In this brief lecture, J. Anthony Allen reviews the core concepts of musical intervals covered up to this point and sets the stage for exploring more unusual, non‑diatonic intervals. He distinguishes melodic intervals (sequential notes) from harmonic intervals (simultaneous notes), defines simple intervals (under an octave) and compound intervals (over an octave, up to thirteenths, common in jazz). He explains inversion rules: major ↔ minor, perfect ↔ perfect, and that the original and inverted interval numbers always sum to nine (e.g., 6 ↔ 3, 5 ↔ 4, 2 ↔ 7, octave ↔ unison). After summarizing these fundamentals, he previews the next topic—non‑diatonic intervals that occur outside a key, such as altered perfect fifths, which have special names and properties.
Chapters
Okay, let's do a quick summary of what we know so far about intervals, because after this I'm going to add some new intervals to your plate and they're going to make you scratch your head kind of weird, because they are kind of weird. So, quick summary. Here's what we know. We know the difference between melodic and harmonic intervals. Melodic intervals happen sequentially, note after note. Harmonic intervals happen at the same time. Simple and compound intervals. I don't think I mentioned simple intervals, but that's what we've been working with. Simple interval is anything smaller than an octave. Compound interval is anything bigger than an octave. So ninths, tenths, elevenths, twelfths, you can get up to thirteenths. You don't really see usually anything bigger than a 13th. But jazz people like thirteenths quite a bit. Jimi Hendrix like thirteenths a bit, things like that. And then my points for inversion. A major inverts to a minor. A minor inverts to a major. A, A perfect inverts to a perfect. And whenever you invert a number, the old number and the new number have to equal nine. So a six inverts to a third, a fifth inverts to a fourth, a third, a fourth inverts to a fifth, a third inverts to a six, a second inverts to a seventh, and a octave inverts to a unison, which the number for unison is one. So. So eight plus one equals nine. Okay, so that's just a quick summary of what we've kind of done with intervals so far. Next we're going to get into some non diatonic intervals. Remember, diatonic means in key. We're going to start looking at some intervals that can happen when we're outside of a key. Such as? Like, what happens if we make our perfect fifth imperfect? You know what if we mess with it? We can. It's possible and it has a special name and some special properties. So let's start looking at some of those non diatonic intervals in the next section here.
