looking at Meantone, (long)

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Greetings, 
    The following was posted by Paul Erlich on the "Tuning" group list.  
Thought it may be of some interest to some.  
   I will be in Austin this weekend, hope all that are in the area and are 
interested in the Temperament Revival will come by for Saturday's class.  
Otherwise, it is on to Reno. 
Regards, 
Ed Foote

       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] . . . "