Inhaltsangabe
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1901 Excerpt: ...historical importance, is to be found in the numerical speculations of Zarlino and Rameau. When we represent the "diatonic scale," not by those numbers by which our experiments with folk songs teach us it must be represented, but by the numbers of Zarlino, 3, 27, 15, 2, 9, 5, 45, 3, which designate pitches differing but slightly from those of the right intonation, then the way for speculation is open. We may with pride point out that our "scale" does not contain any other numbers than products of 2, 3, (2-7) and (2-9), are represented by the tones 21 and 27; the relationship of the third degree, ((2-15)), is represented by the tone 45. The tone 45 does indeed appear in some folk songs. and 5. But what scientific law prohibits the use of 7 in a "scale?" And why is the tone 3 called "tonic" by Zarlino, Rameau, Helmholtz, and their followers? One searches in vain the writings of these theorists for a satisfactory answer to these questions. We saw above that the historic development of music "along the line of least resistance" explains why there is no pure 7--though there is 21 = 3'7--in the so-called diatonic scale, viz., the introduction of the 7 into "simple" melodies would have prohibited the use of two other tones, 9 and 15, in such melodies. Yet there is still another reason for the infrequency of 7 in music. Suppose that one of the early, yet inexperienced, composers had played or sung or simply imagined the following melody: 2, 2, 5, 3, 7, 3, 5, 2,2; suppose, now, that he had happened to replace the last 2 by 4-He must at once have noticed the extraordinary change of aesthetic effect, produced by so small an objective change as the substitution of for the last 2. The new melody must be represe...
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Reseña del editor
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1901 Excerpt: ...historical importance, is to be found in the numerical speculations of Zarlino and Rameau. When we represent the "diatonic scale," not by those numbers by which our experiments with folk songs teach us it must be represented, but by the numbers of Zarlino, 3, 27, 15, 2, 9, 5, 45, 3, which designate pitches differing but slightly from those of the right intonation, then the way for speculation is open. We may with pride point out that our "scale" does not contain any other numbers than products of 2, 3, (2-7) and (2-9), are represented by the tones 21 and 27; the relationship of the third degree, ((2-15)), is represented by the tone 45. The tone 45 does indeed appear in some folk songs. and 5. But what scientific law prohibits the use of 7 in a "scale?" And why is the tone 3 called "tonic" by Zarlino, Rameau, Helmholtz, and their followers? One searches in vain the writings of these theorists for a satisfactory answer to these questions. We saw above that the historic development of music "along the line of least resistance" explains why there is no pure 7--though there is 21 = 3'7--in the so-called diatonic scale, viz., the introduction of the 7 into "simple" melodies would have prohibited the use of two other tones, 9 and 15, in such melodies. Yet there is still another reason for the infrequency of 7 in music. Suppose that one of the early, yet inexperienced, composers had played or sung or simply imagined the following melody: 2, 2, 5, 3, 7, 3, 5, 2,2; suppose, now, that he had happened to replace the last 2 by 4-He must at once have noticed the extraordinary change of aesthetic effect, produced by so small an objective change as the substitution of for the last 2. The new melody must be represe...
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