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. Note that the Harmonic Compatibility and Melodic Compatibility ratings are based on octave-equivalence, and many of the ratings are speculative at this point, adjustments are to be expected in the future. | ||
== Interval chart == | == Interval chart == | ||
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:* It frequently acts as a chromatic 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 | :* It demonstrates 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 | ||
* Is the closest approximation of [[17edo]]'s Minor Second found in this system, and thus… | * 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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* 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… | ||
:* It can be thought of as something along the lines of a "wide semitone" in voice-leading | :* It can be thought of as something along the lines of a "wide semitone" in voice-leading | ||
:* It demonstrates trienthird | :* It demonstrates trienthird functionality—namely in relation to this system's approximation of the Classic Major Third—due to the combination of commas tempered out in this system | ||
* Approximates a complex yet uprooted 17-limit interval relative to the Tonic and can be used… | * Approximates a complex yet uprooted 17-limit interval relative to the Tonic and can be used… | ||
:* As an unexpected option for a Diatonic-type semitone in Western-Classical-based harmony | :* As an unexpected option for a Diatonic-type semitone in Western-Classical-based harmony | ||
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:* 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… | * Approximates the [[13/12|Tridecimal Neutral Second]], and thus… | ||
:* It demonstrates two-third-tone | :* 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 | :* 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 | ||
* Is found in 53edo as that system's Supraminor Second, and can thus be used to create identical-sounding melodic and harmonic gestures in this system | * Is found in 53edo as that system's Supraminor Second, and can thus be used to create identical-sounding melodic and harmonic gestures in this system | ||
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* Is one third of this system's approximation of the Classic Major Sixth as a consequence of the schisma being tempered out in this system | * Is one third of this system's approximation of the Classic Major Sixth as a consequence of the schisma being tempered out in this system | ||
* Is reachable through stacking three of this system's approximation of the Axirabian Limma | * Is reachable through stacking three of this system's approximation of the Axirabian Limma | ||
|- | |- | ||
| 40 | | 40 | ||
| 301.8867925 | | 301.8867925 | ||
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| 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… | ||
:* It is easily very useful when it comes to building chords | :* It is easily very useful when it comes to building chords despite—or perhaps even because of—its dissonance | ||
* Approximates a complex 5-limit interval formed by adding a syntonic comma to a Pythagorean Major Third, and thus… | * Approximates a complex 5-limit interval formed by adding a syntonic comma to a Pythagorean Major Third, and thus… | ||
:* It can be thought of as a type of third when acting in this capacity | :* It can be thought of as a type of third when acting in this capacity | ||
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::* It has the potential to move up towards a Serviant harmony through a Parachromatic quatertone-type motion | ::* It has the potential to move up towards a Serviant harmony through a Parachromatic quatertone-type motion | ||
::* It has the potential to move up towards an Intersubiant harmony through a Parachromatic semitone-type motion, with this move granting additional follow-up options | ::* It has the potential to move up towards an Intersubiant harmony through a Parachromatic semitone-type motion, with this move granting additional follow-up options | ||
* Follows after the pattern of inframinor and ultramajor intervals sounding like members of the adjacent interval | * Follows after the pattern of inframinor and ultramajor intervals sounding like members of the adjacent interval classes—specifically, the paraminor fourth sounds more like a third than a fourth | ||
* Is the closest approximation of 19edo's Diminished Fourth found in this system, and thus… | * Is the closest approximation of 19edo's Diminished Fourth 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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* Approximates the [[27/20|Classic Acute Fourth]], and as such… | * Approximates the [[27/20|Classic Acute Fourth]], and as such… | ||
:* Is one of two xenharmonic intervals that appear in the otherwise traditional settings of Western-Classical-based Diatonic scales | :* Is one of two xenharmonic intervals that appear in the otherwise traditional settings of Western-Classical-based Diatonic scales | ||
::* Specifically, it is found between the Major Third and Major Sixth in the Lydian Mode of the familiar [[Zarlino|Ptolemaic Sequence]], and is ideally in the exact same position for both Ionian and Mixolydian modes, though this technically results in there being Diatonic scales of different | ::* Specifically, it is found between the Major Third and Major Sixth in the Lydian Mode of the familiar [[Zarlino|Ptolemaic Sequence]], and is ideally in the exact same position for both Ionian and Mixolydian modes, though this technically results in there being Diatonic scales of different varieties—namely the Bilawal and Myxian scale types | ||
::* It is useful for overtly making the VImin chord of these modes do what a traditional deceptive cadence normally does | ::* It is useful for overtly making the VImin chord of these modes do what a traditional deceptive cadence normally does | ||
:* Is one of two intervals that can generate an Antidiatonic MOS with a sound and feel that blends in easily with traditional Western-Classical-based Diatonic harmonies | :* Is one of two intervals that can generate an Antidiatonic MOS with a sound and feel that blends in easily with traditional Western-Classical-based Diatonic harmonies | ||
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* Approximates the [[40/27|Classic Grave Fifth]], and as such… | * Approximates the [[40/27|Classic Grave Fifth]], and as such… | ||
:* Is one of two xenharmonic intervals that appear in the otherwise traditional settings of Western-Classical-based Diatonic scales | :* Is one of two xenharmonic intervals that appear in the otherwise traditional settings of Western-Classical-based Diatonic scales | ||
::* Specifically, it is found between the Minor Third and Minor Seventh in the Locrian Mode of the familiar [[Zarlino|Ptolemaic Sequence]], and is ideally in the exact same position for, Phrygian, Aeolian and Dorian modes, though this technically results in there being Diatonic scales of different | ::* Specifically, it is found between the Minor Third and Minor Seventh in the Locrian Mode of the familiar [[Zarlino|Ptolemaic Sequence]], and is ideally in the exact same position for, Phrygian, Aeolian and Dorian modes, though this technically results in there being Diatonic scales of different varieties—namely the Contrazarlino, Contrabilawal and Contramyxian scale types | ||
::* It is useful for overtly making the VImin chord of these modes do what a traditional deceptive cadence normally does | ::* It is useful for overtly making the VImin chord of these modes do what a traditional deceptive cadence normally does | ||
:* Is one of two intervals that can generate an Antidiatonic MOS with a sound and feel that blends in easily with traditional Western-Classical-based Diatonic harmonies | :* Is one of two intervals that can generate an Antidiatonic MOS with a sound and feel that blends in easily with traditional Western-Classical-based Diatonic harmonies | ||
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::* It has the potential to move back down towards a Dominant harmony through a Parachromatic quatertone-type motion | ::* It has the potential to move back down towards a Dominant harmony through a Parachromatic quatertone-type motion | ||
::* It has the potential to move back down towards an Interregnant harmony through a Parachromatic semitone-type motion, with this move granting additional follow-up options | ::* It has the potential to move back down towards an Interregnant harmony through a Parachromatic semitone-type motion, with this move granting additional follow-up options | ||
* Follows after the pattern of inframinor and ultramajor intervals sounding like members of the adjacent interval | * Follows after the pattern of inframinor and ultramajor intervals sounding like members of the adjacent interval classes—specifically, the paramajor fifth sounds more like a sixth than a fifth | ||
* Is the closest approximation of 19edo's Augmented Fifth found in this system, and thus… | * Is the closest approximation of 19edo's Augmented Fifth 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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:* It functions as an Augmented Fifth in Western-Classical-based functional harmony by default, and is the signature interval of certain 5-limit Non-Diatonic modes such as Lydian Augmented | :* It functions as an Augmented Fifth in Western-Classical-based functional harmony by default, and is the signature interval of certain 5-limit Non-Diatonic modes such as Lydian Augmented | ||
:* Can be used in Western-Classical-based harmony as an extension to the simul cadence due to its relationship to multiple notes | :* Can be used in Western-Classical-based harmony as an extension to the simul cadence due to its relationship to multiple notes | ||
:* It is easily very useful when it comes to building chords | :* It is easily very useful when it comes to building chords despite—or perhaps even because of—its dissonance, specifically… | ||
::* It is the basic interval for framing a 5-limit augmented triad, though it can also be used for certain other triads | ::* It is the basic interval for framing a 5-limit augmented triad, though it can also be used for certain other triads | ||
* Approximates a complex 5-limit interval formed by subtracting a syntonic comma from a Pythagorean Minor Sixth, and thus… | * Approximates a complex 5-limit interval formed by subtracting a syntonic comma from a Pythagorean Minor Sixth, and thus… | ||