BETWEEN U S: A HyperHistory of American Microtonalists

Meantone is the name of one of the most elegant tunings in the history of European music, a beautiful tuning that provided near-perfect consonance in a variety of keys. The tuning was first explicitly defined in 1523 by an Italian theorist name Pietro Aaron, though it is suspected that some rough form of meantone had been in use through much of the 15th century. Meantone tuning dominated European music until the early 18th century, and continued being used in certain backwaters, especially England and especially among organ tuners, through the late 19th century. Having lasted some 250 to 400 years, depending on the area, meantone has been the most durable tuning in European history so far. [Ed. Note: It is also, most likely, the tuning that the European colonial settlers brought to America, and its compromises of good and bad triads undoubtedly informed the compositional choices of William Billings, Francis Hopkinson and other early American composers.]

Meantone is basically a 12-pitch keyboard tuning, a workable compromise that allows eight usable major triads and eight minor triads, the other four of each being real howlers. The premise of keyboard tuning in general is that you can have your major thirds in tune or your perfect fifths in tune, but both cannot be in tune, and some compromise is always necessary. Let’s look at why:

A well-tuned perfect fifth = 702 cents.
A well-tuned major third = 386.3 cents.
An octave = 1200 cents.

If we tune our perfect fifths in tune, we’ll have C to G, G to D, D to A, and A to E all 702 cents wide. 4 x 702 = 2808 cents. Therefore the two octaves and a major third from C to E (C G D A E) will be 2808 cents, and, subtracting two octaves or 2400 cents, the major third C to E will be 408 cents. 408 cents is an awfully wide and harsh major third, not really tunable by ear, bad for singing, and inharmonious.

Meantone’s solution is two squeeze down the perfect fifths until the major thirds are perfect. What we want is C to E at 386.3 cents. Therefore, two octaves and a major third will be 2786.3 cents, and each perfect fifth will be 1/4th of that amount, 696.575 cents. (The ratio between pitches of a meantone fifth is actually the fourth root of 5, since if you take the fourth root of 5 to the fourth power, you get 5, which is the ratio of two octaves and a pure major third.) (Don’t worry if you didn’t follow that. Not necessary.) The perfect fifth in meantone is just over 5 cents flat. But acoustically, the ear is less disturbed by out-of-tune fifths than by out-of-tune thirds, since with fifths the out-of-tune harmonics are higher up in register and further away and less obvious.

So meantone strives to give us as many perfect 5-to-4 major thirds as possible, which, when limited to 12 keys per octave on a keyboard, is 8. C, D, E, A, and G are tuned to slightly narrow fifths and slightly broad fourths, and then the rest of the pitches are tuned to pure major thirds: E-G#, F-A, A-C#, Eb-G, G-B, Bb-D, and D-F#. The result, notated in cents above C, is the following scale:

C 0
C# 76.0
D 193.2
Eb 310.3
E 386.3
F 503.4
F# 579.5
G 696.6
G# 772.6
A 889.7
Bb 1006.8
B 1082.9

And, if you’ve tuned your first five pitches right, C-E is a pure major third as well. The other four major thirds are 427 cents wide and sound terrible: G#-C, F#-Bb, C#-F, and B-Eb. In fact, as notated, those aren’t major thirds at all, but diminished fourths. In meantone, there is no such note as Db, but only C#. There is no D#, but only Eb. Unless, that is, you redo the tuning slightly to center it around some key other than C, as was sometimes done.

And so, in meantone, you simply can’t use triads with those unavailable major thirds. During the meantone period, you can’t really use keys with more than three sharps or flats in the key signature. Look through music of the 16th and 17th centuries, and you will find no pieces in Ab major, F# major, or Bb minor. Such keys need pitches that don’t exist in meantone tuning.

BUT – and this is the great advantage, the eight major and eight minor keys you can use sound so much sweeter than they do in our music. Those thirds sound so lovely, and thus all European music from the mid-15th to mid-18th centuries (and beyond) was based on the primacy of thirds. It became excusable to omit the fifth from a triad, but not the third, because the third was in tune and the fifth wasn’t. (I highly recommend Orlando Gibbons‘s Lord Salisbury Pavane and Galliard as a sterling example of exploration of meantone tuning. This late-16th-century work, a masterpiece of early keyboard music, meanders through every possible chord in meantone plus one dissonant B-major triad as a passing chord. Play through it in equal temperament and it sounds OK. Then play it in meantone, and its colors suddenly come alive, and you hear the work’s luscious beauty as Gibbons’s original audience did. Then play it in equal temperament again, and it collapses disappointingly back into black and white, just like Dorothy coming back to Kansas.)

Historically, there are different kinds of meantone, based on their division of the syntonic comma. The syntonic comma is the discrepancy between four perfect fifths and two octaves and a major third, about 21.5 cents. The classic Pietro Aaron meantone I’ve outlined above is called 1/4th-comma meantone, because 1/4 of the comma was subtracted from each perfect fifth. There are less extreme meantones such as 1/5th-comma, 1/6th-comma, even 5/18ths-comma. The less subtracted from each fifth, the more out-of-tune the thirds will be. 1/11th-comma meantone is actually identical to equal temperament. [The classic tuning book from which all this material is drawn is J. Murray Barbour’s Tuning and Temperament (New York: Da Capo Press, 1972).]

I wish I could recommend specific recordings in meantone tuning. I suspect that many exist, but early music groups, even when they are attentive to authentic tunings, are not often in the habit of specifying what keyboard tunings they use. Anyone can contact me at kgann@earthlink.net with information about specific meantone recordings, I will add them to my historical tuning web page.

From BETWEEN U S: A HyperHistory of American Microtonalists
by Kyle Gann
© 2001 NewMusicBox

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