159edo/Interval names and harmonies: Difference between revisions

Aura (talk | contribs)
Need to come up with more xen uses for none other than 12edo's major third...
Aura (talk | contribs)
Finally got to the Pythagorean Major Third...
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| [[121/96]]
| [[121/96]]
| ?
| ?
| ?
| [[34/27]]
| rM3, rKd4
| rM3, rKd4
| Tendomean Major Third, Tendomean Diminished Fourth
| Tendomean Major Third, Tendomean Diminished Fourth
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:* It is useful for evoking the feel of 12edo in various ways, such as...
:* It is useful for evoking the feel of 12edo in various ways, such as...
::* Creating the familiar augmented triads of 12edo
::* Creating the familiar augmented triads of 12edo
::* Being stacked with this system's approximation of the Quasi-Tempered Minor Third to make chords similar in sound to those of 12edo
::* Performing modulatory maneuvers based around the aforementioned triads
::* Performing modulatory maneuvers based around the aforementioned chords
* Is very useful for [[essentially tempered chord]]s such as [[palingenetic chords]], and, oddly...
:* It just so happens that stacking this interval with this system's approximation of the Quasi-Tempered Minor Third makes triads of just this sort in the [[27-odd-limit]]
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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 in building oddly-charming augmented triads.
| This interval...
* Approximates the [[81/64|Pythagorean Major Third]], and as such...
:* Is a viable option in both melodic and harmonic motion in general, and in particular...
::* It is a useful interval in Western-Classical-based Diatonic scales
:* Can easily occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony
:* It differs from the Ptolemaic Minor Third in that...
::* It is very useful as an interpretation of the dissonant Major Third from Medieval music's florid organum  
::* It can be used in creating a subtle instability in certain Diatonic harmonies
* Is one half of this system's approximation of the Classic Minor Sixth as a consequence of the schisma being tempered out in this system, which...
:* Leads to this interval being useful in forming oddly charming augmented triads
* Moving up by seven of these with two octave-reductions is an unexpected alternative means for exploiting the frameshift comma, though this system's approximation of the Axirabian Limma remains essential to the process even in this case
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| [[192/121]]
| [[192/121]]
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