In order to determine what is the pitch-time maximum in any given melodic continuity, sum up all the pitch levels occurring in the continuity; then establish the pitch which has the greatest number value as the primary axis of the melody.

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Our musical memory selects the primary axis through its reactions to a quantity of repeated excitations produced by certain frequencies.

Musical orientation is based on the relations of a melodic configuration to its primary axis, without which melody does not produce any musical reality. A melody without an axis seems “not to hold together,” to have no comprehensible structural constitution. When some of our contemporary composers reject the idea of the primary axis (consciously or unconsciously), they revolt not only against musical traditions but against the laws of nature as well. So-called “atonality”, i.e., the neutral distribution of pitch units within a given tuning system in various arrangements in order to produce a melody, does not make any “musical”, i.e., organic, sense. Listeners usually object to such music and they are perfectly justified in doing so.

Inasmuch as counting pitch units in their time continuity does not present any difficulties, no properly constructed melody will ever leave room for any doubt as to where its primary axis is located. In analyzing music on a geometrical basis, one comes across a number of inconsistencies even in the well-known themes of important composers of the past. If they had known the mechanical specifications of melody, their intentions would have been clearer both to themselves and to their listeners. . . .

Joseph Schillinger