��reproduce his Diagram, before proceeding to the practical application of our subject.
To use this Table, (i) When the name of the Proportion is known, but not its constituents, find the name in the upper part of the Diagram ; follow down the lines of the lozenge in which it is enclosed, as far as the first horizontal line of figures ; and the two required numbers will be found under the points to which these diagonal lines lead. Thus, Tripla Sesquialtera lies near the left-hand side of the Diagram, about mid- way between the top and bottom ; and the diagonal lines leading down from it conduct us to the numbers 2 and 7, which express the re- quired Proportion in its lowest terms. (2) When the constituents of the Proportion are known, but not its name, find the two known numbers in the same horizontal line; follow the lines which enclose them, upwards, into the diagonal portion of the Diagram ; and, at the apex of the triangle thus formed will be found the required name. Thus the lines leading from 2 and 8 con- duct us to Quadrupla.
The uppermost of the horizontal lines comprises all the Proportions possible, between the series of numbers from I to 10 inclusive, reduced to their lowest terms. The subsequent lines give their multiples, as far as 100 ; and, as these multiples always bear the same names as their lowest re- presentatives, the lines drawn from them lead always to the apex of the same triangle.
By means of the Proportions here indicated, the Theorist is enabled to define the difference of pitch between two given sounds with mathema- tical exactness. Thus, the Octave, sounded by the half of an Open String, is represented by the Proportion called Dupla ; the Perfect Fifth, sounded by 2-3 of the String, by that called Sesquialtera; the Perfect Fourth, sounded by 3-4, by Sesquitertia. These Ratios are simple enough, and scarcely need a diagram for their elucidation ; but, as we proceed to more complex Intervals, and especially to those of a dissonant character, the Proportions grow far more intri- cate, and Morley's Table becomes really valuable.
A certain number of these Proportions are also used for the purpose of defining differences of Rhythm; and, in Mediaeval Music, the latter class of differences involves even greater complications than the former.
The nature of MODE, TIME, and PROLATION will be found fully explained under their own special headings ; and the reader who has care- fully studied these antient rhythmic systems will be quite prepared to appreciate the confusion which could scarcely fail to arise from their un- restrained commixture. [See NOTATION.] Time was, when this commixture was looked upon as the cachet of a refined and classical style. The early Flemish Composers delighted in it. Jos- quin constantly made one Voice sing in one kind of Rhythm, while another sang in another. Hobrecht, in his ' Missa Je ne demande,' uses no less than five different Time-signatures at the beginning of a single Stave an expedient which became quite characteristic of the Music of the
1 5th and earlier years of the i6th centuries. It was chiefly for the sake of elucidating the mys- teries of this style of writing that Morley gave his Table to the world ; and, by way of making the matter clearer, he followed it up by a setting of 'Christes Crosse be my speed,' for Three Voices, containing examples of Dupla, Tripla, Quadrupla, Sesquialtera, Sesquiquarta, Quadrupla-Sesqui- quarta, Quintupla, Sextupla, Septupla, Nonupla, Decupla, and Supertripartiens quartas, giving it to his pupil, Philomathes, with the encouraging direction 'Take this Song, peruse it, and sing it perfectly ; and I doubt not but you may sing any reasonable hard wrote Song that may come to your sight.'
Nevertheless, Morley himself confesses that these curious combinations had fallen quite into disuse long before the close of the i6th century.
Ornithoparcus, writing in I5I7, 1 mentions eight combinations of Proportion only, all of which have their analogues in modern Music, though, the Large and Long being no longer in use, they cannot all be conveniently expressed in modern Notation, (i) The Greater Mode Per- fect, with Perfect Time; (2) the Greater Mode Imperfect, with Perfect Time; (3) the Lesser Mode Perfect, with Imperfect Time; (4) the Lesser Mode Imperfect, with Imperfect Time;
(5) the Greater Prolation, with Perfect Time;
(6) the Greater Prolation, with Imperfect Time ;
(7) Perfect Time, with the Lesser Prolation;
(8) Imperfect Time, with the Lesser Prolation.
1. 2. 3. 4. 5. 6. 7. 8.
��Adam de Fulda, Sebald Heyden, and Hermann Finck, use a different form of Signature ; distin- guishing the Perfect, or Imperfect Modes, by a large Circle, or Semicircle ; Perfect, or Imperfect Time, by a smaller one, enclosed within it ; and the Greater, or Lesser Prolation, by the presence, or absence, of a Point of Perfection in the centre of the whole; thus
��In his First Book of Masses, published in 1554, Palestrina has employed Perfect and Imperfect Time, and the Greater and Lesser Prolation, simultaneously, in highly complex Proportions, more especially in the 'Missa Virtute magna/ the second Osanna of which presents difficulties with which few modern Choirs could cope ; while, in his learned 'Missa L'homme arms',' he has produced a rhythmic labyrinth which even Jos- quin might have envied. But, after the pro- duction of the ' Missa Papae Marcelli,' in the year 1565, he confined himself almost exclusively to the use of Imperfect Time, with the Lesser Pro- lation, equivalent to our Alia Breve, with four Minims in the Measure ; the Lesser Prolation, alone, answering to our Common Time, with frfur Crotchets in the Measure; Perfect Time, with 1 the Lesser Prolation, containing three Semibreves
1 Micrologus, lib. 11. cap. 5.