system of electrically controlled tuning-forks. The full demonstration of these facts occupies the larger part of his classical work on 'Sensations of Tone,' and can hardly be given in a brief summary. Pure tones can be obtained from a tuning-fork held over a resonance tube, and by blowing a stream of air from a linear slit over the edge of a large bottle. The quality of tone in struck strings depends on (1) the nature of the stroke, (2) the place struck, and (3) the density, rigidity, and elasticity of the string. In bowed instruments no complete mechanical theory can be given; although Helmholtz's beautiful 'Vibration Microscope' furnishes some valuable indications. In violins, the various parts, such as the belly, back, and soundpost, all contribute to modify the quality; as also does the contained mass of air. By blowing across the f-hole of a Straduarius violin, Savart obtained the note c'; in a violoncello, F; and in a viola, a note one tone below that of the violin.
Open organ pipes, and conical double reed instruments, such as the oboe and bassoon, give all the notes of the harmonic series. Stopped pipes and the clarinet give only the partial tones of the uneven numbers. On this subject, neither Helmholtz nor any other observer has given more detailed information: indeed the distinguished German physicist points out that here there is still 'a wide field for research.'
The theory of vowel-quality, first enunciated by Wheatstone in a criticism on Willis's experiments, is still more complicated. Valuable as are Helmholtz's researches, they have been to some extent corrected and modified of late by R. Koenig in his 'Experiences d'Acoustique.'[1] The latter writer begins by stating that, according to the researches of Donders and Helmholtz, the mouth, arranged to produce a particular vowel-sound, has a powerful resonance-tone which is fixed for each vowel, whatever be the fundamental note. A slight change of pronunciation modifies the sound sufficiently to sustain the proposition made by Helmholtz of defining by these accessory sounds the vowels which belong to different idioms and dialects. It is therefore very interesting to determine the exact pitch of these notes for the different vowels. Helmholtz and Donders however differ considerably in their results. Koenig determines the accessory resonance-tones for the vowels as pronounced by the North-Germans as follows:—
| OU | O | A | E | I | |
| B♭2 | B♭3 | B♭4 | B♭5 | B♭6 | |
| 225 | 450 | 900 | 1800 | 3600 | vibrations. |
The simplicity of these relations is certainly in their favour, and is suggested by M. Koenig as the reason why we find essentially the same five vowels in all languages, in spite of the undoubted powers which the human voice possesses of producing an infinite number and variety of such sounds.
TIME (Lat. Tempus, Tactus; Ital. Tempo, Misura, Tatto; Fr. Mesure; Germ. Takt, Taktart, Taktordnung).
No musical term has been invested with a greater or more confusing variety of significations than the word Time; nor is this vagueness confined to the English language. In the Middle Ages, as we shall show, its meaning was very limited; and bore but a very slight relation to the extended signification accorded to it in modern Music. It is now used in two senses, between which there exists no connection whatever. For instance, an English Musician, meeting with two Compositions, one of which is headed, 'Tempo di Valza,' and the other, 'Tempo di Menuetto,' will naturally (and quite correctly) play the first in Waltz-Time'; that is to say, at the pace at which a Waltz is commonly danced; and the second, at the very much slower pace peculiar to the Minuet. But an Italian Musician will tell us that both are written in 'Tempo di tripla di semiminima'; and the English Professor will (quite correctly) translate this by the expression, 'Triple Time,' or '3-4 Time,' or 'Three Crotchet Time.' Here, then, are two Compositions, one of which is in 'Waltz-Time,' and the other in 'Minuet Time,' while both are in 'Triple Time'; the words 'Tempo' and 'Time' being indiscriminately used to indicate pace and rhythm. The difficulty might have been removed by the substitution of the term 'Movimento' for 'Tempo,' in all cases in which pace is concerned; but this word is very rarely used, though its French equivalent, 'Mouvement,' is not uncommon.
The word Tempo having already been treated, in its relation to speed, we have now only to consider its relation to rhythm.
In the Middle Ages, the words 'Tempus,' 'Tempo,' 'Time,' described the proportionate duration of the Breve and Semibreve only; the relations between the Large and the Long, and the Long and the Breve, being determined by the laws of Mode,[2] and those existing between the Semibreve and the Minim, by the rules of Prolation.[3] Of Time, as described by mediæval writers, there were two kinds—the Perfect and the Imperfect. In Perfect Time, the Breve was equal to three Semibreves. The Signature of this was a complete Circle. In Imperfect Time—denoted by a Semicircle—the Breve was equal to two Semibreves only. The complications resulting from the use of Perfect or Imperfect Time in combination with the different kinds of Mode and Prolation, are described in the article Notation, and deserve careful consideration, since they render possible, in antient Notation, the most abstruse combinations in use at the present day.
In modern Music, the word Time is applied to rhythmic combinations of all kinds, mostly indicated by fractions (38 etc.) referring to the aliquot parts of a Semibreve—the norm by which
- ↑ Quelques Expériences d'Acoustique, Paris 1882 (privately printed). Essay vi. p. 42.
- ↑ Here, again, we meet with another curious anomaly; for the word 'Mode' is also applied, by mediæval writers, to the peculiar forms of Tonality which preceded the invention of the modern Scale.
- ↑ See Mode, Prolation, and Vol. ii. pp. 471b–472a.
