Music Theory/Fundamentals of Common Practice Music/Pitch

The interactions of various pitches are what allow music to be meaningfully interpreted by the human ear.

The Overtone Series

The pitch of sound is measured in Hz (Hertz), which is the number of vibrations per second. Young adults can generally hear from 20Hz-20,000Hz, while older people lose the top part of that range.

When instruments vibrate, they do so at specific intervals, usually at multiples of a whole number. For example, 55Hz, 110Hz, 165Hz, 220Hz, etc (which can be heard here)

Intervals

An interval is the measure of distance between two notes in pitch and in the chromatic scale. The chromatic scale is easy to play on the piano - just play every note, including black keys. It is best to print this page out so that the examples can be played on a piano or keyboard. Or, use the virtual keyboard at [1] /link desn't work/ here's other virtual keyboard [2]

1. Perfect Unison - two notes, equal in pitch (0 half steps apart).
2. Minor Second - two notes, 1 half step apart. e.g. C and D flat/C sharp
3. Major Second - two notes, 2 half steps apart. They are a whole step apart. e.g. C and D
4. Minor Third - two notes, 3 half steps apart. e.g. C and E flat/D sharp
5. Major Third - two notes, 4 half steps apart. e.g. C and E
6. Perfect Fourth - two notes, 5 half steps apart. e.g. C and F
7. Augmented Fourth/Diminished Fifth - two notes, 6 half steps apart. This interval is also known as a Tritone because the notes are also 3 whole-tones/steps apart. e.g. C and F sharp/G flat
8. Perfect Fifth - two notes, 7 half steps apart. e.g. C and G
9. Minor Sixth - two notes, 8 half steps apart. e.g. C and G sharp/A flat
10. Major Sixth - two notes, 9 half steps apart. e.g. C and A
11. Minor Seventh - two notes, 10 half steps apart. e.g. C and A sharp/B flat
12. Major Seventh - two notes, 11 half steps apart. e.g. C and B
13. Perfect Octave two notes, of the same pitch class, one octave apart (12 half steps apart). e.g. C and the next highest C

Note that there are 12 different pitch classes within an octave (the octave is generally not counted because it is the same pitch class as the pitch used as the base for interval measurement, 12 half steps below/above it). This is equivalent to saying that the chromatic scale has 12 pitches with the octave being a repeat of the starting pitch.

Consonance/Dissonance

Consonance is a measure of harmony or lack thereof. There are many definitions, some of which are subjective. In historic Europe, the augmented fourth/diminished fifth was said to be the "Devil in music"! In general, consonant intervals include the octave, perfect fourth, and perfect fifth.