Allen's Master Theory Help & Hints
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Lessons 75-80: Intervals
This series of lessons is divided into three related pairs. Lessons 75 & 76 deal with major and perfect intervals, and are related to the major scale. Lessons 77 & 78 deal with minor and perfect intervals, and are related to the minor scale. Lessons 79 & 80 deal with diminished and augmented intervals, and are probably the thorniest lessons in Book 3.
When working on intervals, it would be good to review a few hard and fast rules:
1. The best way to determine an interval is to start with the bottom note. Start an imaginary scale based on this note, and count the intervals all the way up to the next note. The key signature of the piece is only used to determine the bottom and top note. When you start counting up to find your interval, you are building a major scale based on the bottom note and independent of the piece's key signature.
2. All intervals are numbered for the relative position of the notes on the staff. For example, A# and Bb are the same note, but the interval from E up to A# is an augmented fourth, and from E up to Bb is a diminished fifth. Any E up to any A is always a fourth. Any E up to any B is always a fifth. Modifiers like major, minor, perfect, diminished or augmented are needed to complete the interval name.
3. All primes, octaves, fourths and fifths are perfect, augmented or diminished. They are never major or minor.
4. All 2nds, 3rds, 6ths and 7ths are major or minor initially. A half-step larger than major is augmented, and a half-step smaller than minor is diminished.
This is tedious! Why am I learning all these intervals?
Because intervals have to be understood in order to deal with chords and harmony. Much of this will seem like nonsensical hair-splitting, but the spelling of chords is very important in the writing of piano music and of condensed scores for music groups.
What's with all these double sharps and double flats!? Why not just use a natural note?
This, again is a matter of spelling. Chord tones need to be written so that they stack up vertically in thirds, and involve as few accidentals as possible. In extremely sharp or flat keys, this can be very difficult. Melody writing is also affected. Singers who read music depend on the notes to go up and down with the melody as much as possible. If you're in the key of Db and you want to rise a half-step from Gb, it seems only logical to write G-natural. But, what if you're going right back to Gb? That sequence of Gb-G-Gb just looks like three G's in a row. The first has no accidentals (it's in the key signature) the second has a natural sign, and the third must have a flat sign to cancel out the previous natural. For many singers, this looks like the same three notes, each with different gibberish attached. Now, what if we use Abb instead of G natural? The sequence is now Gb-Abb-Gb, but with two advantages. First, the notes now go up and down on the page. Second, you don't have to draw an accidental for the second Gb. It now looks just like the first one.
Common Snag #1 - There are no minor fourths, fifths, primes or octaves. Remember rules 3 and 4 from above.
Common Snag #2 - Now that we have double sharps and double flats to contend with, each note of an interval can have up to five different pitches. Sometimes that interval can be smaller than diminished or larger than augmented. If E to A is a fourth, then Eb to A is an augmented fourth. What happens when it's Eb to A#? It's a doubly augmented fourth. By the same token, E to Ab is a diminished fourth. What if you have an E# to A--or an E to Abb? A doubly diminished fourth. Heaven help us, but it can get to this point. The book does not mention this, but there are examples of it in Lesson 79.
Common Snag #3 - Don't express intervals with an enharmonic value. E to Ab is a diminished fourth, even though in the world of real sound it is obviously a major third. Don't make these kinds of substitutions. Just stick to the rules. It does matter. Just live with it. You'll see why later on.
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