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

I’ve run into this exact issue before with my own software. I never found the term you’re looking for.

I made up my own term in code, a property of interval number data called IsPerfectable, which was a Boolean value based on (IntervalNumber - 1) % 7 where results of 0, 3, and 4 were True and the others were False.

In the user output, I changed the terminology back into terms normally understood in music, like “A third must be major, minor, diminished, or augmented,” or “Sorry, but a perfect third is invalid.”

Edit: For non-software folks reading this, % is a modulus operator. It's a type of division which gives you a remainder instead of a quotient.

Answer 2

The distinction is roughly about tonal versus modal scale degrees. I say 'roughly' because the supertonic has an ambiguous role...

Revisiting Music Theory: A Guide to the Practice, by Alfred Blatter (Curtis Institute)

So tonal degree are describe as perfect, modal as major/minor, either can be diminished or augmented.

Answer 3

I think your assumption that the two types are mutually exclusive sets and therefore can be labelled as 'something' is not entirely correct.

You can have augmented second, augmented sixth and, hell even third, and so on - it all depends on the musical context or even particular analysis or notation.

That's probably why such label was not yet invented.

Answer 4

Considering the names of the Degrees, I would argue that, except for the tonic, which is your reference, thus by definition perfect, all dominants are also perfect.

The best term I can think of is IsMemberOfDominantFamily which would entail the tonic (1), the dominant (5) and the sub dominant (4).

• tonic perfect
• super tonic
• mediant
• sub dominant perfect
• dominant perfect
• sub mediant
• leading tone

Answer 5

• The term encompassing unisons, fourths, fifths, and octaves (and their compounds) is perfect intervals.

• The term encompassing seconds, thirds, sixths, and sevenths (and their compounds) is imperfect intervals.

A source of confusion is the perfect has two different usages: as an interval quality and as an interval class. This dual usage means one can say that "the class of perfect intervals comprises those intervals which can have the quality of being perfect."

Taking the statement from the question:

a fifth is a foobarian interval, so its quality cannot be minor

it would be more clear to say:

a fifth can be perfect, so its quality cannot be minor

or

the perfect intervals include fifths, so a fifth cannot be minor

For the purposes of computer code, just make sure the naming scheme reflects the distinction: for example, isInPerfectClass(interval) and hasPerfectSize(interval).