A theory of harmony by Ernst Levy, Siegmund Levarie

By Ernst Levy, Siegmund Levarie

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The series of digits being infinite, we have to limit it arbitrarily. 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.

There exists, however, an inherent instability of the triad in respect to its mode, as we shall see in the next chapter. The inner schism of the minor mode is strikingly reflected in the schism existing between its harmonic and melodic projections. In major, the congruence between the two is perfect. The melodic projection of the tones of the basic cadential functionstonic T, dominant D, subdominant Sresults in the establishment of the major scale. Now, applying the polarity principle to the cadence, we obtain a perfect minor cadence (aeolian) where all three functions are represented by minor triads.

The hypothesis I have to offer underlies the theory exposed in this paper. Here it is: The first and most important condition into which we are born is telluric gravity. Gravity permeates our whole beingfirst of all and totally, our imagination. Now in the Pythagorean table there is no such thing as telluric gravity but only gravitation around generatorsa sort of a compound planetary system with the monas as its center. About the multitude of tones we may say that they are different from one another, but we may not say that they are different in pitch, because no concept of altitude has yet entered the system.

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