Since the early 1900s, almost all Western keyboard instruments have been tuned to Equal Temperament, a system in which all of the notes of the chromatic scale are spaced equally between the tonic and its octave. This has led to a common misconception that such a tuning is 'right'. In fact, from a musical perspective EVERY note is in the wrong place and the great composers for these instruments such as Chopin, Liszt, Beethoven and Bach, whilst admiring the quality of modern pianos, would wonder why they were all out of tune!

The exact positioning of the notes within the scale is a complex subject with a long history, especially where the tuning of fixed pitch instruments such organs and keyboards is concerned. This site aims, to provide an introduction to the topic with the help of the interactive diagram at the bottom of this page.

To start at the very beginning, it will be instructive to question the whole concept of notes and scales. Nature produces sounds at every pitch, such as the wind blowing through the trees or the human voice, but musical instruments and almost all modern music is based on sets of discrete notes. In looking at how many notes there should be and how they should be spaced, the driving force turns out to be the ratio between notes. Simple ratios, 2:1, 3:2 etc are pleasing to the ear, complex ratios 78/34 are not! The simplest of the ratios 2:1 (or a doubling of the pitch) produces an octave and it is one of the few almost universally agreed facts that the octave and its tonic must always be in the ratio of 2:1. Since the octave has its own octave at double its frequency, the spectrum of notes can be divided into octave-wide scales which will all have identical properties except for the doubling of pitches.

Music made up simply of octaves would be rather tedious, and so the next task is to divide the scale into a set of discrete notes, and this is where the fun starts!  Once again the ratios between notes come into play and the next simplest ratio, 3:2 gives us a tonic and its 5th which is another 'pleasing' interval and must appear in our new scale. If we make two more seemingly sensible assumption, that all of the notes in the scale should be evenly spaced out and that we need no more than 20 notes, then something very interesting happens. Some simple mathematics will show that there are only two possibilities for the number of notes in a scale, 12 and 17. No other number of notes produces a scale with a 5th in it. Western music has settled on a 12 note scale, both because its 5th is closer to the 'natural' ratio and music based on a 12 note scale is easier to learn and play. However, for anyone interested in a musicological diversion, a move to a 17 note scale (with enharmonics such as Ab and G# seen as separate notes) was seen as the next natural progression from atonal music in the early 20th century and had quite a following.

A 12 note chromatic scale may seem an attractive route to follow, but, and its a big 'but', the 5th does not lie exactly at the same pitch as the 9th note of this evenly spaced scale, even though it is so close that our ears cannot tell the difference in a line of melody. Other simple ratios such as the major 3rd (5:4) are so far out that our ears can detect a distinct difference. This evenly spaced chromatic scale is therefore only an approximation.

To illustrate this problem another way, there are two ways to find the major 2nd of the scale, based on intervals with simple ratios. The first is to go up a 5th and the back down a 4th. The second is to go up a major 6th and back down a 5th. The problem is that these two ways arrive at notes of slightly different pitches. Though this seems odd at first, both notes are right in their own way because it is the interval that is important, not the exact pitch of the note. A good musician will naturally flatten the major 2nd when descending from a 6th to make the interval of a 5th correct. This is why music teachers often want particular notes to be slightly sharpened or flattened. Once again, the conclusion to draw is that there is no 'right answer' when deciding where every note of the scale should sit.

If we accept that it is intervals that we should concentrate on then musicians will have to bend the actual pitch of some notes to make the music sound right. This slight bending of notes is possible with the voice, on string instruments and on most woodwind and brass instruments. The problem comes with fixed pitch instruments such as pipe organs and keyboard instruments. These instruments have to be tuned to one, and only one pitch per note and it is the choice of these pitches that defines each 'Musical Temperament'.

Many different tunings and temperaments have been used through the ages and the chapters that follow will examine the important ones. Before we start, however, it is useful to define the difference between a 'tuning' and a 'temperament'. In a tuning, the notes are tuned using a particular method, based on the ratios of pairs of notes. The notes are in the right place, in theory, and tunings are normally good for playing in the tuning key and for playing the type of music they were intended for (medieval, classical etc.). However, they usually have significant problems either with particular notes in the scale, or with modulations to other keys. A temperament, on the other hand, starts with a tuning and then 'tempers' it by shifting some of the notes slightly from their natural pitch to improve problem intervals or problem keys. The most radical of all of the temperaments is 'Equal Temperament' which shifts every note from its natural position, but creates a set of scales which are all equally good (or bad depending on your point of view) and which allows modulation freely between any keys.