Fifth below F♯ (or G♭) is written \B, and so on till we arrive at \F♯, the Fifth below which is written \\B. The notes B, E, A, D have their Thirds in the same series as themselves, thus D—F♯, \D—\F♯. Other notes have their Thirds in the series next below, thus C—\E, \C—\\E. These marks may be collected at the signature, like sharps and flats. The keys of A and E will be unmarked; the key of C will have three grave notes, \A, \E, \B. When it is necessary to counteract the grave or acute mark and restore the normal note, a small circle (o) may be prefixed, analogous to the ordinary natural.
To apply this mode of tuning to the organ would be expensive without any great advantages in return. Ordinary organ-tone, except in the reed and mixture stops, is too smooth to distinguish sharply between consonance and dissonance, and the pipes are so liable to the influence of heat and cold that attempts to regulate tile pitch minutely are seldom successful. Still less would it be worth while to tune the pianoforte justly. It is chiefly to the orchestra that we must look for the development of just intonation; but among keyboard instruments the most suitable for the purpose is the harmonium, which is specially useful as a means of studying the effects obtainable from untempered chords.
| • | • | • | • | • | /f | • | • | • | • | • | • | • |
| • | • | • | • | • | • | • | • | • | • | /a♭ | • | • |
| • | • | • | /e♭ | • | • | • | • | • | • | • | • | • |
| • | • | • | • | • | • | • | • | /a♭ | • | • | • | • |
| • | /d♭ | • | • | • | • | • | • | • | • | • | • | • |
| • | • | • | • | • | • | /g♭ | • | • | • | • | • | • |
| • | • | • | • | • | • | • | • | • | • | • | b | • |
| • | • | • | • | e | • | • | • | • | • | • | • | • |
| • | • | • | • | • | • | • | • | • | a | • | • | • |
| • | • | d | • | • | • | • | • | • | • | • | • | • |
| • | • | • | • | • | • | • | g | • | • | • | • | • |
| c | • | • | • | • | • | • | • | • | • | • | • | c |
| • | • | • | • | • | f | • | • | • | • | • | • | • |
| • | • | • | • | • | • | • | • | • | • | b♭ | • | • |
| • | • | • | e♭ | • | • | • | • | • | • | • | • | • |
| • | • | • | • | • | • | • | • | a♭ | • | • | • | • |
| • | d♭ | • | • | • | • | • | • | • | • | • | • | • |
| • | • | • | • | • | • | g♭ | • | • | • | • | • | • |
| • | • | • | • | • | • | • | • | • | • | • | \b | • |
| • | • | • | • | \e | • | • | • | • | • | • | • | • |
| • | • | • | • | • | • | • | • | • | \a | • | • | • |
| • | • | \d | • | • | • | • | • | • | • | • | • | • |
| • | • | • | • | • | • | • | \g | • | • | • | • | • |
| \c | • | • | • | • | • | • | • | • | • | • | • | \c |
There is in the South Kensington Museum a harmonium, the tuning of which may be considered identical with the system just explained. The form of keyboard is that which has already been described in connexion with the meantone temperament; and it is equally applicable to the system of perfect Fifths. Being an experimental instrument it was constructed with eighty-four keys in each Octave, but for ordinary purposes it is found that about half that number would be sufficient. The fingering of the Major scale resembles that of A♭ Major on the ordinary keyboard, and is always the same, from whatever note we start as Tonic. Moreover the form which any given chord takes does not depend on theories of tonality, but is everywhere symmetrical. The diagram in the preceding column shows the positions of the notes on the keyboard when applied to the system of perfect Fifths.
It is unnecessary to consider here the objections which might be made to the use of this tuning, as they would, no doubt, be similar to those we have already noticed in dealing with the meantone temperament. But it may be pointed out that the supposed difficulty of enharmonic change no more exists here than elsewhere. We may even modulate through a series of eight Fifths down, and return by a Major Third down, without altering the pitch. The following passage from a madrigal, 'O voi che sospirate,' by Luca Marenzio (died 1590) illustrates this:
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In the 4th bar G♯ and C♯ are written for A♭ and D♭; and in the 5th bar F♯, \B and D for G♭, \C♭, E♭♭, but the confused notation would not affect the mode of performance either with voices or the justly tuned harmonium.
The practical use of this instrument has brought to light certain difficulties in applying just intonation to ordinary music. The chief difficulty comes from the two forms of Supertonic which are always found in a perfectly tuned Major Scale. Thus, starting from C, and tuning two Fifths upwards (C—G—D) we get what might be considered the normal Supertonic (D); but by tuning a Fourth and a Major Sixth upwards (C—F—\D) we arrive at a flatter note, which might be called the grave Supertonic (\D).
