FKH Extended-diatonic Interval Names: Difference between revisions

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*The unison is labelled P1 for perfect unison, and the octave P8 for perfect octave.

*A tuning's best approximation to 3/2 is labelled P5, for perfect fifth, and it's octave-complement labelled P4, for perfect fourth.

*From the Pythagorean diatonic scale ~~using~~ a tuning's best 3/2 fifth, the two sizes of second, third, sixth and seventh are labelled major, or 'M', for the larger, and minor, or 'm' for the smaller.

*From the Pythagorean diatonic scale generated by a tuning's best 3/2 fifth, the two sizes of second, third, sixth and seventh are labelled major, or 'M', for the larger, and minor, or 'm' for the smaller.

*Any perfect or major interval raised by the apotome, the interval between the major and minor intervals of a single interval-class is labelled 'A' for augmented, and any perfect or minor interval lowered by the same is labelled 'd' for diminished.

*Any augmented interval may be made doubly augmented, with short-hand 'AA' by the further raising of an apotome and any diminished interval made doubly diminished, with short-hand 'dd' by the further lowering of an apotome. This process may be iterated ad nauseum. At this stage we have simply rigorously defined diatonic interval names. Thankfully what remains of the definition leads to more desirable alternatives for most occasions in which one might find these iteratively diminished and augmented intervals.

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 *The unison is labelled P1 for perfect unison, and the octave P8 for perfect octave.
 *A tuning's best approximation to 3/2 is labelled P5, for perfect fifth, and it's octave-complement labelled P4, for perfect fourth.
-*From the Pythagorean diatonic scale using a tuning's best 3/2 fifth, the two sizes of second, third, sixth and seventh are labelled major, or 'M', for the larger, and minor, or 'm' for the smaller.
+*From the Pythagorean diatonic scale generated by a tuning's best 3/2 fifth, the two sizes of second, third, sixth and seventh are labelled major, or 'M', for the larger, and minor, or 'm' for the smaller.
 *Any perfect or major interval raised by the apotome, the interval between the major and minor intervals of a single interval-class is labelled 'A' for augmented, and any perfect or minor interval lowered by the same is labelled 'd' for diminished.
 *Any augmented interval may be made doubly augmented, with short-hand 'AA' by the further raising of an apotome and any diminished interval made doubly diminished, with short-hand 'dd' by the further lowering of an apotome. This process may be iterated ad nauseum. At this stage we have simply rigorously defined diatonic interval names. Thankfully what remains of the definition leads to more desirable alternatives for most occasions in which one might find these iteratively diminished and augmented intervals.