Intervals - Repost
So musical pitches are given letter names to distinguish between the different pitches, right? So when you talk about musical intervals you are counting the span of the letter names between each pitch, plus a word (major, minor, perfect, augmented, diminished) that describes something about the quality of the interval.
Perfect unison, prime, first. They all mean the same thing. Same note. Duh.
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The other easy one is the perfect octave. Easy to sing or play, hard to describe. Mathematically, the frequency doubles for an octave. A is 220hz and the A above it is 440hz. An octave is the same note but higher or lower. God just made it that way.
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A perfect 5th is an interval whose span is five notes, i.e. C to G. Count 'em C, D, E, F, G, that's five letters.
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A perfect 4th is an interval whose span is four notes, so C to F, that's C, D, E, F, yeah, four notes.
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These intervals are all called 'perfect.' Why? Well it has to do with the way they sound, and a little history. Early church musicians had some pretty strong opinions about the sounds of different intervals based on their consonance or dissonance. Consonant intervals are ones that sound stable, like they just go together. The dissonant intervals seem to clash and your ear wants to hear them resolve to a more stable, consonant interval. Another way of describing it, dissonant intervals have tension, while consonant intervals are more relaxed. So the church musicians called the unison, octave, 4th and 5th the perfect intervals, because they have the least dissonance and to them that meant holiness, purity, intervals that were suitable for praising God. That's why in early church music, like Gregorian chants, almost all the chords are made up of 5ths and 4ths.
Another thing about perfect intervals has to do with what happens when you invert them. Inversion just means that I take the bottom note and move it up one octave. So if my interval is C to G, a perfect 5th, and I move the C up an octave, I get G to C, which is a perfect 4th. Perfects always invert to perfects.
So the next interval, if you're thinking in terms of consonance anyway, is the 3rd. C to E, count the letters, C, D, E. C to E is a major 3rd. It's fairly stable, sounds nice, so it's a consonant interval. If you lower that top note a half step, C to Eb (remember that b is a flat) you get a minor 3rd. Still pretty stable but a little more dissonant than the major 3rd.
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If you invert that major 3rd you get E to C. Count the letters, E, F, G, A, B, C, that's six. So this is a 6th. If you listen to the quality of the interval, it's a little dissonant. So E to C is a minor 6th. And we've also just learned something about inverting major and minor intervals. If you invert a major, you get a minor, and if you invert a minor, you get a major. So C to Eb was our minor 3rd, inverted Eb to C is a major 6th.
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On to the 2nds. C to D, major 2nd. Invert it? D to C is a minor 7th. Take that D and lower it half a step, like so: C to Db? Minor 2nd. Db to C is a major 7th. Cool?
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That leaves one interval left. There's this nasty little mug that sits right in between the perfect 4th and the perfect 5th. It's called a tritone, or depending on the context an augmented 4th or a diminished 5th. It's pretty much the most dissonant interval in music without adding a third note. Definately hardest to sing.
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