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Computerized real time tuning Ladislav Šipeky Ladislav Šipeky FSTA1/18

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

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Symbolic relationship h + Q = h. Computerized real time tuning Mathematics - music Ladislav Šipeky 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 Šipeky 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 Šipeky FSTA5/18

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Pythagorean comma F G = 1024 / 729 G I = 729 / / Computerized real time tuning Tuning Ladislav Šipeky 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 Šipeky FSTA7/18

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Equal temperament Cents Computerized real time tuning Tuning Ladislav Šipeky FSTA8/18

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Pytagorean tuning [cent] Just intonation [cent] 12-tones equal temperamen[cent] C000 D203, E407,82386,13400 F498, G701, A905, H / B1109,781088, C1200 Computerized real time tuning Tuning Ladislav Šipeky FSTA9/18

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Beats Acoustical effect - interference of close frequences Computerized real time tuning Tuning Ladislav Šipeky 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 Šipeky FSTA11/18

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Computerized real time tuning Fuzzy logic in music Ladislav Šipeky FSTA12/18

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Computerized real time tuning Dissonance curve Spectral analysis of real tone Result of Fourier transform Threshold Taken from: Ladislav Šipeky FSTA13/18

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Dissonance curve Taken from: Computerized real time tuning Dissonance curve Ladislav Šipeky FSTA14/18

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Dissonance curve of real tones Taken from: Computerized real time tuning Dissonance curve Ladislav Šipeky 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 Šipeky 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 Šipeky FSTA17/18

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Thank you for your attention Mgr. art., Mgr. Ladislav Šipeky Department of Mathematics Faculty of Civil Engineering Slovak University of Technology Bratislava Radlinského Bratislava Slovakia Ps. For lunch will be: borshch and something for vegetarians Computerized real time tuning Ladislav Šipeky FSTA18/18

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