Two parts must not move in consecutive octaves or fifths, because by so doing they unaccountably reinforce each other by an amount by which they impoverish the rest of the harmony.
This is of constant occurrence in classical pianoforte music, in which thick chords are subjected to polyphonic laws only in their top and bottom notes, while the inner notes make a solid mass of sound in which numerous consecutive fifths and octaves are not only harmless but essential to the balance of tone.
White is also worn during the octaves of these festivals, on ordinary days (for which no special colour is provided) between Easter and Whitsuntide, at certain special masses connected with the saints falling under the above category, and at bridal masses.
- Sundays and week-days between Epiphany and Septuagesima, and between Trinity and Advent, except festivals and their octaves and Ember days.
It may thus be brought into unison with any sound of which it may be required to determine the corresponding number of vibrations per second, as for instance the note A3, three octaves higher than the A which is indicated musically by a small circle placed between the second and third lines of the G clef, which A is the note of the tuning-fork usually employed for regulating concert-pitch.
The third 4= 5 X Z X z or ascent through an interval 4, which has no special name, and a descent through two octaves, and so on.
Ix.) used a string loaded at the middle point so that the higher tones were several octaves above the fundamental, and so not likely to be mistaken for it; he found that with 37 vibrations per second a very weak sensation of tone was heard, but with 34 there was scarcely anything audible left.
A semitone, give two beats per second, while the same number of beats are given by notes of 32 X 16 (four octaves higher than the first of the preceding) or 512, and 514 vibrations, which are only slightly out of tune.
Robert Smith (Harmonics, 2nd ed., 1 759, p. 95) states that Sauveur " inferred that octaves and other simple concords, whose vibrations coincide very often, are agreeable and pleasant because their beats are too quick to be distinguished, be the pitch of the sounds ever so low; and on the contrary, that the more complex consonances whose vibrations coincide seldom are disagreeable because we can distinguish their slow beats; which displease the ear, says he, by reason of the inequality of the sound.
In the succeeding year he showed, in the same journal, that if the elements be arranged in the order of their atomic weights, those having consecutive numbers frequently either belong to the same group or occupy similar positions in different groups, and he pointed out that each eighth element starting from a given one is in this arrangement a kind of repetition of the first, like the eighth note of an octave in music. The Law of Octaves thus enunciated was at first ignored or treated with ridicule as a fantastic notion unworthy of serious consideration, but the idea, subsequently elaborated by D.