homologue;[1] and, throughout their system, this Hemitone occurred between the first and second sounds of every Tetrachord; just as, in our Major Scale, the Semitones occur between the third and fourth Degrees of the two disjunct Tetrachords by which the complete Octave is represented. Therefore, they ordained that the four sounds of the Tetrachord should be represented by the four syllables, τα, τε, τη, τω; and that, in passing from one Tetrachord to another, the position of these syllables should be so modified, as in every case to place the Hemitone between τα and τε, and the two following Tones between τε and τη, and τη and τω, respectively.[2]
When, early in the 11th century, Guido d'Arezzo substituted his Hexachords for the Tetrachords of the Greek system, he was so fully alive to the value of this principle, that he adapted it to another set of syllables, sufficiently extended to embrace six sounds instead of four. In the choice of these he was guided by a singular coincidence. Observing that the Melody of a Hymn, written about the year 770 by Paulus Diaconus, for the Festival of S. John the Baptist, was so constructed, that its successive phrases began with the six sounds of the Hexachord, taken in their regular order, he adopted the syllables sung to these notes as the basis of his new system of Solmisation, changing them from Hexachord to Hexachord, on principles to be hereafter described, exactly as the Greeks had formerly changed their four syllables from Tetrachord to Tetrachord.
It will be seen, from this example, that the syllables, Ut, Re, Mi, Fa, Sol, La,[3] were originally sung to the notes C, D, E, F, G, A; that is to say, to the six sounds of the Natural Hexachord: and that the Semitone fell between the third and fourth syllables, Mi and Fa, and these only. [See Hexachord.] But, when applied to the Hard Hexachord, these same six syllables represented the notes G, A, B, C, D, E; while, in the Soft Hexachord, they were sung to F, G, A, B♭, C, D. The note C therefore was sometimes represented by Ut, sometimes by Fa, and sometimes by Sol, according to the Hexachord in which it occurred; and was consequently called, in general terms, C sol-fa-ut. In like manner, A was represented either by La, Mi, or Re; and was hence called A la-mi-re, as indicated, in our example, by the syllables printed above the Stave. But, under no possible circumstances could the Semitone occur between any other syllables than Mi and Fa; and herein, as we shall presently see, lay the true value of the system.
So long as the compass of the Melody under treatment did not exceed that of a single Hexachord, the application of this principle was simple enough; but, for the Solmisation of Melodies embracing a more extended range, it was found necessary to introduce certain changes, called Mutations, based upon a system corresponding exactly with the practice of the Greeks. [See Mutation.] Whenever a given Melody extended (or modulated) from one Hexachord into another, the syllables pertaining to the new series were substituted for those belonging to the old one, at some convenient point, and continued, in regular succession, until it became convenient to change them back again; by which means the compass of the Scale could be enlarged to any required extent.
For instance, in the following example the passage begins at (a), in the Natural Hexachord of C, but extends upwards three notes beyond its compass, and borrows a B♭ from the Soft Hexachord of F. As it is not considered desirable to defer the change until the extreme limits of the first Hexachord have been reached, it may here be most conveniently made at the note G. Now, in the Natural Hexachord, G is represented by the syllable Sol; in the Soft Hexachord, by Re. In this case, therefore, we have only to substitute Re for Sol, at this point; and to continue the Solmisation proper to the Soft Hexachord to the end of the passage, taking no notice whatever of the syllable printed in Italics.
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At (b), on the other hand, the passage extends downwards, from the Hexachord of G, into that of C. Here, the change may be most conveniently effected by substituting the La of the last-named Hexachord for the Re of the first, at the note A.
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- ↑ The Diatonic Semitone is represented by the fraction 1516; the Greek Hemitone by 248⁄256, that is to say, by a Perfect Fourth, minus two Greater Tones.
- ↑ Though the true Pronunciation of the Greek vowels is lost, we are eft without the means of forming an approximate idea of it, since Homer uses the syllable βὴ, to imitate the bleating of the sheep.
- ↑ Gerard Vossius, in his tract 'De quatuor Artibus popularibus' (Amsterdam 1650), mentions the following Distich as having been written, shortly after the time of Guido, for the purpose of impressing the six syllables upon the learner's memory—
'Cur adhibes tristi numeros cantumque labori?
UT RElevet MIserum FAtum SOLitosque LAbores.'
