noun: how much there is of something that you can quantify
noun: musical notation for a repeating pattern of musical beats
noun: measuring instrument having a sequence of marks at regular intervals; used as a reference in making measurements
noun: the act or process of measuring ("The measurements were carefully done")
noun: a basis for comparison; a reference point against which other things can be evaluated ("They set the measure for all subsequent work")
verb: have certain dimensions ("This table surfaces measures 20 inches by 36 inches")
verb: determine the measurements of something or somebody, take measurements of ("Measure the length of the wall")
verb: place a value on; judge the worth of something
verb: express as a number or measure or quantity

This tune is in the key of E♭ Major, and the key into which it moves for a passage is the next above it, B♭ Major. The first chord, E♭ G B♭, is the tonic; the second and third are the tonic and dominant; the fourth, C E♭ G, whose full form would be C E♭ G B♭, is the compound subdominant of the new key, which suggests the approaching modulation. The next two chords, in which the measure closes, may either be viewed as the tonic and dominant of the key, or the subdominant and tonic of the new key. The second measure opens with the same chord which closes the first measure, and is best defined as the tonic of the new key; the second chord is clearly the dominant of the new key, and the whole of the second measure is in the new key, and reads, T. D. S. T. compound D. T. Some of these chords might be read as chords of the old key, so near to each other and so kindred are the contiguous keys. All contiguous keys to a certain extent overlap each other, so that some of the chords may be variously read as belonging to the one or to the other. [Scientific Basis and Build of Music, page 94]

In the opening of the third measure the tune returns to its own key by striking the tonic. This case is a very simple illustration of how a composition will move with perfect naturalness in more keys than one, the keys so grow out of each other, and may either merely snatch a passing chord from a new key, or pass quite into it for a phrase or two, or for a whole measure, then return as naturally, either by a smooth and quiet or by a strongly contrasted turn, according to the chords between which the turn takes place. In such modulation there may or there may not be marked a sharp, , or , in the air itself; the note which Nature raises in the new key may occur in one of the other parts of the harmony. In Watchman it is A, the fourth, which is altered; from being it is made . The change which takes place in the sixth of the scale, which is C in Watchman, is only one comma, the ratio of 80 to 81, and it slips into the new key as if nothing had happened. No mark is placed to it, as the comma difference is never taken notice of, although it is really and regularly taking place, with all the precision of Nature, in every new key. It is, however, only the note which is altered four commas, which is marked by a sharp, , or , as the case may be. [Scientific Basis and Build of Music, page 94]

The Octave being divided into 53 commas, the intervals are measured, as usual, by these, the large second having 9-commas, the medium second having 8, and the small second 5. These measures are then made each the radius by which to draw hemispheres showing the various and comparative areas of the seconds. The comparative areas of the thirds are shown by the hemispheres of the seconds which compose them facing each other in pairs. The comma-measures of the various thirds thus determined are then made the radii by which to draw the two hemispheres of the fifths. The areas of the three fifths are identical, as also the attitudes of their unequal hemispheres. The attitude of the six thirds, on the other hand, in their two kinds, being reversed in the upper and under halves of the scale, their attitude gives them the appearance of being attracted towards the center of the tonic; while the attitude of the three fifths is all upward in the major, and all downward in the minor; their attraction being towards the common center of the twelve scales which Nature has placed between the second of the major and the fourth of the minor, as seen in the two D's of the dual genetic scale, - the two modes being thus seen, as it were, revolving [Scientific Basis and Build of Music, page 113]

with her irrevocable proportions to measure his scales for him. The stars at the C of the first scale and at the B# of the last show the coincidence of 12 fifths and 7 octaves. The number of B# is 3113 467/512; C24 multiplied 7 times by 2 brings us to the number 3072; these two notes in the tempered system are made one, and the unbroken horizon of the musical world of twelve twofold keys is created. The very small difference between these two pitches is so distributed in the 12 tempered scales that no single key of the 12 has much to bear in the loss of perfect intonation. [Scientific Basis and Build of Music, page 118]

I enter upon the subject with the deepest sense of my own inability to do justice in any measure to the grandeur of the topic; but I trust that my remarks may prove suggestive to others of far higher truths. They are the result of the leisure hours of nearly fifty years, during which the conviction has ever deepened, that "philosophy of the natural kind does but push man's ignorance farther back," and that, in the concluding words of Sir John Lubbock's inaugural address to the British Association at York in 1881, "the great lesson which Science teaches is, how little we yet know, and how much we have still to learn." [Harmonies of Tones and Colours, Introduction2 - Harmonies, page 10]

"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]

R. A. Schwaller de Lubicz
"Measure can be considered the quantitative definition of irreducible magnitudes." [R. A. Schwaller de Lubicz, The Temple in Man, page 57]

"Proportion belongs to geometry and harmony, measurement to the object and to arithmetic; and one necessitates the other. Proportion is the comparison of sizes; harmony is the relationship to measures; geometry is the function of numbers." [R. A. Schwaller de Lubicz, The Temple in Man, page 61]

See Also

Experimental Measurements of Ion Emission
Interaction of Intense Laser Pulses with Atomic Clusters - Measurements of Ion Emission Simulations and Applications
Quantize to One
Quantum Arithmetic
Sound Measurements
Test and Measurement

Created by Dale Pond. Last Modification: Wednesday April 7, 2021 05:02:08 MDT by Dale Pond.