Base-40 Arithmetic Implications for Notation-Oriented Applications.

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Presentation transcript:

Base-40 Arithmetic Implications for Notation-Oriented Applications

Music ; rev 2010 Eleanor Selfridge-Field Overview Base-40 definition Base-40 and MIDI I/O Base-40 and Notation Base-40 and MIDIPlus file format Base-40 and musical-data interchange 2

Music ; rev 2010 Eleanor Selfridge-Field What is Base-40? A scheme for pitch representation suited to Music which is tonal Notation which is conventional Repertories widely referenced in professional environments including Research Teaching Performance Publishing 3

Music ; rev 2010 Eleanor Selfridge-Field Where did Base-40 come from? Conceived by Walter Hewlett (1986) Used extensively at CCARH in data operations (not in encoding per se) Explanation published in Musikometrika (1992) Reproduced at Further elaborated in U.S. Patent 5,675,100 (7 October 1997) 4

Music ; rev 2010 Eleanor Selfridge-Field Why Base-40? Musical literacy Tonal legibility (common practice era) Musical computation in integer arithmetic Intervallic complementarity Base-10 complementarity (not for music) : If interval = 3, complement = 7 If interval = 6, complement = 4 5

Music ; rev 2010 Eleanor Selfridge-Field Enharmonic-notation tiers Physical instrument Cultural apparatus Letter names Base-7 (0 #s/bs) Octave numbers Base-12 (1#/b) Inflection names Bases > 12 (>1#/b)

Music ; rev 2010 Eleanor Selfridge-Field Enharmonic-notation tiers, cont. Third tier ## # - b bb Fourth tier ### ## # - b bb bbb C## / D / Ebb D## / E / Fb A# / Bb / Cbb (7 x 5) + 5 7

Music ; rev 2010 Eleanor Selfridge-Field MIDI I/0 vs. Graphical Notation MIDI to base-7 MIDI to base-12 MIDI to base-21 MIDI to base-40 Solution: Translate from symbolic code to MIDIPlus 8

Music ; rev 2010 Eleanor Selfridge-Field What is MIDIPlus? A binary implementation of base-40 Replaces last 3 bits of velocity byte Used to interpret key number 9

Music ; rev 2010 Eleanor Selfridge-Field MIDIPlus in Printing Raw MIDI to Notation (Bach Prelude in E Minor, BWV 855 Translation from symbolic code (MuseData) to MIDIPlus to notation 10

Music ; rev 2010 Eleanor Selfridge-Field Base-40 in Music Theory Scales Intervals 11

Music ; rev 2010 Eleanor Selfridge-Field Chords (interval complementarity) Intervallic complementarity Chord definitions 12

Music ; rev 2010 Eleanor Selfridge-Field Summary Enharmonic details matter! Where? Music notation Music theory Cultural discussions of tonal music When? In symbolic code In graphical output 13