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Home | Music Theory | Frequency and pitch

Music Theory - Frequency and pitch

To develop a good understanding of how music works it is necessary to start with the basics of sound, pitches and notes.

Frequency and Vibration

All sound is vibration, and the frequency of the vibration (i.e. how fast it is vibrating) determines its pitch. The faster it is vibrating the higher the sound will appear to the human ear. There are an infinite number of frequencies that something can vibrate at and so there are also an infinite nymber of possible pitches.

In terms of pitch big means low and small means high. If you strike two metal rods of equal thickness but differing lengths the longer one will produce the lowest note. This is true whether the vibration is in a metal rod, a string or a column of air.

Pitch

In music, however, there are a finite number of pitches. How then do we make the transition from frequencies into musical pitches?

To some extent the relationship between the note pitches of Western Music and the natural frequencies of sound is arbitrary in the sense that there are other ways of doing it. There are good reasons for the chosen relationship, however, and these are outlined below.

The most obvious limit to impose on the infinite frequencies of nature is that of mortal hearing. There is little point incorporating pitches into a musical system if they are above or below our hearing spectrum.

The Octave

The second logical organisation of natural pitches rests on a phenomenon known as the octave. This is a naturally occurring law that means that if you double the frequency of a note you will get a note that sounds the same only higher. Thus if we pick a frequency of 110Hz and call it "Note A" we will find that 220Hz gives another, higher A as does 440Hz etc. Using our analogy of metal rods again a rod twice the length of another should produce the same note but an octave lower.

We now have a very simple basis for mapping out frequencies in terms of musical pitch:

DIAGRAM OF OCTAVE

Below Human Hearing---------------------------------------------------------------------------------------------------Above Human Hearing
<---------------------------A-----A----------A--------------------A----------------------------------------A------------------------------------>
Frequency Doubles with each octave ->

Splitting the Octave into Musical Intervals

Clearly a tune with only one note (even with high and low versions) would be pretty dull. To create a usable set of musical pitches it is necessary to subdivide the octave. While the octave is common to all cultures different musical systems have differing approcahes when it comes to dividing it up. The octave and its subdivisions are known as musical intervals.

Our ability to hear different musical intervals is due to the harmonic series and the fact that notes are actually composite sounds made up of a root frequency and many fainter multiples of that frequency.

Diagram Of Harmonic Series

Western music splits the octave into 7 basic notes and calls them by the letters of the alphabet.

A B C D E F G

(NOTE: For historical reasons the musical alphabet is actually started on the letter C - CDEFGAB)

The spliting, like the octave, is based on frequency ratios. Simple frequency ratios produce consonant (or pleasing) intervals and more complex ratios (with closer frequencies) produce dissonant(less pleasing) sounds. The different intervals and their frequency ratios are outlined below:

Perfect
consonances:

1:1 Unison (two of the same note)
1:2 Octave
2:3 Fifth
3:4 Fourth

Imperfect consonances:

4:5 Major Third
5:6 Minor Third
3:5 Major Sixth
5:8 Mnor Sixth

Dissonances:

8:9 Major Second (Tone)
15:16 Minor Second (Semitone)
9:16 Minorr Seventh
8:15 Major Seventh





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