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  Interval proofs - importance.  StephenJMacko at 05:37 on 30 January 2011

Upon the use of interval rationales for proofs of composition, the work must first be analyzed for musical keys, transitions, and chord progressions throughout. The proof that interval rationales give to performers, composers, and theorists, is not based on theory alone, but, fact of note placement and important interval events within the composition.

With this in mind intervals and transitions are proven to be required, because of interval rational proofs, giving performers and composers both positions and fingerings, based on proof for intervals and important interval happenings i.e. transitions. for each composition, possibly even 12-tone compositions that do not use key signatures in order to provide positions and fingerings for performers.

Because interval rationales are not proven to for chords, interval rationales are only proven for two part inventions only at this time. Much work in the clarification of chords is possible with proof of two part interval rational proofs to date.

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