A Question of Temperament

Temperaments have an enormous impact of the sound and interpretation of music, particularly music for keyboards. As the name implies, temperaments describe ways in which pitches are tempered, or mis-tuned so that the instrument can be used to play music in a wider variety of keys.

More specifically, temperaments deal with some specific mathematical problems which prevent a keyboard instrument from ever being perfectly in tune with itself. A temperament which has perfectly tuned fifths cannot also have perfectly tuned major thirds, for example. Some fifths must be “narrowed” (made flat) to allow for better major thirds, or the thirds have to be widened (made sharp) to allow for better fifths. Some temperaments favor fifths, and others favor purely tuned major thirds. In either case, some intervals must be “tempered”, hence the term “temperament.”

Tuning an instrument involves setting the pitches of a middle octave of the keyboard, then tuning the rest of the keys (up and down the scale) in octaves from the tuned pitches in the middle. Tuning is accomplished by starting with a reference pitch (e.g. A=440) and tuning the next pitch, typically a fifth, fourth, or major third away from the reference. A temperament is basically a scheme which prescribes whether the tuning between these two notes is to be pure, or tempered by a measurable amount. The newly tuned pitch is then used as the new reference pitch, and the next note is tuned – a fifth, fourth or major third away – according to the temperament rules. This process is repeated until the pitch of all 12 notes in the central octave are set.

In equal temperament, used on almost all keyboards today, all 12 fifths are equally narrowed (made flat) by a small amount, which causes all major thirds to be equally wide (made sharp) but by a larger amount. Tempering fifths equally is a characteristic of mean-tone temperament, which uses the term “mean” to indicate averaging, or equalizing. Equal temperament is rather bland and rather useful for the same reason: all keys sound alike, and every chord of every key is equally out of tune. We’ve gotten used to it!

One can also equally temper a subset of the fifths of a temperament. In the case of quarter-comma mean tone temperament, the most commonly-used fifths, which outline the triads of C, D, F, and G, are equally narrowed enough so that the major thirds of these triads (E in C-major, for example) can be tuned pure. The remaining pitches in the octave are tuned as pure thirds as well, creating a temperament which strongly favors the sound of a purely tuned major third.

Temperaments have a huge effect on organ sound because the organ’s sound is constant, and does not die away like that of a piano or harpsichord.

More importantly, the majority of stops on an organ play something other than normal “piano pitch” – instead these “mutation” stops sound pure octaves, pure fifths and pure major thirds above the note played. While the organ is purely in tune with itself when one note is played at a time, these stops will be out of tune with any tempered interval (two or more notes, played together). The purely tuned intervals in the “mutations” stops will clash with the same tempered/unpure pitches played on the keyboard.

This means that the best temperament for the organ is one that has the most “pure” intervals, to match the tuning of mutation stops. Quarter-comma mean tone, with its large number of pure thirds, sounds particularly well on organs. When the temperament and the pipework are both purely in tune, it causes a change in the perceived timbre of the sound. This change in the timbre can be readily experienced by the average listener.

Other characteristics

Mean tone gives composers devices for creating expressive works that are inexorably tied to the temperament. For example, on quarter-comma mean tone organs, there are two different sizes of half-step intervals. The interval of F to F# is small, and the interval between A and B-flat is larger. Special effects can be created by crafting a musical theme which ascends or descends through the scale chromatically, shifting back and forth between large and small minor seconds.

The use a sharp accidental or flat accidental in the score can also assert a significant effect in the harmonic progression---effects which simply do not exist on an equal-tempered instrument. The extensive use of chromatic pitches on a mean tone organ can give the composer or improviser tools for truly bizarre, and shocking chord progressions, or ones that are strangely beautiful.

Limitations with quarter-comma mean tone temperaments

The most significant problem with quarter-comma mean tone is imposed by the number of keys per octave. Each raised key (the black notes of a standard piano) is tuned to be either a sharp (i.e. A-sharp) or a flat (B-flat); that raised key cannot be used for both pitches in mean tone. To have access to both pitches you need to have a key for each – two raised keys---so that when the music calls for an A-sharp, you can play one, and when the music calls for a B-flat, you can play that as well using a different key.

For a period of time, this problem was addressed through the use of subsemitones – a second set of raised keys that were higher than the standard sharps, and placed slightly rearward (away from the organist). Through the use of subsemitone keys, additional pitches can be available, making a mean tone organ playable in more keys. However, additional keys on the manuals and pedals of the organ requires many more pipes, and considerably increased complexity for the organist.

For mean tone organs with the traditional 12 keys per octave, the instrument cannot play in all keys. The rarely used keys with three or more sharps or flats will sound out of tune—an effect that a composer may choose, but which most will avoid. However, the vast majority of organ works written during the mean tone era are in keys which are compatible with the temperament. The use of mean tone is a particularly good fit for pieces written in the modal systems (Dorian, Lydian, etc.)