Musical interval

“ The pitch of a sound depends wholly upon the number of vibrations per second that produce it; and if one of two sounds consists of twice as many vibrations per second as the other one, they differ in pitch by the interval called in music an octave, this latter term merely signifying the number of intervals into which the larger interval [65] is divided for the ordinary musical scale. The difference between a high and a low sound is simply in the number of vibrations of the air reaching the ear in a given time. ”

“ The fixation of a definite interval-order which shall serve as the scale of their performances is the starting-point of Chinese musical theory. All the different pitches which are used in a given piece of music, taken together embody a certain set of intervals arranged in a certain order from low to high. The fact of scale in music is the fact that in general in the music of one age and race different pieces embody in this way the same order of intervals, or one or other of a few different orders. ”

“ When we know more of overtones we shall see that the tempo of every masterpiece is absolute, and is exactly set by some further law of rhythmic accord. Whence it should be possible to show that any given rhythm implies about it a complete musical form, fugue, sonata, I cannot say what form, but a form, perfect, complete. ”

“ The orderly beauty which the tonal relations confer upon music is further enriched and complicated by rhythm. Rhythm in music is of two sorts: a rhythm of time and a rhythm of accent, or increased loudness. Through the one, the duration of a musical composition is divided up into approximately equal parts filled by notes and rests of definite length, and through the other, the light notes are subordinated to the heavy notes. ”

“ Time is that quantity which admits of the necessary reduction to units (like the feet and inches of a yardstick) , whereby a System of Measurement is established that shall determine the various lengths of the tones, define their rhythmic conditions, and govern the co-operation of several melodies sung or played together. Time is the canvas upon which the musical images are drawn—in melodic lines. ”

“ Even the tiny baby responds to rhythm and to melody. Rhythm brings “a cadence to the soul”, to use G. Stanley Hall’s phrase; it relaxes and soothes both mind and body; it has far-reaching significance as a spiritual and moral force. Chanting any rhythmic poem or jingles, singing, rhythmic performing of physical exercises, are the beginnings of music as a rhythmic art. When the noise-enjoying age arrives, at about six months, a string of soft-toned, musical sleigh bells, or later in the first year, at the pounding stage, a tubephone, will give as much enjoyment as harsh noises ”

“ Time may well be called the pulse of music. Upon some occasions the pulse beats more rapidly than others. It is incumbent on the interpreter of music to ascertain the harmonic and other causes which determine the tempo of a musical composition, as well as those which make slight variations from it admissible. ”

“ In primitive states of music rhythmic sounds were heard, defined by the pulses but with little or no change of pitch, and sounds varying in pitch without regularity of impulse. A high degree of intellectuality was reached before our modern scales were evolved from long-continued attempts at making well-balanced successions of sounds. As musical art advanced rhythm and melodic expression became united. ”

“ Rhythm, Melody, Harmony, and Timbre (or tone-color) .
179. Rhythm is the regular recurrence of accent. In music it is more specifically the regular recurrence of groups of accented and non-accented beats (or pulses) —according to some specified measure-system. Since rhythm implies continuity, there must usually be at least two such measure groups in order to make musical rhythm possible. (See p. 44, Sec. 97.)
180. A melody is a succession of single tones of various pitches so arranged that the effect of the whole will be unified, coherent, and pleasing to the ear. ”

“ The principle of Unity dictates that the beats which are associated in one and the same musical sentence shall be of equal duration. Every musician admits the necessity of keeping "strict time"—that is, marking the beats in regular, equal pulses. ”

“ Not only does the rhythmic impulse precede the other musical elements, but the superiority of sonant rhythm is such as to serve as an incitement to tone-production. Rhythm tends to set the voice going ”

“ This progress has gone on until the present time, when two particulars of our music are exactly recorded—the pitch and the rhythm. The exact relation of every tone to the key note is ascertainable from our musical notation, and the precise degree of rhythmic importance appertaining to each tone according to its place in measure and in the larger rhythms. ”

“ Rhythm is the oldest of the musical elements and there is no question but that the rhythmic appeal is still the strongest of all for the majority of people. Rhythm is the spark of life in music, therefore, woe to the composer who attempts to substitute ethereal harmonies for virile rhythms as a general principle of musical construction. Mere tones, even though beautiful both in themselves and through effective combination, are meaningless, and it is only through rhythm that they become vitalized. ”

“ For non-psychiatric patients, musical programming should be based upon patient requests. For stimulation the important factors are rapid tempo, accentuated rhythm, and elevated volume. For sedation, slow tempo and reduced volume are indicated, as well [Pg 43] as simple recognizable melodies. Some discussion of the selection to follow is a valuable aid to the enjoyment of listening. Live musicians should be used as often as possible. ”

“ Time may be a substitute for stress and vice versa. A subjective rhythm is richer and far more realistic than the physical rhythm. The quality of tone is heard in relation to its musical meaning. To the musician, the hearing is not so much a question of true pitch, formal accent, temporal rhythm, or vowel quality as it is a matter of musical balance and a recognition of artistic deviation from the true. Meticulously exact performance of a Bach score would be musically intolerable. Notes are frail symbols. The performer must interpret even the shortest measure rhythm or single note value. ”

“ Whether the minuter intervals would ever be useful in melody is a question which experience alone can decide. It rests with the composer to apply the material of mean and just intonation, with which he is now provided. The possibility of obtaining perfect tuning with keyed instruments is one result of the recent great advance in musical science, the influence of which seems likely to be felt in no branch of the art more than in Temperament. ”

“ At some points in the musical series the several movement cycles may appear in the same phase, and at these points the same irregularities as in verse are possible, as in the case of pauses at the ends of periods and the irregularities of phrasing. It is evident in cases of expressional variations of tempo that a single broad rhythm is dominating and serving as a cue for the other more elaborate rhythmic processes, instead of being regulated by them. ”

“ On account of the long, uninterrupted continuance of this 3⁄2 rhythm its character as a syncopation is entirely lost and it becomes simply an augmentation of the preceding and following 3⁄4 rhythm, and all of the best orchestral conductors I have seen always give out the beat accordingly—that is, in a manner equivalent to simply doubling the rate of speed in the 3⁄4 from that of the 3⁄2 movement. ”

“ This source of pleasure received from the melodious succession of colours or of sounds must not be confounded with the pleasure received from the repetition of them explained above, though the repetition, or division of musical notes into bars, so as to produce common or triple time, contributes much to the pleasure of music; but in viewing a fixed landscape nothing like musical time exists ”

“ For a single sound to become a musical sound, that is to say, a tone corresponding to one of the intonations of the musical scale, it is necessary that the impulse and, consequently, the undulations of the air should be exactly similar in duration and intensity, and that they should return after equal intervals of time. ”

“ The time-beat goes either by twos or some multiple of two, or by threes or some multiple of three, and the accent recurs at regular intervals of time, and is marked by dividing off the music into bars of equal length. Nothing is more important for a beginner to learn, and yet from the point of view of rhythm nothing could be more inadequate. ”

“ In musical time we have a power which exerts such a fascination upon us, that, so far from being able to treat it with indifference, we not unfrequently find ourselves beating time quite unconsciously with it while listening. This constant recurrence of equal lengths of time according to a definite measure has nothing to do with tones and their duration as we find them in Nature. Tone simply as musical sound and time abstractly regarded, are both of them equally indifferent to such uniform divisions and repetitions. Musical time is consequently something wholly created by the human mind ”

“ Usually in teaching the divisions of musical time, it has been the custom to play forte the time called theoretically tempo forte: in other words, to strike hard on the first note of every rhythmic measure. In fact, teachers of children or young people can often be heard playing a tune with special emphasis on the first note of every measure and playing the successive notes pianissimo. Naturally the motory action corresponds to this: it will be tense for the strong beats and light for the weak beats. But what value has all this in relation to the feeling of the rhythmic measure? ”

“ Although musical factors such as pitch, intensity and melody can contribute to mood effect when isolated, the reaction to an entire composition is quite different from reaction to tones of chords. It may depend upon environment or association with the situation in which the selection was first heard or is being heard. It may be altered by the length of the composition or unanticipated contrasts of intensity or the use of unusual patterns, rhythm or tempo. In listening to music, expectation plays an important role. A sudden change or interruption is apt to excite surprise. ”

“ In any case, the only “ultimate” rhythmic element is the tendency to mark off rhythmic beats into pairs, with a stress on the first of each pair. Where this tendency is resisted, the mind will follow the line of least resistance, which will vary according to the pace and detail of the music. Thus in rapid triple time it is easier to seek duple rhythm in the grouping of bars than in the details within the bars ”

“ TEMPO.—This refers to the degree of motion. The musical picture is not constant, but panoramic; we never hear a piece of music all at once, but as a panorama of successive sounds. Tempo refers to the rate of speed with which the scroll passes before our minds. Thus we speak of rapid tempo (allegro, and the like) , or slow tempo (adagio) , and so forth.
BEATS.—The beats are the units in our System of Measurement,—as it were, the inches upon our yardstick of time; they are the particles of time that we mark when we "count," or that the conductor marks with the "beats" of his baton. ”

“ The one fact upon which Spencer always seems to rely is that the intervals of speech and the intervals of the most primitive chant are both indefinite. Even here, however, Sir Hubert Parry's book is unpropitious to him, for Sir Hubert insists on the obvious fact that indefiniteness [215] of intervals in early music is entirely a matter of lack of instruments by which to fix the various notes of a scale. ”

“ Let any one attempt to follow a symphony with a metronome in his hand, and he will soon discover that if the metronome represents the æsthetically perfect rhythm, the orchestra represents a more pleasurable imperfection. Its accelerations and retardations carry on a continual conflict with the typical time of the music, yet that typical time is not only printed on every sheet, but is in the mind of every player. It is precisely so with verse.
It is true, of course, that the variations from regularity of rhythm are more numerous and conspicuous in verse than in music. ”

“ The first likings for musical composition are based on this instinctive feeling for rhythm. It is the simple tunes, with well-marked, easily recognizable time divisions, which first take the child's fancy, and he knows the quieting and the exciting qualities of different rhythms and times. Where rhythm is less marked, or grows highly complex, the motor responses being confused, the pleasurable interest declines. ”

“ It was in this apartment, also, that there stood against the western wall, a gigantic clock of ebony. Its pendulum swung to and fro with a dull, heavy, monotonous clang; and when the minute-hand made the circuit of the face, and the hour was to be stricken, there came from the brazen lungs of the clock a sound which was clear and loud and deep and exceedingly musical, but of so peculiar a note and emphasis that, at each lapse of an hour, the musicians of the orchestra were constrained to pause, momentarily, in their performance, to harken to the sound; ”

“ Modern musical rhythm is so complex in its frequent employment of syncopations, "cross accents," et cetera, that the prospective conductor must study indefatigably if he is to unravel its apparently inextricably snarled-up threads. We assume, however, that detailed study of rhythm has constituted a part of the student's work in piano, singing, et cetera, and shall therefore not attempt to treat the matter further. ”