Enharmonic keyboard.

A keyboard with more than 12 keys and sounding more than 12 different pitches in the octave. Such keyboards may serve various purposes, to make available mean-tone temperament in tonalities involving more than two flats or three sharps (see Temperaments); to make possible the playing of a number of chords in Just intonation; and to produce microtones.

In many mean-tone tuning systems none of the usual chromatic degrees, C, E, F, G and B, can serve as its enharmonic equivalent. Tonalities involving more than these five chromatic degrees would not be playable on keyboard instruments so tuned without a retuning of some of the raised keys. The simplest enharmonic keyboards merely duplicate one or more of the raised keys in order to provide additional chromatic degrees, making these retunings unnecessary. Thus the G key may be divided into two parts sounding G and A respectively; E may be split in order to gain D, etc. Enharmonic keyboards with one or two split keys per octave were not uncommon in 16th- and 17th-century Italy and some are recorded north of the Alps, for example Father Smith’s organ in the Temple Church, London, or Zumpe's square piano of 1766 in the Württembergisches Landesgewerbemuseum, Stuttgart. They extended the range of playable modulations to tonalities involving up to three flats or four sharps. It should be observed, however, that the more extended the range of modulations becomes within one piece, the more need may arise for an enharmonic modulation. Because the enharmonic keyboard introduces an intervallic difference between enharmonic equivalents, it makes enharmonic modulations impossible if by this is understood a change of note name without change of its pitch. For instance, John Bull's famous chromatic fantasy on Ut re mi fa sol la (Fitzwilliam Virginal Book, vol.i, no.51), which starts in the mode of G and returns to that mode after 12 modulations, could be played on a keyboard of 17 notes in the octave but would sound awkward at the point where there is an enharmonic modulation, with an A major triad including a D instead of a C. Only a well-tempered tuning could smooth that passage.

Prosdocimus de Beldemandis's Libellus monocordi (1413) and Ugolino of Orvieto's Tractatus monocordi (c1430) seem to imply a keyboard with the five raised keys divided. The tuning is described as a mere extension of the regular Pythagorean tuning up to five sharps and five flats. However, such notes as A, G or D could hardly have been used in the early 15th-century repertory: they were most probably intended to be played as B, F and C respectively, forming major 3rds below D and above D and A. (A Pythagorean diminished 4th, such as A–D, D–G or A–D, is an excellent approximation of a pure major 3rd.) This keyboard thus provided the pure 5ths of the Pythagorean system and, for the chromatic degrees, alternative forms sounding pure 3rds to some of the diatonic degrees. It must therefore be ranged among the enharmonic keyboards aiming at just intonation for certain triads.

To achieve an extended just intonation on a keyboard instrument is a much more ambitious aim. A problem arises from the fact that, ideally, triads formed of pure 3rds and 5ths on such an instrument should also be connected to each other by pure 3rds and 5ths. If one connects chords on, say, C and E in just intonation, the one on E should be a pure major 3rd above the one on C, for E, the common note, is a pure 3rd above C in the C chord. But if elsewhere the chord on E is connected to the one on C through a root succession of 5ths as C–G–D–A–E, then E will have to be a Pythagorean 3rd above C if all five chords are to be connected by common notes a pure 5th apart. Thus the keyboard would need two E chords a comma apart, and an inordinate number of keys would be needed to permit completely just intonation in any one tonality. A related problem is that a few chord successions might cumulatively shift the pitch level by several commas, rendering participation in ensemble music prohibitively awkward.

Zarlino mentioned a harpsichord made by Domenico da Pesaro with raised keys inserted between E and F and between C and D, in addition to the five regular raised keys split into two. According to Zarlino, this keyboard was intended to permit the playing of quarter-tones – although Praetorius described a similar harpsichord owned by Karel Luython where the additional raised keys were tuned as E and B, thus permitting the tonalities of F and C. Many such keyboards with a large number of keys in the octave would appear to be able to fulfil more than one function, permitting for instance both just intonation and microtones. As shown above, however, even a large number of keys in the octave would not produce a complete solution of the problem of just intonation, a fact of which few ancient writers were aware. Keyboards with any number of keys between 24 and 60 in the octave were advocated by Salinas (1577), Fabio Colonna (1618), Mersenne (1636–7), G.B. Doni (1635–40), Galeazzo Sabbatini (c1650, quoted by Kircher), Athanasius Kircher (1650) and others. Interest in the enharmonic keyboard for just intonation was rekindled in the 19th century, often with a suitable understanding of the limited possibilities of such instruments. A.J. Ellis discussed experiments, often applied to reed organs, made by Helmholtz, Colin Brown, Liston, Poole, Perronet Thompson, Bosanquet and J.P. White.

Nicola Vicentino, who described his Arcicembalo with 35 keys in the octave in 1555, appears to have been one of the very few Renaissance or Baroque theorists to realize that the best purpose of an enharmonic keyboard would be the playing of microtones, and some of his compositions use the quarter-tone as a melodic interval. Several keyboards have been conceived to divide the octave into more than 12 equal parts. Best known is the 24-note division, producing equal quarter-tones. A division into thirds of a tone could include either 17 or 19 notes in the octave, depending on whether one or two thirds of a tone be taken to stand for the diatonic semitone (for other likely multiple divisions Interval, Table 1). Some multiple divisions have been thought to correspond to exotic or ancient musical systems, but actually they appear to represent new systems which, though essential to the music written for them, have not been shown to form a significantly better compromise for general use than ordinary 12-note equal temperament.

All the enharmonic keyboards have been built on the same general principles: black key levers are split longitudinally and the front end of the block (the part the player sees) overlaps the adjacent sharp or flat, making it look as if each black key were divided into a front and a back part (see fig.1). Often, when the total number of keys is more than 19 per octave, it has been found expedient to divide some of the white keys or to build two keyboards one above the other, as in Vicentino’s arcicembalo. An enharmonic harpsichord made by Vito Trasuntino in 1606, and now in Bologna (fig.2) has 31 keys per octave; each regular accidental key is divided into four parts, and additional keys divided into two are inserted between E and F and between B and C. The playing and tuning of such instruments are of course particularly difficult. This, together with the fact that the multiple divisions that they make possible often do not seem to correspond to any profound musical necessity, explains why they rarely passed the experimental stage. For further discussion of unusual keyboards, see Microtonal instruments.

BIBLIOGRAPHY

MersenneHU

PraetoriusSM

Prosdocimus de Beldemandis: Libellus monocordi, 1413, CoussemakerS, 248–58

Ugolino of Orvieto: Tractatus monocordi [appx to Declaratio musice discipline], ed. in CSM, vii/3 (1962)

N. Vicentino: L'antica musica ridotta alla moderna prattica (Rome, 1555, 2/1557; ed. in DM, 1st ser., Druckschriften-Faksimiles, xvii, 1959)

G. Zarlino: Le istitutioni harmoniche (Venice, 1558/R, 3/1573/R; Eng. trans. of pt iii, 1968/R as The Art of Counterpoint; Eng. trans. of pt iv, 1983 as On the Modes)

F. de Salinas: De musica libri septem (Salamanca, 1577/R, 2/1592; Sp. trans., 1983)

F. Colonna: La sambuca lincea, overo dell'istromento musico perfetto (Naples, 1618/R)

G.B. Doni: Compendio del trattato de'generi e de'modi della musica (Rome, 1635); Annotazioni sopra il Compendio (Rome, 1640); extracts ed. C. Gallico in RIM, iii (1968), 286–302

A. Kircher: Musica universalis (Rome, 1650/R)

A.J. Ellis: ‘Experimental Instruments for Exhibiting the Effects of Just Intonation’, On the Sensations of Tone (London, 2/1885/R) [trans. of H. Helmholtz: Die Lehre von den Tonempfindung, Brunswick, 1863, 4/1877], appx XX F

J.M. Barbour: Tuning and Temperament: a Historical Survey (East Lansing, MI, 1951/R, 2/1953)

C. Stembridge: ‘Music for the Cimbalo Cromatico and Other Split-Keyed Instruments in Seventeenth-Century Italy’, Performance Practice Review, v/1 (1992), 5–43

C. Stembridge: ‘The Cimbalo Cromatico and Other Italian Keyboard Instruments with Nineteen or More Divisions to the Octave (Surviving Specimens and Documentary Evidence)’, Performance Practice Review, vi/1 (1993), 33–59

D. Wraight and C. Stembridge: ‘Italian Split-Keyed Instruments with Fewer than Nineteen Divisions to the Octave’, Performance Practice Review, vii/2 (1994), 150–81

NICOLAS MEEÙS