Yahoo Tuning Groups Ultimate Backup tuning tense diatonic

Hello, there, and I'd like to try briefly to address some of the
remarks about Zarlino and the syntonic diatonic tuning, which can be
applied either to the variety of modes prevailing in the 16th century,
or to the major/minor system which emerged in the later part of the
17th century, as Kirnberger (1771) and others did -- partially, and
"in theory."

First of all, while it is a commonplace of musical history that
Zarlino was "the first to address triads rather than intervals," this
statement may create the misleading impression that Zarlino was the
first to address combinations of three or more voices, a feature of
Gothic theory also (e.g. Coussemaker's Anonymous I, c. 1290 or 1300;
AnonymousJohannes de Grocheio, c. 1300; Jacobus of Liege, c. 1325;
Johannes Boen, 1357).

What Zarlino did do was to address saturated _5-limit_ triads in the
Erlichan sense of three-voice combinations of "third plus fifth or
sixth" -- in other words, combinations with an outer fifth plus a
major and minor third, or an outer sixth plus a major or minor third
and a fourth. Zarlino describes such saturated combinations as
representing _harmonia perfetta_ or "complete harmony," as they do in
a 5-limit context.

In fact, in a Gothic 3-limit context, theorists around 1290-1357
discuss stable three-voice trines (outer octave, lower fifth, and
upper fourth -- or the converse arrangement with the fourth below the
fifth), and Anonymous I and Jacobus find the arrangement with the
fifth below and the fourth above more smooth and pleasing.

Johannes de Grocheio says that it takes _three_ voices to "perfect a
consonance," e.g. D3-A3-D4 (MIDI notation with C4 as middle C), and
describes this trinic sonority as _consonantia perfectissma_ or "most
perfect consonance" -- a very similar description to Zarlino's 5-limit
_harmonia perfetta_ about 250 years later.

Anonymous I and Jacobus additionally note that the bare major ninth
(9:4) "seems to concord better" when a middle voice is added to
produce 9:6:4 (or, in frequency-ratio terms, 4:6:9) with two
concordant fifths, e.g. F3-C4-G4. They are addressing what Paul might
call "triadic harmonic entropy," and going beyond a theory of simple
intervals or dyads.

In discussing the unstable _quinta fissa_ or "split fifth" sonority
where an outer fifth is "split" by a third voice into a ditone or
major third and a semiditone or minor third, Jacobus expresses a
preference for the former arrangement but notes that the latter is
also used, e.g. A3-C4-E4, the opening sonority in a 13th-century motet
which he cites and is happy preserved in the Bamberg and Montpellier
Codices for our admiration.

Note that Jacobus discusses these three-voice sonorities in a setting
where they are _unstable_ 3-limit combinations, in contrast to
Zarlino's stable 5-limit _harmonia perfetta_ involving the same types
of intervals (in 5-limit JI or meantone, rather than Gothic
Pythagorean). This is the distinction between medieval theory and
Zarlino: both discuss three-voice combinations, but in different
systems of musical and intonational practice and theory.

Around 1357, Johannes Boen (in a "modern" 14th-century stylistic
setting) finds the tritone or diminished fourth dissonant in itself,
but a consonance "by situation" (_per accidens_) in a sonority such as
D3-F3-B3 (tritone with minor third below) or E3-G#3-C4 (diminished
fourth with major third below). Again, this clearly goes beyond a
theory of simple intervals or dyads, and within a 3-limit setting as
opposed to Zarlino's 5-limit system.

Recognizing these Gothic 3-limit theories of complete stable trines,
and also of "triadic harmonic entropy" as we might term it for some
unstable sonorities, doesn't in any way diminish Zarlino's
accomplishments in describing _5-limit_ sonorities.

As for the syntonic diatonic, Zarlino himself indeed credits it to
Ptolemy, and Fogliano (1529) provided an earlier 5-limit use of this
scheme in the new stylistic setting of the 16th century to obtain pure
major and minor thirds at 5:4 and 6:5.

Note that Zarlino's basic scheme might best be defined in terms of
solmization syllables: 9:8 whole-tones appear immediately above mi-fa
semitones, and also at A-B, leaving 10:9 whole-tones at other
locations. The solmization system, with its hexachords, can be used to
sing in any of the 12 modes recognized by Zarlino, following Glareanus
(1547). A diatonic semitone is always sung mi-fa, and "mutations" from
one hexachord to another are required to cover a complete octave, as
here from the natural (C-A) to the "hard" (G-E) hexachord:

C D E F G A B C
ut re mi fa sol re mi fa
9:8 10:9 16:15 9:8 10:9 9:8 16:15

People curious about solmization and hexachords might visit:

http://www.medieval.org/emfaq/harmony/hex.html

Paul, you are quite correct that Zarlino regards temperament much more
practical for keyboard instruments, and champions 2/7-comma meantone
(1558), although in 1571 he additionally recognizes that 1/4-comma
meantone is pleasant and easy to tune, and somewhere as I recall
describes 1/3-comma as "somewhat languid." For the lute, as I recall,
he follows the consensus of middle to late 16th-century theory and
favors 12-tone equal temperament (12-tET).

It is for unaccompanied singers that Zarlino regards 5-limit JI (the
syntonic diatonic) as the best model, and it's an interesting question
how he might view an adaptive JI system such as Vicentino's. He also
describes a 16-note classic JI keyboard (two D's, Bb's, Eb's, and
F#'s), but recognizes that it is difficult to play, and favors
meantone in practice.

For Zarlino, there are 12 modes, with the Ionian mode (C-C) regarded
by 1573 or so as "first among equals," as one might say. However,
16th-century Ionian is not the same thing as major tonality, because
the late 17th-century constraints of key don't apply. Beautiful
3-limit progressions such as M3-5 by contrary motion continue to guide
motion in the new setting of textures moving between saturated 5-limit
sonorities. Degrees such as B/Bb and F/F# are fluid and flexible in
various modes, including Ionian. These comments apply to early
17th-century music also.

As the Monz has correctly observed, the German theorist Johannes
Lippius (1610, 1612) followed Zarlino both in advocating Ptolemy's
syntonic diatonic and in much of his approach to the 12 modes.
Additionally, he made Zarlino's 5-limit _harmonia perfetta_ the
centerpiece of his approach to music, both theological and practical,
apparently coining the term _trias harmonica_ or "harmonic triad" for
a saturated 5-limit sonority.

At any rate, I'm quite confident that Zarlino would _not_ consider
40:27 an appropriate tuning for the main fifth of the Dorian mode
(D-A), a mode being largely defined by its consonant species of fifth
and fourth, so his JI scheme is more a model than a fixed "scale."

Although earlier authors, especially Fogliano and Vicentino (1555), had
discussed 5-limit JI and Ptolemy, Zarlino does deserve to have this
tuning system associated with his name, given his rich contributions
to the art, including his comparison of 5-limit saturated sonorities.

It's interesting that in 1771, Kirnberger describes two ideal tuning
systems: the "modern" system of Zarlino, and the older one of
Pythagoras. At the same time, he notes that singers must sometimes
make compromises, and like Zarlino endorses temperament for keyboard
instruments (in Kirnberger's case, unequal well-temperament with its
distinctions of keys).

As far as Zarlino's championship of _diatonic_ music goes, he indeed
argues in his _Harmonic Institutions_ of 1558 that the diatonic genus
is basic to modern polyphonic music in the various modes, unlike the
situation with Greek music (presumably monophonic for the most part)
where the chromatic or enharmonic genus could have been used to better
effect.

In attacking the "chromaticists" -- likely Vicentino in particular --
he argues that intervals such as the chromatic semitone or enharmonic
diesis must have a bad effect in polyphony because they are
disproportionate to the proper vertical concords. He also argues --
taking the same position as Lusitano in the Vicentino/Lusitano
disputation of a few years earlier (1551?) -- that the mere use of a
melodic minor third or major third does not change the genus from
diatonic to chromatic or enharmonic, as claimed by the "chromaticists"
(specifically the unnamed Vicentino).

This does not mean that Zarlino is opposed to the use of accidentals,
which he finds indispensable (for example to make a sixth major before
an octave), only that such accidentalism should have what he considers
a "reasonable" or "justifiable" basis. He clearly takes the view that
the "chromaticists" have gone beyond such bounds.

In short, Zarlino (1558) is the first theorist to discuss and analyze
multi-voice combinations at length in a _5-limit_ setting, in contrast
to a Gothic 3-limit setting, although brief remarks in the earlier
treatise of Vicentino (1555) urge a "richness of harmony" based on
guidelines which essentially prescribe saturated 5-limit sonorities.
He champions both the syntonic feature of Ptolemy's tuning (the pure
5-based ratios) and the diatonic genus as the norm in polyphonic music,
based on a system of 12 modes.

Most respectfully,

Margo Schulter
mschulter@value.net

tense diatonic

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