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159edo/Interval names and harmonies: Difference between revisions

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Finished the section between Minor and Major Thirds...
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Finally covered the Classic Major Third...
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::* It is a staple interval in Western-Classical-based Diatonic scales
::* It is a staple interval in Western-Classical-based Diatonic scales
:* Readily occurs as the distance between two notes in a single chord in Western-Classical-based polypedal harmony
:* Readily occurs 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 differs from the Pythagorean Minor Third in that...  
::* It is one of four perfect consonances in this system, rendering it extremely suitable for use in a Tonic triad in Western-Classical-based polypedal harmony
::* It is one of four perfect consonances in this system, rendering it extremely suitable for use in a Tonic triad in Western-Classical-based polypedal harmony
* Is reachable through stacking three of this system's approximation of the Octave-Reduced Seventeenth Harmonic
* Is reachable through stacking three of this system's approximation of the Octave-Reduced Seventeenth Harmonic
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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, thus facilitating the formation of strange-sounding triads.
| This interval...
* Approximates the [[56/45|Marvelous Major Third]], and as such...
:* Is the narrowest interval that can reasonably be used in Western-Classical-based harmony and Neo-Medieval harmony as a type of Major Third
* Is one half of this system's approximation of the Just Paramajor Fifth
* Is the closest approximation of 16edo's Major Third 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 the closest approximation of 19edo's Major Third found in this system, and thus...
:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, since such moves on their own don't work the exact same way in this system
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| Ptolemaic Major Third, Pythagorean Diminished Fourth
| Ptolemaic Major Third, Pythagorean Diminished Fourth
| Gb, F#↓
| 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.
| This interval...
* Approximates the [[5/4|Classic Major Third]] or Octave-Reduced Fifth Harmonic, and as such...
:* Is one of the staples of both melodic and harmonic motion in general, and in particular...
::* It is a staple interval in Western-Classical-based Diatonic scales
:* Readily occurs as the distance between two notes in a single chord in Western-Classical-based polypedal harmony
:* It differs from the Pythagorean Major Third in that...
::* It is one of four perfect consonances in this system, rendering it extremely suitable for use in a Tonic triad in Western-Classical-based polypedal harmony
* Approximates the [[8192/6561|Pythagorean Diminished Fourth]], and as such...
:* Serves as an enharmonic substitution for the Classic Major Third when building chords for purposes of voice-leading, in which case it counts as an unresolved interval
* Is the closest approximation of 22edo's Lesser Major Third 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 such moves on their own don't work the exact same way in this system
* Is the closest approximation of 31edo's Major Third 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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