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Clavicymbalum Universale
Translating the provided text from German to English:
For both music theorists and practitioners, a seemingly eternal and unresolved problem has emerged since the renewed interest in ancient authors like Pythagoras: the pure tempering of intervals. How could one create a possibility on a musical instrument to distinguish between tones like dis and es, which, depending on the context (dis as a leading tone to e, es as a fourth above b), ought to be different in pitch?
The modern equal temperament, which after long centuries became a compromise, is in many respects the most unsatisfactory of all solutions, as it makes all intervals, except the octave, equally mistuned, thus distributing the error of the so-called Pythagorean comma evenly across all intervals. The only advantage of this temperament is the unlimited possibility of modulation and the freedom to choose keys. The price for this includes some particularly impure intervals like thirds and sixths, for example, the major third, which is about one-sixth of a semitone too high.
However, equal temperament has certain technical and practical advantages, as a look at other approaches to solving the problem demonstrates. This is particularly illustrated by an instrument type, generally referred to in literature as the Clavicymbalum Universale, based on a description by Michael Praetorius.
At first glance, the keyboard of this instrument, built in 1606 by Vito de Trasuntino in Venice, following the model of music theorist Nicola Vicentino (now housed in the Museo di Musica in Bologna), stands out: It spans 4 octaves, but each octave has 31 keys, meaning the instrument has a total of 125 keys (a modern concert grand piano has only 88)! Instead of the usual black key, there are four keys here, and between the semitone steps e-f and b-c, there are additionally two extra upper keys. Each usual upper key tone is split with a separate key for each single sharped/flattened and double sharped/flattened tone; additionally, between e and f and between b and c, the eis and fes, and the his and ces are included. Incidentally, the builder provided a specially made and calibrated monochord to accurately determine the individual pitches.
| deses | disis | geses | asas | aisis | ||||||||||
| C𝄪 | E♭♭ | F𝄪 | G𝄪 | B♭ | ||||||||||
| D♭ | D♯ | F♭ | G♭ | A♭ | A♯ | C♭ | ||||||||
| cis | es | eis | fis | gis | b | his | ||||||||
| C | D | E | F | G | A | H | (C) |
Other universal harpsichords, such as the one owned by the imperial chapel master Carl Luython in Prague, which Praetorius himself saw, had only 19 keys per octave, thus forgoing the double-offset notes in comparison to the instrument by Trasuntino, and provided only one key between e-f and b-c.
There are indeed some compositions for such instruments, as well as vocal works with similar intonation demands on the singers, which, however, only require a very good ear to meet these demands, like madrigals by the aforementioned Nicola Vicentino or by Luzzasco Luzzaschi, who was also praised as a player of such an instrument.
Undoubtedly, the demands on the players as well as on the piano tuners presented by such a construction were immense and did not exactly contribute to this at least approximately ideal solution to the problem of pure intonation in music becoming widely adopted.
However, the principle of split black keys, though realized less extremely, persisted until the 18th century, for instance to provide alternatives for certain semitone steps (most commonly D-sharp/E-flat) or to insert the semitones that would actually be expected at those points in the case of a short octave in the bass.