Deductive Reasoning Set 1

Tempo exclusions for quadruplets (4/4 with prevailing sixteenth-note motion) using deductive reasoning. The “since” half expresses a tempo “x” in terms of every possible note value from one to sixteen sixteenth notes. The “then” half expresses the equivalent quarter-note tempo, which represents the sequence “ax/4” where “a” = 1, 2, 3, etc.

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

Since e = x must be excluded, then q = x/2 must also be excluded.

Since de = x must be excluded, then q = 3x/4 must also be excluded.

Since q = x must be excluded, then q = x must also be excluded.

Since q + s = x must be excluded, then q = 5x/4 must also be excluded.

Since dq = x must be excluded, then q = 3x/2 must also be excluded.

Since q + de = x must be excluded, then q = 7x/4 must also be excluded.

Since h = x must be excluded, then q = 2x must also be excluded.

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

Since h + e = x must be excluded, then q = 5x/2 must also be excluded.

Since h + de = x must be excluded, then q = 11x/4 must also be excluded.

Since dh = x must be excluded, then q = 3x must also be excluded.

Since dh + s = x must be excluded, then q = 13x/4 must also be excluded.

Since dh + e = x must be excluded, then q = 7x/2 must also be excluded.

Since dh + de = x must be excluded, then q = 15x/4 must also be excluded.

Since w = x must be excluded, then q = 4x must also be excluded.

(etc., infinite progression)