246 HAND-BOOK OF ACOUSTICS.
succession of True Fifths, but those of the one manual are tuned a comma sharper than those of the other. A full description will be found in Helmholtz's " Sensations of Tone."
2. Bosanquet's Harmonium, which possesses eighty-four tones to the Octave and a specially constructed key-board. A full account may be found in "Proceedings of the Eoyal Society," vol. 23.
3. General Thompson's Enharmonic Organ, which possesses 3 manuals and seventy-two tones to the Octave. For particulars of its construction the reader is referred to General Perronet Thompson's work " On the Principles and Practice of Just Intonation."
4. Colin Brown's Voice Harmonium, the finger-board of which differs entirely from the ordinary one. The principles of its construction are given in " Music in Common Things," parts I&II.
To perform music with true Intonation in one key only, without using Chromatics and in the Major Mode, eight tones to the Octave are required.
In general, every transition of one remove, either way, from the original key and still keeping to the Major Mode only, requires two new tones. In changes of three or more removes, the number of new tones required is not quite so large as if the changes were made through the intervening keys.
To modulate therefore in all keys and in both the Major and Minor Mode in true intonation requires a very large number of tones to the Octave—between 70 and 80, in fact.
This presents no difficulty in the case of the voice and stringed instruments of the Viobln Class, f )r such instruments can produce tones of any required gradation of pitch ; the difficulty is only felt in instruments with a limited number of fixed tones ; and for such instruments some system of Temperament is necessary.
A Temperament is any system of tuning other than true intonation; Intervals tuned on any such system are termed tempered intervals. The object of temperament is so to tune a certain limited number of