159edo/Interval names and harmonies: Difference between revisions
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| D/ | | D/ | ||
| This interval... | | This interval... | ||
* Approximates the [[rastma]] | * Approximates the [[rastma]], and thus... | ||
* Approximates the [[marvel comma]] | :* Is useful for defining [[11-limit]] subchromatic alterations in the Western-Classical-based functional harmony of this system | ||
* Approximates the [[marvel comma]], and thus... | |||
:* Can function as both a type of subchroma and a type of reverse diesis in this system | |||
* Is useful for slight dissonances that convey something less than satisfactory | * Is useful for slight dissonances that convey something less than satisfactory | ||
* Can only be approached in melodic lines indirectly with one or more intervening notes | * Can only be approached in melodic lines indirectly with one or more intervening notes | ||
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| D↑\ | | D↑\ | ||
| This interval... | | This interval... | ||
* Approximates the [[ptolemisma]] | * Approximates the [[ptolemisma]] and the [[biyatisma]] | ||
* Is useful for slight dissonances that create noticeable tension | * Is useful for slight dissonances that create noticeable tension | ||
* Can only be approached in melodic lines indirectly with one or more intervening notes | * Can only be approached in melodic lines indirectly with one or more intervening notes | ||
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| D↑ | | D↑ | ||
| This interval... | | This interval... | ||
* Approximates the [[syntonic comma]] | * Approximates the [[syntonic comma]], and as such... | ||
* Approximates the [[Pythagorean comma]] | :* Is especially useful as a basis for defining [[5-limit]] subchromatic alterations in the Western-Classical-based functional harmony of this system | ||
* Approximates the [[Pythagorean comma]], and thus... | |||
:* Can be considered a type of reverse diesis | |||
* Is a dissonance to be avoided in Western-Classical-based harmony unless deliberately used for expressive purposes | * Is a dissonance to be avoided in Western-Classical-based harmony unless deliberately used for expressive purposes | ||
* Is useful in melody as... | * Is useful in melody as... | ||
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| This interval... | | This interval... | ||
* Approximates the [[45/44|Undecimal Fifth-Tone]] | * Approximates the [[45/44|Undecimal Fifth-Tone]] | ||
* Approximates a complex | * Approximates a complex 11-limit paradiatonic quartertone that is the namesake of 24edo's own Inframinor Second | ||
* Is the closest approximation of | * Is the closest approximation of [[31edo]]'s own Superprime found in this system, and thus... | ||
:* Is capable of being used in progressions reminiscent of that system's [[SpiralProgressions|spiral progressions]] | :* Is capable of being used in progressions reminiscent of that system's [[SpiralProgressions|spiral progressions]] | ||
* Is a dissonance to be avoided in Western-Classical-based harmony unless... | * Is a dissonance to be avoided in Western-Classical-based harmony unless... | ||
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| This interval... | | This interval... | ||
* Approximates the [[33/32|Al-Farabi Quartertone]], and as such... | * Approximates the [[33/32|Al-Farabi Quartertone]], and as such... | ||
:* It functions as the default parachromatic quartertone in Western-Classical-based | :* It functions as the default parachromatic quartertone in Western-Classical-based Paradiatonic functional harmony, and thus... | ||
::* Can be used more overtly in both melodic and harmonic voice-leading in general, though doing so in Western-Classical-based music requires a proper set-up | ::* Can be used more overtly in both melodic and harmonic voice-leading in general, though doing so in Western-Classical-based music requires a proper set-up | ||
::* Cannot occur as the distance between any two notes in a single chord in Western-Classical-based polypedal harmony due to its dissonance | ::* Cannot occur as the distance between any two notes in a single chord in Western-Classical-based polypedal harmony due to its dissonance | ||
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::* Has the potential to move away from the Tonic towards either a Contralead or Supertonic harmony through a diatonic or paradiatonic motion | ::* Has the potential to move away from the Tonic towards either a Contralead or Supertonic harmony through a diatonic or paradiatonic motion | ||
* Is one fifth of this system's approximation of the Septimal Subminor Third | * Is one fifth of this system's approximation of the Septimal Subminor Third | ||
* Is the closest approximation of [[22edo]]'s | * Is the closest approximation of [[22edo]]'s Lesser Minor Second in this system, and thus... | ||
:* Can be used in Superpyth-based 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 Superpyth-based 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 24edo's own Ultraprime in this system, and thus... | * Is the closest approximation of 24edo's own Ultraprime in this system, and thus... | ||
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:* Is the narrowest interval that can be used in Western-Classical-based harmony and Neo-Medieval harmony as a proper leading tone | :* Is the narrowest interval that can be used in Western-Classical-based harmony and Neo-Medieval harmony as a proper leading tone | ||
::* Compared to other options, it has a markedly more tense feel | ::* Compared to other options, it has a markedly more tense feel | ||
* Is the closest approximation of | :* Can be used as an unexpected option for a chromatic-type semitone in Western-Classical-based harmony | ||
* Is the closest approximation of [[19edo]]'s Augmented Prime found in this system, and thus... | |||
:* Is capable of being used for similar modulatory moves, albeit with caveats, since such moves on their own don't work the exact same way in this system | :* Is capable of being used for similar modulatory moves, albeit with caveats, since such moves on their own don't work the exact same way in this system | ||
* Is one third of this system's approximation of the Ptolemaic Major Second | * Is one third of this system's approximation of the Ptolemaic Major Second | ||
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| This interval... | | This interval... | ||
* Approximates the [[25/24|Classic Chroma]], and thus... | * Approximates the [[25/24|Classic Chroma]], and thus... | ||
:* It frequently acts as a semitone in Western-Classical-based harmony | :* It frequently acts as a chromatic semitone in Western-Classical-based harmony | ||
* Approximates the [[26/25|Large Tridecimal Third-Tone]] and the [[27/26|Small Tridecimal Third-Tone]], and thus... | * Approximates the [[26/25|Large Tridecimal Third-Tone]] and the [[27/26|Small Tridecimal Third-Tone]], and thus... | ||
:* It demonstrates third-tone functionality- especially in relation to this system's approximation of the Pythagorean Major Second- due to the combination commas tempered out in this system | :* It demonstrates third-tone functionality- especially in relation to this system's approximation of the Pythagorean Major Second- due to the combination commas tempered out in this system | ||
* Is the closest approximation of | * Is the closest approximation of [[17edo]]'s Minor Second found in this system, and thus... | ||
:* Is capable of being used for similar modulatory moves, albeit with caveats, since such moves on their own don't work the exact same way in this system | :* Is capable of being used for similar modulatory moves, albeit with caveats, since such moves on their own don't work the exact same way in this system | ||
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:* In Western-Classical-based harmony as part of the simul cadence due to it providing a smooth option for both voice-leading and chord construction | :* In Western-Classical-based harmony as part of the simul cadence due to it providing a smooth option for both voice-leading and chord construction | ||
:* As an unexpected option for a chromatic-type semitone in Western-Classical-based harmony | :* As an unexpected option for a chromatic-type semitone in Western-Classical-based harmony | ||
* Is the closest approximation of | * Is the closest approximation of 31edo's Subminor Second found in this system, and thus... | ||
:* Is capable of being used in certain similar melodic and harmonic gestures, albeit with caveats, since such moves on their own don't work the exact same way in this system | :* Is capable of being used in certain similar melodic and harmonic gestures, albeit with caveats, since such moves on their own don't work the exact same way in this system | ||
* Is the closest approximation of | * Is the closest approximation of [[16edo]]'s Subminor 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 | :* 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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| Eb, D#↓ | | Eb, D#↓ | ||
| This interval... | | This interval... | ||
* Approximates the [[256/243|Pythagorean Limma]], and as such... | * Approximates the [[256/243|Pythagorean Limma]] or Pythagorean Minor Second, and as such... | ||
:* It serves as a Diatonic semitone in both Western-Classical-based harmony and Neo-Medieval harmony, 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 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 | ::* 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 reverse leading-tone, 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 reverse leading-tone, 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 | ||
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:* Can be used as an unexpected option for a chromatic-type semitone in Western-Classical-based harmony | :* Can be used as an unexpected option for a chromatic-type semitone in Western-Classical-based harmony | ||
* Approximates the [[128/121|Axirabian Limma]], and thus... | * Approximates the [[128/121|Axirabian Limma]], and thus... | ||
:* Can be used as a type of | :* Can be used as a type of Diatonic semitone in undecimal harmony | ||
:* Is one of two in this system that are essential in executing the [[Frameshift comma #Frameshift cedence|frameshift cadence]] | :* Is one of two in this system that are essential in executing the [[Frameshift comma #Frameshift cedence|frameshift cadence]] | ||
* Is the closest approximation of the [[12edo]] Minor Second found in this system, and thus... | * Is the closest approximation of the [[12edo]] Minor 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 | :* 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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| This interval... | | This interval... | ||
* Approximates the [[17/16|Large Septendecimal Semitone]] or [[Octave-Reduced]] Seventeenth Harmonic, and thus... | * Approximates the [[17/16|Large Septendecimal Semitone]] or [[Octave-Reduced]] Seventeenth Harmonic, and thus... | ||
:* Can be used as an unexpected option for a | :* Can be used as an unexpected option for a Diatonic-type semitone in Western-Classical-based harmony | ||
* Approximates the [[1089/1024|Parapotome]] and thus... | * Approximates the [[1089/1024|Parapotome]] and thus... | ||
:* Can be used as a type of chromatic semitone in undecimal harmony | :* Can be used as a type of chromatic semitone in undecimal harmony | ||
* Is the closest approximation of 22edo's | * Is the closest approximation of 22edo's Greater Minor Second 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 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 | :* 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 | ||
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| 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 thus... | |||
:* It serves as the 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 reverse leading-tone, though in non-meantone systems like this one, such a gesture using this interval has a slightly more lax and natural feel | |||
::* 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... | |||
:* Is generally the interval that defines the default value of [[Wikipedia: Sharp (music)|sharps]] and [[Wikipedia: Flat (music)|flats]] in this system, and is thus very helpful as a reference interval | |||
:* Is one of two in this system that are essential in executing the frameshift cadence | |||
* Is the closest approximation of 31edo's own Minor 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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| 16 | | 16 | ||