Costeley the Co-Inventor of the 19-tone Equal

It is something of a mystery how a tuning so poor as the 12-tone equal
was able to drive out the 1/4 comma mesotonic system, whose harmonies
are so dramatically smoother, and altogether more poignant and
affecting. But one should remember that fretted instruments had been
tuned either in Pythagorean tuning or in an approximation of the 12-tone
equal tuning since the Middle Ages - perhaps since antiquity. The
possibility of using the 1/3 comma mesotonic (or the virtually identical
19-tone equal system,) whose invention is usually attributed to
Francisco Salinas (1571) , seems to have remained quite unknown to most
composers, and never became widespread, probably through conservatism
and the attachment of musicians to the 12-tone keyboard.

As will shortly be seen, Guillaume Costeley (pronounce: coat-lay)
expressly states that he used an octave divided into equal 1/3 tones,
and also expressly refers to 19 pitches in the octave, in a preface of
1570, a year before Salinas mathematically defined the 1/3 comma
mesotonic, which is aurally absolutely identical to the 19-tone equal.
Probably this tuning was 'in the air', and both men independently
discovered slightly different ways of defining the same system. Costeley
finds the 19-tone equal far superior to any other tuning.

The relevant passage is printed in Les Ma?tres Musiciens de la
Renaissance Fran?aise, and precedes Costeley's celebrated chromatic
motet "Seigneur Dieu Ta piti?". I give a translation:

[After a greeting to his friends, and a general praise of music, there
follows:]

"Now I do not doubt that you gentlemen find it strange that I should
have exceeded in certain of my compositions the usual limits of the
tones [i.e. the diatonics plus C#, Eb, F#, G# or Ab, & Bb - he implies
that he has used Db, D#, E#, Fb, Gb,A#, B# & Cb in some of his
compostions, which exceed the usual limits of the mesotonic tuning then
prevailing on keyboards, and the usual limits of the pythagorean as
well] of which usual limits I am not ignorant.

"I reply to these possible criticisms, first, that I have wished to
provide the most excellent choristers of our Most Christian, Magnanimous
and most Royally Born King of FRANCE (whom may God long preserve among
us) with all that which might most please our Master. But I have done
this [i.e. added these new tones to music] without ever going out of the
key [this phrase admits of differing interpretations, but probably means
that by the use of 1/3 tones he can more exactly preserve the mode when
it has been modulated to a new key], and withal so that I might render
our music more airy [he probably means, more harmonious, or perhaps less
polyphonic and more dramatic, or else more freely modulated].

"As for the song that follows, I composed it 12 long years ago as an
experiment, to render more practical an idea that I had, which I hoped
should give a sweeter and more agreeable music than the diatonic,
provided it were well and skillfully handled. This new music has its
voices separated by intervals of one-third tone [instead of by unequal
fractions of a tone, or else by more or less equal semitones]. And this
[possibility] points up how far from perfection are the designs of our
organs and spinets, inasmuch as they have but 7 diatonics and 5
accidentals in the octave, whereas perfection requires not 5, but 12
accidentals, which a good workman [with a skilful] design can introduce
into the keyboard without making it unplayably complex. And when by
these equal 1/3 tones we dispose the diatonics and accidentals in their
natural order, we possess a marvelously new and pleasing instrument,
without which the song which I have composed for it cannot be played.

"By using this 19-tone instrument tuned by 1/3 tones, we can always
modulate [d?tonner] without discord [for the requisite accidental is
always present, just as it is on the 12-tone keyboards, but with far
less sweetness in the harmony, and the requisite accidental is by no
means available in the 1/4 comma mesotonic, unless it be carried to an
unmanageable 31 tones in the octave]. For we can always lower or raise a
note by 1/3 or 2/3 of a tone as needed [to fit the new key].

"There is no further need to speak of semitones, for in this tuning
there are none [he means, the chromatic and diatonic semitones are no
longer equal, the former being but half the width of the latter]. Our
lutes as usually tuned suffer from the same imperfection as our keyboard
instruments, although by its natural sweetness even the most delicate
ears rarely find anything amiss with it. [He means perhaps that good
players adjust the unequal semitones of the mesotonic as needed, it
being remembered that the lute's tones are not prolonged, which tends to
mask bad harmony - or perhaps he even means that lute-players used an
approximation of 12-tone equal temperament, though this is very
doubtful.] Therefore the perfect music such as I have suggested has not
been more practiced on the lute than on organs or spinets [despite the
lute's movable frets], for it imperatively requires the use of all the
1/3 tones. Well-played violins have the advantage over the
above-mentioned instruments in this regard, inasmuch as they can be
played justly without the division of the octave into any particular
intervals.

"Now the true difference between flats and sharps, between flats and
naturals, or between sharps and naturals, is 1/3 tone. For example,
between Bb and B is 1/3 tone, and between Eb and E is 1/3 tone again.
But on the other hand between F# and G is 2/3 tone. I have marked this
distinction whenever necessary for the sake of clarity. For most
musicians and singers have hitherto confounded sharps and flats. But
only when a G for example is twice flatted, is it the same as F#.

"As for all other information regarding this matter, I leave it sirs, to
your most reliable and equitable judgement, which will permit you to
benefit from my labors, both now and in the future. And in this spirit I
pray God that He may keep you ever in His peace.

Paris, 1 January 1570

[End of Costeley's Preface}

It would appear from the preceding that in part to Guillaume Costeley,
and not entirely to Salinas (or Zarlino) must be attributed the signal
honor of first devising the 19-tone equal temperament, or a very close
approximation thereto. Costeley's report however does not mention his
procedure for obtaining 19 equal tones, and so remains less useful to
the theorist than the careful studies of Salinas, which is perhaps why
his contribution has been hitherto ignored, even by the French.

Salinas, by the way, clearly recognized that his 1/3 comma mesotonic
amounted to a virtually equal division of the octave into 19 tones. He
expressly states this, and comments on the relevance of this to
enharmonic melody, even though the legend has grown up (presumably
propagated by an imperfect or cursory reader of the Latin) that he never
realized the virtually equal nature of the 1/3 comma mesotonic division.
This piece of impudence has been carried so far as to conjecture that he
never noticed the equal appearance of the 1/3 commatic intervals on his
own diagram (Salinas was blind.)

I have been able to find no references to Costeley's invention, either
in the well-known article "Costeley's Chromatic Chanson", which
inexplicably seems to assume that Costeley used 12-tone equal
temperament in that piece. Malherbe's article "Syst?me Musical et
Clavier ? Tiers-de-Ton' (le M?nestrel, XXIX, July 19, 1929, page 329 sq.
I have not yet seen - perhaps he mentions Costeley - one may be
permitted to hope.

Costeley also deserves credit for being perhaps the first to suggest
modulation of a mode to a different pitch by the introduction of alien
tones, the resources of which procedure are now well known, but were not
always so apparent.

The present writer has discovered that by stretching the octave by 2 or
3 cents the 19-tone harmonies can be made virtually as smooth as those
of the 1/4 mesotonic. This writer has examined this 19-tone equal
temperament at great length, and believes it to be as perfect, and
indeed as marvelous, as Costeley suggests.

I hope to publish from my extremely voluminous notes, additional
articles on this matter, but for now I have thought it important to make
more widely known the existence of this temperament, and the
extraordinary possiblities which it unfolds.


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