159edo/Interval names and harmonies: Difference between revisions

Aura (talk | contribs)
No edit summary
Aura (talk | contribs)
No edit summary
Line 261: Line 261:
| 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...
:* 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 semitone in both Western-Classical-based functional harmony and Neo-Medieval harmony in general, and thus...
:* It serves as a Diatonic semitone in both Western-Classical-based functional harmony and Neo-Medieval harmony in general, and thus...
::* 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
::* Has the potential to move directly back down to the Tonic as a Contralead, though in non-meantone systems like this one, such a gesture using this interval has a slightly more tense feel
::* Has the potential to move directly back down to the Tonic as a Contralead, though in non-meantone systems like this one, such a gesture using this interval has a slightly more tense feel
::* Can serve as a possible interval between the Tonic and the root of a Neapolitan chord
::* Can serve as a possible interval between the Tonic and the root of a Neapolitan chord
Line 322: Line 322:
| D#, Eb↑
| D#, Eb↑
| This interval...
| This interval...
* Approximates the [[16/15|Classic Minor Second]] or Ptolemaic Minor Second, and thus...  
* Approximates the [[16/15|Classic Minor Second]] or Ptolemaic Minor Second, and thus...
:* 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 causes crowding, and thus requires resolution
:* It readily serves as the traditional leading tone in 5-limit Western-Classical-based functional harmony and thus...
:* It readily serves as the traditional leading tone in 5-limit Western-Classical-based functional harmony and thus...
::* 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 causes crowding, and thus requires resolution
::* Has the potential to move directly back down to the Tonic as a Contralead, though in non-meantone systems like this one, such a gesture using this interval has a slightly more lax and natural feel
::* Has the potential to move directly back down to the Tonic as a Contralead, 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 Serviant due to being located at roughly a Ptolemaic Major Third away from it
::* Can serve as a possible interval between the Tonic and the root of a Neapolitan chord
::* Can serve as a possible interval between the Tonic and the root of a Neapolitan chord
* Approximates the [[2187/2048|Apotome]] or Pythagorean Augmented Prime, and thus...
* Approximates the [[2187/2048|Apotome]] or Pythagorean Augmented Prime, and thus...
Line 400: Line 401:
| 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...
:* It can be thought of as something along the lines of a "wide semitone" in voice-leading
:* 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 smaller and more dissonant of two Neutral Seconds in Western-Classical-based Paradiatonic functional harmony, and thus...
:* It serves as the smaller and more dissonant of two Neutral Seconds in Western-Classical-based Paradiatonic functional harmony, and thus...
::* It can be thought of as something along the lines of a "wide semitone" in voice-leading
::* 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
::* Has the potential to move to the Pythagorean Minor Third through a Paradiatonic "narrow whole tone" motion  
::* Has the potential to move to the Pythagorean Minor Third through a Paradiatonic "narrow whole tone" motion  
::* Has the potential to move to the Lesser Subminor Second through a type of Chromatic semitone motion  
::* Has the potential to move to the Lesser Subminor Second through a type of Chromatic semitone motion  
Line 422: Line 423:
| 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...
:* It can be thought of as something along the lines of a "narrow whole tone" in voice-leading
:* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this causes crowding, and thus requires resolution
:* It serves as the larger and more consonant of two Neutral Seconds in Western-Classical-based Paradiatonic functional harmony, and thus...
:* It serves as the larger and more consonant of two Neutral Seconds in Western-Classical-based Paradiatonic functional harmony, and thus...
::* It can be thought of as something along the lines of a "narrow whole tone" in voice-leading
::* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this causes crowding, and thus requires resolution
::* Has the potential to move to the Pythagorean Minor Third through a Paradiatonic "wide semitone" motion  
::* Has the potential to move to the Pythagorean Minor Third through a Paradiatonic "wide semitone" motion  
::* Has the potential to move to the Lesser Subminor Second through a type of Chromatic semitone motion
::* Has the potential to move to the Lesser Subminor Second through a type of Chromatic semitone motion
Line 494: Line 495:
| E↓, Fb
| E↓, Fb
| This interval...
| This interval...
* Approximates the [[10/9|Classic Major Second]] or Ptolemaic Major Second, and thus...  
* Approximates the [[10/9|Classic Major Second]] or Ptolemaic Major Second, and thus...
:* It readily serves as a Diatonic whole tone in Western-Classical-based functional harmony, and thus...
:* Can be used readily in both melodic and harmonic voice-leading in general
::* 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 crowding, and thus requires resolution
::* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this causes crowding, and thus requires resolution
:* Is one the intervals in this system that are essential in executing any sort of variation on Jacob Collier's "Four Magical chords" from his rendition of "In the Bleak Midwinter"  
::* Is one the intervals in this system that are essential in executing any sort of variation on Jacob Collier's "Four Magical chords" from his rendition of "In the Bleak Midwinter"
:* It readily serves as a Diatonic whole tone in Western-Classical-based functional harmony, since...
::* It has close affinities with the Serviant due to being located at roughly a Ptolemaic Minor Third away from it
* Is one half of this system's approximation of the Octave-Reduced Thirteenth Subharmonic
* Is one half of this system's approximation of the Octave-Reduced Thirteenth Subharmonic
* Is one fifth of this system's approximation of the Pythagorean Major Sixth
* Is one fifth of this system's approximation of the Pythagorean Major Sixth
Line 519: Line 521:
* Is one third of this system's approximation of the Classic Augmented Fourth
* Is one third of this system's approximation of the Classic Augmented Fourth
* Is the closest approximation of [[19edo]]'s Major Second found in this system, and thus...
* Is the closest approximation of [[19edo]]'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
|-
|-
| 26
| 26
Line 531: Line 533:
| Tendomean Major Second
| Tendomean Major Second
| E\, Fb↑\
| E\, Fb↑\
| In addition to being the closest approximation of the 31edo Major Second found in this system, it is one of two intervals that come the closest to approximating the 12edo Major Second found in this system.
| This interval...
* Approximates the [[28/25|Middle Major Second]]
* 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
* 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
|-
|-
| 27
| 27
Line 543: Line 550:
| Pythagorean Major Second
| Pythagorean Major Second
| E, Fb↑
| E, Fb↑
| This interval is the standard-issue whole tone in this system as it is one of two intervals that come the closest to approximating the 12edo Major Second, and the only one of the two that actually approximates the Pythagorean Major Second; furthermore, it is the whole tone that is used as a reference interval in [[Diatonic, Chromatic, Enharmonic, Subchromatic|diatonic-and-chromatic-style]] interval logic in this system as it pertains to both semitones and quartertones.
| This interval...
* Approximates the [[9/8|Pythagorean Major Second]], and thus...
:* 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 causes crowding, and thus requires resolution
:* It readily serves as a Diatonic whole tone in Western-Classical-based functional harmony, since...
::* It functions as a Double Dominant due to being the result of stacking two Perfect Fifths and octave-reducing
:* Is the whole tone that is used as a reference interval in [[Diatonic, Chromatic, Enharmonic, Subchromatic|diatonic-and-chromatic-style]] interval logic in this system as it pertains to both semitones and quartertones, and thus...
::* It sees usage in Paradiatonic and Parachromatic harmonies in addition to the more obvious Diatonic-related uses
* 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 an interval with unexpected xenharmonic potential in this system despite its familiarity as...  
:* It can be exploited in Oneirotonic harmonies due to being reachable through stacking three of this system's approximation of the Septimal Subfourth and octave-reducing
|-
|-
| 28
| 28