153/128
| [[153/128]]
| rKm3
| rKm3
| Tendomean Minor Third  
| Tendomean Minor Third  
| F↑\
| F↑\
| This interval...
| This interval...
* Approximates the [[153/128|Septendecimal Tendomean Minor Third]]
* Is one half of this system's approximation of the Greater Septimal Tritone, and thus...
* Is one half of this system's approximation of the Greater Septimal Tritone, and thus...
:* Is used accordingly as part of a diminished triad
:* Is used accordingly as part of a diminished triad
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* Is the closest approximation of 31edo's Minor Third found in this system, and thus...
* Is the closest approximation of 31edo's Minor Third 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
:* 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
* Can easily be used in modulatory maneuvers similar to those performed by Jacob Collier
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:* Readily occurs as the distance between two notes in a single chord in Western-Classical-based polypedal harmony
:* Readily occurs as the distance between two notes in a single chord in Western-Classical-based polypedal harmony
:* It differs from the Pythagorean Minor Third in that...  
:* It differs from the Pythagorean Minor Third in that...  
::* It is one of four perfect consonances in this system, rendering it extremely suitable for use in a Tonic triad in Western-Classical-based polypedal harmony
::* It is one of four imperfect consonances in this system, rendering it extremely suitable for use in a Tonic triad in Western-Classical-based polypedal harmony
* Is reachable through stacking three of this system's approximation of the Octave-Reduced Seventeenth Harmonic
* Is reachable through stacking three of this system's approximation of the Octave-Reduced Seventeenth Harmonic
* Is the closest approximation of 19edo's Minor Third found in this system, and thus...
* Is the closest approximation of 19edo's Minor Third found in this system, and thus...
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:* Readily occurs as the distance between two notes in a single chord in Western-Classical-based polypedal harmony
:* Readily occurs as the distance between two notes in a single chord in Western-Classical-based polypedal harmony
:* It differs from the Pythagorean Major Third in that...  
:* It differs from the Pythagorean Major Third in that...  
::* It is one of four perfect consonances in this system, rendering it extremely suitable for use in a Tonic triad in Western-Classical-based polypedal harmony
::* It is one of four imperfect consonances in this system, rendering it extremely suitable for use in a Tonic triad in Western-Classical-based polypedal harmony
* Approximates the [[8192/6561|Pythagorean Diminished Fourth]], and as such...
* Approximates the [[8192/6561|Pythagorean Diminished Fourth]], and as such...
:* Serves as an enharmonic substitution for the Classic Major Third when building chords for purposes of voice-leading, in which case it counts as an unresolved interval
:* Serves as an enharmonic substitution for the Classic Major Third when building chords for purposes of voice-leading, in which case it counts as an unresolved interval
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| Artomean Major Third, Artomean Diminished Fourth
| Artomean Major Third, Artomean Diminished Fourth
| Gb/, F#↓/
| Gb/, F#↓/
| As this interval is situated between the Ptolemaic Major Third on one hand and the familiar major third of 12edo on the other, this interval can easily be used in modulatory maneuvers similar to those performed by Jacob Collier.
| This interval...
* Approximates the [[64/51|Septendecimal Artomean Major Third]]
* Is reachable through stacking two of this system's approximation of the Middle Major Second
* Can easily be used in modulatory maneuvers similar to those performed by Jacob Collier
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| Tendomean Major Third, Tendomean Diminished Fourth
| Tendomean Major Third, Tendomean Diminished Fourth
| F#\, Gb↑\
| F#\, Gb↑\
| As none other than the familiar major third of 12edo, this interval is useful for creating the familiar augmented triads of 12edo, performing modulatory maneuvers based around said triads, and evoking the feel of 12edo in other ways.
| This interval...
* Approximates the [[63/50|Quasi-Tempered Major Third]]
* Is none other than the familiar major third of 12edo, and thus...
:* It is useful for evoking the feel of 12edo in various ways, such as...
::* Creating the familiar augmented triads of 12edo
::* Being stacked with this system's approximation of the Quasi-Tempered Minor Third to make chords similar in sound to those of 12edo
::* Performing modulatory maneuvers based around the aforementioned chords
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