devil's advocate

[Susan Kline]

Stephen, is this book available? Has the English translation 
been published?

Thanks.

Susan

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At 08:41 AM 3/17/98 -0500, Stephen wrote:
>Read on, and note the date.
>I pass this on with no comment for now. (Bill Garlick are you there?)
>
>Stephen
>--------------------------------------------------------
>
>Montal, L'Art d'accorder soi-meme son piano 
>Paris: Meissonnier, 1836).
>(Annotated translation excerpts courtesy of Sandra Rosenblum)
>---------------------------------------------------
>
>Montal begins by discussing the tuning instructions in a number of recent
>books and describing the defect(s) of each. He states that there are two
>types of temperament: egal (moyen), which creates equality between the
>dozen half-steps of the scale, and inegale, in which some half-steps are a
>little different and which favors the purity [justesse] of certain keys to
>the detriment of others. In effect, he writes, the true purpose of
>temperament ought to be to apportion the alteration among the largest
>number of intervals possible in order to make it less perceptible. Today
>our pianists play unconcernedly in all the keys, thus equal temperament
>ought to be an absolute necessity. And composers follow their inspirations
>and write just as well in F-sharp as in F-natural, in D-flat and A-flat as
>well as in C and G-natural. Finally Montal acknowledges that he is happy
>to have made a special study of mathematics and of music before devoting
>himself to the art of tuning pianos, "for it is from the alliance of these
>three types of knowledge that I have deduced the reliable, straighforward,
>and easy method that I offer to the public today". 
>
>Equal temperament consists of changing intervals by the same quantity in a
>manner that divides the octave into twelve equal half steps. This
>makes all the keys equally perfect or, rather, equally out of tune, for
>none ought to be exactly perfect, but only tolerable. According to
>montal's method, one learns the degree of alteration of major thirds
>necessary in equal temperament by tuning three successive major thirds
>equally, and just enough wider [forte] than than perfect, so that the top
>note forms a perfect octave with the bottom note. Four successive minor
>thirds must be made slightly narrow [faible] to accomodate then within a
>perfect octave.  If four successive fifths, starting on c1, are each tuned
>to be perfect, the top note of the series, e3, if lowered two octaves,
>would make too wide a major third with the bottom c1. Therefore, the
>fifths must be made narrow by lowering their top notes and this alteration
>must be equally apportioned so that the top and bottom notes of the series
>form a major third exactly as wide as those within an octave. Finally, for
>teaching purposes, this process is repeated with descending fifths, which
>are made narrow by raising thier lower notes. 
>
>The progression for Montal's tuning is a series of descending fifths, with
>ascending octaves interspersed as needed to keep the setting of the
>temperament within the range f-b1. One tunes in succesion a1, the "lower"
>a as a perfect octave, and d1 as a slightly narrow fifth down from a1. The
>purity of the fifth is disturbed only "by a very light beating". The test
>of a wide fourth (a-d1) is then applied.  From here the succession for
>tuning is d1-g,g-g1,g1-c1,c1-f,f-f1 / f1-a#(bflat),
>a#-a#1,a#1-d#1,d#1-g#,g#-g#1,g#1-c#1 / c#1-f#,f#-f#1,f#1-b,b-b1,b1-e1.
>Finally one tests the fifth e1-1. 
>
>The two slashes (/) in the series show where Montal interrupts the tuning
>progression to apply tests for accuracy. At the first slash the tests
>include the major thirds f-a and f1-a1, and triad f-a-c1, but particularly
>the six-four chord c1-f1-a1, the arrangement of which - with the major
>third on top - allows the ear to detect the degree of alteration more
>precisely than in other position. At the second slash Montal urges testing
>with the three major thirds within the octave f-f1. These thirds, f-a,
>a-c#1, and dflat-f1 ought to be "equally wide" and when "struck one after
>the other ought to produce exactly the same effect on the ear".
>Interestingly, after the fifth c#1-f# is tuned, Montal suggests trying the
>chord f#-a#-c#1 which "ought to produce the same effect as the chord
>f-a-c1". This statement acknowledges the lack of key colour that results
>from equal temperament. 
>
>Similar tests apply at the end of the tuning.  For those who may not have
>achieved an accurate enough temperament Montal gives the entire tuning
>progression in reverse order, with rising fifths, allowing the tuner to
>retrace the steps to find and repair any error(s). When the temperament
>has been set successfully, the remainder of the piano is tuned in octaves
>and tested with the fifth below. The final verification includes playing
>four-part chords around the circle of fifths, during which all the keys
>should sound "equally tolerable", followed by playing chromatic scales in
>octaves, first in the treble, then in the bass. 
>
>After a long section on repairing pianos, Montal presents a chapter on
>acoustics, in which he included the fractions that express the precise
>physical relationships of all chromatic intervals, with the distinctions
>between enharmonic tones. 
>
>Stephen
>
>Stephen Birkett Fortepianos
>Authentic Reproductions of 18th and 19th Century Pianos
>464 Winchester Drive
>Waterloo, Ontario
>Canada N2T 1K5
>tel: 519-885-2228
>email: birketts@wright.aps.uoguelph.ca
>
>
>
Susan Kline
P.O. Box 1651
Philomath, OR 97370
skline@proaxis.com		

"Time will end all my troubles, but I don't always
approve of Time's methods."
		-- Ashleigh Brilliant