Technical Library TEMPERAMENTS VIII: Quarter-comma Meantone Entire Contents Copyright © 2013 CBH

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Pietro Aron (c1480–after 1545)

Fasten your seatbelt for Meantone now. This term is too often misused for any other sort of tuning than equal temperament. Working again from your Kirnberger III base, here’s how to tune the Quarter-comma Meantone as proposed by Pietro Aron in his Toscanello in musica (Venice, 1523):

1. Instead of determining all the notes outside the C to E on the circle by tuning pure fifths, find them by tuning absolutely perfect thirds. The g♯ is a perfect third above e. (If you do most of your meantone tuning in the octave below middle c', you may find these perfect thirds a little easier to hear.)

2. Find the c♯' a perfect third above a, and the f a perfect third below a.

3. The b will come from the g, and tune down a perfect third for the e♭.

4. Your f♯ comes from the d, as does the b♭ from d'.

Once more, you’re done. Enjoy the pure sound of perfect thirds in all the easy keys, but don’t try to play Brahms’ Waltz in A♭, or you will fall victim to the wolf: It is not a perfect fifth from G♯ to e♭, but a diminished sixth, and it sounds absolutely hideous. But instead of that, you should focus on the beauty of the many perfect Major thirds: Look at all of them shown in the temperament diagram by those straight lines, and in the notation at the right.

Meantone is all very well if you want to play by yourself. It is especially useful for a lot of the virginal music, Frescobaldi, Sweelinck etc, but music was meant to be sociable afterall: Here’s where you can get into trouble if you have been following all the tuning directions above and beginning your tunings from c'', because sooner or later your diverse instrumental pals—instead of being overcome by the beauty of your harpsichord tuning—are going to politely complain about how flat your a' is, the traditional note most instruments tune from. (Nowadays supposedly the standard A440, although often creeping higher. For our modern baroque convenience, a halftone lower at A415.) You can eliminate this conflict by starting your Quarter-comma Meantone from the usual a' tuning fork, tuning down the octave to a, then the perfect Major third down to f. Divide that third into your four, quarter-comma fifths.

If you want to play in keys further afield, you can still do so in Quarter-comma Meantone, but you must either retune a little, or fiddle around trying to reduce the effects of the wolf. We can examine some possibilities next.

Further discussion
Anonymous [Kayano, Moxzan] Dodecagon — Chi-s akt temo Tokyo 2012, p19
Asselin, Pierre-Yves Musique et Tempérament Éditions Costallat, Paris 1985, p75
Barbour, J Murray Tuning and Temperament Michigan State College Press, East Lansing 1951, p26
Jorgensen, Owen The Equal-beating Temperaments The Sunbury Press, Raleigh 1981, p16
Klop, G C Harpsichord Tuning Werkplaats voor Clavecimbelbouw, Garderen 1974, p12
Kottick, Edward L Harpsichord Owner’s Guide University of North Carolina Press, Chapel Hill & London 1987, p152
Padgham, Charles The Well-Tempered Organ Positive Press, Oxford 1986, p50
Veroli, Claudio di Unequal Temperaments Artes Graficas Farro, Buenos Aires 1978, p41
Zuckermann, Wolfgang Joachim The Modern Harpsichord, New York 1969, p243

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