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159edo/Interval names and harmonies: Difference between revisions

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:* It differs from the Ptolemaic Minor Third in that...  
:* It differs from the Ptolemaic 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
* Is the closest approximation of 19edo's Minor Third found in this system, and thus...
* Is the closest approximation of 19edo's Minor 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
:* 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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* Approximates the [[135/112|Marvelous Minor Third]], and as such...
* Approximates the [[135/112|Marvelous Minor Third]], and as such...
:* Is the widest interval that can reasonably be used in Western-Classical-based harmony and Neo-Medieval harmony as a type of Minor Third
:* Is the widest interval that can reasonably be used in Western-Classical-based harmony and Neo-Medieval harmony as a type of Minor Third
* Is used in the formation of various strange-sounding triads, including...
* Is one half of this system's approximation of the Just Paraminor Fifth
:* A triad in which two of these add up to this system's approximation of the Just Paraminor Fifth
* Is one third of this system's approximation of the Neapolitan Augmented Sixth as a consequence of the [[hemimage comma]] being tempered out in this system
* Is one third of this system's approximation of the Neapolitan Augmented Sixth as a consequence of the [[hemimage comma]] being tempered out in this system
* Is the closest approximation of 22edo's Greater Minor 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
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| Lesser Supraminor Third, Infra-Diminished Fourth
| Lesser Supraminor Third, Infra-Diminished Fourth
| Ft>↓, Gdb>
| Ft>↓, Gdb>
| This interval is mainly of interest due to the fact that it's exactly twice the size of it's fourth complement- the approximation of the Undecimal Submajor Second- and its interesting properties as a type of supraminor third.
| This interval...
* Approximates the [[40/33|Undecimal Supraminor Third]], and thus...
:* It functions as the [[fourth complement]] to this system's approximation of the Undecimal Submajor Second
* Is one half of this system's approximation of the Undecimal Diminished Fifth
* Is one third of this system's approximation of the Pythagorean Minor Seventh
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| Greater Supraminor Third, Diretroptolemaic Diminished Fourth
| Greater Supraminor Third, Diretroptolemaic Diminished Fourth
| Ft<\, F↑↑, Gdb<↑\, Gb↓↓
| Ft<\, F↑↑, Gdb<↑\, Gb↓↓
| This interval is of interest because not only does it have 13-limit interpretations, but it also has usage as a 17-odd-limit interval, and all while being easily reached by stacking three Ptolemaic Minor Seconds.
| This interval...
* Approximates the [[39/32|Lesser Tridecimal Neutral Third]], and thus...
:* It serves as the [[fifth complement]] of the Octave-Reduced Thirteenth Subharmonic
* Approximates the [[17/14|Septendecimal Supraminor Third]], and thus...
:* Is very useful for essentially tempered chords such as [[273/272|tannic chords]]
* Is reachable through stacking three of this system's approximation of the Classic Minor Second
* Is found in 53edo as that system's Supraminor Third, and can thus be used to create identical-sounding melodic and harmonic gestures in this system
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