Just intonation: Encyclopedia II - Just intonation - Why isn't just intonation used much?

Just intonation - Why isn't just intonation used much?

Some fixed just intonation scales and systems, such as the diatonic scale above, produce wolf intervals. The above scale allows a minor tone to occur next to a semitone which produces the awkward ratio 32:27 for C:A, and still worse, a minor tone next to a fourth giving 40:27 for E:A. Moving A down to 10/9 alleviates these difficulties but creates new ones: D:A becomes 27:20, and A:F# becomes 32:27.

You can have more frets on a guitar to handle both A's, 9/8 with G and 10/9 with G so that C:A can be played as 6:5 while D:A can still be played as 3:2. 9/8 and 10/9 are less than 1/53 octave apart, so mechanical and performance considerations have made this approach extremely rare. And the problem of how to tune chords such as C-E-G-A-D is left unresolved (for instance, A could be 4:3 below D (making it 9/8, if G is 1) or 4:3 above E (making it 10/9, if G is 1) but not both at the same time, so one of the fourths in the chord will have to be an out-of-tune wolf interval). However the frets may be removed entirely -- this, unfortunately, makes in-tune fingering of many chords exceedingly difficult, due to the construction and mechanics of the human hand -- and the tuning of most complex chords in just intonation is generally ambiguous.

For many instruments tuned in just intonation, you can't change keys without retuning your instrument. For instance, if you tune a piano to just intonation intervals and a minimum of wolf intervals for the key of G, then only one other key (typically E-flat) can have the same intervals, and many of the keys have a very dissonant and unpleasant sound. This makes modulation within a piece, or playing a repertoire of pieces in different keys impractical to impossible.

Synthesizers have proven a valuable tool for composers wanting to experiment with just intonation. Many commercial synthesizers provide the ability to use built-in just intonation scales or to program your own. Wendy Carlos used a system on her 1986 album Beauty in the Beast, where one electronic keyboard was used to play the notes, and another used to instantly set the root note to which all intervals were tuned, which allowed for modulation. On her 1987 lecture album Secrets of Synthesis there are audible examples of the difference in sound between traditional equal temperament and just intonation.

There were several other systems in use before equal temperament. Pythagorean tuning was perhaps the first to be theorized, which is a system in which all tones can be found using the ratios 3:2 and 4:3. It is easier to think of this system as a cycle of fifths, but it must be noted that because a series of 12 fifths does not reach the same tone it began with, this system produces "wolf fifths" in the more distant keys (which were consequently unused).

Another system that was popular for keyboards through the Renaissance was meantone temperament. In this system the simpler ratios of 3:2 and 4:3 were compromised in favour of exact 5:4 (major thirds) ratios. Specifically, the fifth (3:2) was slightly narrowed so that a series of four narrowed fifths would produce 5:4 exactly (at some octave transposition). Again, this system is not circular and produced some unplayable keys. (Some keyboards of the 18th century featured split keys to differentiate between sharp and flat notes to expand the range of useable keys.)

The most common tuning today began as well temperament, which was replaced by the more rigorous equal temperament in the early 20th century. Well temperament largely abandoned just intonation by applying small changes to the intervals so that they became more homogenized and eliminated wolf intervals. In systems of well temperament, and there were many, the goal was to make all keys useable by compromising each of them slightly. Its development was necessary as composers moved toward expression through large harmonic changes (modulation), and required access to a wider realm of tonality. Bach's "The Well-Tempered Clavier", a book of compositions in every key, is the most famous example, but the compositions of Chopin, for instance, rely much more on the devices of expression only allowed by well temperament.

Equal Temperament is essentially the most homogenized form of well temperament, in that it tunes an actual circle of fifths by narrowing each by the same amount. In equal temperament, every interval is the same as all other intervals of its type. There are no longer pure and "wolf" fifths, or even good and bad fifths, but simply fifths (or thirds, or seconds, et cetera). Equal temperament is not a form of just intonation.

Today, the dominance of repertoire composed under well tempered systems, the prominence of the piano in musical training, the lack of just-intonation capable instruments, and the way that tuning is not normally a significant part of a musician's education have made equal temperament so prevalent that alternatives are not often discussed.

Despite the obstacles, many today find reasons to pursue just intonation. The purity and stability of its intervals are found quite beautiful by many, but this stability also allows extreme intonational precision as well. The practical study of just intonation can greatly increase ones analytical ability with respect to sound, and yield improvement to musicianship even in well temperament repertoire.

In practice it is very difficult to produce true equal temperament. There are instruments such as the piano where tuning is not up to the performer, but these instruments are a minority. The main problem with equal temperament is that its intervals must sound somewhat unstable, and thus the performer has to learn to suppress the more stable just intervals in favour of equal tempered ones. This is counterintuitive, and in small groups, notably string quartets, just intonation is often approached either by accident or design because it is much easier to find (and hear) a point of stability than a point of arbitrary instability.

Adapted from the Wikipedia article "Why isn't just intonation used much?", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki