From: mclaren
Subject: William Sethares' request for info...
--
In Topic 3 of Tuning Digest 684, 6 April 1996,
William Sethares requested a body of musical
literature which would sound particularly
godawful if Pythagorean 3rds were substituted
in place of the "usual" 12-TET thirds.
IMHO, the body of musical literature most clearly
illustrating this effect is the keyboard music
written for meantone tuning. Tudor music of
England composed between 1520 and 1620 shows
this property of Pythagorean thirds with particular
clarity. Compositions like William Byrd's "The
Carman's Whistle," when played with an organ
timbre in Pythagorean tuning, sound remarkably
bad ( to these old ears).
(Incidentally, the English virginal music of this
period is one of the great undiscovered bodies
of keyboard masterworks in the European canon.)
The reason why these compositions sound so icky
of keyboard masterworks in the European canon.)
The reason why these compositions sound so icky
when played in Pythagorean is that Byrd, Bull,
Gibbons, Ferrabosco, Tomkins and the rest of the
16-century English Tudor composers used meantone
tuning. Their virginals and their foot-pump reed chamber
organs boasted long chains of pure just major 3rds
along with considerably tempered fifths; thus, Byrd's
compositions generally sound painful on modern pianos
tuned to the usual Railsback-stretch 12-TET.
Byrd, Bull, Gibbons et al. favored long passages of
eighth- and sixteenth-note major third 5/4s
arabsequed around, over and underneath a much
slower cantus firmus. While this style of composition
clearly shows the influence of vocal music from
Dunstable's time, it even more clearly illustrates
the adventurous nature of the Tudor composers--
because these strings of 5/4s were a new resource
in meantone virginal tuning. They let the composers
because these strings of 5/4s were a new resource
in meantone virginal tuning. They let the composers
of that period show off the extraordinary sweetness
of just thirds on the harmonic-series timbres of the
English viriginal and chamber pump organ.
Retuning these just 5/4s to Pythagorean goes just
as about as far as possible in violating the composers'
original intentions. It sounds godawful--but does not,
of course, prove that Pythagorean thirds are wretchedly
dissonant intervals. Rather, this perverse exercise
demonstrates only that the intonation in which a piece
of music was historically composed is as much a part
of a truly musical performance as is technical skill
on a pianist's part, knowledge of the ornaments typical
to a period, understanding of figured bass conventions,
etc., etc.
Retuning Bach's chorales to Pythagorean would likely
produce less grating results. The evidence appears to
indicate that Bach used one of the circulating irregular
produce less grating results. The evidence appears to
indicate that Bach used one of the circulating irregular
temperaments rather than straight meantone; thus fewer
of Bach's major thirds were tuned to 5/4 vs. almost all just
major thirds in music of the English Tudor composers. (This
is primarily due to the fact that Tudor composers didn't
need to modulate nearly as much or as often as did Bach.) The
advantage of the Kirnberger/Werckmeister intonations
is less the superb sweetness of their major thirds on
a harmonic-series instrument than the intonation's
ability to distribute usable triads over many more
keys and thus allow much wider modulation than did
classic 1/3-comma or 1/4-comma meantone. By way of
comparison, Don Hall has calculated that 1/4-comma
meantone has 14 awful-sounding keys and 10 very smooth
keys; Werckmeister II has 14 reasonably good-sounding
keys, 10 dubious-sounding keys, but no truly godawful
ones. (This is due to the "wolf" in 1/4-comma meantone--
which arises ONLY when you limit meantone to 12 pitches.
ones. (This is due to the "wolf" in 1/4-comma meantone--
which arises ONLY when you limit meantone to 12 pitches.
In a gamut of 27 pitches, as A. J. Ellis pointed out in
Helmholtz's "Sensations of Tone" on page 452, if memory
serves, 1/4-comma meantone would produce *no* godawful-
sounding keys and *no* "wolf" fifths in 18 of the 24 possible
major and minor keys.)
Alas, to uncover the facts of historical intonation, a student
is FORCED to burrow into the library stacks for hi/rself.
Until you read the original texts of the original authors
of the period, it isn't at all obvious that 12-TET piano
performances of Renaissance keyboard compositions are
about as intonationally and musically accurate to the
composers' intentions as performing Beethoven's fifth
with a Balinese gamelan.
--mclaren
