Jablonski, Marek (Michael)

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2. Instruments.

Rameau reported (1737) that some masters of the violin and basse de viol tempered their open-string intervals – an idea also found in the writings of Werckmeister (1691) and Quantz (Versuch einer Anweisung die Flöte traversiere zu spielen, 1752). But Boyden has shown (1951) that evidence from the writings of 18th-century violinists, particularly Geminiani and Tartini, points to a kind of just intonation flexibly applied to successive intervals with adjustments when necessary both melodically and harmonically on each of the four strings, tuned in pure 5ths, as points of reference. In the 1760s Michele Stratico, a former pupil of Tartini, worked out a fairly efficient system of notation for this kind of just intonation, including septimal intervals (ex.3).

To model a fretted instrument upon just intonation entails the use of zig-zag frets. Dirck Rembrandtsoon van Nierop, a mathematician who favoured just intonation for all sorts of instruments as well as voices, worked out (1659) an exact fretting scheme for a cistern (fig.4a), according to which, if the open-string intervals were tuned as in fig.4b, then each position on the highest course could be supplied with one or more justly intoned chords as shown in ex.4. Some other devotees of just intonation who designed fretted instruments were Giovanni Battista Doni, Thomas Salmon and Thomas Perronet Thompson (see fig.5).

The simplest way to provide all possible pure concords among the naturals of a keyboard instrument with fixed intonation is to have two Ds, one pure with F and A and the other, a comma higher, pure with G and B (see fig.6a). (The concept of a diatonic scale in just intonation with two Ds a comma apart goes back to Lodovico Fogliano's Musica theorica, 1529.) If this group of eight notes is then provided with a complement of ten chromatic notes as indicated in fig.6b, each natural will have available all six of its possible triadic concords. This scheme was described by Mersenne and employed by Joan Albert Ban for a harpsichord built in Haarlem in 1639 (for illustration see Ban, Joan Albert). Mersenne stated that on a keyboard instrument of this type the ‘perfection of the harmony’ would abundantly repay the difficulty of playing, ‘which organists will be able to surmount in the space of one week’.

The ‘justly intoned harmonium’ of Helmholtz (in mathematical terms not exactly embodying just intonation, but deviating from it insignificantly from a practical and acoustical point of view) combined two normal keyboards for the scheme shown in fig.7. The 12 pitch classes shown to the left are on the upper manual, the 12 to the right on the lower manual. No justly intoned triadic note is present beyond the lines along the top and bottom of the diagram, but the three notes at the right end (A, C or D, and E) make justly intoned triads with the three at the left (E, G or A, and C). Thus the major and minor triads on F, A, and D or C require the use of both manuals at once. The 12 pitch classes shown in the upper half of the diagram are each a comma lower in intonation than their equivalents in the lower half of the diagram. Every 5th except C–G or D–A is available at two different pitch levels a comma apart, and the same is true of six triads: the major ones on E, B and F, and the minor ones on G, D or E, and B. In the case of triads on C, D, F, G and A, however, the major triad is always intoned a comma higher than its parallel minor triad.

Various other elaborate keyboard instruments capable of playing in just or virtually just intonation have been built by Galeazzo Sabbatini, Doni, H.W. Poole, H. Liston, R.H.M. Bosanquet, S. Tanaka, Eitz, Partch, the Motorola Scalatron Corporation and others (see Microtonal instruments). Playing such an instrument involves choosing which form of each note to use at which moment. If the proper choice is consistently made, impure vertical intervals will be avoided and the occurrence of impure melodic ones minimized. The criteria for choosing, which differ in detail with each kind of elaborate keyboard pattern, are intricate but capable of being incorporated in a pattern of electric circuits amounting to a simple computer programme. In 1936 Eivind Groven, a Norwegian composer and musicologist, built a harmonium with 36 pitches per octave tuned to form an extension of Helmholtz's quasi-just-intonation scheme, but with a normal keyboard, the choice of pitch inflections being made automatically while the performer plays as on a conventional instrument. He later (1954) devised a single-stop pipe organ of the same type, now at the Fagerborg Kirke in Oslo, a complete electronic organ with 43 pitches per octave (1965), now at the Valerencen Kirke in Oslo, and a complete pipe organ incorporating his invention (c1970, built by Walcker & Cie.). Groven's work has made just intonation practicable on keyboard instruments that are no more difficult to play than ordinary ones.

While the distinctive quality of justly intoned intervals is unmistakable, their aesthetic value is bound to depend upon the stylistic context. In 1955 Kok reported, on the basis of experiments with an electronic organ capable of performing in various tuning systems, that musicians, unlike other listeners, heard the difference between equal and mean-tone temperaments, giving preference to the latter, ‘and a fortiori the just intonation, but only in broad terminating chords and for choral-like music. However, they … do not like the pitch fluctuations caused by instantaneously corrected thirds’. According to McClure (‘Studies in Keyboard Temperaments’, GSJ, i, 1948, pp.28–40), George Bernard Shaw recalled that in the 1870s the progressions of pure concords on Bosanquet's harmonium (with 53 pitches in each octave) had sounded to him ‘unpleasantly slimy’. E.H. Pierce (1924), describing the 1906 model of the Telharmonium, which was capable of being played in just intonation with 36 pitches in each octave, reported:

The younger players whom I taught … at first followed out my instructions, but as time went on they began to realize (as in fact I did myself) that there is a spirit in modern music which not only does not demand just intonation, but actually would suffer from its use, consequently they relapsed more and more into the modern tempered scale.

The composer and theorist J.D. Heinichen remarked (Der General-Bass in der Composition, 1728, p.85) that because keys with two or three sharps or flats in their signature were so beautiful and expressive in well-tempered tunings, especially in the theatrical style, he would not favour the invention of the ‘long-sought pure-diatonic’ keyboard even if it were to become practicable. These remarks suggest that the recently achieved technological feasibility of just intonation on keyboard instruments is but a step towards its musical emancipation and that further steps are likely to depend on the resourcefulness of composers who may be inclined in the future to discover and exploit its virtues.

Just intonation

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