78 MUSIC [HISTORY. of percussion, having the hammer of the drum to strike the string of the lyre. Inter- Musical intervals are named numerically from any given vals. note, say C as the 1st, the note next to which is thus D the 2d, the one beyond is E the 3d, and so on to another C, the 8th. Beyond the 8th, numerical names are only used for the rare combinations of the 9th, the llth, and the 13th. This is because the 8th is in some sense a reproduction of the 1st, as all intervals beyond it are reproductions of the 8th below them reproductions, that is, uniting identity and difference, the relation of tones in the higher octave being just what it is in the lower, while each tone is so or so much more acute than its under 8th, an analogy to which may be sought in the reduction of any visual object to half its size while all its propor tions are preserved, the larger and the smaller, as in the interval of the 8th, thus uniting identity with difference. When two voices or instruments produce the same sound they are in unison; the unison or 1st 1 is styled perfect; so too is its reproduction, the 8th ; the 8th is unequally divisible into a 5th and a 4th, and these two are classed with the 1st and 8th as perfect. There are many specialities that distinguish the four perfect intervals in music from every other. The two notes of which each is constituted are, save in one instance, of the same quality as natural, or sharp, or flat ; to raise or lower either of the two notes by a chromatic semitone 2 changes a perfect interval into a dis cord, whereas the other intervals are elastic, that is, they may be major or minor from having a chromatic semitone more or less in their extent, and are not changed from concords to discords, or the reverse, by the modification. To invert a perfect interval by placing the higher note beneath the lower produces another perfect interval, whereas to invert any of the other intervals reverses its character of major or minor. The progression of two parts together from one to another 1st or 8th, from one to another 5th or 4th, has, save in excep tional instances, the bad effect that all musical grammar forbids, whereas the progression of two parts in 3ds or 6ths with each other has a good effect. In the resolution of funda mental discords the progression of perfect intervals is free, whereas that of the imperfect intervals is restricted ; and further, in the relation of subject and answer in a fugue, one perfect interval may be changed for another, but never for an imperfect interval. Many technicalities are antici pated in the foregoing which can only be explained in the sequel, but present mention of them is unavoidable in reference to a position now to be stated. The Egyptians perceived the distinction of the perfect intervals from others, if not all the above specialities, and regarded them as typical of the seasons, spring bearing the proportion of a 4th to autumn, of a 5th to winter, and of an 8th to summer. The distinction, then, has been observed for many centuries, but neither ancients nor moderns have adduced any explanation of the phenomenon, and the wondrous fact that perfect intervals differ in constitution and treatment from other intervals appears to defy reason, and not even to incite speculation. Analogy The anciently supposed affinity of music to astronomy to astro- was taught by Pythagoras (585 B.C.), who derived the
- notion from the Egyptians, and exemplified it by com
parison of the lyre of seven strings with the planetary system. The Sun, then believed to rotate round the 1 Literally, the 1st is not a musical distance ; but, as it is a fre quent combination in counterpoint, and as its repetition is not rare in melody, it is conveniently classed as an interval. 2 A chromatic or minor semitone is between two notes of the same alphabetical name, as C and $C, or D and >D ; a diatonic or major semitone is between two notes of different alphabetical names, as C and bD, or C and B ; the ratio of the latter is |f, and that of the former varies with the place of the interval in the chromatic scale. earth, was deemed the chief planet, next to which were, on the one side Mercury, Venus, and the Moon, and on the other side Mars, Jupiter, and Saturn. The strings of the lyre, not the notes they sounded, were thus named : Mese (middle), being the principal or keynote, corresponding with our A on the fifth line with the bass clef, and likened to the Sun ; Paramese (next to middle) or B flat, likened to Mercury; Paranete (next to lowest, i.e., shortest = highest in pitch) or C, likened to Venus ; and Nete or Neate (lowest) or D, likened to the Moon ; these constituted the upper tet- rachord or scale of four notes, to which the lower tetrachord was conjoined by having Mese for its acutest note, which was the gravest of the other tetrachord ; next to it was Lichanos (forefinger string) or G, likened to Mars ; then Parhypate (next to highest, i.e., longest = lowest in pitch) or F, likened to Jupiter ; and lastly Hypate (highest) or E, likened to Saturn. The Moon being of all the planets the nearest to, and Saturn the farthest from, the earth, they are analogous to the shortest and the longest string. The Greek lyre (see LYRE, vol. xv. p. 113) had at first Greek four strings, to which subsequently were added the longest ly re - three; then an 8th, corresponding with our E, tuned to an 8th above Hypate ; then three below the latter, which took the scale down in pitch to B on the second line with the bass clef ; afterwards three above the former, which took the scale up to A in the second space with the treble clef ; and finally Proslambanomenos, corresponding with our A in the first space with the bass clef, extended the "greater system " of fifteen notes to an 8th below Mese and an 8th above it. 3 Tradition has it that Pythagoras made his discovery of Pythagc the ratios of the perfect intervals by listening to some rean svs smiths who struck the iron on their anvil with hammers em of different weights, and thus produced different notes from the metal. But the narrator of the tale has disregarded the obvious fact that, save for slight variation due to the greater or less heat of its different parts, a metallic bar, like a string, always sounds a note of the same pitch whatever be the weight of the instrument with which it is struck. 4 The smithy wherein Pythagoras worked his musical problems was the land of Egypt, where he is said to have acquired and whence he imported his knowledge. His division of the 1st and 2d degrees and the 2d and 3d degrees of the tetrachord, counting downward in pitch into equal intervals of a major tone, left but a leimma (remnant), which was less than a semitone between the 3d and 4th degrees. Aristoxenus (300 B.C.), who has been called the father of temperament, discovered the difference between the major and minor tones, the first having the ratio I, and the second having that of V. His followers formed a school opposed to that of Pythagoras, and there was severe contention between the two. Subsequent theorists disputed whether the major or the minor tone should be above the other, and it was Claudius Ptolemy (c. 150 A.D.) who enunciated that the major tone should be below the minor, which is the prin ciple that directs the intonation of our present scale. This intonation may account for the difference between the effect in proceeding from the minor chord of the supertonic to the major chord of the tonic, and the effect in proceeding from the minor chord of the submediant to the major chord of the dominant, of which the latter, at the interval of a minor tone, is acceptable and the former, at the interval of a major tone, is repugnant to cultivated ears. 3 Terpander (700 B.C.) was the first of whom it is said that "he added a new string to the lyre, " but the ascription to him was probably figurative and not literal, for the proverbial expression was applied to any one who discovered a novelty in science or excelled in art. 4 Not only was this manifest fiction repeated from age to age, but it was transferred from the ancient philosopher to Handel by a writer of some sixty years since, who assumed that the composer derived a melody from the various sounds of smiths hammers on one piece of iron.
