David Ryan's notation
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A system of notating any fractional frequency in Just Intonation, created by the musician and theorist David Ryan * Preprint: http://arxiv.org/pdf/1508.07739 Abstract: Musical notation systems provide ways of recording which notes musicians should play at which times. One essential parameter described is the frequency. For twelve-note tuning systems the frequency can be described using letters A to G with sharp or flat symbols. For Just Intonation tuning systems these symbols are insufficient. This paper provides a system for describing any frequency which is a rational number multiplied by a suitable base frequency. Explicit notation is given for low prime numbers, and an algorithm for higher primes described. Key features: Can be inputted by computer keyboard alone (ASCII characters) Can freely transpose keys in JI - done by multiplying notations - any two notations can be easily multiplied Simple notations exist for 3-limit, 5-limit, 7-limit JI notes Look-up table for providing ASCII notation for higher primes (11/8, 109/100, etc) Algorithm for deriving these notations Very compact notation for octave equivalence classes Good for describing all the notes on a 5-limit or 7-limit tone lattice Challenges: Octaves are not sequential - easier to understand octave equivalence classes than exact notes . ( Example: C = 1/1 F = 4/3 G = 3/4 but 3/2 = `G so 3/2 requires an octave modifier to describe.)
Original HTML content:
<html><head><title>David Ryan's notation</title></head><body>A system of notating any fractional frequency in Just Intonation, created by the musician and theorist David Ryan<br /> <br /> <ul><li>Preprint: <!-- ws:start:WikiTextUrlRule:20:http://arxiv.org/pdf/1508.07739 --><a class="wiki_link_ext" href="http://arxiv.org/pdf/1508.07739" rel="nofollow">http://arxiv.org/pdf/1508.07739</a><!-- ws:end:WikiTextUrlRule:20 --></li></ul><br /> Abstract:<br /> Musical notation systems provide ways of recording which notes musicians should play at which times. One essential parameter described is the frequency. For twelve-note tuning systems the frequency can be described using letters A to G with sharp or flat symbols. For Just Intonation tuning systems these symbols are insufficient. This paper provides a system for describing any frequency which is a rational number multiplied by a suitable base frequency. Explicit notation is given for low prime numbers, and an algorithm for higher primes described.<br /> <br /> Key features:<br /> Can be inputted by computer keyboard alone (ASCII characters)<br /> Can freely transpose keys in JI - done by multiplying notations - any two notations can be easily multiplied<br /> Simple notations exist for 3-limit, 5-limit, 7-limit JI notes<br /> Look-up table for providing ASCII notation for higher primes (11/8, 109/100, etc)<br /> Algorithm for deriving these notations<br /> Very compact notation for octave equivalence classes<br /> Good for describing all the notes on a 5-limit or 7-limit tone lattice<br /> <br /> Challenges:<br /> Octaves are not sequential - easier to understand octave equivalence classes than exact notes . ( Example: C = 1/1 F = 4/3 G = 3/4 but 3/2 = `G so 3/2 requires an octave modifier to describe.)</body></html>