Sonata, by means of which the two last movements are made continuous. Two very remarkable and unmistakeable instances occur also in the first movement of the Sonata in E (op. 109), one of which has already been quoted in the article Cadence. Another instance occurs in the Quartet in A (op. 132), where the 'working out' commences; the cadence of F major is interrupted at *, and the 'working out' commences in the next bar, proceeding immediately with modulation, as follows:
etc.
Wagner has made great use of this device, and by it secures at once the effect of a conclusion and an uninterrupted flow of the music; the voice or voices having a form which has all the appearance of a full cadence, and the instruments supplying a forcible Interrupted Cadence which leads on immediately and without break to the succeeding action. An example which will probably be familiar is that at the conclusion of the chorus at the beginning of the 4th scene of the 2nd act of Lohengrin, where Ortruda suddenly steps forward and claims the right to precede Elsa into the cathedral. Another instance which illustrates the principle very clearly is the following from the 3rd scene of the 1st act of Tristan und Isolde:—
etc.
Beethoven also made occasional use of this device in Fidelio. One specially clear instance is in the Finale of the last act, at the end of Don Fernando's sentence to Leonora—'Euch, edle Frau, allein, euch ziemt es, ganz ihn zu befrei'n.' By such means as this, one scene is welded on to another, and the action is relieved of that constant breach of continuity which resulted from the old manner of coming to a full close and beginning again.
INTERVAL. The possible gradations of the pitch of musical sounds are infinite, but for the purposes of the art certain relative distances of height and lowness have to be definitely determined and maintained. The sounds so chosen are the notes of the system, and the distances between them are the Intervals. With different objects in view, different intervals between the sounds have been determined on, and various national scales present great diversities in this respect—for instance the ancient Gaelic and Chinese scales were constructed so as to avoid any intervals as small as a semitone; while some nations have made use of quarter-tones, as we have good authority for believing the Muezzins do in calling the faithful to prayer, and the Dervishes in reciting their litanies. The intervals of the ancient Greek scales were calculated for the development of the resources of melody without harmony; the intervals of modern scales on the other hand are calculated for the development of the resources of harmony, to which melody is so far subordinate that many characteristic intervals of modern melody, and not unfrequently whole passages of melody (such as the whole first melodic phrase of Weber's Sonata in A♭), are based upon the use of consecutive notes of a single chord; and they are often hardly imaginable on any other basis, or in a scale which has not been expressly modified for the purposes of harmony. Of the qualities of the different intervals which the various notes form with one another, different opinions have been entertained at different times; the more important classifications which have been proposed by theorists in mediæval and modern times are given in the article Harmony.
The modern scale-system is, as Helmholtz has remarked, a product of artistic invention, and the determination of the intervals which separate the various notes took many centuries to arrive at. By the time of Bach it was clearly settled though not in general use, and Bach himself gave his most emphatic protest in favour of the equal temperament upon which it is based in his Wohltemperirte Clavier, and his judgment has had great influence on the development of modern music. According to this system, which is specially calculated for unlimited interchange of keys, the semitones are nominally of equal dimensions, and each octave contains twelve of them. As a consequence the larger intervals contained in the tempered octave are all to a certain extent out of tune. The fifth is a little less than the true fifth, and the fourth a little larger than the true fourth. The major thirds and sixths are considerably more than the true major thirds and sixths, and the minor thirds and sixths a good deal less than the true minor thirds and sixths. The minor seventh is a little larger than the minor seventh of the true scale, which is represented by the ratio 9:16, and is a mild dissonance; and this again is larger than the harmonic sub-minor seventh which is represented by the ratio 4:7; and this is so slight a dissonance that Helmholtz says it is often more harmonious than the minor sixth.
The nomenclature of intervals is unfortunately in a somewhat confused state. The commonest system is to describe intervals which have two forms both alike consonant or dissonant as 'major' and 'minor' in those two forms. Thus major and minor thirds and sixths are consonant, and major and minor sevenths and ninths are dissonant; and
