I am looking for some piano instruction books and I was reading the first pages of the Alfred Adult All-in-One Course vol. 1, they are available on Google Books.
The book defines a second interval as "the distance from any white key to the next white key, up or down" and a third interval "when you skip a white key" (p.25). Although they are not considering major and minor, those definitions sounds good, perhaps incomplete.
The problem arises when they define a fourth "when you skip 2 white keys" (p.29). It sounds very weird to me and, moreover, the first example is "F B". I know "F B" is an augmented fourth but perhaps it should be better to explain intervals on halftones as usual, I don't know if an explanation based on "white keys" is enough or they are hiding important issues for the future.
BTW it is a very basic concept and I already know it but I am afraid the rest of the book includes similar oversimplified explanations.
It is incomplete, and inaccurate in some situations.
Interval names depend on what you call the notes. When they say a fourth skips two white keys, that can be dead wrong - that F to B interval can also be a second, a third, a fifth or a sixth. What you CALL those notes matters:
Gbb to Ax is a second
Gbb to B is a third
F to B is a fourth
F to Cb is a fifth
E# to Cb is a sixth
All of those skip over exactly two white keys, and all of them sound exactly the same.
All intervals have two parts to their name: one is based on letter distance, the other on sound quality compared to the major scales. The distance part simply counts letters, ignoring all accidentals. Then we apply the quality rules:
If BOTH notes are in the major scale of the other, the interval is perfect. This can only happen when the letters are the same (unisons or octaves) or when they are a fourth or fifth apart.
If the UPPER note is in the major scale of the lower, but the reverse isn't true, it's a major interval.
If the LOWER note is in the key of the upper, but the reverse isn't true, it's a minor interval. (another way to look at this is that it's one half step smaller than a major interval)
If it is one half step smaller than a minor or perfect interval, it's diminished.
If it is one half step larger than a major or perfect interval, it's augmented.
If it's one half step smaller than a diminished interval, it's doubly-diminished; one half step larger than an augmented interval is doubly-augmented.
You can, in theory, make intervals triply or quadruply altered (like the Gbb to Ax example). In practice I've never seen them.
The reason the letter names are so important is because of temperament history - at one point in time, F# and Gb were different sounds. So C to F# was an augmented fourth, and that sounded different from C-Gb, a diminished fifth. Even though that hasn't been the case for about five centuries or so, the theory remains the same.
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Perfect! Thank you very much.
I didn't know the important part is what you call the notes, it explains many things to me. For example, I never understood why were used several names for the same (sounded?) interval: F to Bb is a perfect fourth and F to A# is an augmented third. They are (or were) different intervals.
Intervals are just the distances between notes in a 7 note scale. Anything that says otherwise is not really using them the right way.
That's Not true, or at least it's not complete.
The distance between C and E can be a third or a tenth. Intervals larger than an octave are called "compound intervals", and are often - but not always - reduced to place both pitches within a seven note scale. But there are exceptions, particularly for ninths and tenths, and particularly in arranging vocal music for choirs. Understanding intervals larger than an octave is also the theoretical foundation of extended chords, like 11ths and 13ths - even if they're not actually voiced according to theory.
It's useful in many situations to simplify things to understand them. But it's also dangerous to think of the simplification as the whole picture.
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