and the Small Room
Arthur M. Noxon
Acoustic Sciences Corporation
Eugene, Oregon USA
This paper first presented at the 85th AES Convention
Los Angeles, CA, November 6, 1988
The Modulation Transfer Function (MTF) is used in room acoustics
as a descriptor of the effectiveness of transmission down the signal
path, between the speaker and listener. A major application for
this has been speech intelligibility. Basis for MTF analysis is
the signal to noise ratio. Noise can be any sound masking effect,
steady state noise, transient noise of reverberation or apparent
noise due to adjacent octave sound levels.
Narrow band MTF is used in the present work. This is in contrast
to the octave band methods common to traditional speech intelligibility.
Here, pure tone modulation used to develop spectral response detail.
A rapidly gated, slow sine sweep is the test signal for the articulation
response curve. This technique allows blurred transmission bands
to be specifically identified. These narrow ranges of poor articulation
are both audible to the listener and visible in hard copy data.
Changes to the room acoustic are also easily documented. The responsiveness
of this test to room acoustics in addition to the fine grain spectral
information in the articulation response curve suggests that this
system be used as a diagnostic tool. Although originally developed
to demonstrate small room acoustics in the lower registers, it has
found use in the full range of room sizes from the amphitheater
and auditorium right through to recording studio vocal booth.
I ARTICULATION RESPONSE CURVE (ARC)
The Modulation Transfer Function (MTF) is used in room acoustics
as the descriptor of effective signal transmission between speaker
and listener. A popular application of the MTF is for speech intelligibility.
Here we look at an application of MTF developed for precision playback
environments such as the hi-end, hi-fi listening room and the recording
studio. The suitability of the standard Speech Transmission Index
(STI) approach falls short on numerous points in these smaller spaces
that have high musical articulation requirements.
The spectrum segment useful for STI prediction or measurement starts
at the 125 Hz band and each octave band is weighted for significance
in speech recognition. Music occupies two octaves lower than the
range used for STI work, half the keyboard is below Middle C 2 5
2 . The weighting of these and other octaves in a calculation is
not yet established. The musical spectrum and the relative significance
of each octave band may well not be the same as for speech. The
Music Transmission Index (MTI) may be convertible to STI, but the
converse may not be possible. This would be due to the relative
lack of full bandwidth information in the STI. Clearly, research
remains to be done in this area.
The STI joins the group of single index acoustic descriptors, such
as NRC, dB, A, IIC, RT60, et. al. Architectural specifications can
be satisfied with a single index indicator. Acoustical engineers
and consultants engaged in diagnosis and remedy have always required
spectral detail and the subject of intelligibility is no different.
Measured STI only needs the signal to noise ratio to be detected.
Tracking octave band decay rates is one method used and monitoring
modulated octave band noise levels is another. Both use selected
octave bandwidths and yield a single intelligibility rating. The
approach contributes little to the diagnosis of room acoustics.
The present technique provides narrow band spectral articulation
information. This facilitates diagnostic efforts and evaluation
The predictive side of MTF analysis requires the ability to accurately
estimate the signal to noise ratio. The noise level is due to the
reflections in the room and due to its reverberation. Predictive
methods that use room reverberation decay rates have the prerequisite
imposed that the room sound field is instantaneously diffuse and
has an exponential decay rate.
A non-linear method of predicting noise levels is to use ray tracing
of the first 30 reflections. This method better correlates with
measured STI. Complex room geometry limits this method. Neither
linear acoustics nor ray tracing can be used for predicting in small
rooms dominated by room resonant mode decays.
The musical line is characterized as a rapid staccato of complex
tone bursts. Music then is a set of musical lines, overlaid and
intertwining one another. The basic element of this woven fabric
of music is the tone burst. The acoustic descriptor that relates
to musical articulation may well be the tone burst, indeed a rapid
staccato of bursts. Such a signal has been used for harmonic distortion
analysis room acoustic transmission path. Here we only desire measurement
of the signal envelope and the faithfulness of its modulated transmission.
Wave form reproduction, although important, is not the issue addressed.
A synthesis of these constraints and requirements is embodied in
the present approach to MTF. The Articulation Frequency Response
Curve (AFC) is a relatively simple, direct physical measurement.
Equally important is the subjective aspect. The auditor in a precision
listening setting can play the test signal over headphones and hear
the rapid, clean staccato of tone bursts whose frequency is slowly
varied. The auditor expects the room acoustic to play this signal
accurately. By removing the headphones and listening to the same
signal in the playback room, defects in the transmission path become
quite audible. In a small room, articulation dramatically varies
with frequency. Typically, there are tenth-octave bands of totally
garbled transmission adjoining similar sized bands of quite intelligible
transmission. The Articulation Response Curve is a fine-grained
quantification of the “fast tracking” ability of a listening
II COMPARISON WITH TRADITION
DEFINITION OF STANDARD TERMS
1. Signal Intensity (I)
Standard MTF format assumes the sound intensity envelope is a modulated
cosine with a DC offset.
The mean signal intensity (Io) is modulated by the modulation amplitude
2. Modulation Index (m)
The modulation index is defined as the ratio of the intensity of
the modulation to the mean intensity of the signal, modulation plus
It is also expressed in terms of the signal level Is
= mIo and the noise level IN = Io
3. Modulation Transfer (MT)
This is the attenuation in dB of the modulated signal. It is a function
of the modulation index.
MT = 20 log m
4. Signal to Noise Ratio (SNR)
The signal to noise ratio is the level of difference between the
signal and the noise (LS/N).
It can also be expressed in terms of the modulation index.
Transmission Index (TI)
The transmission index is the SNR measured in dB and expressed in
percent. To do this the SNR is offset to a practical zero % level
and then proportioned to the range of effective SNR. These are subjectively
determined constants that relate the perceived threshold of modulation
to the maximum value of modulation.
The offset is 12 dB and the range is 30 dB.
6. Speech Transmission Index (STI)
This is compiled as the sum of the weighted TI for each of the 7
octave bands and expressed in percent.
The weighting factors (WK) normalize to 1.
7. Octave Masking Effect (mO)
This occurs when the lower octave is louder than the measured one.
0.3% of the lower octave intensity is considered noise acting on
the test signal.
The impact of simultaneous independent masking effects is carried
by multiplying their independent modulation indices together.
m = m1 x m2
MTF IN PRESENTLY MEASURED TERMS
1. Signal Modulation Level (La)
Separated signal and noise levels are not directly measured in the
present test method. The articulation response curve is the timewise
evolution of the received sound levels. This easily allows measurement
of La, the fluctuation in dB of the test signal.
2. Modulation Index m(La)
The modulation level (La) can be expressed in terms of
modulation index by rewriting its definition.
Upon rearrangement, the modulation index is resolved solely in
terms of measured level fluctuation (La).
3. Modulation Transfer (MT)
The reduction in modulation can be related to the modulation level
at the receiver La.
4. Signal to Noise Ratio (SNR)
The signal to noise ratio is developed by using the new expression
of the modulation index.
5. Transmission Index (TI)
The transmission index remains except as the SNR term is above has
6. Mean Transmission Index (TI)
The concept is to sum the various TI values similar to that as done
with the STI. Data collected here is not from octave bands but from
small bandwidths of tones having similar modulation levels.
The STI octave band weighting factor (WK) here is undefined.
It will be carried in the form of (Wi) to suggest that a listener
based preference fit option still remains open.
The octave bandwidth weighting actor in STI appears here as a “log
frequency” term in the averaged 5.
7. Octave Masking Index (mo)
This effect is left out of the current presentation. However, it
should be thoroughly investigated and ultimately included. It clearly
is an operative with small room acoustics. It is easy to find bandwidths
with low level articulation and low mean sound level that are just
upfrequency from a loud and strongly fluctuating signal.
A given mean intensity level is given by the mean sound level (L)
for example, equal octave fraction band widths for a low frequency
75 dB level followed by a weaker 65 dB level
This single level shift is of small consequence but cumulative
effects can occur due to a very rough response curve loaded with
room resonances. Only 4 such 10 dB shifts would produce a 90% masking
THE TEST SIGNAL
1. The Burst
The MTF (Modulation Transfer Function) method of testing for articulation
uses a gated audio signal. For musical playback in listening rooms,
a pure tone is gated 8 times per second. Shown in the figure is
one burst, it lasts about 60 ms. The sweeping frequency changes
about 1 Hz during each burst. This particular burst started at 183
Hz and over 60 ms has shifted to 184 Hz.
2. Duty Cycle
Each tone burst is separated by a dwell time. We use here a 50%
duty cycle: 60 ms on and 60 ms off. During the silent period the
signal generator continues to change frequency. The next burst after
the 184 Hz signal would start at about 185 Hz and slide upwards
to 186. Here we show three distinct tone bursts spread out over
a 4/10 second time window. These bursts are clearly 60 ms long followed
by a 60 ms dwell.
The burst has a square wave modulation. Typical MTF bursts are
sine wave modulated, either amplitude or level. Here the square
wave modulation has ringing in it, visible in both the on and the
off parts of the duty cycle. A ramped attack and decay would reduce
the ringing effect. Although the pure tone quality of each burst
is degraded by the low level ringing, this coloration provided unique
cues for the subjective perception of attack transients. At about
2 dB articulation level, the LF ringing loses audibility—this
may suggest a method to evaluate perception thresholds of tonal
The tone generator is set to be a linear ramp. The signal starts
at about 20 Hz and sweeps with a rate of 20 Hz/sec up to 800 Hz
and back down to 20 Hz. This symmetrical format has proven easy
to read. The ramp up frequencies are not identical to those on the
ramp down. This method also serves as a check on the repeatability
and accuracy of the test.
Next is shown the test signal as seen by a dB meter. If each burst
is clean and each dwell period quiet, the dB meter output will alternate
between loud and quiet levels. The signal rises in the presence
of a burst and falls during the dwell time. There are 2 seconds
shown and the 16 sound burst level peaks due to the 8 bursts/second
test rate. The actual electric signal level shifts some 50 dB. The
damping factors in the analyzer circuitry limit the level swing
to only 17 dB. However, this seems to be more range than adequate
for the analysis of most rooms.
5. The Complete Test
The entire test lasts about 75 seconds. The frequency from 20 Hz
through 800 Hz and back down to 20 Hz again. The full test is shown.
The level swing of each successive tone burst is clearly visible
in this display. The burst’s tone raises steadily to the 800
Hz peak frequency and then drops back down during the second half
of the test. By listening to this signal on headphones, an articulate
audition of the test tone is available.
B. THE RECEIVED SIGNAL
1. The Test Setup
The gated set of tone bursts is played into the room. This allows
the distinct features of playback articulation to be observed. A
good way to record the effect is with an omni mic and tape recorder
without AGC (automatic gain control). Once the listener’s
signal is captured on tape, it can be played back through an analyzer
circuit at a later date.
2. Articulation Response Printouts
The articulation response curve is developed by plotting the recorded
sound level vs. time. This is most directly accomplished by running
the signal into a chart level recorder. Another method uses the
dB level output from a meter to feed the vertical sweep of a storage
scope set at very slow horizontal sweep and a printout on an x-y
A closeup of consecutive tone bursts shows substantial acoustic
energy can occupy the dwell period. There are 4 bursts in this 8/10
second display. Notice how the burst is deformed. What used to be
a sharp attack, flat sustain and abrupt decay has been turned into
a pulse that has lost distinctive features.
Ramps, both up and down take the place of the sharp attack and
decay of the articulate signal. The sustain does not hold flat,
it is foreshortened by the ramping transitions. In this inarticulate
space, the room mumbles, slurs and often will “double-tongue”
the rapidly gated signal.
4. Articulation Response Curve
Here is what a typical hi-fi demo room does to the fully articulate
signal. The signal received by the listener will display some ranges
of articulation but most of the test data looks very thin. When
the vertical strokes are short, the articulation is weak. There
will be little sound level difference between successive tone bursts
and dwells. The only way to improve articulation is to “clear
the air” between bursts by adding acoustic control.
IV ANALOG TRANSMISSION INDEX
A. APPROXIMATION TO TI
1. Fitted Curve
The STI or as generalized here the TI is an equation based on clear
definitions. The weighting factor feature (WI) can be
set and prorated to bandwidths used to convert the TI into the STI.
However the data taken must be converted into a computer and processed
to calculate the STI. An analog electronic circuit approximation
to this equation is desired.
key is the TI term. Within the range of desired values a simple
expression has been found to closely match within a few percent.
Also note the expression is in terms of La, the presently
measured modulation variable.
2. Circuit Diagram for Measurement
The circuit diagram for the analog approximation equation is shown.
The first stage develops the level of modulation (La).
The second stage develops the dB level of the modulation (Log La).
These two frequency dependant parts are properly ratioed and added
to a DC offset then integrated against log frequency. Regardless
of the reference level of either term, the DC offset can be scaled
If the frequency sweep is a log sweep instead of linear, then log
frequency weighting will be maintained by integrating over time.
Substantial signal conditioning has been left out of this circuit
to retain a sense of propriety integrity but the basic elements
B. DISCUSSION OF La AND Log La
1. Modulation Level (La, dB)
Articulation is measured here in terms of the modulation level in
acoustic dB’s. The weighting scale dB,A or dB,C doesn’t
affect articulation. Articulation is merely a difference in sound
It is semantically possible to propose that an effect of negative
articulation could exist and not be detected by the present circuit.
This occurs whenever sound levels in the dwell period exceed levels,
attained during the burst. This seems to be able to happen at a
frequency for which sound cancellation occurs. The modulation transfer
function is not defined in this situation of negative modulation
Negative modulation is physically improbable. It takes time for
resonant conditions, strong enough to cancel a direct signal, to
be developed inside the room. The direct signal will exceed reverb
levels during this initial energy buildup period in the room. During
this transition period, the direct signal will be heard. Energy
is always split between the burst and dwell periods.
2. Articulation Level (10 Log La, dB)
This is also measured in dB and the scale is adjusted so that 1.0
dB articulation is equal to zero articulation level (Ref, 1dB).
This is really mathematically arbitrary but set here with considerations.
The listener’s minimum perceived level change is 0.4 to 0.5
dB for any tone. For the practical purpose of signal burst reproduction
1 dB level differences though audible have little to no perceived
value for depicting quality music transition detail. Therefore,
it was chosen as zero dB. Regardless, this is an empirical curve
fitting arrangement and a different reference here would be reflected
in a different DC offset constant than 0.08 above.
L, La AND Log La OF TEST SIGNAL
1. Constant Modulation Test Signal
The test signal has a constant signal to noise ratio of at least
45 dB or the full dynamic range of the test cassette tape. The corresponding
articulation level shows as the solid, slightly fluctuating dark
line. It is overlaid against the back drop of its gated sweep response
Two curves are shown here. The sound L(t) level vs. time articulation
response curve is the wide4 fluctuating line. Overlaid on it is
a solid, slowly changing and relatively flat line, the Modulation
2. Upper Limits to Sound Level
The sound level curve is not fully accurate because of the ballistics
in the electronic detection circuits. For this data run the upper
limit is about 20 dB. The real 40 dB signal modulation does not
show. This is of no practical concern because 15 dB to 20 dB differences
between peaks and valleys in the modulation envelope are subjectively
quite adequate. Most of the data is often on the order of a 5 dB
to 10 dB articulation level (La).
In future work a 1K test tone should be modulated at zero, 1, 5,
10, 15 and 20 dB modulation levels. This will allow calibration
of testing circuits. An alternative to this is to step the 1K tone
level (zero modulation) to develop calibration at the above -1,
-5, -10, -15, -20 levels.
L, La AND Log La OF RECEIVED SIGNAL
1. Modulated Sweep Response Curve
This shows the signal to noise ratio spectral response of the room
to the rapidly gated tone sweep. The actual received signal level
L(t) is the wide, rapid fluctuating line.
The overlaid solid line is the transmission index vs. frequency
at the 8 Hz gated modulation rate. The mean TI would be the averaged
value of this curve.
2. This curve is a linear frequency sweep and the mean TI requires
log frequency weighting. If a log frequency sweep was used instead
of linear, then straight integration of the TI in time would produce
the mean TI.
Linear sweep is often used in low frequency room measurements.
It is said the ear hears quasi-linear frequency scale below 200
Hz. The log sweep spends ¾ of the time below 170 Hz about
¼ of the frequency range to be explored. The remainder ¼
test time packs the remaining ¾ frequency range (200 to 800
Hz). Although log frequency sweep accommodates a simple integration
scheme for the mean TI, it most likely is not sampling sufficiently
the room articulation. A more sophisticated integration must be
V SAMPLE TESTS
A. ROOM SEQUENCE
A listening room, 8’ x 14’ x 18’ with double
sheetrocked walls and concrete floor is tested at various stages
of acoustic treatment. Fundamental, is the use of corner-loaded
bass traps. The mic is placed at the hi-fi listener’s position
and two speakers, in phase are located at the opposite end of
the room in a stereo setup.
Bare Room Response
To read this type of printout, we focus on the percentage of the
test frequency sweep that has a wide (10 dB) swing, peak to peak.
Marginally acceptable is a medium swing (5 dB). Real garbling
occurs with less than a 2 dB swing. Note also the irregular “median
line.” It is the average about which jitters the articulation
signal. The terrain looks like a lot of steep hills and valleys
covered with very little articulation.
2. Absorption Added in Stages
a. Here, a simple Tx6 set has been added to the front of the
room behind the speakers. Already a substantial pattern of low
level articulation is established throughout the entire test.
The hills and valleys have grown less severe and are covered better
with a wider articulation band. Note also the overall flatness,
the room is being acoustically EQ’d.
b. The next setup adds traps (16x3 plus 11x3 pair stacks) at
the back of the room. Again, the frequency bands of improved articulation
widen. The severity of the peaks and valleys is more reduced.
A few peak/valley patterns have even disappeared.
The softening of the peak/valley profiles means the “Q”
of the room, the sharpness of its resonance responses, have been
lowered. As the room resonances are damped, the peaks drop, the
valleys rise and there is an overall softening effect to the room
Next is added a side wall treatment, 4 sets of 9” x 5’
½ Rounds. This controls stage width and imaging, lateral
flutter and cross talk. It develops overall a much deeper articulation.
It produces wide bands of continuously full articulation, some 200
Hz wide between 400 and 600 Hz. Yet, curiously there seems to be
some areas of thinning, reduced articulation around 150 Hz.
d. The head wall traps are the next to be set, 6-11x5 ½
Rounds plus a single column of 11x6 Full rounds in the center. This
develops stage depth, clarity and imaging detail. Dramatic articulation
improvement is seen broadband, the peak/valley terrain flattens
substantially. The width of the articulation patterns have grown
quite wide and improvement is seen in the mid-bass. The front/rear
energy storage system of the room has been dampened to make this
e. Finally we have added the rear wall. A 16x3 + 11x5 center column
and 4 sets of 11x5 ½ Rounds with one more pair on the front
wall. The result is a very wide and steady articulation pattern
that extends even into the deepest bass. Peaks and valleys now even
more are soft, rounded. The room still retains a strong, comfortable
If you compare the overall before and after room articulation signatures,
you will see that the sound levels below 100 Hz have not changed
and those above 100 Hz are depressed by about 5 dB. In addition,
we see that below 400 cycles the articulation signature increases
from 2 to 8 dB and above 400 from 10 to 18 dB.
The effects of equalizing the signal were explored. The effort was
made to get the trapped, articulate room to have an over flutter
response. A 1/3 octave equalizer was set with pink noise and headphones.
The following articulation test results. For better results, a parametric
equalizer could be used. With this equalizer a noticeable ringing
effect occurs, most likely not desirable in quality audio. Nonetheless,
the response curve has been flattened, peaks lowered, valleys raised.
Notice however, that there is “zero effect” on articulation.
Electronic EQ only adjusts levels, not articulation.
4. Full Acoustics Plus Equalizer
a. The “full on” room has also been tested. This is
not too unlike the typical dedicated Hi-end reference listening
room. Basically, a carpet has been added along with floor bounce
traps. All the traps of the prior setup (#6) have been elongated
from their 5-foot height to a full floor to ceiling length. A major
articulation improvement is noted, especially in the 20 to 400 Hz
range. The natural acoustic #Q is taking a strong control, the low-end
boom below 100 is almost gone.
b. Finally, to this “ultra” system, we degrade its
sonics but add equalizer effects. Again the EQ is set with pink
noise, RTA and 1/3 octave equalizer. The result is pretty flat,
and articulate response. There are a few small band widths with
poor articulation remaining. Even these may well be cleaned up with
additional tweaking. Again the ringing effect of the equalizer is
clearly audible in this test, something undesired in precision audition.
1/3 OCTAVE PINK NOISE, RTA
1. RTA and Room Treatment Sequence
For the entire series of test just described, 1/3 octave RTA was
also taken. Above 40 Hz the overall levels are reduced by 2 dB.
If we overlay and line up the mid-range levels, we see a relative
increase in the lower octaves below 70 Hz by 2 dB. This is the acoustic
EQ effect. This acoustic treatment brought the deep bass 2 dB closer
to the mid bass levels.
Relatively minor corrections towards flattening the spectrum sound
levels with no loss of deep bass sound power is how RTA sees the
effects of the full on acoustics. Clearly RTA doesn’t begin
to suggest the fast tracking ability of the listening room.
2. RTA and Slow Sine Sweep
The narrow band frequency sweep room response curve is compared
to the 1/3 octave pink noise levels. The frequency range is 20 to
800 Hz. The frequency scale is linear, this stretches the 1/3 octave
bandwidths as the frequency goes higher.
The RTA levels are weighted higher with increasing frequency. This
is due to wider bandwidths, more 1 Hz levels being added together.
The equivalent narrow band spectrum can be had by subtracting the
bandwidth weighting term from each bandwidth level.
L = 10log f + 10log 23%
The 1/3 octave has 23% bandwidth. When the two curves are overlaid
the general tendency is seen but the detailed narrow band sweep
cannot be even inferred by the 1/3 octave measurement.
RTA and Articulated Sweep
Not unlike the vague relationship between the frequency response
of the room and the RTA, so it is with the articulated sweep. Overall
trends do track, but the RTA gives no indications by which features
in the articulated sweep response curve can be derived.
For example, 1/3 octave EQ suggests that the 250 Hz band should
be cut some 5 dB. However, the articulated sweep response shows
that the problem high sound level is a 1/3 octave band centered
at 180 Hz.
C. SLOW SINE AND MODULATED SWEEPS
Here we compare the slow sine sweep to the modulated sweep. The
sound levels at the listener’s position are recorded in both
cases between 20 and 800 Hz.
Observations and Tendencies
Tendencies are noticed. The trend of the slow sine sweep matches
the trend of the articulated sweep.
a) Articulation levels La of 12 to 15 dB attain peak
sound levels equal to that of the slow sine sweep levels.
b) Articulation levels that are less than 12 dB fall short of the
slow sine sweep level by an amount approximately equal to: 15 -
c) Strong articulation is associated with wide bandwidths of relatively
uniform sound level on the slow sine sweep response curve.
d) The lower the “Q” of sine sweep response curve the
stronger the articulation signal.
e) Very low articulation levels are always accompanied by a very
sharp, high “Q” room resonance section of the room response
f) Rapid sound level changes in the slow sine sweep curve mark
frequency bands with poor articulation response.
C. ROOM MODES AND “Q”
From the above it is clear that room mode spacing and the adjustment
of room resonance “Q” are controlling variables in the
development of articulation response in small rooms.
To illustrate by contrast, it can be safely concluded that a group
of closely spaced high “Q” resonances will produce stronger
articulation than if that given group was well separated having
well isolated resonance peaks. The tight grouping of some modes
leave more spaces between other modes. The real answer to an articulate
room will be to have a set properly spaced and damped room resonances.
2. Modulation Level La and Room “Q”
It is straight forward to expect that the higher the “Q”
for a particular room resonance, the lower the articulation levels
would be. For the data presented above in Section V-B, an interesting
curve “Q” vs. La is produced. The room “Q”
has an almost exact inverse relationship with the articulation level
La. The empirical data is found to lie on the curve of:
Q x La = 180
Since the minimum La for acceptable listening is about 5 dB, the
most probable maximum acceptable “Q” will be about 36.
For the very desirable La of 10 dB we have room resonance
“Q” of 18. The “Q” of a typical room is
often 40 to 50 prior to specific acoustic conditioning.
D. LINEAR “Q” VS La
The classic sabine equation uses diffuse exponent sound fields.
The “Q” vs. La relationship can be predicted,
it is seen to not fit the measured relationship. This is expected
because the sound field in small rooms and lower octaves does not
“Q” and RT60
There exists a group of “Q” relationships dependant
on a variety of variables. The RT60 is no exception.
The frequency of the resonance (f) part of the dependant variables.
Q = 1/22 RT60
La and RT60
For linear RT60, the diffuse exponential decay sound
field level drops proportional to time.
The gated tone burst has burst rate (F) and its dwell period is
the time allowed for sound level decay.
An 8 Hz gated frequency yields an equation relevant to the present
3. Linear “Q” and La
By combining the above equations the frequency dependant “Q”
x La relation is developed.
For linear decay the Cis directly proportional to frequency. This
is not what is measured, a constant. Since both definitions used,
“Q” and La assume a linear acoustic relationship
with RT60, neither can be identified as the non linear
term at this point.
The goal of this project has been to explore the Transmission Index
of small rooms in the lower octaves. The rapidly gated slow sine
sweep is an effective test signal. Although envelope shaping of
the attack and decay should be explored, the existing coloration
led to the observation that low level coloration becomes inaudible
at a higher modulation level than does the modulation itself. This
suggests that “quality” detection thresholds may well
be much different from “quantity” detection. Research
in perception along the lines of complex signal detection thresholds
needs to be applied to the present work.
The difference between the linear and measured QLa term stands
to illustrate that the prediction of TI in the lower octaves in
small rooms has yet to be accomplished. More empirical work also
needs to be done in this area. The observation presented here is
only based on one data run.
A new, complex test signal and detection method may be considered
to directly measure the masked partial signal level. A correlation
between pure tone modulation levels at the partially frequency and
the masking level of the partial wherein a complex tone burst ie.
Linear, additive effects, may be fruitful.
The TI equation has been approximated here by a fitted curve using
the same single variable. The only reason for this is to access
the convenience of a relatively simple analog circuit.
Further work with the exact equation ought to be completed using
analog or computational methods to develop the TI. There also may
be additional terms added to reduce the error of the approximation
There lies ahead a great opportunity to work on the theoretical
side of the Transmission Index at lower frequencies in small rooms.
The first step aside from large halls in linear acoustics was the
ray tracing method, but this is not applicable to small room resonant
The relative level effect needs to be factored into the present
TI approach. A room with strong level changes in a slow sine sweep
must be penalized when compared to a room with a relatively flat
response. A method to isolate this effect needs to be developed
and produce an independent modulation index.
In general, standards for speech in small rooms need to be applied
to this work. The performance of STI analyzers needs to be compared
to traditional listening tests in small classrooms where modes exist
in the speech range. In large halls, little emphasis is given to
the lower speech octave, 125 Hz. Small rooms, with their room modes
and typical lack of low frequency absorption, may well require re-assessment
of this weighting.
A method that develops spectral response curves for articulation
has been demonstrated. The measure variables have been written into
the equations that define the Modulation Transfer Function and the
corresponding Transmission Index. The signal to reverberant noise
level is directly measured and there is no conversion of data that
requires the assumption of linear acoustics.
The equipment used to make this test is relatively common. The
source is a pre-recorded cassette test signal. Analysis will use
as little as a sound meter and strip chart recorder. By adding a
circuit for signal processing, the Transmission Index response curve
can be developed. With additional circuits even the STI can be stated.
The STI is fast becoming a standard specification. Engineers and
consultants require a spectral version of the Transmission Index
in order to remedy the acoustics. Now that this simple and low cost
articulation test method has been shown to produce detailed spectral
information, it is hoped that this technique will be the forerunner
of a new class of sound system analysis.
(The following were used in the preparation of the paper)
Houtgast, T. and Steeneken, H.J.M., Predicting Speech Intelligibility
in Rooms from the Modulation Transfer Function Parts I, and II.
ACUSTICA VOL 46, 1980.
Houtgast, T. and Steeneken, H.J.M., A Review of the MTF Concept
in Room Acoustics and Its Use for Estimating Speech Intelligibility
in Auditoria. JASA 77 (3) March 1985.
Schroeder, M.R., Modulation Transfer Functions: Definition and
Measurement. ACUSTICA Vol 49 (1981) 179.
Houtgast, T. and Steeneken, H.J.M., A Physical Method for Measuring
Speech-transmission Quality. JASA 67 (1) Jan 1980.
Houtgast, T. and Steeneken, H.J.M., The Modulation Transfer Function
in Room Acoustics as a Prediction of Speech Intelligibility. ACUSTICA
Vol 28, 1973.
Kryter, Karl., Methods for the Calculation and Use of the Articulation
Index. JASA 34 (II) Nov 1962.
Polack, J.D., Alrutz, H. and Schroeder, M.R., The Modulation Transfer
Function of Music Signals and its Application to Reverberation Measurements.
ACUSTICA 54 (1984).
Demany, L. and Semal, C., Amplitude and Frequency Modulation. ACUSTICA
Fastl, H. and Hesse, A., Frequency Discrimination for Pure Tones
at Short Durations. ACUSTICA 56 (1984).
© 2009 Acoustic Sciences Corporation.
All Rights Reserved.