A Dictionary of Music and Musicians/Interval
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 where they are capable of further reduction they are called 'diminished,' as diminished thirds and sevenths; and when of further enlargement as 'augmented,' as augmented sixths. With intervals which have only one normal form the terms 'major' and 'minor' are not used; thus fifths and fourths lose their consonant character on being either enlarged or reduced by a semitone, and in these forms they are called respectively 'augmented' and 'diminished' fifths and fourths. The interval of the augmented sixth is indifferently called 'superfluous' or 'extreme sharp' sixth; and the same terms are applied to the fifth; the term 'false' is also used for diminished in relation to the fifth and for augmented in relation to the fourth.
The term 'Imperfect' is used in two senses in relation to Intervals. In the classification of Consonances it was common to divide them into perfect and imperfect, or perfect, middle and imperfect; but as the classification varied at different times reference must be made for details to the article Harmony (vol. i. pp. 669—685). On the other hand, when an interval is commonly known in its normal condition as perfect, such as a fourth or a fifth, it is natural per contra to speak of the interval which goes by the same name, but is less by a semitone, as 'imperfect.'
For further details on the subject see Temperament.