James Huntingford

Equal Temperament

Equal Temperament, or ET, is the most well known, most widely utilised and most versatile tuning system in the world today. Its standardised intervals make it the easiest tuning system to adapt to different performance situations and to transpose to different keys or pitches, and it is arguably the easiest temperament for a young musician to learn to use.
Despite all of this, ET, like all tuning systems, has its drawbacks. The most common criticism of equal temperament almost invariably comes from players and listeners of renaissance, baroque and galante (classical) repertoire. The three main issues that are taken with ET are:
1. Its total lack of key colour (all keys are identical with respect to tuning, and thus have no individual flavour other than that which may be afforded them by other variables),
2. Its lack of pure intervals (save for the octave, every single interval in the scale is out of tune), and most critically
3. Its significantly out-of-tune major and minor thirds (the basis of triadic harmony, upon which much of the beauty of western art music harmony has rested for centuries).
For these earlier musics, other systems are almost invariably preferred, including well temperaments, meantone temperaments and, for non-fixed pitched instruments, just intonation.

So how does ET work? As you will have read in basics of tuning, a perfect octave is defined as two sounds, one of which vibrates at precisely double the frequency of the other. Equal temperament is theoretically very simple. It divides this perfect octave into twelve equally spaced (equidistant) semitones. This makes an ET scale entirely based on the interval of 1/12 of an octave, also known as an ‘ET semitone’. A distance of 4 ET semitones will roughly correspond to an interval of a major third (M3), 9 ET semitones will be roughly a major sixth (M6), and 12 ET semitones should give the full octave. The problem here is the word roughly. This is because the truth is that, save for the octave itself, every single one of these intervals will be out of tune, and some of them quite significantly so. Pure intervals (P3, P6 etc.), upon which much of the beauty of early music is based, simply cannot be enjoyed in ET. The mathematical reason for this is demonstrated by clicking the link below.

The Mathematics of Equal Temperament