That's one of the many things that makes transpositions counter-intuitive for me. Down a fifth (gratuitous Cabbage set up line) really means down four intervals.
-----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Steve Haflich Sent: Saturday, August 07, 2010 11:33 PM To: The Horn List Subject: Re: [Hornlist] NHR Short Monograph on Number System Indeed, the lack of a concept for zero has maimed music terminology for more than two millenia. Common interval nomenclature makes no sense. Start with the interval of a unison. "Unison" derives from the number 1. But two notes that are a unison have a zero interval (distance) between them. Adjacent diatonic scale steps have a distance on 1, but we call that interval a "second". Take an interval of a third, and continue with an interval of another third. The resultant interval is a fifth, but 3+3=6. We musicians are so familiar with intervals that we need not and do not use arithmetic to calculate compound intervals relations. But notation, description, and "theory" would be more elegantly expressed if the Greeks had a zero, and had given us a system where the interval between two identical pitches were a "naught", two adjacent scale steps had the interval of a "unit", and the notes of a triad were a "second" and a "fourth". An octave would then have been called a seventh. _______________________________________________ post: [email protected] unsubscribe or set options at https://pegasus.memphis.edu/cgi-bin/mailman/options/horn/bgross%40airmail.ne t _______________________________________________ post: [email protected] unsubscribe or set options at https://pegasus.memphis.edu/cgi-bin/mailman/options/horn/archive%40jab.org
