��ascertain the exact proportions, in Just In- tonation, of the Diatonic Semitone, the Greater and Lesser Tone, the Major and Minor Third, the Perfect Fourth, and the Perfect Fifth, in different parts of the Octave. Like Pietro Aron ('Toscanello della Musica/ Venice, 1523), Ludovico Fogliano ('Musica teoretica,' Venice, J5 2 9) an< ^ other theoretical writers of the i6th century, Zarlino was fond of illustrating his theses by diagrams of this kind : and it was, no doubt, the practical utility of the custom that tempted Des Cartes to illustrate this self-same system by the Canonical Circle (Fig. 2), which later theorists extended, so as to include the proportions, in commas, 1 of every possible Diatonic Interval within the limits of the Octave (Fig. 3).
���Acute Maj.2 d ^- Grave
��It needs but a very slight examination of the foregoing diagrams to prove that the Syntonous Diatonic of Ptolomy, coincided, to the minutest particular, with the system advocated by Kepler (Harmonices Mundi, Lib. Ill, Cap. 7.) Mersenne (Harm. Univers. Lib. II), Des Cartes (Compen- dium Musi cae), and all the most learned theoretical writers of later date, who, notwithstanding our acceptance of Equal Temperament as a practical necessity, entertain but one opinion as to the true division of the Scale in Just Intonation the opinion defended by Zarlino, three centuries ago.
Lib. III. of the ' Istitutioni ' treats of the laws of Counterpoint, which, it must be confessed, are not always set forth, here, with the clearness for which Zacconi is so justly remarkable. In the examples with which this part of the work is illustrated, an interesting use is made of the well- known Canto fermo which forms so conspicuous a feature in ' Non nobis Domine,' and so many other works of the i6th and i ;th centuries.
��Lib. IV. treats of the Modes: more es- pecially in the later forms introduced by the Early Christians, and systematised by S.Ambrose, and S. Gregory. In common with Glareanus, and all the great theorists of the Polyphonic
��is the ninth part of a Greater Ton*.
School, Zarlino insists upon the recognition of twelve Modes, and twelve only ; reject- ing the Locrian and Hypolocrian forms as inadmissible, by reason of the False Fifth in- separable from the one, and the Tritonus which forms an integral part of the other. But, though thus entirely at one with the author of the Dodecachordon on the main facts, he arranges the Modes in a different order of succession. 9 Instead of beginning his series with the Dorian Mode, he begins with the Ionian, arranging his series thus :
I. Ionian. Final, C.
III. Dorian. Final, D.
V. Phrygian. Final, E.
VIL Lydian. Final, F.
IX. Mixolydian. Final, G.
XL .Eolian. Final, A.
��Plagal Modes. II. Hypoionian.
Final, 0. IV. Hypodorian.
Final, D. VI. Hypophrygian.
Final, E. VIII. Hypolydian.
X. Hypomixolydian. Final, G. XII. Hypojeolian.
��This arrangement which no other great theorist of the century has followed 3 would almost seem to have been dictated by a prophetic- anticipation of the change which was to lead to the abandonment of the Modes, in favour of a newer tonality : for, the series here begins with a form which corresponds exactly with our modern Major Mode, and ends with the prototype of the descending Minor Scale of modern music.
In the course of the work, Zarlino introduces some very valuable memoranda, and occasionally records as facts some very curious superstitions. In one place he tells us that the human pulse is the measure of the beats in music a state- ment fortunately corroborated by other early writers, and furnishing us with a comparative estimate of the duration of the two beats which are included in the normal Semibreve. In another, he asserts that Josquin treated the Fourth as a Consonance. In a third, he records his observation that untaught singers, always sing the Third and Sixth Major which is in all probability true. Occasionally, too, he diverges into the region of romance, and assures us that deer are so delighted with music that hunters use it as a means of capturing them.
The ' Dimostrationi annoniche,' occupying 312 folio pages, is disposed in the form of five Dialogues, carried on by Adriano Willaert, Claudio Merulo, and Francesco Viola, Maestro di Cappella of Alfonso d'Este, Duke of Ferrara. Zarlino tells us, that, in the year 1562, the friends met at the house of Willaert, who was then laid up with the gout ; and, that their con- versation is faithfully reported in the five Ra- gionamenti of the Dimostrationi. The first of these treats chiefly of the Proportions of In- tervals ; the second, and third, of the ratios of the Consonances, and Lesser Intervals ; the fourth, of the division of the Monochord ; and the fifth, of the Authentic and Plagal Modes.
See LIB. IV. cap. x. p. 399, in edition of 1588.
See MODES, THE ECCLESIASTICAL.