Loading...
 

Period

The time required for a complete oscillation or for a single cycle of events. The reciprocal of frequency. [Bentley Nevada Corporation; Field of Rotating Machinery Measurement, Monitoring and Analysis]

Ramsay
"The numbers which express the motions of these twenty-five quantities have among themselves nineteen different ratios, or rates of meeting; and when these ratios are represented by the oscillations of twenty-five pendulums, at the number of 64 for the highest one, they will all have finished their periods, and meet at one for a new series. This is an illustration, in the low silence of pendulum-oscillations, of what constitutes the System of musical vibration in the much higher region of vibrating strings and other elastic bodies, and determines the number of undeveloped sounds which form the harmonious halo of one sound, more or less faintly heard, or altogether eluding our dull mortal ears; and which determines the number of sounds which, when developed, constitute the System of musical sounds." [Scientific Basis and Build of Music, page 16]

of twelve mathematical scales is that F# and G♭, which in the tempered system are one, being counted the same, are made two scales in the mathematical; but it is a needless nicety. Twelve is the natural number and period for both mathematical and tempered scales. And as the system of twelve Fifths contains the key system of music four times, only three of these twelve Fifths being required for any one key, it follows that the tempered key is affected by only one-fourth part of the small amount to be tempered into the whole twelve. [scientific Basis and Build of Music, page 30]

Well, how are we to get the true minor scale? There is a remarkable fact, and a beautiful one, which suggests the method. Such is the economy of Nature, that from one system of proportion employed in two different ways, in the one case as periods of vibrations and in the other as quantities of strings, everything in Music's foundation is produced. It is a remarkable fact that the numbers for the lengths of the strings producing the major scale are the numbers of the vibrations producing the minor scale; and the numbers for the lengths of the strings for the minor scale are the numbers of the vibrations of the notes of the major scale. Here Nature reveals to us an inverse process for the discovery of the minor scale of notes. [Scientific Basis and Build of Music, page 31]

Such is the economy of Nature, that from one system of proportions employed in two ways - in the one case as periods of vibrations, and in the other case as quantities of strings - everything in music is derived. The numbers which are the periods in the one are the numbers which are the quantities in the other. And abundantly throughout Creation reigneth the Law of Duality, which thus reigneth here in this region of most perfect response.2[Scientific Basis and Build of Music, page 44]

"To say that I was surprised at what Mr. Keely has discovered would be saying very little indeed ... It would appear that there are three different spheres in which the laws of motion operate.
1 - The first is the one in which Nature plays her grand fugue on the silent harp of Pendulums. In one period of Nature's grand fugue, as illustrated by pendulums, there are 19 ratios in 25 circles of oscillations ranging over 6 octaves; but all in silence. [Scientific Basis and Build of Music, page 86]

are always when they have returned to the side from which they were started. The Pendulugrapher, also, when writing the beautiful pictures which the musical ratios make when a pen is placed under the control of the pendulums, always finds his figure to begin again when the pendulums have finished their period, and have come for a fresh start to the side from which the period began. This confirms our author's definition of an oscillation of a pendulum. Fig. 3 is an illustration of the correct definition of a Musical Vibration, as also given in this work. Although the definition of an oscillation is not identical with that of a vibration, yet on account of their movement in the same ratios the one can be employed in illustration of the other as we have here done. Fig. 4 is a uniform rod suspended from the end as a pendulum; it will oscillate, of course, at a certain speed according to its length. In such a pendulum there are three centers related in an interesting way to the subject of Music in its three chords - subdominant, tonic, and dominant, which roots are F, C, and G. The center of gravity in the middle of the rod at 2, suspended at which the rod has no motion, corresponds to F, the root of the subdominant, in which there is the maximum of musical gravity. The center of oscillation at 3, which is one-third of the length of the rod from the end, is like the root of the tonic whose number is 3 in the genesis of the scale from F1. In this point of suspension the oscillations are the same as when suspended from the end at 1. The point at 9 is at a ninth from the center of oscillation. Our author discovered that, if suspended at this point, the pendulum had its highest rate of speed. Approaching the end, or approaching the center of oscillation from this point, the rate of speed decreases. Exactly at one-ninth from the center of oscillation, or two-ninths from the end, is this center of velocity, as Ramsay designated it; and it corresponds in some sort also to the root of the dominant G, which is 9 in the genesis of the scale from F1; its rate of vibration is nine times that of F1. The dominant chord is the one in which is the maximum of levity and motion in music. [Scientific Basis and Build of Music, page 105]


When 25 pendulums are arranged and oscillated to represent the different musical ratios in their natural marshalling, they will all meet at 1 when 64 of the highest is counted. This plate is intended to show that there are two kinds of meeting and passing of the pendulums in swinging out these various ratios. In the ratio of 8:9 the divergence goes on increasing from the beginning to the middle of the period, and then the motion is reversed, and the difference decreases until they meet to begin a new period. This may be called the differential way. In the ratio of 45:64 there is an example of what may be called the proximate way. In this kind of oscillations meet and pass very near to each other at certain points during the period. In 45:64 there are 18 proximate meetings; and then they exactly meet at one for the new start. This last of the ratios, the one which finished the system, is just as if we had gone back to the beginning and taken two of the simplest ratios, [Scientific Basis and Build of Music, page 105]

save the octave, and made them into one, so that in its proximate meetings during its period it seems composed of the ratio 2:3 twelve times, and 3:4 seven times; twelve times 2 and seven times 3 are 45; twelve times 3 and seven times 4 are 64. This long period of 45 to 64 by its proximate meetings divided itself into 19 short periods, and oscillates between the ratios of 2:3 and 3:4 without ever being exactly the one or the other; the difference being always a very small ratio, and the excess of the one being always the deficiency of the other. This fifth, B to F, has been misnamed an "imperfect fifth." When these two notes in the ratio of 45:64 are heard together, the oscillating proximately within it of the two simple ratios gives this fifth a trembling mysterious sound. [Scientific Basis and Build of Music,page 106]


Hughes
"Harmony must be looked at in two ways at least: first, up the score from bottom to top—the perpendicular view; second, along the score from side to side—the horizontal view. Then as to its periods or pulsations—its to and fro, its flow and ebb. This brings us to rhythm and measure. At the bottom of these lie what is called stress or accentemission and remission—strong and weak: of these the bar in modern music is an outward and visible sign of certain facts which ought to be in the music, but which, if not in the music, the presence of the bar is of no avail. The bar cannot give stress or accent. 'Wherever there is time, there must be accent;'* but the tick of a clock has no accent. Hullah (or Chorley) should have said life." "The semitone makes music. What operation has it upon the accent or to and fro? It creates the call, it supplies the answer." [This point, I believe, Dr. Gauntlett never alluded to with me, and I have feared that making no difference between tones and semitones might be considered a difficulty with regard to the scheme. In the working of the natural laws of harmony, they must all equally be employed.—F. J. H.] "Art (grand and true) does not depend upon the teaching of facts. The head is of less importance than the heart. Unless the tone of feeling, the habit and disposition, be well fixed, nothing enduring can come out of the misdirected artist." [Harmonies of Tones and Colours, Fragments from the Last Note-book, page 50]

WaveLength

See Also


differential period
Figure 7B.08 - Russells Periodic Chart of the Elements
Figure 7B.10 - Russells Periodic Chart of the first four octaves of proto-matter
Figure 9.13 - Wave Flow as function of Periodic Attraction and Dispersion
Law of Assimilation
periodic
periodicity
Periodic Table Set to Music
proximate period
Rhythmic Balanced Interchange
Time
Wave Number
WaveLength
7.2 - Rhythmic Balanced Interchange

Created by Dale Pond. Last Modification: Wednesday April 7, 2021 04:58:03 MDT by Dale Pond.