computerized real time tuning ladislav Šipeky
DESCRIPTION
Computerized real time tuning Ladislav Šipeky. Computerized real time tuning. Mathematics-Music Tuning Fuzzy logic in music Dissonance curve Algorithms Future work. Computerized real time tuning Mathematics - music. Symbolic relationship h + Q = h. Computerized real time tuning - PowerPoint PPT PresentationTRANSCRIPT
Computerized real time tuning
Ladislav Šipeky
Ladislav Šipeky 31.1.2012 FSTA 1/18
Mathematics-Music Tuning Fuzzy logic in music Dissonance curve Algorithms
Future work
Computerized real time tuning
Ladislav Šipeky 31.1.2012 FSTA 2/18
Symbolic relationship
h + Q = h.
?4
1
2
1
Computerized real time tuningMathematics - music
Ladislav Šipeky 31.1.2012 FSTA 3/18
Tuning- terminology
Tuning: Tuning is an exact definition of the pitch of one or more tones.
Octave: Given two sounds with frequencies f1 and f2, we say that f2 is one octave higher than f1 if f2 is twice f1.
Interval:2
1
f
f
Computerized real time tuningTuning
Ladislav Šipeky 31.1.2012 FSTA 4/18
Pythagorean tuning
2/1 - Octave / 12 semitones
3/2 - Fifth (perfect) /7 semitones
4/3 - Fourth (perfect) /5 semitones
2p3q
p, q ϵ Z
Computerized real time tuningTuning
Ladislav Šipeky 31.1.2012 FSTA 5/18
Pythagorean comma
FG = 1024 / 729
GI = 729 / 512
524288 / 531441
712
22
3
Computerized real time tuningTuning
Ladislav Šipeky 31.1.2012 FSTA 6/18
Just intonation
major third / 4 semitones
2p3q5r
p, q, r ϵ Z
4
5
Computerized real time tuningTuning
Ladislav Šipeky 31.1.2012 FSTA 7/18
Equal temperament
Cents
12 2
2
1221 log1200,
f
fffd
Computerized real time tuningTuning
Ladislav Šipeky 31.1.2012 FSTA 8/18
Pytagorean tuning [cent]
Just intonation[cent]
12-tones equal temperamen[cent]
C 0 0 0
D 203,91 203,91 200
E 407,82 386,13 400
F 498,04 498,04 500
G 701,96 701,96 700
A 905,86 905,86 900
H / B 1109,78 1088,26 1100
C 1200 1200 1200
Computerized real time tuningTuning
Ladislav Šipeky 31.1.2012 FSTA 9/18
BeatsAcoustical effect - interference of close frequences
21 fffbeats
Computerized real time tuningTuning
Ladislav Šipeky 31.1.2012 FSTA 10/18
INTERVAL DEVIATION
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 tuningTuning
Ladislav Šipeky 31.1.2012 FSTA 11/18
Computerized real time tuningFuzzy logic in music
Fuzzy logic in music
0
2222
2221
2222
2
(x)
else
fxfff
xffxf
fxfff
fx
2ff2f 2f 2f
Ladislav Šipeky 31.1.2012 FSTA 12/18
Computerized real time tuningDissonance curve
Spectral analysis of real toneResult of Fourier transform
Threshold
Taken from: http://www.phys.unsw.edu.au/jw/sound.spectrum.html
Ladislav Šipeky 31.1.2012 FSTA 13/18
Dissonance curve
Taken from: http://eceserv0.ece.wisc.edu/~sethares/consemi.html
1212
212121 ),,,( ffbsffas eellllffd
Computerized real time tuningDissonance curve
Ladislav Šipeky 31.1.2012 FSTA 14/18
Dissonance curve of „real“ tones
Taken from: http://eceserv0.ece.wisc.edu/~sethares/consemi.html
Computerized real time tuningDissonance curve
Ladislav Šipeky 31.1.2012 FSTA 15/18
Real time tuning algorithms
Hermode Tuning system (Werner Mohrlok)
Adaptive tuning (William A. Sethares)
Computerized real time tuningAlgorithms
Ladislav Šipeky 31.1.2012 FSTA 16/18
Usage Interpretation Evaluation of musicians ...
Future work “More” correct formula of dissonance curves Implementation of musical analysis to existing algorithms Else
Computerized real time tuningFuture work
Ladislav Šipeky 31.1.2012 FSTA 17/18
Thank you for your attention
Mgr. art., Mgr. Ladislav Šipeky
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 Šipeky 31.1.2012 FSTA 18/18