Deductive Reasoning Set 2

Tempo exclusions for triplets (6/8 with prevailing eighth-note motion) using deductive reasoning. The “since” half expresses a tempo “x” in terms of every possible note value from one to six eighth notes. The “then” half expresses the equivalent dotted-quarter-note tempo, which represents the sequence “ax/3” where “a” = 1, 2, 3, etc.

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

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

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

Since h = x must be excluded, then dq = 4x/3 must also be excluded.

Since h + e = x must be excluded, then dq = 5x/3 must also be excluded.

Since dh = x must be excluded, then dq = 2x must also be excluded.

(etc., infinite progression)