Why I hate Vallotti – cont.

I believe the answer is 1/6 comma meantone, a regular meantone system where all the fifths but one (the wolf) are narrowed by 1/6 of a sytonic comma. The resultant temperament has several keys that are equally consonant, several M3rds of good quality, predictable semitones of two different sizes–one for diatonic and one for chromatic semitones–as well as other musical assets. Threaded throughout the discussion in Bruce Haynes’s superb 1991 Early Music article (pp. 357–81), “Beyond temperament: non–keyboard intonation in the 17th and 18th centuries,” is the frequent re–appearance of 1/6 comma meantone. Already widely known today as Silbermann’s temperament (after the organ builder and friend of J. S. Bach), it corresponds to ideals for temperaments given by Telemann, Tosi, Quantz, and Geminiani, among others, and is described by the French theorist Sauveur (1707) as the temperament of “ordinary musicians”. The historical evidence as presented by Haynes speaks for itself, and is a stunning endorsement. What better temperament to use as a standard for Baroque music than the one employed by everyday musicians at the time? So, from an historical standpoint for music from the earlier 18th century, 1/6 comma beats Vallotti and Young. Its cents chart (with rounded approximations) is given here:

Furthermore, it is clear from the many references to major and minor (diatonic and chromatic) semitones and particularly the distinction between sharp and flat versions of a note in woodwind fingering charts well into the 18th century–not to mention Peter Prelleur’s violin fingerboard illustration of 1731–that some form of regular meantone temperament is being assumed as a standard. Vallotti and Young have major and minor semitones in some places, it’s true, but the whole point of a circulating temperament is that the notes can remain fixed and still be usable. Distinctions between G# and Ab are unnecessary because the compromise position of the note in Vallotti and Young is meant to serve for both harmonic contexts. In other words, if Baroque musicians were thinking in terms of circulating temperaments as a standard, then they wouldn’t need to distinguish between enharmonic notes in fingering charts, and they wouldn’t need to build keyboards with split keys, for which there is still some scattered evidence in the 18th century. In addition, the difference between the major and minor semitone in 1/6 comma meantone is very close to a syntonic comma, which lends an extra degree of melodic elegance in a system based on divisions of that interval. The fact that diatonic semitones are always the same size and chromatic semitones are always the same size, however, creates a predictability as to where the notes will be found that Vallotti and Young simply cannot provide. Furthermore, this regularity enables fretted instruments to play fairly easily with the temperament–setting major and minor semitones on the fingerboard–whereas trying to set frets to match an irregular temperament can be hopelessly frustrating.

The large number of good M3rds, meanwhile, and the keys that use them, mean that the possibilities for transposition are superior in 1/6 comma over Vallotti and Young. Pitch standards like Chorton (A=ca.460) and Kammerton (A=ca.415) in Germany must have required frequent transposition by whole tone up or down. In 1/6 comma, this can often be done with no change in the relative position of the notes. But in an irregular system, the tempering is always different for a transposed key from its written version. “Hey, don’t forget, we’re playing in G at A=415 but the organ is in Young at A=460 with the player transposing to F, so that G is going to be lower (or the B and D higher) than you expect, heh, heh.” Such conversations were unnecessary with 1/6 comma, but must have taken place, even among muscians familiar with the temperament, when irregular temperaments were in use.

The good M3rds of 1/6 comma are, of course, balanced by four that are so wide as to be unusable (although only 5 cents wider than the worst and supposedly usable M3rds of Vallotti and Young). The classic case is the need for both G# and Ab. Most instruments (and singers) aren’t going to have a problem with that since they can make diatonic semitones, etc. wherever they are needed–hence the distinctions in the fingering charts noted above and references by some theorists to a “55 division” where the octave is divided into 55 commas (basically a fully extended 1/6 comma meantone)–but continuo keyboards with only twelve notes to the octave are stuck with whichever note was chosen when the temperament was set. There are some practical solutions to this problem in performance, some of which may be possible in various circumstances, and all of which can help to extend the utility of 1/6 comma:

1. Choose pieces that need only one note or the other.
2. Retune the note as needed for a piece or group of pieces.
3. Avoid the “wrong” notes and leave them to more flexible instruments.
4. Tune the notes differently in various octaves and avoid the “wrong” versions in the realization.
5. Tune the notes differently on each manual, using one manual for flat–leaning keys and another for sharp–leaning keys.
6. Use a keyboard with split keys.

Finally, there is one last musical reason why I think 1/6 comma is so satisfying. Complex harmonies so typical of Baroque music–including 7th chords and diminished triads–simply sound more satisfying in 1/6 comma. I could never understand why this should be so until I realized that the tritone in 1/6 comma meantone has about as much claim to harmonic purity as could be made. At 590.2 cents (again, a rounded approximation), the 1/6 comma tritone is virtually a combination of the pure (5:4) M3rd at 386.3 cents, and the pure (9:8) major whole tone at 203.9 cents. This is a rationalization, of course, since the interval itself (45:32) does not occur at an audible place in the harmonic series, and yet it may explain why the interval and its reciprocal diminished 5th (64:45) are so completely satisfying, and thus why the tension and release of Baroque harmonic progressions sound especially fine in 1/6 comma.

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