Enharmonically equivalent Interval usage

Question

So I was thinking, similar to sharp and flat notes, interval usage is contextual. In the same way that Bb is the same as A#, a diminished fifth is the same as an augmented fourth, etc. I understand when you would use flats or sharps, but I am a little more confused on intervallic values.

I understand how they would work in a scale: if the note is the fifth degree of the scale and a tritone above the root, then you would clearly refer to it as a diminished fifth rather than an augmented forth; but what happens when there is no scale to base the intervals upon? Does it even matter?

Answer 1

Letter names.Count from whatever letter is underneath.This is why there are two or three different names for the same sounding interval.Where the notes are written on a stave will dictate the naming.So, I suppose you could say that the bottom note of an interval can be regarded as the root note of its scale, and the upper note will be determined from that standpoint.It's theory that tries to explain what is happening.Rules are made, and then have to be adhered to as best as possible. Just playing two notes and asking what the interval is will never work, as much as hearing a note D#/Eb, and being able to say which it is. (equal !)You need to know parameters like what key are we in.

Answer 2

I usually think of it contextually, and try to make my choices based on the harmony I want to imply.

In a C diminished chord, you'd call the note at the diminished fifth Gb because it's derived that way—a diminished triad is two major thirds, which add up to a diminished fifth, and that's that.

On the other hand, a Cmaj7#11 chord comes by that same interval a different way. It's derived from the Lydian mode, in which the fourth is augmented. So, in that case, I'd call the note F#.

In the same sort of vein, I could indicate a dominant chord as G7b5, or G7#11. Identical, at first glance, but when I use the 7b5 notation, I'm asking for a whole tone sound or perhaps an altered scale sound (though my preference is to notate that G7alt instead), whereas when I use the 7#11 notation, I'm asking instead for a Lydian Dominant sort of sound. The choice really depends on the parent scale of the chord and the function of that interval in the chord.

Answer 3

There are two important "out of context" (i.e., outside of a scale) uses for intervals:

1. Basic ear training. When students learn to identify intervals by ear, there's a general tendency to give intervals without context and only to use perfect, major, and minor intervals. For example, students would be tested on minor thirds but not augmented seconds. Tritones are the exception, and generally either "augmented fourth" or "diminished fifth" is an acceptable answer. And of course, if tests are "in context", then differentiating minor thirds and augmented seconds (for example) would be expected.

2. Serial music. The whole reason serialism came into being (in the form of 12-tone music) was to remove the context from intervals and have them function in a "pure" way. For that reason, spelling is a matter of convenience, and interval naming is done numerically: 3 designates both a minor third and augmented second, regardless of their use; 6 designates both an augmented fourth and a diminished fifth.