Tuesday, October 13, 2009

Intervals in music

Second, third, fourth, fifth... sounds kinda like people are waiting in line. But actually we're talking about intervals, which means pairs of notes and their pitch relationship to each other.

If you're an experienced musician, you know this stuff backwards and forwards, and you can skip this post. If you're a beginner, this part of musical terminology takes a bit of explaining, and you should read on.

There's no way to talk about the specifics of music without using metaphors. We say that one pitch is higher than another, but pitch is a metaphor, and so is higher.

A sound is actually a vibration in the air. In a timescale of thousands of a second, some sounds have a regular, repeating waveform, which we hear as a musical tone. A regular waveform has a frequency, which we define as the number of cycles per second. Another word for cycles per second is hertz, abbreviated Hz. Our ears are especially attuned to repeating waveforms, and we hear the frequency as musical pitch.

The A below middle C is traditionally defined as a musical tone with a frequency of 440 Hertz. That means the waveform of the A note has a cycle that repeats 440 times per second.

If a frequency has a higher number, we hear it as a higher pitch. A tone of 880 Hz has a frequency twice as high as the A at 440 Hz. We hear the 880 Hz tone as another A tone, exactly one octave higher that the 440 Hz tone. Twice the frequency equals an interval of one octave.

Our musical system is based on dividing the octave into 12 equal parts. Each 1/12 of an octave is called a half-step or semitone. Musical intervals are defined as the number of semitones you have to travel to get from the first note to the second note. (This is easiest to see on a piano keyboard or a guitar fretboard, where the semitones are clearly marked off.)

If two notes are at the same pitch, the distance is 0 semitones, and the interval is called unison. (For shorthand, unison can be abbreviated P1).
1 semitone is called a half-step or a minor second, abbreviated m2.
2 semitones is called a full-step or a major second, abbreviated M2. (Capital M for major, small m for minor.)
3 semitones is a minor third (m3).
4 semitones is a major third (M3).
5 semitones is a perfect fourth (P4)
6 semitones (half an octave) is an augmented fourth or diminished fifth (A4/d5).
7 semitones is a perfect fifth (P5).
8 semitones is a minor sixth (m6).
9 semitones is a major sixth (M6).
10 semitones is a minor seventh (m7).
11 semitones is a major seventh (M7).
12 semitones is an octave (P8).

The names of these intervals might make more sense if you think about the notes that make up the major and minor scales, and each note's interval to the keynote (the first note) of the scale.

The major scale contains P1, M2, M3, P4, P5, M6, M7.
The minor scale contains P1, M2, m3, P4, P5, m6, m7.

With the sole exception of the M2 in the minor scale, you can see that the major scale contains all the major version of the intervals, and the minor scale contains the minor versions of the intervals.

With this handy vocabulary of intervals, we can also describe the different kinds of chords as the intervals between each note in the chord and the chord's root. So far we've talked mainly about major and minor chords.

The major chord contains P1, M3, and P5.
The minor chord contains P1, m3, and P5.

If you are new to reading music, this vocabulary of musical intervals might seem like a whole lot of details to try to learn. Don't worry! Like everything else in music, it just requires practice.

Tuesday is Beastly Fundamentals Day.

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