Deductive Reasoning Set 4

Tempo exclusions for nonuplets (9/16 with prevailing sixteenth-note motion) using deductive reasoning. The “since” half expresses in terms of “x” every possible note value from one to nine sixteenths. The “then” half expresses the equivalent tempo for one measure, which represents the sequence “ax/9” where “a” = 1, 2, 3,etc.

Since s = x must be excluded, then h + s = x/9 must also be excluded.

Since e = x must be excluded, then h + s = 2x/9 must also be excluded.

Since de = x must be excluded, then h + s = x/3 must also be excluded.

Since q = x must be excluded, then h + s = 4x/9 must also be excluded.

Since q + s = x must be excluded, then h + s = 5x/9 must also be excluded.

Since dq = x must be excluded, then h + s = 2x/3 must also be excluded.

Since q + de = x must be excluded, then h + s = 7x/9 must also be excluded.

Since h = x must be excluded, then h + s = 8x/9 must also be excluded.

Since h + s = x must be excluded, then h + s = x must also be excluded.

(etc., infinite progression)