If you like to go to the root of musical terms, then this one's for you.
In a recent post on the WL forum, a member asked the following question:
"Hofnarr" asked: "Why is a perfect fourth or a perfect fifth called "perfect?" Why isn't a major third called "perfect third?", or likewise, a major sixth "perfect sixth," etc.?"
Our theory expert Charlton answered:
Like a lot of things in music, the naming followed the usage, and the theory was an effort to name and categorize what people were already doing.
First off, the number refers to the number of notes making up the interval. So, for example, any interval involving an A note up to a C note is a third (A, B, C). Any interval involving an F up to a D is a sixth (F, G, A, B, C, D). This is true no matter whether the notes are sharp, flat, double-sharp, double-flat, natural, or whatever. This is important to remember, and later on I'll point out what sorts of mistakes you can make later (and how composers disregard this at will!).
So, we're looking at what people actually do, so we'll start with the C major scale, and all the intervals we find there. I'm going to avoid using "major," "minor," "perfect," and the like, and count half-steps. This is not something I recommend doing if you're trying to recognize intervals -- more on that in a bit -- but it's useful for explaining why we use the other terms.
First, we look at all the seconds. There are two kinds: some are a half-step wide, and others are a whole step wide. The half-steps are E-F and B-C, and the whole steps are C-D, D-E, F-G, G-A, A-B.
Next, thirds. There are also two kinds: some are three half-steps wide, and others are four half-steps wide. The three half-steps are D-F, E-G, A-C, B-D, and the four half-steps are C-E, F-A, G-B.
Fourths. Again, two kinds: 5 and 6 half steps. 5 half-steps are C-F, D-G, E-A, G-C, A-D, B-E; 6 half-steps are F-B.
Fifths. Again, two kinds: 6 and 7 half-steps. 6 half-steps are B-F; 7 half-steps are C-G, D-A, E-B, F-C, G-D, A-E.
Sixths. Two kinds: 8 and 9 half-steps. 8 half steps are E-C, A-F, B-G; 9 half steps are C-A, D-B, F-D, G-E.
Sevenths. Two kinds: 10 and 11 half-steps. 10 half-steps are D-C, E-D, G-F, A-G, B-A; 11 half-steps are C-B and F-E.
So, if all the intervals of a certain type that we can find in the major scale are the same size except for one, we call that size perfect and the other size augmented (if it's larger than the perfect interval) or diminished (if it's smaller). If the intervals are a mix of two types, we call them major (for the larger version) and minor (for the smaller version).
Now, I promised to explain why counting half-steps is dangerous (or at least likely to get you marked down on theory exams, and likely to confuse any other musicians you're working with). Two intervals that are different can have the same number of half-steps in them, and so if you only count half-steps you're going to come up with the wrong answer as soon as you start running into interesting cases.
Consider a diminished seventh chord, the notes B D F A-flat. If you count half-steps, you can see that the interval from B to A-flat has 9 half-steps in it. 9 half steps is a major sixth, right? That's what we figured out above! Except that, well, B to A-flat is a seventh because it encompasses seven note names. And the diminished seventh chord is a particularly useful example because the way you write it indicates how you expect it to resolve: a B diminished seventh chord (B D F A-flat) should resolve to some sort of C chord, and a D diminished seventh chord (D F A-flat C-flat) wants to resolve to some sort of E-flat chord, even though if you play them on the piano, you hit the same keys. It's the same set of notes, but how you write it communicates to the musicians what its function is.
There's also the special exception, near and dear to my heart, of other tuning systems: the reason I said "if you play them on the piano, you hit the same keys," and not "they are the same notes." In many tuning systems, especially ones used in early music, two notes that are the same key on the piano are actually different notes in performance. The term for this is enharmonic -- C-flat and B are not the same note, but they are enharmonic with each other.
(Another reason to not approach this by counting half-steps is that it takes a LOT longer to work out how many half steps there are than to recognize an interval by sight, and this is the sort of thing that practicing musicians need to do fluently -- at least the ones interested in communicating with other musicians!)
And now, as promised, an example of how composers violate this, and it's one of my favorites.
One of the things Schubert experimented with was sonata form. Traditionally, sonatas are written with one theme in the key of the piece and another theme in a closely related key. But in his great Sonata in B-flat, Schubert threw in a substantial theme in a third key. So the first theme of that sonata is in B-flat major, and so because it's in major, you expect the second theme to be in F major. But Schubert interrupts the route there with a substantial theme, but it's still closely related -- it's an interruption in G flat minor. But any pianist will tell you that G flat minor is a chore to play in - six flats and a double flat to keep track of! So Schubert notated it in F sharp minor instead -- because, after all, on the piano, you can't tell the difference between F sharp and G flat. Confuse the theorists, but make things easier on the performer!
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