IVOR DARREG

ANOTHER ANALOGY FOR TEMPERAMENT

In printing, the letters have different widths, but on ordinary typewriters, every character must occupy the same space. Therefore this type that you are now reading has been seriously distorted, so that all the capital and small letters and punctuation marks take up exactly the same horizontal space. In the present instance, this horizontal equal space is one-tenth of an inch.

To be specific, the letter M should take up at least 1 1/2 times that space, while the letter I should have little more than 1/2 the space of average letters such as o n u e &c. Depending on the style of lettering, the capital W should be even wider, or as wide as M.

This distortion-for-practical-reasons is an excellent analogy for what happens in the 12-tone equal temperament, used for tuning pianos, organs, xylophones, marimbas, and now for synthesizers. Nearly all guitars, banjos, mandolins, and other fretted instruments are put into 12-tone equal temperament at the factory by the positions in which the frets are set into the fingerboard.

The excessively wide small i and 1 have their counterparts in the excessively sharp major third and major sixth in 12-tone tuning, while the cramped, squeezed-up m and w have their counterparts in the too-small minor third and minor sixth of 12-tone. The overall effect is to introduce a roughness and restlessness into the music played in this ordinary tuning system.

For certain types of music this does not matter; for others it is very serious indeed. There are other tuning-systems besides 12 equal, and all of them have some kind of distortion except the one kind called just intonation. However, the less distortion the more complicated the system may be to use on keyboard instruments.

In particular, the piano and pipe-organ would be impractical if tuning-systems with large numbers of tones per octave were insisted on. Happily, we now have computers and synthesizers and other new means of dealing with the less-distorted or undistorted tunings, so the obstacles have begun to vanish.

Compare the words below as typewritten and as set with proportionally-spaced lettering: