A Case For Nineteen

This is the first in a series on the more important non-twelve-tone tuning systems. We begin with 19 tones per octaves because (1) this is the 50th anniversary of the publication of Joseph Yasser's book advocating the 19-tone equal temperament, Theory of Evolving Tonality; (2) this is the 21st anniversary of Dr. M. Joel Mandelbaum's Thesis on Multiple Division of the Octave and the Resources of the Nineteen-Tone Temperament, which was accompanied by a tape of 9 Preludes in this system; (3) 19-tone happens to be compatible with existing musical notation to such an extent that fully 80% of the existing musical literature can be read off from printed sheet music and played in 19 without notational changes; (4) the 19-tone system is compatible with guitars and other fretted instruments; (5) the 19-tone system is practical in the piano tone-quality, so that two pianos can be tuned to it in Dr. Mandelbaum's layout scheme, and this scheme can also be used on two-manual organs and two-manual harpsichords.

All of the above factors recommend 19 as the first, but not the only, system to begin exploring the vast unoccupied territory outside the familiar 12-tone equal temperament. 19 has a very pronounced MOOD, which was not predicted by any theorist or mathematician, and which could not have been predicted without composing in the system and hearing the results.

Just 20 years ago, Tillman Schafer provided me with the Mandelbaum tape, and I was struck by the peculiar impact of the music and its strange insistent quality which I had never heard before. At first I thought this was the composer's style, but I tuned my own electronic organ to 19 and started composing and lo and behold, my compositions had this same new mood. So it was the system, and this led to my discovery that at least eleven of the systems with reasonable numbers of tones per octave, and the untempered just intonation system as well, had their distinctive personalities or moods. Since then, I have interviewed about 200 persons and found that certain personality types prefer 19 and others prefer the 22-tone temperament, and it is difficult to be impartial about them, but I do my best. Someday this might become a standard psychological personality test.

The book by the late Joseph Yasser did not predict any such mood, but presented an intricate dialectic theory as to the past and future evolution of musical scales. This book has been reprinted in recent years and can be consulted in many libraries. We do not have space here to give it the review and critique that it deserves. Suffice it to say that my 20 years' experience composing, performing, and building instruments in 19 did not bear out many of Yasser's predictions, but instead continually presented me with a number of pleasant surprises and the paradoxical fact that 19 has more resources than 24!

The composer Ferrucio Busoni narrowly missed 19: he advocated the third-tone (18 tones per octave) 75 years ago as a melodic interval awaiting its place in the musical scene, but unfortunately did not live long enough to pursue his experiments. Julian Carrillo, the Mexican composer, had third-tone pianos constructed and did compose in the system. Neither of these artists got around to the 19-tone system next door, so never experienced the compelling dynamic MOOD of 19 as against the vague low-profile mood of 18.

I bring up the third-tone and the 18 system because the 19th of an octave, the unit-interval of the system, functions melodically as a "third-tone" fully as much as the third4one of 18 does, thus realizing Busoni's dream now that there are a number of 19-tone composers and a number of instruments, especially refretted guitars.

The 19-tone system is a member of the Meantone Family of Temperaments. It can be considered an exaggerated meantone or the practical end of the meantone spectrum. The Spanish organist Francisco Salinas, a long time ago, figured out what is called the one-third-comma meantone temperament, because its fifths are flat by one-third of the syntonic comma, and this 1/3-comma temperament fails to close its circle of fifths by less than a cent, which means that the difference between a l9-tone-equal fifth and a one-third-comma fifth is 1/19th of that tiny inaudible interval, so there is no practical difference between the two systems. Also, 19 minor thirds in just intonation, ratio 5:6, fail to return to the original starting pitch by about 3 cents (1/400 Octave) and the difference between those perfect minor thirds and the l9-tone-equal minor thirds is about a fifth of a cent, so never could be heard and could be tuned only with Sophisticated laboratory equipment. All we need care about here is that the major sixth, and that the errors of the major third of 19-tone temperament favors the minor third and the and the fifth are almost equal and thus cancel out almost perfectly.

The error of the major third is about one-half the error of the 12-tone major third, and in the Opposite direction: the 12-tone major third is exactly one-third octave and is too sharp, whereas the 19-tone major third is too flat by half that amount. The result of these flat major thirds is that, instead of the 12-tone symmetry of pattern, where three major thirds or four minor thirds make exactly one octave, a pile of 19-tone major thirds falls one degree short of the octave, giving an exciting new dissonance, the augmented seventh, then one more major third on top of those gives you a minor, not a major, tenth! This further means that whereas in 12-tone, a chain of major thirds does not use up more than 3 of the 12 pitch-classes, repeating indefinitely, a chain of major thirds in 19 must go through all 19 pitches before it returns to the starting note. Mathematically this has to do with 12 being a divisible number and 19 a prime number. If we pile up minor thirds, four of them exceed the octave by one degree, and five of them give a major tenth instead of the minor tenth you get in 12-tone. Again, a chain of minor thirds uses up only 4 of the 12 pitch-classes and creates that overworked exhausted cliche, the diminished~seventh chord, whereas in 19-tone, the diminished seventh chord comes in four exciting new flavors and gives you variety instead of monotony and will take some time to be exhausted.

We are all familiar with the equivalents in 12, such as C-sharp equalling D-flat Since the 19-tone circle of fifths closes at B-double-sharp instead of B-single-sharp, the 19-tone equivalents (I do not want to say "enharmonics" here because I wish to reserve that term for the Ancient Greek genus and its small intervals) the 19-tone synonyms or equivalents are going to be different. This leads to a possibility, which Mandelbaum chose, of not using any equivalents, but just the one designation for each pitch-class, F-flat through A-sharp.

The Wilson-Hackelman keyboard for 19-tone is laid out in such manner that the equivalents F-flat E-sharp and C-flat B-sharp are recognized -- in effect a 7 + 7 + 7 or 21-digital layout. For many people, it will be convenient to use double-sharps and double-flats, as is done in ordinary 12, but with the different sets of synonyms, such that F-double-sharp is G-flat and G-double-flat is F-sharp. That is, it will take F-triple-sharp to get up to G and G-triple-flat to get down to F. Since the key-signature system in 12-tone goes beyond the circle of fifths and six sharps in 12 equals six flats, or the key of F-sharp major equals the key of G-flat major and the signatures run one step beyond the closure in each direction and there is C-sharp with 7 sharps and C-flat with 7 flats, we could use such remote keys as A-sharp or even E-sharp major with double-sharps in the key signature and keys like G-double-flat major with six double-flats in its signature, but in practice this is confusing and clutters up the page, as well as annoying those of us who have been brought up on a diet of traditional 12-tone. It is perhaps more sensible to stop using any key signatures, in order to avoid cluttering up the page with clouds of naturals -- and save the space all these key signatures occupy at the beginning of each music line. I am sure that the formidable chart of key signatures in Yasser's book has frightened hundreds of potential composers and performers away from 19, and this is a shame.

The Meantone Family was mentioned above partly to point out the relation of 19 to 31-indeed, some people regard 19 as the Poor Man's 31-but it is not a poor relation at all-the moods of the two systems are very different and we need BOTH moods for their valuable contrast. Briefly, 31 favors harmony over melody while 19 has a much stronger melodic impact, but both systems are varieties of meantone and so mathematically related. Both fit ordinary musical notation.

The fact that 19 fits existing notation so well, making efficient use of the distinction between sharps and flats, is generally a powerful advantage to using the system and being able to play one's already mastered repertoire in 19. However, there is one misleading aspect about it. If a chromatic pattern such as Bach's mordent-like trademark, e.g. G -- G is played as written, then the semitone in it is TWO third-tones or two degrees of 19, and this makes it have less impact than the corresponding figure in 12 or in 17. So if you are too much a slave to playing everything exactly as written, you may complain of the leading tone being too flat. The solution is very easy, but it goes against ordinary complain of the leading-tone being too flat. The solution is very easy, but it goes against ordinary musical training and tradition: play such figures in a melody with only ONE degree of 19, the small semitone or rather third-tone in this case. Play G-G-flat-G instead of G-F-sharp-G and it will be brilliant and have much more zonk. Do this even though it makes a dissonance with the accompanying chord! It is all the difference between a sparkling performance and the blahs.

In popular music there is much tone-bending, and them as degrees of the 19-tone scale. At the same some of these bends are made systematic by doing time, we should make it clear that there is almost as much tolerance of pitch-deviation in 19 as there is in 12, and vibrato is still effective as it is in 12. There is no need to be stuffy or perfectionist about exact tuning of 19. The serious performer, especially on the violin family, will make various expressive deviations, and this works as well in 19 as it does in 12 -- in fact we could never have endured 12 for two centuries, if solists hadn't made those deviations!

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There is a very serious risk of misunderstanding when one does what you see just above: that anyone reading the ntoation will try to force it to its usual 12-tone-system meaning. Not only that: the synonyms shown above obtain only in 19. In the 31-tone system, F-flat and E-sharp are different pitches.

Another point that must be repeated over and over in the hope that someone will eventually heed it, is: the term EQUAL TEMPERAMENT does not necessarily mean 12 tones per octave -- the following are also equal temperaments: 7 5 14 15 17 18 19 22 24 29 31 34 36 41 43 46 50 53 and there are manyother equal temperaments possible.

Do not judge anything about 19-tone equal temperament till you have heard its sounds! This is imperative and crucial!