Teaching of Intonation After Mozart's Death

This is a summary of some interesting points from Chesnut, John
Hind. "Mozart's teaching of intonation", Journal of the American
Musicological Society vol. 30 no. 2, summer 1977, pp. 254-271.

Shortly after Mozart's death there began to appear an advocacy of
Pythagorean-type tunings by some string players -- in other words,
sharps were, for the first time since the Middle Ages, supposed to be
played slightly _higher_ than the enharmonically equivalent flats.
Chesnut, echoing Anton's recent postings about Ogolevets, writes,

"It may be that the disposition of some nineteenth-century string
players to use a system of intonation approximating Pythagorean
tuning -- a tuning system based on pure fifths -- was influenced by
the fact that the standard orchestral stringed instruments are tuned
in fifth (basses in fourths). Several nineteenth-century violin
teachers, however, including one of Joachim's teachers, explicitly
recommended shading pitches in the direction of their "attachment",
as defined by harmonic context, in order to achieve an "animated"
performance. In other words, they explained this practice in terms of
the structure of music, not in terms of the structure of stringed
instruments. We might call such a system "functional intonation". In
such a system, tendency tones, such as the leading tone and the
seventh of the dominant-seventh chord, are inflected in the direction
of their tendency to resolve, diatonic half steps are smaller than
chromatic half steps, and sharped notes are higher than
enharmonically equivalent flatted notes. Present-day string
intonation seems to follow this nineteenth-century practice. And the
present author's observation is that other non-keyboard performers of
our own time tend to play these small half steps. According to Louis
Richardson, Pablo Casals called the hightening of melodic tendencies
through intonation 'la justess expressive' (expressive intonation)."

Later I'll try to post summaries of this article's point on the
teaching of intonation shortly _before_ Mozart (that is, by those who
would have influenced Mozart and his father), and of course by Mozart
himself. The short answers are:

Before Mozart -- Meantone temperament, specifically something close
to 55-tone equal temperament;
Mozart -- Meantone temperament, but M. was unspecific as to the exact
amount of tempering.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> Before Mozart -- Meantone temperament, specifically something close
> to 55-tone equal temperament;

So you mean somewhere between 1/6 and 1/5 comma, i.e. away from 1/4
comma in the direction of 12-tET (1/11 comma)?

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
These two passages appear to contradict each other. the first says
"harmonic context", the second "melodic tendencies". Clearly melodic
tendencies explain it, harmonic context does not (at least not 5-limit
harmonic context).

1.
> Several nineteenth-century violin
> teachers, however, including one of Joachim's teachers, explicitly
> recommended shading pitches in the direction of their "attachment",
> as defined by harmonic context, in order to achieve an "animated"
> performance.

...

2.
> In
> such a system, tendency tones, such as the leading tone and the
> seventh of the dominant-seventh chord, are inflected in the
direction
> of their tendency to resolve, diatonic half steps are smaller than
> chromatic half steps, and sharped notes are higher than
> enharmonically equivalent flatted notes. ... According to Louis
> Richardson, Pablo Casals called the hightening of melodic tendencies
> through intonation 'la justess expressive' (expressive intonation)."

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:

> > Before Mozart -- Meantone temperament, specifically something
close
> > to 55-tone equal temperament;
>
> So you mean somewhere between 1/6 and 1/5 comma, i.e. away from 1/4
> comma in the direction of 12-tET (1/11 comma)?

Specifically, in the period and culture immediately preceding Mozart,
sharps were said to be a comma lower than the enharmonically
equivalent flats. "Comma" did not differentiate between Pythagorean
comma and syntonic comma. The whole tone was said to contain nine
commas. So the diatonic half step would be five commas. Thus the
octave was fifty-five commas.

--- In tuning@y..., "Dave Keenan" <D.KEENAN@U...> wrote:
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
> These two passages appear to contradict each other. the first says
> "harmonic context", the second "melodic tendencies". Clearly
melodic
> tendencies explain it, harmonic context does not (at least not 5-
limit
> harmonic context).

"Harmony" doesn't just mean verticality . . . except for Partch and
for some of us when we get too consonance-focused.

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

/tuning/topicId_23952.html#23952

> This is a summary of some interesting points from Chesnut, John
> Hind. "Mozart's teaching of intonation", Journal of the American
> Musicological Society vol. 30 no. 2, summer 1977, pp. 254-271.
>

Hi Paul!

I just forwarded this interesting post on to my friend Anton, so that
he's sure to get it when he gets back. He's still at the
contemporary music festival in Odessa and not back in Moscow yet...

_______ ______ ____
Joseph Pehrson

This is a summary of some interesting points from Chesnut, John
Hind. "Mozart's teaching of intonation", Journal of the American
Musicological Society vol. 30 no. 2, summer 1977, pp. 254-271.

Quoting from Chesnut:

"The type of tuning we presently call 'meantone temperament' is not
called a 'temperament' in the eighteenth-century terminology we find
here. Only the compromise tuning used at the keyboard [well-
temperaments] are called 'temperaments' in these sources. In fact,
the writers of these sources were so unconscious of alternatives to
what we call 'meantone temperament' for the uncompromised tuning of
non-keyboard instruments that they had no name for this system at
all; they thought of what we call 'meantone temperament' simply as
correct intonation. [Not surprising since it had flourished since the
late fifteenth century.] But let us now examine these sources more
specifically.

"Leopold Mozart refers to Tosi in general terms as an authoritative
source in a letter to Wolfgang from Salzburg dated June 11, 1778.
Tosi, in 1723, considered the correct tuning system to be what we
would today call a form of regular meantone temperament with more
than twelve notes to the octave, or what we might call for
short 'extended regular meantone temperament'. He says that this
temperament should be employed by bowed instruments. Tosi does not
tell us specifically what tuning one would expect to find on the
keyboard instruments of his time, but only that they are not capable
of playing more than twelve notes to the octave without split
keys. . . . according to Tosi, the large diatonic half step is
theoretically equal to five ninths of a whole step, and the small
chromatic half step is theoretically four-ninths of a whole step.
Tosi thereby divides the octave into fifty-five equal parts [Monz,
take note]. This is equivalent to tempering the perfect fifth by
approximately one-sixth of a 'comma,' [footnote explains that this is
approximately correct with regard to either Tosi's comma (=1/55
octave), the syntonic comma, or the pythagorean comma] . . . Many
other divisions were considered in the eighteenth century, as were
irregular keyboard tuning systems that do not divide the octave into
a multitude of equal parts, but the fifty-five-part division had
prominent adherents. Georg Andreas Sorge, in particular, attributed
it to Telemann, explaining that in its complete state it could not be
used on the clavier; but it might be applied to the violin and to
certain wind instruments and was easiest for singers. In its
incomplete state, Sorge attributed the fifty-five-part division to
the organ builder, Gottfried Silbermann. According to Mark Lindley,
Sauveur and his editor Fontanelle, writing ca. 1700, described the
1/6-comma temperament as that most favored by musicians in general,
as distinguished from keyboard musicians in particular, some of whom
tuned differently. The 1/6-comma temperament is the one implied by
Türk's statement of 1791, previously cited from Boyden, that sharps
are a 'comma' lower than the equivalent flats; it also seems to be
the most common basis fro the irregular temperaments described by
Barbour in _Tuning and Temperament_.

"Although the Mozarts, certainly Leopold Mozart, seem to have been
very well read, no mention of Quantz is found in their writings. We
shall discuss him here, however, as an important figure continuing
the tradition of Tosi. Quantz, in his flute method of 1752, advocates
a tuning system for the flute identical to that recommended by Tosi.
He gives the flutist a wealth of practical advice on how to obtain
correct intonation, even suggesting a mechanical improvement for the
flute, but admits that only a minority of flutists of his time
observed those rules. Most of his contemporary flutists he considered
to be quite bad, not even knowing how to obtain a pleasant tone
quality on high notes. Quantz tells us that keyboard instruments, not
being able to make pitch distinctions in the manner of the flute,
resort to tempering [i.e., well-tempering] . . .

"Leopold Mozart, in his violin method of 1756 -- which happens to be
the year of Wolfgang's birth -- also describes what we have
called 'extended regular meantone temperament' as the correct
intonation for the violin; he tells us that keyboard instruments of
his time were played with some form of tempered [i.e., well-tempered]
tuning, but that in the "right ratio" [i.e., meantone] tuning that he
recommends for the violin, flats are higher by a comma than
enharmonically equivalent sharps. It can be shown that for whichever
of the standard commas we choose, the perfect fifths in Leopold
Mozart's system were theoretically flattened by about one-sixth of
that comma . . . Leopold Mozart wrote down a couple of scales
specifically intended for practice in intonation, one leading through
the flats, the other through the sharps. In practicing these scales,
the student is supposed to learn to distinguish between the large
diatonic half steps and the small chromatic half steps. It is
important to emphasize that these scales are not abstractions but
exercises to be mastered . . .

"That the use of keyboard accompaniment for the strings was
conditional, and not inevitable, is implicit in Leopold Mozart's own
discussion of the subject. The point is also illustrated by an
anecdote of André Schachtner. According to Schachtner, immediately
after the Mozarts' return from Vienna early in 1763, Wolfgang, to the
astonishment of those present, took part in playing certain trios by
Wentzel, even though he had had no instruction in the violin.
Schachtner names the musicians taking part -- Leopold Mozart
performed the bass part, Wentzl played first violin, and Schachtner
himself (later Wolfgang) played second violin. Schachtner makes no
mention of any keyboard accompanist. According to James Webster, 'the
evidence that the continuo had been abandoned in secular Austrian
chamber music by 1750 is overwhelming.' For this reason, the problem
of reconciling the pitch of keyboard and non-keyboard instruments
would not have arisen very often in small ensembles in W. A. Mozart's
time. And Quantz tells us that these fine distinctions of pitch are
only perceptible in small ensembles, so the problem of reconciling
the pitch of the two types of instrument can be disregarded where the
clavier plays with a full orchestra, as in Mozart's piano concertos.

[...]

"Horst Walter reports that surprisingly late in the eighteenth
century there were still attempts to circumvent the physical
limitations of the keyboard that normally require compromise tunings
of enharmonically equivalent sharps and flats. The Londoner, Charles
Clagget, invented a piano tuned without such compromise temperament,
providing unaltered chromatic tones with pedals (operating like the
pedals of a harp, according to Lindley). Joseph Haydn visited
Clagget's shop in 1792 and reportedly gave high praise to Clagget's
improvements on the piano and harpsichord (which was apparently still
in use in 1792). In October of 1796, there was a demonstration in
Vienna of a new kind of piano built by Johann Jakob Könnicke in 1795
according to the plans of Johann Georg Roser, music director of the
cathedral in Linz. Beethoven, Joseph Haydn, and several music
directors and composers are said by Roser's son, Franz de Paula
Roser, to have played on this piano, a six-manual instrument with a
range of six octaves that allowed playing in all keys in their pure
[i.e., meantone] tuning . . . [putative connections with Mozart
described] . . . "

--- In tuning@y..., "Paul Erlich" <paul@s...> wrote:

> This is a summary of some interesting points from Chesnut, John
> Hind. "Mozart's teaching of intonation", <etc.>

Thanks for posting this, Paul. I've had this article for
several years, but your post prompted me to finally make
a webpage about it:

"Mozart's Tuning: a 12-tone subset of 55-EDO"
http://www.ixpres.com/interval/monzo/55edo/55edo.htm

-monz
http://www.monz.org
"All roads lead to n^0"

--- In tuning@y..., "monz" <
joemonz@y...> wrote:
>
> --- In tuning@y..., "Paul Erlich" <paul@s...> wrote:
>
> > This is a summary of some interesting points from Chesnut, John
> > Hind. "Mozart's teaching of intonation", <etc.>
>
>
> Thanks for posting this, Paul. I've had this article for
> several years, but your post prompted me to finally make
> a webpage about it:
>
> "Mozart's Tuning: a 12-tone subset of 55-EDO"
> http://www.ixpres.com/interval/monzo/55edo/55edo.htm
>
The article makes it clear that
neither on his keyboard nor in his
teaching of string intontation did
Mozart use a 12-tone subset of
55-EDO.