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Computerized real time tuning Ladislav Šipeky Ladislav Šipeky31.1.2012 FSTA1/18

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Mathematics-Music Tuning Fuzzy logic in music Dissonance curve Algorithms Future work Computerized real time tuning Ladislav Šipeky31.1.2012 FSTA2/18

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Symbolic relationship h + Q = h. Computerized real time tuning Mathematics - music Ladislav Šipeky31.1.2012 FSTA3/18

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Tuning- terminology Tuning: Tuning is an exact definition of the pitch of one or more tones. Octave: Given two sounds with frequencies f 1 and f 2, we say that f 2 is one octave higher than f 1 if f 2 is twice f 1. Interval: Computerized real time tuning Tuning Ladislav Šipeky31.1.2012 FSTA4/18

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Pythagorean tuning 2/1 - Octave / 12 semitones 3/2 - Fifth (perfect) /7 semitones 4/3 - Fourth (perfect) /5 semitones 2 p 3 q p, q Z Computerized real time tuning Tuning Ladislav Šipeky31.1.2012 FSTA5/18

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Pythagorean comma F G = 1024 / 729 G I = 729 / 512 524288 / 531441 Computerized real time tuning Tuning Ladislav Šipeky31.1.2012 FSTA6/18

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Just intonation major third / 4 semitones 2 p 3 q 5 r p, q, r Z Computerized real time tuning Tuning Ladislav Šipeky31.1.2012 FSTA7/18

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Equal temperament Cents Computerized real time tuning Tuning Ladislav Šipeky31.1.2012 FSTA8/18

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Pytagorean tuning [cent] Just intonation [cent] 12-tones equal temperamen[cent] C000 D203,91 200 E407,82386,13400 F498,04 500 G701,96 700 A905,86 900 H / B1109,781088,261100 C1200 Computerized real time tuning Tuning Ladislav Šipeky31.1.2012 FSTA9/18

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Beats Acoustical effect - interference of close frequences Computerized real time tuning Tuning Ladislav Šipeky31.1.2012 FSTA10/18

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INTERVALDEVIATION prime / unisono(-12, 12) major second (160, 230) major third(372, 430) perfect fourth(472, 530) perfect fifth (672, 730) major sixth (866, 930) major seventh (1066, 1136) Garbuzov zones Computerized real time tuning Tuning Ladislav Šipeky31.1.2012 FSTA11/18

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Computerized real time tuning Fuzzy logic in music Ladislav Šipeky31.1.2012 FSTA12/18

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Computerized real time tuning Dissonance curve Spectral analysis of real tone Result of Fourier transform Threshold Taken from: http://www.phys.unsw.edu.au/jw/sound.spectrum.html Ladislav Šipeky31.1.2012 FSTA13/18

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Dissonance curve Taken from: http://eceserv0.ece.wisc.edu/~sethares/consemi.html Computerized real time tuning Dissonance curve Ladislav Šipeky31.1.2012 FSTA14/18

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Dissonance curve of real tones Taken from: http://eceserv0.ece.wisc.edu/~sethares/consemi.html Computerized real time tuning Dissonance curve Ladislav Šipeky31.1.2012 FSTA15/18

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Real time tuning algorithms Hermode Tuning system (Werner Mohrlok) Adaptive tuning (William A. Sethares) Computerized real time tuning Algorithms Ladislav Šipeky31.1.2012 FSTA16/18

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Usage Interpretation Evaluation of musicians... Future work More correct formula of dissonance curves Implementation of musical analysis to existing algorithms Else Computerized real time tuning Future work Ladislav Šipeky31.1.2012 FSTA17/18

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Thank you for your attention Mgr. art., Mgr. Ladislav Šipeky ladislav.sipeky@stuba.sk Department of Mathematics Faculty of Civil Engineering Slovak University of Technology Bratislava Radlinského 11 813 68 Bratislava Slovakia http://www.math.sk Ps. For lunch will be: borshch and something for vegetarians Computerized real time tuning Ladislav Šipeky31.1.2012 FSTA18/18

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