Term for distinguishing dim/perfect/aug intervals from dim/min/maj/aug ones?

Question

There are two types of intervals, distinguished by their possible qualities: - Unisons, fourths, fifths, and octaves (and their compound variants) may be of perfect or (multiply) diminished/augmented quality - Seconds, thirds, sixths, and sevenths (and their compound variants) may be of minor, major, or (multiply) diminished/augmented quality Is there an established term for distinguishing these two categories? Something like "a fifth is a *foobarian* interval, so its quality cannot be minor". If there is no established term, what would be a good choice? ^{Background: I'm writing some music software and this distinction comes up a lot in my code so I'd like to use the appropriate terminology.}

Answer 1

You can track the distinction if you look at the harmonic (aka overtone) series. If you look at the second and third partials – the lowest ones above the first partial (or fundamental) – they give us the fifth and octave (and the interval of a fourth between the fifth and the octave formed by the interval between the third and fourth partials). These are either perfect or not, and they were the first intervals used as European harmony developed. Raise or lower them and you lose stability, hence their designations as perfect (stable), and either diminished (lowered) or augmented (raised), both unstable.

Major and minor thirds, generated higher up the harmonic series by the fourth and fifth partial (major) and between the fifth and sixth partial (minor), were both originally considered dissonances. And they either don't lose stability (the major third) or do so only minimally (the minor third, but only in the context of a minor triad, where it conflicts with the naturally major third in the harmonic series of the root note) and can be raised or lowered as desired. Hence their qualities of major and minor, as opposed to perfect or not-perfect.

Answer 2

I think the root of this lies in tuning of acoustically "pure" fifths (and octave) above a tone. The fourth just tuning a fifth down, naturally.

I am not aware of a particular term that clusters them together, but your programming jargon might include "pure" intervals, I would suggest. :-)