Mathieu on chromatic scales, superdiesis, Medieval music

A while back I had a debate with Daniel Wolf on chromatic passages in
Mozart. W. A. Mathieu, in _Harmonic Experience_, backs up my point of view
perfectly (the beginning of chapter 42):

". . .an entirely new musical force.

"_The Equal-Tempered Chromatic Scale_

"The new force arises from the ear's response to a succession of tones
equidistant from one another. On the equal-tempered keyboard, play a
chromatic scale evenly, without particularly choosing where you begin or
end. The ear hears the even spacing between the pitches with the same kind
of perception with which the eye sees the even spacing of a picket fence or
the lines of type on the printed page.
In just intonation, no such thing occurs. A just chromatic scale is
quite uneven, containing a wide variety of semitones depending on the
tuning, potentially including not only the [5-limit] 16:15, 25:24, 135:128,
and 27:25 but also the Pythagorean 256:243, as well as the septimal 28:27
and 21:20. To hear such chromatic scales played smoothly and rapidly sounds
haphazard and unmusical; indeed, they have the cumulative effect of a poorly
constructed picket fence. Even in the various unequal temperaments
(including meantone and Bach's well temperaments), a chromatic scale has
nothing of the smooth sheen ours possesses.
Before the days of equal temperament, the tones of a chromatic passage
were heard in terms of their harmonic function. . . . sing each tone of the
slowly rising scale in just intonation as a functional resonance (including
the dissonant but compelling 45:32 F#). The issue of equal distance is
nowhere in sight. What we get is a cogently bonded melodic ascent
accompanied by wildly divergent harmonic contrasts: rare, but dramatically
useful when used in moderation. Likewise, if you tune a keyboard (electronic
or chromatic) to some version of the just chromatic scale and play it slowly
over the tonic or dominant, you can also hear the widely divergent harmonic
effects; if you play the same just scale rapidly over several octaves but
out of tonal context, the harmonic effect disappears and the melodic residue
is simply uneven -- in fact, it sounds out of tune. Now play the scale
rapidly on the equal-tempered keyboard and hear how the various harmonic
functions simply disappear beneath the gloss of evenly spaced percussive
events
. . . .
An equal-tempered chromatic scale out of context is purely melodic and
_merely_ chormatic (see chapter 35); it has no tonal function and no proper
spelling. It is difficult for the modern ear, which takes such things for
granted, to imagine how the new aural artifact was heard by the
eighteenth-century ear, but the surviving literature tells much of the
stort. Chromatic flourishes in Bach are rare (and usually appear in the
context of descending diminished triads), but by Mozart's time, chromatic
scales in cadenzas were common. Between 1750 and 1790, as equal temperament
became more the rule than the exception in Europe, and as it became more
familiar, composers and improvisors gradually began to resond to its newly
available effects. By the early nineteenth century, chromatic scales were
part of the compositional fabric.
Play an equal-tempered chromatic scale again, up and down several
octaves in one hand, not too fast, and let your ear savor its regularity,
its newfangled, manufactured, precisely measured _sameness_. Don't be bored,
be fascinated, mesmerized. This sensibility opens the door for the more
complex symmetrical forces hidden inside the Trojan horse of equal
temperament."

In a later chapter, Mathieu introduces a new definition for the
"superdiesis", contradicting the one he introduced earlier (that I quoted a
few weeks ago). The new definition is the same as what others have called
the "major diesis" arising from a chain of four 6:5 minor thirds, and
Mathieu finds it as an interval of equivalence in Bartok's "In the Style of
a Folk Song" from _Microcosmos_.

Mathieu uses a modified type of standard notation called "tone lattice
notation" to represent 5-limit JI. He writes,

"Tone lattice notation is most suitable for music that can be performed with
few or no Didymic [=syntonic] commas, and the Medieval literature abounds
with such pieces. _Fumeux fume_ by Solage, a French composer who flourished
in the late fourteenth century, is a remarkable mix of architectural
subtlety and pentamerous sweetness. This rondeau was evidently composed for
a "society of smokers" -- possibly of opium or hashish -- who no doubt
delighted in the stylistic whimsy and intricate design. . . .
The harmonic motion of Solage's piece is almost grotesquely extended,
yet the journey through the vast territory is beautifully balanced and
etirely believable. The net result is hardly caprice, but rather, deep
satisfaction. A most wonderful thing is that there is no harmonic ambiguity.
No singer or player needs to sing or play through a single comma, and each
part has modal as well as melodic intergrity. . . ."

It would be wonderful to have a MIDI file of this piece (which is written
out in the book). Also, we might ask Margo, isn't the late fourteenth
century a bit early for a French composer to be using 5-limit so
extensively? Was Solage ahead of the currents of his time?

Paul:

If you sort out the topoi in which chromatic scales are used in Mozart (and
Haydn) you will find nothing of the romantic steely precision found in
later, romantic musics (or even in Bach, for that matter). Instead,
chromatic textures are used for exoticism, danger, or catastrophe (i.e.
accompaning the Stone Guest in _Don Giovanni-). For these purposes, the
uneven patterns of meantone chromatic scales are ideal.

There is also a technical argument to be made: Viennese classical fingering
avoided the thumb, thus passage work was continuously broken into grupetti
of two or three pitches, yielding anything but the smooth effect of high
romantic pianism. (in contrast, Bach famously used his thumb!).

Coincidentally, I hope to find the time in the next month or so to offer the
list a review of the three volumes of Herbert Kelletat's "Zur musikalischen
Temperatur. The first (1992) deals with "Bach and his time", the second with
Viennese classicism, and the third with Franz Schubert.

Daniel Wolf

>Are we talking about the same Mozart and Bach??? I hear plenty of chromatic
>runs in Mozart that sound perfect as even, featureless ascents or descents,
>but none in Bach. I suppose we'll have to agree to disagree.

What Bach are you listening to?

Although there is never a way to be sure how something was played 200 years
ago, everybody seems to agree that runs, both diatonic and chromatic, were
not played smoothly, but instead played as strings of tiny phrases, up
until Beethovan, at least. It is true that historical fingering leads
naturally to grupetti, but just because Bach used his thumb doesn't mean
that he played runs smoothly.

-Carl

On Tue, 1 Feb 2000, Carl Lumma wrote:
>> Are we talking about the same Mozart and Bach??? I hear plenty of chromatic
>> runs in Mozart that sound perfect as even, featureless ascents or descents,
>> but none in Bach. I suppose we'll have to agree to disagree.
>
> What Bach are you listening to?
>
> Although there is never a way to be sure how something was played 200 years
> ago, everybody seems to agree that runs, both diatonic and chromatic, were
> not played smoothly, but instead played as strings of tiny phrases, up
> until Beethovan, at least.

Erh? These are the runs that Mozart said must "flow like oil"?

--pH <manynote@library.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Foul? What the hell for?"
-\-\-- o "Because you are chalking your cue with the 3-ball."