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

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.

• I think the distinction in perfect and imperfect intervals is describing what you are looking for. The broader term of INTERVAL doesn't comprehend the difference. I'm not quite sure what you mean by foobarian. I looked it up in wiki but to me it doesn't make sence. Feb 15, 2019 at 10:28
• Don't think there will be separate terms. Unison, 4th, 5th and octave intervals are what they are. One semitone bigger, and they're aug., one smaller, they're dim. 4th and 5th are perfect in their normal state. That's it. You could say 'a fifth is perfect, so its quality cannot be minor'.
– Tim
Feb 15, 2019 at 10:36
• @AlbrechtHügli "foobarian" is a non-sense term I made up to illustrate the usage of the term I'm looking for. "foobar" is a common dummy-name in software development. And I know that I'm looking at the right distinction, but I'm not sure how to call it ;) Feb 15, 2019 at 11:05
• @Tim: But, in general, a fifth is not perfect -- it may very well be, say, augmented. So I can't just say "A fifth is perfect, ..." when talking about fifths in general. It's like talking about pitches vs. talking about pitch spaces. Feb 15, 2019 at 11:09
• In general fifths are perfect. In their natural (sic) state that's what they are. seven semitones gap. I know it's not the reason, but 4ths and 5ths are the same in both major and minor scales, and whilst they may be aug or dim, the vast majority are perfect.
– Tim
Feb 15, 2019 at 11:17

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.

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.

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.

• As I've written, I know that any interval can be diminished/augmented (possibly multiple times). But a unison/fourth/fifth/octave (and their compound variants) can never be minor or major, and a second/third/sixth/seventh (and their compound variants) can never be perfect. So any interval "class" (unison/second/third/...) either belongs to the category "can be perfect" or to the category "can be minor/major", and these categories are mutually exclusive. I'm looking for a name for these categories. Feb 15, 2019 at 12:57
• Indeed, apologies, I did't fully grasp your classification. If as it seems there's no term the 'bimodal' and 'unimodal' might be good candidates... Feb 15, 2019 at 13:14

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
• This answer is confusing. I've never heard anyone talk about a dominant family of scale degrees. On the other hand, there is a dominant family of chords, but this family consists of the V and VII chords. Do you have some reference or support for your terminology?
– user39614
May 4, 2019 at 12:34
• 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)`.