Intro to theory

This is the first lesson in a series on music theory. This lesson and others can be found at

Music Theory is the part of music that is used for the comprehension, analysis, and synthesis of music.

We will start with sound.
Sound is a wave phenomena that is created from a vibrating object. The object vibrates producing waves, that are carried through the air to some sort of reciever (such as your ears), which then converts the waves into the experience of sound.

We can see sound as having qualities relating to time and space.

We will briefly discuss 4 qualities of sound, namely: pitch, intensity, duration, and timbre.

Pitch is the highness or lowness of a sound. The pitch is related to the frequency of a soundwave.

The frequency of a wave is the number of cycles per unit time. ( A cycle is the distance from a waves crest to crest or trough to trough).

The standard frequency measurement we will use will be the hertz (Hz).
The hertz is defined as 1 cycle per second.
1Hz = 1cycle/second.

For example: A = 440Hz is a tone (pitch) that most western musicians tune to (from which the other pitches/tones are created). 440Hz means that 440cycles pass through an arbitrary given point within one second.

Given two pitches of different frequencies, we can describe the distance between them (called an interval), and the relative highness or lowness of the pitches. The pitch with the higher frequency is said to be higher or sharper. The pitch with the lower frequency is said to be lower or flatter.

Intervals (the distance between two pitches) can be classified by ratios of their frequecies.

The ratio of 2:1 defines an octave.
A = 220Hz and A = 440Hz are octaves of each other.

The word toned is often used instead of pitch to refer to the pitch or frequency of a sound (or even a set of pitches).

Another quality of sound is intensity. The intensity of a sound is related to the loudness of the sound. The loudness and intensity are related to the energy in a wave, and the waves amplitude. The greater the energy (and thus the amplitude of the waveform), the greater the intensity of the sound (the louder the sound).

An exercise:
1.) lightly tap on a surface.
2.) heavily knock on a surface.
3.) ask yourself:
a.) which one was louder?
b.) whcih one took more energy?

Duration is the quality of sound having to do with time and rhythm.
Duration refers to amount of time that a sound lasts.

Rhythm is the element of music dealing with patterns of duration.

Question: Is it necessary for there to be a sound in order for there to be rhythm?

The last quality of sound we'll briefly consider is the timbre. The timbre (pronounced Tam-buhr), is also called the tone quality or the tone color, and is the quality produced by the particular sound source.

So sounds produced by different sources (wood, steel, brass, glass, etc.) sound different because most sounds are produced by a combination of pitches called partials, or harmonics. Partials or harmonics are created by vibrations of fractions of the sounding body as well as the entire body itself. The number, intensity, and distribution of these partials is largely responsible for the sound's timbre.

The combination of simultaneous pitches generated from a fundamental (pitch) of a tone is called the harmonic series, these pitches determine the timbre of the sound.

The lowest harmonic in the harmonic series is called the fundamental.
All higher harmonics can be refered to as overtones (or just harmonics).

Below are the first 16 harmonics of the harmonic series.

Partial#  ratio	 name
1	  1:1    Fundamental (also unison)
2	  2:1    Octave  
3	  3:2    Perfect 5th
4	  4:2    Octave
5	  5:4    Major 3rd
6	  6:4    Perfect 5th
7         7:4    Minor 7th
8	  8:4    Octaves
9	  9:8    Major 2nd (major tone) 
10	  10:8   Major 3rd
11        11:8   Tritone
12        12:8   Perfect 5th
13	  13:8   Major 6th
14	  14:8   Minor 7th
15	  15:8   Major 7th
16	  16:8   Octave

note: partials 1-2 occur between 1st octave, 2-4 occur between 2nd octave, 4-8 occur between 3rd octave, and 8-16 occur between 4th octave, etc.

Nowadays we in the western world typically use a tempered tuning system so that when we tune our notes (such as tuning strings, or boring holes, etc.) they don't actually correspond with these intervals. More on this at an appropriate time; however these are the partials being created from a vibrating object (and more above this).

note: the typical human ear can hear a spectrum between the range of 20Hz to 20kHz.

if A = 440Hz. Six octaves up is A = 28160Hz out of the hearing range.
(5th octave is A = 14080 is in the hearing range)
Although an infinite number of harmonics are theoretically possible.

next lesson is on pitch notation.

Christopher Roberts

How do I change all those numbers to letters (for notes, chords, etc.)? Here's a transposition chart

Back to theory index
Next lesson - Notating pitch

Last updated January 23, 2003
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