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159edo/Interval names and harmonies: Difference between revisions

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Aura (talk | contribs)
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Trying to get a handle on the types of diminished fourth in here- I need to catch up on this before I start working with major thirds...
Aura (talk | contribs)
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5,920 edits
Finally finished listing all the major third intervals in this system... There's clearly still work ahead of me though...
Line 368: Line 368:
| Narrow Supermajor Second
| Narrow Supermajor Second
| E↑\, Fd>↓
| E↑\, Fd>↓
| This interval is of note because it is utilized in approximations of the [[17-odd-limit]]; what's more, it is also the whole tone in this system's superpyth diatonic scale, and in fact, 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 such a good superpyth whole tone that two of these add up to the approximation of the Septimal Supermajor Third in this system.
|-
|-
| 30
| 30
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| Pythagorean Minor Third
| Pythagorean Minor Third
| F
| F
| This interval approximates the Pythagorean Minor Third, and since this system does not temper out the syntonic comma, this interval- in contrast to the Ptolemaic Minor Third- is very useful as an interpretation of the dissonant Minor Third from [[Wikipedia: Medieval music #Early_polyphony: organum|Medieval music's florid organum]].
| This interval approximates the Pythagorean Minor Third, and since this system does not temper out the syntonic comma, this interval- in contrast to the Ptolemaic Minor Third- is very useful as an interpretation of the dissonant Minor Third from [[Wikipedia: Medieval music #Early_polyphony: organum|Medieval music's florid organum]], and can thus be used in creating a subtle instability in certain Diatonic harmonies.
|-  
|-  
| 40
| 40
Line 593: Line 593:
| '''[[16/13]]'''
| '''[[16/13]]'''
| [[21/17]]
| [[21/17]]
| kkM3, RN3
| kkM3, RN3, kd4
| Lesser Submajor Third
| Lesser Submajor Third, Retroptolemaic Diminished Fourth
| Ft>/,  F#↓↓, Gb↓
| Ft>/,  F#↓↓, Gb↓
| As both the approximation of the octave-reduced thirteenth subharmonic, and ostensibly one of the easiest 13-limit thirds to utilize in chords framed by some type of sharp wolf fifth, this interval is used accordingly.
| As both the approximation of the octave-reduced thirteenth subharmonic, and ostensibly one of the easiest 13-limit thirds to utilize in chords framed by some type of sharp wolf fifth, this interval is used accordingly.
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| ?
| ?
| 68/55
| 68/55
| Kn3
| Kn3, Rkd4
| Greater Submajor Third
| Greater Submajor Third, Artoretromean Diminished Fourth
| Ft<↑, Gb↓/
| Ft<↑, Gb↓/
| In addition to its properties as a type of submajor third, this interval is also one third of a Pythagorean Major Seventh in this system and is thus used accordingly.
| In addition to its properties as a type of submajor third, this interval is also one third of a Pythagorean Major Seventh in this system and is thus used accordingly.
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| ?
| ?
| ?
| ?
|  
| rkM3, KN3, rd4
|  
| Narrow Major Third, Tendoretromean Diminished Fourth
|  
| 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.
|-
|-
| 51
| 51
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| ?
| ?
| ?
| ?
|  
| kM3, d4
|  
| Ptolemaic Major Third, Pythagorean Diminished Fourth
|  
| Gb, F#↓
|  
| This interval is none other than the approximation of the octave-reduced fifth harmonic- that is, the traditional 5-limit major third- and thus, it one of four imperfect consonances in this system, and, unsurprisingly, is used accordingly; however, this interval is also the approximation of the Pythagorean Diminished Fourth in this system, which sometimes leads to interesting enharmonic substitutions when building chords for purposes of voice-leading.
|-
|-
| 52
| 52
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| ?
| ?
| [[64/51]]
| [[64/51]]
|  
| RkM3, Rd4
|  
| Artomean Major Third, Artomean Diminished Fourth
|  
| 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.
|-
|-
| 53
| 53
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| ?
| ?
| ?
| ?
|  
| rM3, rKd4
|  
| Tendomean Major Third, Tendomean Diminished Fourth
|  
| 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.
|-
|-
| 54
| 54
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| ?
| ?
| ?
| ?
|  
| M3, Kd4
|  
| Pythagorean Major Third, Ptolemaic Diminished Fourth
|  
| 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.
|-
|-
| 55
| 55
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| [[33/26]]
| [[33/26]]
| 108/85
| 108/85
|  
| RM3, kUd4
|  
| Wide Major Third, Lesser Super-Diminished Fourth
|  
| F#/, Gd<↓, Gb↑/
|  
| This interval is of particular interest because it is the approximation of the Neo-Gothic Major Third and is used accordingly; what's more, this interval has additional applications in Paradiatonic harmony, particularly when such harmony is found in what is otherwise the traditional Diatonic context of a Major key.
|-
|-
| 56
| 56
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