PREDICTION OF ROOM ACOUSTICS PARAMETERS Acoustics of Concert Halls and Rooms PREDICTION OF ROOM ACOUSTICS PARAMETERS Handbook of Acoustics Gade, Chapter 9 (2007)

•REVERBERATION TIME (RT) •STRENGTH (G) •CLARITY (C) SEVEN OBJECTIVE ROOM ACOUSTICS PARAMETERS IMPORTANT IN SUBJECTIVE QUALITIES OF A CONCERT HALL •REVERBERATION TIME (RT) •EARLY DECAY TIME (EDT) •STRENGTH (G) •CLARITY (C) •LATERAL ENERGY FRACTION (LEF) •INTERAURAL CROSS CORRELATION (IACC) •EARLY SUPPORT (STearly) Gade, 2007

REVERBERATION TIME SABINE EQUATION: RT = 0.161 V/(ΣSiαi + 4mV) V is volume, Si is area of surface with absorption coefficient αi and m is air absorption per unit volume. Sabine equation applies quite well to rooms whose dimensions are larger than the sound wavelength and whose absorption is well distributed throughout the room. NORRIS-EYRING EQUATION: RT = - 4v/cS ln(1-<α>) <α> is average random-incidence absorption coefficient For rooms with one or more very absorbing surfaces the Norris-Eyring equation usually gives a better RT value.

IMPULSE RESPONSE THE BASIC SOURCE OF INFORMATION ABOUT THE AUDIBLE PROPERTIES OF THE SOUND FIELD IN A ROOM IS THE IMPULSE RESPONSE SIGNAL. WHEN RECORDED WITH A MULTICHANNEL TECHNIQUE TO PRESERVE THE INFORMATION ABOUT DIRECTION OF INCIDENCE IT CONTAINS ALL AVAILABLE INFORMATION FOR A GIVEN SOURCE AND RECEIVER LOCATION.

PREDICTION OF RELATIVE STRENGTH G: PREDICTION OF CLARITY CLARITY---The degree to which every detail of the performance can be perceived With exponential decay, the expected value of C becomes a function of RT alone: Cexp = 10 log [exp(1.104/RT) – 1] dB PREDICTION OF RELATIVE STRENGTH G: In a diffuse field: G = 10 log (RT/V) + 45 dB Sound strength G decreases with distance. The rate of decrease ΔG can be modeled in several ways.

SUGGESTED VALUES OF OBJECTIVE ROOM ACOUSTIC PARAMETERS IN UNOCCUPIED CONCERT HALLS FOR CLASSICAL MUSIC (Gade, 2007)

To minimize sound absorption in order to obtain strong reverberance (for classical music): •Keep the row-to-row distance and chair width small •Seat design: minimum absorption with minimum difference between occupied and empty seats (low back rests and upholster only surfaces covered by seated person) •Thick upholstery on seat (~80 mm) and back rest (~50 mm) to minimize difference between empty and occupied seats)

ABSORPTION COEFFICIENTS OF SEATING AREAS IN CONCERT HALLS FOR THREE DIFFERENT DEGREES OF UPHOLSTRY, BOTH EMPTY AND OCCUPIED (Gade, 2007)

PREDICTION BY COMPUTER SIMULATION COMPUTER SIMULATIONS TAKE INTO ACCOUNT THE GEOMETRY AND ACTUAL DISTRIBUTION OF THE ABSORPTION MATERIALS IN A ROOM AS WELL AS THE ACTUAL SOURCE AND RECEIVER POSITION. ROOM GEOMETRY IS REPRESENTED BY A 3-D CAD MODEL WHICH MAY ALREADY HAVE BEEN CREATED BY THE ARCHITECTS WHEN GEOMETRY IS COMPLETE, THE ABSORPTION VALUES FOR EACH OCTAVE BAND, THE SCATTER, AND THE ACOUSTIC TRANSPARENCY ARE ASSIGNED TO EACH SURFACE. SOURCE AND RECEIVER ARE ENTERED MOST MODELS DISREGARD PHASE AND USE AN ENERGY APPROXIMATION. THE SOUND PROPAGATION IS STUDIED BY (MILLIONS OF) RAYS DRAWN FROM SOURCE TO RECEIVER.

SCALE MODEL PREDICTION SCALE MODELING IS MORE EXPENSIVE AND TIME-CONSUMING THAN COMPUTER MODELING, BUT IS REGARDED AS MORE RELIABLE IN LARGE ROOMS WITH A LOT OF IRREGULAR SURFACES OR OBJECTS THAT DIFFRACT SOUND WAVES. IN TESTING A 1 : m SCALE MODEL, THE ACOUSTIC TEST FREQUENCY IS INCREASED BY A FACTOR m SO THAT THE RATIO OF WAVELENGTH TO LINEAR DIMENSIONS REMAINS THE SAME

RELATIONSHIPS BETWEEN ROOM ACOUSTIC PARAMETERS AND ROOM DESIGN VARIABLES (AS DERIVED FROM DATA FROM MORE THAN 50 HALLS ) Gade, 2007

LISTENER ENVELOPMENT (LEV), THE IMPRESSION OF BEING INSIDE AND SURROUNDED BY THE REVERBERANT SOUND FIELD, IS ONE IMPORTANT ASPECT OF SPACIOUSNESS. LATERAL ENERGY FRACTION (LEF) MEASURES THE AMOUNT OF EARLY ENERGY ARRIVING FROM THE SIDES INTERAURAL CROSS- CORRELATION COEFFICIENT (IACC) MEASURES THE SIMULARITY OF EARLY SOUND AT THE TWO EARS. (A SMALL VALUE OF IACC CONTRIBUTES TO SPACIOUSNESS).

EARLY and LATE SUPPORT EARLY SUPPORT LATE SUPPORT (Gade, 2007) EASE OF ENSEMBLE (HOW WELL THE MUSICANS CAN HEAR EACH OTHER) IS ANOTHER IMPORTANT PARAMETER FOR MUSICIANS THAT RELATES TO STearly

TIMBRE or TONE COLOR TIMBRE DESCRIBES THE ROOM INFLUENCE ON THE BALANCE BETWEEN HIGH, MIDDLE, AND LOW FREQUENCIES (whether the sound is harsh, bright, hollow, warm, etc.) BASS RATIO (BR) IS A GOOD MEASURE OF WARMTH (In these equations, T is the REVERBERATION TIME (RT)) INTIMACY, ANOTHER IMPORTANT QUALITY, IS RELATED TO INITIAL TIME DELAY GAP

SPEECH INTELLIGIBILITY THE MOST COMMON WAY TO ASSESS SPEECH INTELLIGIBILITY IS BY THE SPEECH TRANSMISSION INDEX (STI). THIS IS BASED ON THE IDEA THAT SPEECH CAN BE MODELED AS AN AMPLITUDE-MODULATED SIGNAL IN WHICH THE DEGREE OF MODULATION CARRIES THE SPEECH INFORMATION. STI IS MEASURED BY USING 7 BANDS OF NOISE EACH MODULATED BY 14 FREQUENCIES A FASTER MEASUREMENT METHOD USING ONLY TWO CARRIER BANDS AND FOUR PLUS FIVE MODULATION FREQUENCIES IS CALLED RAPID STI (RASTI)

THEORY AND PRINCIPLE IN MEASUREMENT OF RASTI Gade