Re: TD 411 -- Reply to zHANg: What is microtonality?

Hello, there, and in Tuning Digest 411, zHANg, Zhang2323@aol.com writes:

> microtone - an interval smaller than a semitone (according to some
> theories & practises - 111.7 cents & smaller; by 12tET standards -
> smaller than 100 cents)

> with that definition in mind, _microtonal music_ is any music that
> is based on semitones smaller than those stated above...

You raise some very interesting issues here, and I'll try to address two
points: first, the question of how small an interval should be in order to
be regarded as "microtonal"; and secondly, the presence of "microtonal
nuances" in some musics which may not use direct intervals of this kind.

From an historical point of view, I might observe that 111.7 cents
likely represents the 16:15 diatonic semitone of 5-limit just
intonation (JI) described by such Renaissance theorists as Ramos
(1482) and Zarlino (1558), and advocated by the latter as the ideal
tuning for vocal music. Zarlino and others took the syntonic diatonic
division of the tetrachord or fourth by Ptolemy, 9:8 10:9 16:15, as
the basis for this system of intonation, which from a Renaissance
standpoint had the advantage of providing pure major and minor thirds
at 5:4 and 6:5 -- now the most favored consonances.

However, if we take anything smaller than 16:15 (or the 100 cents of
12-tet) as a "microtonal" interval, then conventional medieval
European music in 3-limit JI (Pythagorean tuning) is "microtonal,"
since it uses a diatonic semitone of 256:243, about 90.224 cents.

Further, by this "smaller than 16:15 or than 100 cents" definition,
any Renaissance piece using direct chromatic semitones (e.g. G-G#)
would be "microtonal," since the 5-limit chromatic semitone is 25:24,
~70.67 cents, while the same interval in 1/4-comma meantone is about
76.05 cents.

If we assume that a "microtonal" interval should be somewhat smaller
than a usual diatonic or chromatic semitone in the most common
European historical tunings, then the exact place to draw the line
remains unclear, although I would draw it on the narrow side of 25:24.

For example, I am not sure whether I would describe Guillaume
Costeley's 1/3-tone interval of 1/19 octave (~63.16 cents), or almost
exactly 28:27 (~62.96 cents), as a "microtone" or simply as a "very
narrow semitone." Anything narrower than this I would consider a
"microtone."

> though some would disagree with including quartertone music as being
> microtonal arguing that quartertone music is just an extension of
> 12tET resources.

To those asserting such an opinion, I might reply that 1/24 octave
should be considered a "microtone" if it is noticeably narrower than a
usual semitone, regardless of whether it is related to 12-tet, n-limit
JI, or some other tuning system. In challenging the uniquely
privileged position of 12-tet, I can at the same time respect it as
_one_ valid alternative in an open universe of tunings.

Since 24-tet is a very popular microtonal system for 20th-century
composed music, I would want to recognize it rather than exclude it
from a definition of "microtonality."

Incidentally, I wonder if "direct microtonality" might be a useful
term for the melodic use of "microtonal" intervals of the kind we are
discussing here. Other kinds of music may engage in what I might call
"microtonal distinctions" without necessarily using direct
microtonality:

(1) Medieval or Renaissance music realized in an extended tuning
system such as 3-limit JI or meantone may involve microtonal
distinctions between such notes as G# and Ab, the former note being a
Pythagorean comma (531441:524288, ~23.46 cents) higher in 3-limit, and
a diesis (128:125, ~41.06 cents) lower in 5-limit JI or 1/4-comma
meantone. If these notes are both used in the same piece, but are not
directly juxtaposed, then we have a microtonal distinction without
direct microtonality.

(2) Certain tuning systems, for example a 12-note version of 3-limit
JI popular in the early 15th century with a chain of fifths Gb-B, may
involve microtonally distinct "flavors" of the same basic vertical
interval, for example a contrast in this case between major thirds at
the usual 81:64 (~407.82 cents) and 3-limit diminished fourths at
8192:6561 (~384.36 cents, a Pythagorean comma smaller, and very close
to 5:4). Likewise, the well-temperaments of the late 17th-19th
centuries involve contrasting sizes of perfect fifths and thirds.

(3) Some tuning systems may also engage in microtonal adjustments of
certain notes for the sake of just intonation: for example,
Vicentino's adaptive JI tunings on his archicembalo, where certain
notes are apparently shifted by about 1/4 syntonic comma (~5.38 cents)
in order to permit the tuning of certain sonorities with pure 3:2
fifths and 6:5 minor thirds as well as 5:4 major thirds.

Thus one might say, for example, that early 15th-century keyboard
music in a Gb-B 3-limit tuning or Bach's keyboard music in a period
well-temperament indeed makes use of "microtonal nuances," although it
does not involve "direct microtonality" of the kind found in
Vicentino's enharmonic music or 20th-century compositions in 24-tet,
not to mention many world musics using smaller direct intervals than a
semitone.

Most respectfully,

Margo Schulter
mschulter@value.net