More on the 19-tone Equal Temperament

My comments on the intervals of 19-tone equal at the limit of human
perception seem to have provoked some disbelief. I am indeed serious. Of
course anyone can distinguish between tones as little as 5-10 cents
apart in successive hearings. But if one substitutes one such tone for
the other in a given melody, not one person in a thousand will identify
that _melody_ as different. This is what I mean. I can make myself no
plainer. I grant that melodies wherein one substitutes one of the
degrees of the 22-tone or 24-tone equal for an adjacent degree, do
occasionally (not usually) produce a change in melody if one of the
degrees is highly consonant. Adjacent degrees of the 31- and 34-tone
equal _never_ produce such a change in melody to my ears. Naturally
there may be exceptional individuals with more acute powers of
discrimination, though I doubt it. But music is written for the many,
not the few.

55-60 cents as the limen of intervallic perception is well-established
in the literature. Pratt for example in his Meaning of Music, as I
recall, found a value "just wider than a quarter-tone", and Seashore &
Jenner found a value between 53 and 61 cents.
Naturally no one should accept these results without making trial for
himself. I find however that my own ears are fully in agreement with
these results.

There is nowadays a disposition to be suspicious of anyone who ventures
to condemn _any_ system of tuning. The presumption seems to be that
everything is good for something. The advocates of the 12-tone equal
have often been willing to use any argument to defend their chosen
system (e.g. the egregious Barbour, who ventured to write a book on
tuning, having never heard any tuning system other than the 12-tone
equal) and this perhaps, by a kind of reaction in favor of
experimentation, has induced many to doubt that any standard tuning
system should exist. This is emphatically not the attitude of the great
artists of the past, whose work depends as much on calculated limits as
on absolute freedoom. Nor was this the attitude of musical theorists of
the past, who tended rather to automatically dismiss all tunings that
did not conform to quite specific and demanding requirements. And I am
far from certain that their attitude was merely benighted. A temperament
which results in continual whining dissonances in place of consonances
may interest a few, but will never displace the 12-tone equal, nor
should it. Music which innovates too radically is somewhat in the case
of poetry which should adopt so many new words that the sense is
obscured.

I have observed that rock singers use a great many third tones; there is
seldom a popular melody nowadays without them. This perhaps is what
makes rock melody so much more pleasing to the masses than the 12-tone
melodies of the last century, which are now almost wholly disregarded. I
suspect that if 12-tone equal is ever dethroned, it will be by rock
instrumentalists wishing to reproduce the subtler, necessarily 19-tone
melodies of their vocalists.

All tuning systems which are not mere noise, reduce approximately either
to the 12-tone or the 19-tone equal, melodically considered. This
follows inescapably from the principle of the melodic limen. 31-tone
equal for example reduces melodically to the 12-tone equal (with a few
exceptions where the augmented tone occurs, where it has rather a flavor
of the 19-equal), because the adjacent degrees of the 31-tone equal are
confounded in melody. 17- and 22-tone equal do possess a certain melodic
independance, but are so seething with sour dissonances that they are
really not worth discussing.

I have used tree diagrams to examine all the possible heptatonic modes
of the 19-tone equal that have a modicum of consonant intervals and
chords, hence the four new modal genera, which I have previously
suggested might profitably be added to the diatonic. In harmony these 28
new modes constitute what may be called the chromatic music, whose
existence has been hitherto intuited, but never plainly defined.

It is fascinating that Francisco Salinas in the 16th century in his De
Musica observed that the 1/3 comma mesotonic (virtually equivalent to
the 19-tone equal) would alone permit the realization of the enharmonic
genus of the ancients. This is indeed the case, of which more
later.


SMTPOriginator: tuning@eartha.mills.edu
From: Aline Surman
Subject: lutes again
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>Ed's comments on moveable fret lutes were interesting...I must admit
>that I was thinking of the hard fretted variety. I have an album by lute
>virtuoso Lutz Kirchhof, and the frets are not moveable.

In most cultures I'm aware of frets started out as gut or wire ties
around the neck, thereby allowing for the possibility of being movable. I
think it's worth pointing out though that, if a fretted instrument is to
adhere precisely to anything other than an equal temperament, either its
strings have to be tuned in octaves (or whatever interval the tuning
repeats itself in), or its frets have to be placed in different positions
on each string.


SMTPOriginator: tuning@eartha.mills.edu
From: "Bob Lee"
Subject: Re: Liminatory Fulminations
PostedDate: 15-12-97 03:23:04
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