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159edo/Interval names and harmonies: Difference between revisions

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Finally finished listing all the major third intervals in this system... There's clearly still work ahead of me though...
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Line 80: Line 80:
| Inframinor Second, Wide Superprime
| Inframinor Second, Wide Superprime
| Edb>, Dt>↓
| Edb>, Dt>↓
| By default, this interval is a type of paradiatonic quartertone, and indeed, the [[11-limit]] ratio this interval approximates is the namesake of [[24edo]]'s own Inframinor Second; however, in a higher-fidelity system such as this, one will notice that this syntactic second is actually noticeably narrower than 24edo's quartertone.
| By default, this interval is a type of paradiatonic quartertone, and indeed, the [[11-limit]] ratio this interval approximates is the namesake of [[24edo]]'s own Inframinor Second; in addition, it is also the closest approximation of the [[31edo]] Superprime found in this system.
|-
|-
| 6
| 6
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| [[26/25]], [[27/26]]
| [[26/25]], [[27/26]]
| ?
| ?
| km2, rKU1, kkA1
| km2, RuA1, kkA1
| Greater Subminor Second, Diptolemaic Augmented Prime
| Greater Subminor Second, Diptolemaic Augmented Prime
| Eb↓, Dt<↑\, D#↓↓
| Eb↓, Dt<↑\, D#↓↓
| Although this interval frequently acts as the Diptolemaic Chroma, it can also act as a trienstone- that is, a third of a tone- since it's one third of the Pythagorean Major Second.
| Although this interval frequently acts as the Classic Chroma due to consistently approximating it, it can also act as a trienstone- that is, a third of a tone- since it's one third of the Pythagorean Major Second.
|-
|-
| 10
| 10
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| Wide Subminor Second, Lesser Sub-Augmented Prime
| Wide Subminor Second, Lesser Sub-Augmented Prime
| Eb↓/, Dt<↑
| Eb↓/, Dt<↑
| This interval acts as a type of semitone, however, whether it's a diatonic or chromatic semitone depends on the situation.
| This interval acts as a type of semitone, however, whether it's a diatonic or chromatic semitone depends on the situation; in addition, it is also the closest approximation of the 31edo Subminor Second found in this system.  
|-
|-
| 11
| 11
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| Artomean Minor Second, Artomean Augmented Prime  
| Artomean Minor Second, Artomean Augmented Prime  
| Eb/, D#↓/
| Eb/, D#↓/
| This interval is one of two in this system that are essential in executing the [[Frameshift comma #Frameshift cedence|frameshift cadence]]; it is also the closest approximation of the [[12edo]] semitone found in this system.
| This interval is one of two in this system that are essential in executing the [[Frameshift comma #Frameshift cedence|frameshift cadence]]; it is also the closest approximation of the [[12edo]] Minor Second found in this system.
|-
|-
| 14
| 14
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| Ptolemaic Minor Second, Pythagorean Augmented Prime
| Ptolemaic Minor Second, Pythagorean Augmented Prime
| D#, Eb↑
| D#, Eb↑
| This interval approximates the Ptolemaic Minor Second- that is, the traditional [[5-limit]] leading tone- as well as the Pythagorean Augmented Prime, and thus, is used accordingly; however, this interval is also one of two in this system that are essential in executing the frameshift cadence.
| This interval approximates the Ptolemaic Minor Second- that is, the traditional [[5-limit]] leading tone- as well as the Pythagorean Augmented Prime, and thus, is used accordingly; however, this interval is also useful for evoking the feel of 31edo due to approximating that system's Minor Second, and is also one of two in this system that are essential in executing the frameshift cadence.
|-
|-
| 16
| 16
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| Lesser Submajor Second, Diretroptolemaic Augmented Prime
| Lesser Submajor Second, Diretroptolemaic Augmented Prime
| Ed>/, E↓↓, Dt#>↓/, D#↑↑
| Ed>/, E↓↓, Dt#>↓/, D#↑↑
| In addition to its properties as a type of Submajor Second, this interval is also one half of a Ptolemaic Minor Third in this system and is thus used accordingly.
| In addition to being a type of Submajor Second and the closest approximation of the 31edo Middle Second found in this system, two of these add up to the approximation of the Ptolemaic Minor Third.
|-
|-
| 22
| 22
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| Tendomean Major Second
| Tendomean Major Second
| E\, Fb↑\
| E\, Fb↑\
| This interval is created from stacking two of this system's closet approximation of the 12edo semitone, and thus, it is one of two intervals that come the closest to approximating the 12edo whole tone found in this system.
| 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.
|-
|-
| 27
| 27
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| 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 whole tone, 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 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.
|-
|-
| 28
| 28
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| Narrow Supermajor Second
| Narrow Supermajor Second
| E↑\, Fd>↓
| E↑\, Fd>↓
| This interval is interesting not only because it is utilized in approximations of the [[17-odd-limit]], but also because it is such a good superpyth whole tone that two of these add up to the approximation of the Septimal Supermajor Third in this system.
| This interval is interesting not only because it is utilized in approximations of the [[17-odd-limit]], but also because it is the whole tone found in this system's Superpyth scale, and is of such quality that two of these add up to this system's approximation of the Septimal Supermajor Third.
|-
|-
| 30
| 30
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| Lesser Subminor Third, Wide Ultramajor Second
| Lesser Subminor Third, Wide Ultramajor Second
| Et>, Fd>↑, F↓\
| Et>, Fd>↑, F↓\
| As the approximation of the Septimal Subminor Third, this interval is used accordingly; what's more, due in part to both the [[keenanisma]] being tempered out and the fact that three of these add up to the Pythagorean Minor Sixth, this interval can be used to great effect in chords.
| As the approximation of the Septimal Subminor Third, those who are not already familiar with septimal harmony will find this interval useful in forming not only strident-sounding triads framed by the Perfect Fifth, but also other, ambisonant triads framed by the Perfect Fourth; in addition, three of these add up to the Pythagorean Minor Sixth.
|-
|-
| 36
| 36
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| Greater Subminor Third
| Greater Subminor Third
| F↓, Et>/, E#↓↓, Gbb
| F↓, Et>/, E#↓↓, Gbb
| This interval can be interpreted as a type of third on the basis of it approximating the result of subtracting a syntonic comma from a Pythagorean Minor Third; however, it most frequently appears in approximations of [[5-limit]] Harmonic scales as the interval between the Ptolemaic Minor Sixth and the Ptolemaic Major Seventh, making it double as a type of augmented second.
| This interval is useful for evoking the feel of 31edo due to approximating that system's Subminor Third, and even approximates the result of subtracting a syntonic comma from a Pythagorean Minor Third; however, it most frequently appears in approximations of [[5-limit]] Harmonic scales as the interval between the Ptolemaic Minor Sixth and the Ptolemaic Major Seventh, making it double as a type of augmented second.
|-
|-
| 37
| 37
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| Wide Subminor Third
| Wide Subminor Third
| F↓/, Et<↑
| F↓/, Et<↑
| This interval is utilized in approximations of the [[17-odd-limit]], courtesy of acting as the [[fourth complement]] to the Narrow Supermajor Second.
| This interval is utilized in approximations of the [[17-odd-limit]], courtesy of acting as the [[fourth complement]] to the Narrow Supermajor Second; it is also good for evoking the feel of [[17edo]] due to approximating that system's Minor Third.
|-
|-
| 38
| 38
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| Tendomean Minor Third  
| Tendomean Minor Third  
| F↑\
| F↑\
| The main thing of note concerning this interval is that two of these add up to this system's approximation of the Greater Septimal Tritone.
| In addition to being the closest approximation of the 31edo Minor Third found in this system, this interval is also half of this system's approximation of the Greater Septimal Tritone and is thus used accordingly as part of a triad.
|-
|-
| 42
| 42
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| Wide Minor Third
| Wide Minor Third
| Ft<↓, F↑/, Gdb<
| Ft<↓, F↑/, Gdb<
| The main thing of note concerning this interval is that two of these add up to this system's approximation of the Paraminor Fifth.
| The main thing of note concerning this interval is that two of these add up to this system's approximation of the Paraminor Fifth, thus facilitating the formation of strange-sounding triads
|-
|-
| 44
| 44
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| Tendoneutral Third, Greater Sub-Diminished Fourth
| Tendoneutral Third, Greater Sub-Diminished Fourth
| Ft>, Gdb>↑
| Ft>, Gdb>↑
| As one of two neutral seconds in this system, this interval is notable for being one half of a possible generator for this system's superpyth diatonic scale.
| As one of two neutral seconds in this system, this interval is notable for being one half of a possible generator for this system's superpyth scale.
|-
|-
| 48
| 48
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| Narrow Major Third, Tendoretromean Diminished Fourth
| Narrow Major Third, Tendoretromean Diminished Fourth
| Ft>↑, F#↓\, Gb\
| Ft>↑, F#↓\, Gb\
| The main thing of note concerning this interval is that two of these add up to this system's approximation of the Paramajor Fifth.
| The main thing of note concerning this interval is that two of these add up to this system's approximation of the Paramajor Fifth, thus facilitating the formation of strange-sounding triads.
|-
|-
| 51
| 51
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| Pythagorean Major Third, Ptolemaic Diminished Fourth
| Pythagorean Major Third, Ptolemaic Diminished Fourth
| F#, Gb↑
| F#, Gb↑
| This interval approximates the Pythagorean Major Third, and, since this system does not temper out the syntonic comma, this interval- in contrast to the Ptolemaic Major Third- is very useful as an interpretation of the dissonant Major Third from Medieval music's florid organum, and can thus be used in creating a subtle instability in certain Diatonic harmonies, though it's also useful building cool augmented triads.
| This interval approximates the Pythagorean Major Third, and, since this system does not temper out the syntonic comma, this interval- in contrast to the Ptolemaic Major Third- is very useful as an interpretation of the dissonant Major Third from Medieval music's florid organum, and can thus be used in creating a subtle instability in certain Diatonic harmonies, though it's also useful in building oddly-charming augmented triads.
|-
|-
| 55
| 55
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| 143/112
| 143/112
| 51/40
| 51/40
|  
| rKM3, RkUd4
|  
| Narrow Supermajor Third, Greater Super-Diminished Fourth
|  
| F#↑\, Gd>↓
|  
| This interval is useful for evoking the feel of 31edo due to approximating that system's Supermajor Third, and is even better for evoking the feel of [[17edo]] due to approximating that system's Major Third.
|-
|-
| 57
| 57
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| ?
| ?
| ?
| ?
|  
| KM3, rUd4, KKd4
|  
| Lesser Supermajor Third, Diptolemaic Diminished Fourth
|  
| F#↑, Gd<\, Gb↑↑
|  
| This interval is easily very useful due to it being a consistent approximation of the Classic Diminished Fourth; despite its dissonance- or perhaps even because of said dissonance- this interval is even useful when it comes to building chords.
|-
|-
| 58
| 58
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| ?
| ?
| ?
| ?
|  
| SM3, kUM3, rm4, Ud4
|  
| Greater Supermajor Third, Ultra-Diminished Fourth
|  
| Gd<, F#↑/
|  
| This interval is the approximation of the Septimal Supermajor Third and is directly on this system's Superpyth scale as well; those who are not already familiar with septimal harmony will find this interval useful in forming not only strident-sounding triads framed by the Perfect Fifth, but also different types of superaugmented triad.
|-
|-
| 59
| 59
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