User:VectorGraphics/Vector's introduction to 15edo/Temperaments
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The "intervals" section describes the intervals that 15edo uses. This section describes the relationships between intervals. All descriptions here will be "octave-reduced" - that is, "returns you to the root" may mean "returns you to a note some number of octaves above the root". Each tuning has a different combination of temperaments, and the ones here are different from the ones you get when using 12edo.
A note about nomenclature: several of the equivalences described here come from the same underlying "regular temperament", which is why the same name is listed twice in some cases, but for transparency I've listed them separately.
The fundamentals
- Blackwood: Stacking 5 fifths returns you to the root.
- Augmented: Stacking 3 major thirds returns you to the root.
- Porcupine: The intervals between the wolf and minor thirds, and between the minor and major thirds, are the same interval. In other words, you only need 1 set of accidentals to notate 15edo's diatonic scale, while in other tunings like 34edo you'd need two.
Other curiosities
- Valentine: The large whole-tone is found at 3 chromatic scale steps, the major third at 5, and the perfect fifth at 9.
- Porcupine: The minor third can be split into two equal intervals, while the major third cannot.
- Semaphore: Stacking two large whole-tones gives you a perfect fourth.
- Slendric: Stacking three large whole-tones gives you a perfect fifth.
- Blackwood: The perfect fourth is, consequently, 2/3 of a perfect fifth.
- Blackwood: The octave is split into five parts; the perfect fifth is found at the third.
- Cloudy: Each of the five parts is also a large whole tone; large whole tones close the octave.
- Kleismic: By stacking six minor thirds, you reach the perfect fifth.
- Augmented: By stacking two major thirds, you get a minor sixth.
- Augmented: The diatonic and chromatic semitones are the same size.
- Archy: By stacking two perfect fourths, you get a harmonic seventh.
- Keegic: By stacking three large tritones, you get a perfect fifth.
- Paralimmic: By stacking three large tritones, you get a perfect fifth.
- Trust me, the RTT gods say these are different things for some reason