Very Brief History of the 19-tone Equal Temperament

This post is meant to assist students of the 19-tone equal temperament.

M. Joel Mandelbaum's doctoral treatise "Multiple Division of the Octave
and the Tonal Resources of 19-tone Temperament" (1961) is the single
best treatment of the 19-tone equal I have found in English. It is not
highly original, nor is it at all complete; nevertheless it is a very
convenient summary of part of the history of the 19-tone equal.

Francisco Salinas' De Musica, in Latin (16th century) is the first known
mathematically reference to the 1/3 comma mesotonic, which very closely
approximates the 19-tone equal.

Zarlino (16th century) reports on the 1/3 comma mesotonic, which he
found (in comparison to the 2/7 comma and 1/4 comma mesotonics) "a
little languid, but... quite usable."

Mersenne (17th century) briefly mentions 'a certain organist'
(Titelouze) who enthusiastically used 1/3 tones.

The celebrated French composer Costeley in a famous preface (1570) which
has been hitherto ignored by anglophones, specifically refers to his use
of 1/3 tones, which he praises as the ultimate perfection of the tuning
art. I shall give the complete translation (it is not terribly long) in
another post.

Gesualdo is said to have owned a 19-tone clavier; his master, Nenna, is
known for certain to have used the 19-tone equal, as did many of the
17th-century Neapolitans. The German Luython, who as I recall had links
with this school, owned a 19-tone keyboard.

The modern advocates of the 19-tone equal tend to be much more
fantastical than the older writers, and prone to all kinds of dubious,
extravagant assertions - the bane of our age is self-exhibitionism.
Yasser in his Theory of Evolving Tonality seethes with ideas, some
wonderful, others absurd. But he is well worth reading.

In antiquity it is known that the Greeks definitely used 1/3 tones (the
references are a commonplace, both in Aristoxenos and the Arabs who
preserve many of the lost Greek writers). Whether the Greeks made the
next logical step to 19-tone equal is open to debate, but this is by no
means an abstruse or difficult step. But the vast majority of their
musical writings have perished, so we shall never know for sure. Very
probably at least a few of them used approximations to the 19-tone
equal, just as some of them certainly used approximations to the 12-tone
equal.

For anyone wishing to inform himself concerning the 19-tone equal, this
will do to begin with, in the way of history and basic references.


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