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A theory of harmony by Ernst Levy, Siegmund Levarie PDF

By Ernst Levy, Siegmund Levarie

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The Triad To Shang-Ti, the Highest, To the Six Honoured Ones, To the Mountains and Waters, and To the host of Spirits.... Shu-King Page 21 What is a chord? An organized agglomeration of tones. What does that mean? If you depress the white keys of a piano with a ruler, you have a nonorganized agglomeration of tones; if you sit on the keyboard, you have another one. Yet we may write: The first example shows an agglomeration containing all the diatonic tones; the second, one composed of all twelve tones.

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. Now of course we cannot actually multiply the string, but we can imitate the results by using a little trick.

In sonometer experiments, absolute pitch is irrelevant, as we are interested only in tone relations. For reasons of convenience, we tune the string (or strings) to C. We are now ready for a series of experiments whose purpose is to show what happens to a tone when the length of the string is varied. Page 5 It is at once apparent that we need a guiding principle, for the "glissando" effect produced by a continuous shortening of the string does not lead us beyond the not very revealing discovery that pitch rises with the shortening and falls with the lengthening of the string.

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