By Ernst Levy, Siegmund Levarie
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Extra resources for A theory of harmony
The limiting number we call index. For our purpose the index 16 is sufficient. : The tones 1/7, 1/11, 1/13 are not used in our tone system. Therefore we have no name for them and can describe them only by referring them to the nearest known tone. The signs ÙandÚ indicate that they are, respectively, higher or lower than the note referred to. We write the series on graph paper, in one line from left to right, using one square (inch or centimeter) for each tone, and next proceed to multiply the string by the same series of digits.
I suggest that the concept pair consonance-dissonance be reserved for the natural qualifies, and that the current pair ontic-gignetic be adopted for the parallel interpretive qualities. The following diagram will illustrate the relationship between the two concept pairs. Let me offer the following explanation of the diagram. The realm of dissonance is illimited. The radius of the outer circle should be imagined as infinite, r= ¥. In he midst of that immense mass of dissonance lies the one consonant chord, the triad, not unlike a crystal within a mountain.
Normally, one should use two of them to proceed towards C; the two others, to get away from C. That provides two normal, "falling" cadence chains, and two cadence chains in contrary Page 28 motion giving the impression not of a fall but of an expenditure of energy to keep up the motion: Page 29 Following the numbers in their natural array, we obtain a zig-zag motion, consisting of triad pairs having a common generator: Page 30 The better a cadence is balanced, the more convincing and definite it is.
A theory of harmony by Ernst Levy, Siegmund Levarie