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THE SONG OF GLASSES LAIN - UMR CNRS 5011 Univ. Montpellier 2 - cc 82 34095 MONTPELLIER cedex 5 FRANCE Ing. Jean-Yves Ferrandis Pr. Gerard Leveque Pr. Jacques Attal

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GOAL: STUDY OF THE HARMONY OF GLASSES n GOAL: STUDY OF THE HARMONY OF GLASSES Acoustical criteria the strike note : pitch and sound decay timbre consonance and dissonance Subjective approach

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n I. Sound analysis : theoretical background n II. Experiences on glasses and crystal glasses n III. Discussion n IV. Test of listening n V. Conclusions FRAME WORK

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n Harmonic partials : string instruments n Inharmonic partials : infinite cylindrical pipes n Spectral analysis n Circular plates n Vibration of bells n Consonance intervals I. Sound analysis : theoreticalbackgrond

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Harmonic partials : string instruments n String equation Solutions density S cross-area T strain force n order of the mode frequency n = 1, 2, 3, 4 . z TTx

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Inharmonic partials : infinite cylindrical pipes n Infinite cylindrical pipes z : axis of the pipe : angle in the shear cut e : thickness of the pipe e, : Young modulus, Poisson coefficient R : radius of the pipe : density The partial mode are not harmonic frequency intervals [1, 8/3, 5, 8, 35/3 ]

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1234567 8 Cylinders Fondamental frequency m=2m=3 m = 1 m = 2 Spectral analysis m=4m=5 String vibrations 8/3

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Circular plates Chladni s law (empirical relation ship) where c is the sound velocity (n,m) is the mode numbers for flat plates p = 2 for non flat plates (cymbals, bells) p < 2

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Vibration of bells n The bells can be tuned on harmonic partials

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Consonance intervals for bells

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n Pitch n Sound decay n Warble II. Experiences on glasses and crystal glasses

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Sound analysis : Typical response

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: Time constant for a decay 0.368 Sound decay

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Beats due to a dissimetry of the sample B A B A B A BWarble Tea cup

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n Shape n Materials n Manufacturing III. Discussion : Effects of

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Shape dependance The thicker the glass the higher the pitch f 2 /f 1 = 2.35 (tenth = 2.4 ) can be adjusted from 2 to 2.5 according to ellipticity f 2 /f 1 = 1.48f 3 /f 1 = 2.01 (quint = 1.5) can be adjusted with the opening angle ELLIPTICAL CONICAL

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Materials dependance The time constant of the decay is four times as large for the crystal glass with same shape. The pitch and the timbre are correctly appreciated when the decay is small. Verre blancCristal

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Spreading of the measurements (fundamental and first harmonic) Repeatability on a serial of identical glasses Manufacturing

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Test procedure n Collect opinion from an audience of 25 people n Listening to synthetic sounds which simulates glass strikes : effect of pitch, timbre, time decay... u Note : This test has been performed on non informed audience, but is dependant on the musical background of each one IV. Test of listeing

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V. Test and results Q : PITCH EFFECT : thickness and shapeA1B1 A : Preference for bass tones Q : TIME DECAYA2B2 A : Large agreement for long decay : crystal glass is unanimously appreciated Q : RATIO f 2 /f 1 A4B4B5B6 A : Audience can make difference between consonance and dissonance but does not agree on the appreciation Q : NUMBER OF PARTIALSA7B7 A : Slight preference for few partials

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F PSYCHOLOGICAL IMPACT OF THE SONG OF THE GLASS PITCH TIMBRE TIME DECAY F MANUFACTURING QUALITY CONTROL F NEW DESIGN OF GLASS CONSONANT SERIALS NEW SHAPES WHICH ENHANCE SPECIFIC MODES Conclusions