��The first form will necessarily be employed in chords which contain the Dominant (G), the second form in chords which contain the Sub- dominant (F) or the Superdominant (\A). Other- wise, false Fifths or Fourths (G \D; D \A) would be heard. The result is that certain chords and progressions are unsuitable for music which is to be performed in perfect tuning. Let us take the following example and arrange it in its four possible forms : d) (a)
���All of these are equally inadmissible ; No. I being excluded by the false Thirds (F A; A C) ; No. 2 by the false Fourth (\A D) ; No. 3 by the false Fifth (G \D) ; No. 4 by the sudden fall of the pitch of the tonic. If this kind of progression is employed, all the advan- tages of just intonation are lost, for the choice only lies bet ween mistuned intervals and an abrupt depression or elevation of the general pitch.
The idea of writing music specially to suit different kinds of temperament is a somewhat un- familiar one, although, as already remarked, Bach employed a narrower range of modulation in his works for the meantone organ than in those for the equally tempered clavichord. The case has some analogy to that of the different instruments of the orchestra, each of which demands a special mode of treatment, in accordance with its capa- bilities. The same style of writing will evidently not suit alike the violin, the trombone, and the harp. In the same way, just intonation differs in many important features both from the equal and from the meantone temperament ; and before any one of these systems can be used with good effect in music, a practical knowledge of its peculiarities is indispensable. Such knowledge can only be gained with the help of a keyed instrument, and by approaching the subject in this manner, the student will soon discover for himself what modulations are available and suit- able in perfect tuning. He will see that these restrictions are in no sense an invention of the theorist, but are a necessary consequence of the natural relations of sounds.
If just intonation does not permit the use of certain progressions which belong to other sys- tems, it surpasses them all in the immense variety of material which it places within the composer's reach. In many cases it supplies two or more notes of different pitch where the or- dinary temperament has but one. These alter- native forms are specially useful in discords, enabling us to produce any required degree of roughness, or to avoid disagreeable changes of pitch. For instance, the Minor Seventh may be taken either as C /Bb (ten Fifths up), or as C Bb (two Fifths down), or as C \Bb (four- th Fifths down). When added to the triad
C \E G, the acute Seventh, /Bb, is the roughest, and would be used if the Minor Third G /Bb should occur in the previous chord. The intermediate form, Bb, would be used when suspended to a chord containing F. The grave Seventh, \Bb, is the smoothest, being an ap- proximation to the Harmonic Seventh. Many other discords, such as the triad of the Aug- mented Fifth and its inversions, may also be taken in several forms. But this variety of material is not the only merit of perfect tuning. One of the chief sources of musical effect is the contrast between the roughness of discords and the smoothness of concords. In equal tempera- ment this contrast is greatly weakened, because nearly all the intervals which pass for consonant are in reality more or less dissonant. The loss which must result from this in the performance of the simpler styles of music on our tempered instruments, will be readily understood. On the other hand, in just intonation the distinction of consonance and dissonance is heard in its full force. The different inversions and distributions of the same chord, the change from Major to Minor Modes, the various diatonic, chromatic, and enharmonic progressions and resolutions have a peculiar richness and expressiveness when heard with untempered harmonies.
There is yet another advantage to be gained by studying the different kinds of tuning. We have seen that even in those parts of the world where equal temperament has been established as the trade usage, other systems are also em- ployed. Many countries possess a popular or natural music, which exists independently of the conventional or fashionable style, and does not borrow its system of intonation from our tempered instruments. Among Oriental nations whose culture has come down from a remote antiquity, characteristic styles of music are found, which are unintelligible to the ordinary European, only acquainted with equal temperament. Hence transcriptions of Oriental music, given in books of travel, are justly received with extreme scep- ticism, unless the observer appears to be well acquainted with the principles of intonation and specifies the exact pitch of every note he tran- scribes. As illustrations of these remarks we may cite two well-known works on the history of the art, Kiesewetter's 'Musik der Araber/ and Villoteau's ' Musique en Egypte.' Both of these authors had access to valuable sources of information respecting the technical system of an ancient and interesting school of music. Both failed to turn their opportunities to any advan- tage. From the confused and contradictory state- ments of Kiese wetter only one fact can be gleaned, namely, that in the construction of the lute, the Persians and the fLrabs of the Middle Age em- ployed the approximately perfect Major Third, which is got by eight downward Fifths. From the work of Villoteau still less can be learnt, for he does not describe the native method of tuning, and he gives no clue to the elaborate musical notation in which he attempted to record a large number of Egyptian melodies. Yet it would