PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Progress in Tonality Calculation
Julian BECKER1; Roland SOTTEK2; Thiago LOBATO3
1,2,3

HEAD acoustics GmbH, Germany

ABSTRACTThe perception of tonal sounds is one of the most important psychoacoustic sensations for product soundquality and environmental noise. In the past, a lot of work has been carried out to quantify tonal sound events
automatically. This work resulted in several methods for quantifying tonalities, such as Tone-to-Noise Ratio,
Prominence Ratio or the Psychoacoustic Tonality, which was standardized in the 15th Edition of the
ECMA-74 standard. The Psychoacoustic Tonality is based on a hearing model which emulates the processingof human hearing. Thus, it is able to predict human perception better than other methods which are only
partly based on psychoacoustics.
Since the publication of the Psychoacoustic Tonality, the algorithm is constantly being improved. In thispaper, the latest progress in the calculation of the Psychoacoustic Tonality is presented. The newdevelopments include improvements for low frequencies, identification of tonal components and a higher
frequency resolution of the detected tonalities.
These improvements will likely be included in future editions of the ECMA-74 standard.

1. INTRODUCTION
Technical and natural sounds frequently contain prominent tonal components. These sounds areoften either produced by periodicity, for example by a rotating device, or by narrowband noise s which
can for example be generated by air flow.
Tonal components are perceived very prominently by a human listener and thus significantly
influence the individual perception and evaluation of a sound event. Tonal sounds significantly
increase annoyance, if they are perceived as unwanted. Hence, the quantification of tonal sounds has
been an important topic for a long time. The topic currently gains even more attention due to theincreasing importance of electric vehicles. While these vehicles produce less overall noise, electricmotors do produce a rather tonal sound.
Several attempts have been made in the past for the automatic quantification of tonalities. Methods
like the Prominence Ratio (PR) [1] or the Tone-to-Noise Ratio (TNR) [2] have already been in use fora while, but they often lead to unsatisfactory results, because they do not consider human perception.
As a consequence, both methods produce implausible results in certain scenarios. For example, thesame signals with different sound pressure levels lead to the same result when using these methods
even though the perception of tonality has a level-dependence.
Research results show a strong correlation between tonality perception and the partial loudness of
tonal sound components [3]-[5]. Recently a new method, the Psychoacoustic Tonality, has been
published in the 15 th edition of the ECMA-74 standard [6]. This method is based on a psychoacoustic
hearing model and thus takes into account several psychoacoustic effects that are not considered in
PR and TNR. The applicability of the model was investigated for technical sounds and compa red toestablished methods [7,8].
Besides the quantification of tonality, recent research also deals with the quantification of tonalannoyance [9]. The ECMA-74 tonality can also be modified to describe this sensation [10].
While the Psychoacoustic Tonality shows a better performance than other established methods [11],1julian.becker@head-acoustics.deroland.sottek@head-acoustics.de3
thiago.lobato@head-acoustics.de25820

it is constantly being revised to further improve the results and to include additional features. These
improvements are presented in this paper. Recently, it was shown that the ECMA -74 Psychoacoustic
Tonality tends to overestimate tonalities of tonal components at low frequencies [10]. To avoid thiseffect, the outer and middle ear filtering of the algorithm was revised. New or improved features are
introduced to the algorithm by identifying tonal components and increasing the frequency resolutionof the detected tonalities. If not otherwise mentioned, ECMA-74 refers to the 15 th Edition of the
ECMA-74 standard [6] throughout this document.

2. PSYCHOACOUSTIC HEARING MODEL BASED ON ECMA-74
The basis for the tonality calculation is a model of the human hearing which transforms soundpressure to perceived loudness. This model was first described in [12] and later improved further. In
the 15 th edition of the ECMA-74 standard [6] it is described in Annex F and used as basis for further
calculation of psychoacoustic analyses. In this section the hearing model according to ECMA-74 isfirst described and improvements which were recently applied to the model are presented.
Figure 1 shows the structure of the hearing model. The sound pressure input signal ‫݌‬ሺ݊ሻ isprocessed according to the signal processing of the human hearing. Finally, the model results in thespecific loudness ܰǯሺ‫ݖ‬ሻ . The processing steps of the hearing model are briefly discussed in thefollowing and recent improvements to the algorithm are described. Specific information about theexact implementation can be found in the ECMA-74 standard [6]. Since the definition of the criticalbands in the hearing model differs slightly from the commonly used definition by Zwicker [ 13], theunit  ୌ୑ୗ (bark according to the hearing model of Sottek) is used in the following.
Correspondingly the unit ୌ୑ୗ is used for the loudness calculated by the hearing model.
The processing starts with outer and middle ear filtering. In ECMA-74, this filter is defined suchthat the resulting loudness of the hearing model fits well to the equal loudness contours (ELCs) of
ISO 226:1987 for frequencies below 1 kHz and to the ELCs of ISO 226:2003 for higher frequencies.

Figure 1 – Basic hearing model structure
Since the results of ECMA-74 tend to overestimate tonalities at low frequencies, this filter was
revised such that the results also match the ELCs of ISO 226:2003 for frequencies below 1 kHz.
Additionally, a peak at frequencies above 10 kHz was removed since it artificially added tonal effects
to some signals. Also, the filter was designed such that it can be described as two serial filters
corresponding to the influence of the outer ear and of the middle/inner ear. The outer ear filter can bedivided into a filter considering the diffuse field influence and a filter considering additional effects
in free field. With this definition, it is possible to differentiate between free field and diffuse field

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conditions. In free field conditions, the complete filters need to be considered, while in diffuse field
conditions only the diffuse field part of the outer ear needs to be used together with th e filter of theinner/middle ear.
Figure 2 shows the original filter as described in ECMA -74 (left) and the modified filter with thetwo serial filters corresponding to the outer ear and to the middle/inner ear for free field condition.

Figure 2 – Left: Outer and middle ear transfer function according to ECMA-74,
Right: Revised outer and middle/inner ear transfer function
In the next step, the signal is processed by an auditory filter bank consisting of 53 overlapping
filters corresponding to critical bands from ‫ ݖ‬ൌ ͲǤͷ to ‫ ݖ‬ൌ ʹ͸Ǥͷ with a step size of ο‫ ݖ‬ൌ ͲǤͷǤ This
step together with the subsequent half-wave rectification remains unchanged and is calculated exactly
as described in ECMA-74. The resulting 53 rectified band-pass signals ‫݌‬௭ ሺ݊ሻ are later used as basis
for the calculation of the tonality.
To calculate the specific loudness, blockwise root-mean square (RMS) values are taken from ‫݌‬௭ ሺ݊ሻand transformed nonlinearly to result in specific loudness without consideration of the thresh old inquiet. These steps are calculated unmodified according to ECMA-74. For the calculation of theblockwise root mean square values, a frequency-dependent block length ‫ݏ‬ୠ ሺ‫ݖ‬ሻ is used. The block
length is 8192 for the lowest critical bands and is decreased stepwise by a factor of 2 until it reaches
a length of 1024 samples.
Finally, the effect of the threshold of hearing is applied to the loudness values. The function
describing the specific loudness threshold needs to be modified to fit to the outer and m iddle ear filters.
Figure 3 shows the specific loudness thresholds according to ECMA-74 (left) and the modified one(right).

Figure 3 – Left: Loudness threshold according to ECMA-74, Right: Revised loudness threshold
The results of this calculation are 53 specific loudness values ܰԢሺ‫ݖ‬ሻ for each time block, which
are used as basis for the tonality calculation process.

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3. CALCULATION OF TONALITY
The calculation of tonality is based on the rectified band-pass signals ‫݌‬௭ ሺ݊ሻ which were calculated
in the hearing model. Additionally, the final result of the hearing model, the specific loudness ܰԢሺ‫ݖ‬ሻis used. The basic structure of the tonality calculation is shown in Figure 4.

Figure 4 – Basic structure of the tonality calculation
3.1 Estimation of Tonal Loudness.
Tonality is calculated from the tonal loudness of the signal. The estimation of tonal loudness isdone similarly to ECMA-74 but with minor modifications. The first step to estimate the tonal loudness
is to calculate blockwise scaled autocorrelation functions (ACF). The block size ‫ݏ‬ୠ ሺ‫ݖ‬ሻ which wasused for the calculation of the RMS values in the hearing model is used. The calculation of the
autocorrelation function is done according to ECMA-74.
In ECMA-74, ACFs of neighboring bands and of neighboring blocks are averaged to reduce noise
effects. This averaging step is skipped since noise reduction is inherently performed in a new grouping
step which will be described later.
Next, a window is applied to the ACFs as described in ECMA-74. Since signal energy of noisy
signal parts only appears for low lags of the ACF, the window is placed such that lower lags are
ignored. Tonal loudness is then estimated by first removing the mean of the windowed ACF. The
windowed ACF with removed mean is analyzed by a Discrete Fourier Transform (DFT). In
ECMA-74, a ʹ‫ݏ‬ୠ ሺ‫ݖ‬ሻ-point DFT is used, resulting in different frequency resolutions depending on theband ‫ ݖ‬, with the highest frequency resolution for the lowest bands. To obtain a constantly highfrequency resolution, a 16384-point DFT is now used independently of the block size. This size
corresponds to the ʹ‫ݏ‬ୠ ሺ‫ݖ‬ሻ-point DFT for the lowest frequency bands but results in a higher resolution
for higher bands. Tonal loudness is then estimated as the maximum of this spectrum. In ECMA -74, afrequency range is defined to limit the maximum search. This frequency range is no longer used inorder to provide consistent results for the entire audible frequency range between (specific) loudnessand (specific) tonal loudness. Apart from this, the tonal loudness is estimated as described in
ECMA-74. Additionally, the frequency at which the maximum occurs is saved as the f requency
corresponding to the tonal sound.
Since the block size used for the ACF differs for different frequency bands, the temporal resolutionof the blocks is also different. Thus, the estimated tonal loudness and the corresponding frequencies
are resampled to a common time basis as explained in ECMA-74. With this resampling step, all results
have a common time index ݈ . Since the next steps are independent of this time index, it will be
neglected for the description of the algorithm and only be reintroduced for the description of the timeᇱ෡୲୭୬ୟ୪
ሺ‫ݖ‬ሻ and the corresponding
dependent tonality. This first estimate of the tonal loudness is named ܰ5823

frequencies ݂௧ ሺ‫ݖ‬ሻ. The resampling is also applied to the specific loudness of the signal ܰԢሺ‫ݖ‬ሻ, resultingᇱ෡ୱ୧୥୬ୟ୪
ሺ‫ݖ‬ሻ.
in the estimated loudness of the signal ܰ
3.2 Low-pass Filtering
In ECMA-74, the first estimate of the tonal loudness is refined by low-pass filtering and a noise
reduction step by applying a sigmoid function depending on a SNR estimate. The low-pass filtering
is performed in the same way as described in ECMA-74, resulting in the final estimate of the specificᇱᇱ෡ୱ୧୥୬ୟ୪
ሺ‫ݖ‬ሻ. The low-pass filtering is also applied to ܰሺ‫ݖ‬ሻ, resulting in the final
tonal loudness ܰ୲୭୬ୟ୪
ᇱ
estimate of the loudness of the signal ܰୱ୧୥୬ୟ୪ ሺ‫ݖ‬ሻ.
The application of the sigmoid function is skipped because a new grouping step is introduced which
will be described in the next section. This grouping step inherently performs noise reduction.
3.3 Grouping of Tonal Componentsᇱሺ‫ݖ‬ሻ and the corresponding high-resolution
In the grouping step, the specific tonal loudness ܰ୲୭୬ୟ୪
frequency ݂௧ ሺ‫ݖ‬ሻ are used to group the specific loudness of tonal components into the total loudnessᇱሺ‫ݖ‬ሻ and ݂௧ ሺ‫ݖ‬ሻ are described as a functionof those components. To describe the grouping step, ܰ୲୭୬ୟ୪ᇱሺ݅ሻ
of an index ݅ ranging from 1 to 53 rather than a function of the critical band number ‫ݖ‬, i.e. ܰ୲୭୬ୟ୪
and ݂௧ ሺ݅ሻ are used. The resulting tonal loudness values of the components are stored in ܰ୲୭୬ୟ୪େ୭୫୮ ሺ݅ሻ,which is first initialized with zeros for each index ݅ and then filled with the corresponding tonal
loudness values in an iterative process as described below. ܰ୬୭୧ୱୣେ୭୫୮ ሺ݅ሻ is the corresponding
variable for the noise loudness in the bands of the tonal components.
First, the frequencies corresponding to the tonal content of each band, ݂௧ ሺ݅ሻ, are transformed to ୌ୑ୗ values ‫ݖ‬௧ ሺ݅ሻ according to Equation (F.6) of the ECMA-74 standard (15 th Edition).
Next, the iterative process starts. For the first iteration, a set of indices ‫ ܫ‬is defined, which firstcontains all indices ݅ which belong to a defined frequency range:‫ ܫ‬ൌ ሼ݅ ȁ ‫ݖ‬௧ ሺ݅ሻ ൒  ‫ݖ‬୫୧୬  ‫ݖ ٿ‬௧ ሺ݅ሻ ൏  ‫ݖ‬୫ୟ୶ ሽ,(1)

where ‫ݖ‬୫୧୬ and ‫ݖ‬୫ୟ୶ are critical band values corresponding to the range of human hearing. Values
corresponding to a lower limit of 16 Hz and an upper limit of 20 kHz are used. The grouping is only
performed if the overall tonal loudness of all ݅ ‫ ܫ א‬exceeds 0.01 ୌ୑ୗ:ᇱሺ݅ሻ ‫ڄ‬ᶭ ‫ ݖ‬൐ ͲǤͲͳ ୌ୑ୗ Ǥ෍ ܰ୲୭୬ୟ୪

(2)

௜‫א‬ூ

Next, new sets of indices are defined for each index ݆ ‫ܫ א‬, containing all indices with a criticalband value ‫ݖ‬௧ ሺ݅ሻ which is close to the value ‫ݖ‬௧ ሺ݆ሻ of the specific band index ݆:‫ܥ‬௝ ൌ ሼ݅ ‫ ܫ א‬ȁ ‫ݖ‬௧ ሺ݅ሻ ൒  ‫ݖ‬௧ ሺ݆ሻ ‫ݖ  ٿ‬௧ ሺ݅ሻ ൏  ‫ݖ‬௧ ሺ݆ሻ ൅ᶭ ሽ,(3)

where ᶭ  is the maximum allowed deviation. A value of ᶭ  ൌ ͲǤʹ  ୌ୑ୗ is used.
Each set of indices ‫ܥ‬௝ stands for one potential group corresponding to one tonal component. Only thegroup corresponding to the highest tonal loudness is considered as a tonal component in this iteration step.
This is the set ‫ܥ‬௝ౣ౗౮ , corresponding to the index ݆୫ୟ୶ maximizing the tonal loudness of the group:ᇱሺ݅ሻ ‫ڄ‬ᶭ ‫ݖ‬݆୫ୟ୶ ൌ   ෍ ܰ୲୭୬ୟ୪
௝‫א‬ூ

(4)

௜‫א‬஼ೕ

The set ‫ܥ‬௝ౣ౗౮ is only accepted as a tonal component if it contains at least 3 elements for ݆୫ୟ୶ ൐ ʹ, resp. 2
elements for ݆୫ୟ୶ ൑ ʹሻ. The reason for this limitation is that a tonal component will usually appear at leastin the directly neighboring bands. If it does not appear in the neighboring bands, it can be assumed that thehigh loudness originates from a noisy sound and should not be considered as a tonal component. If the set is
accepted as tonal component, the corresponding critical band number is estimated by a weighted average ofthe critical band numbers ‫ݖ‬௧ ሺ݅ሻ in ‫ܥ‬௝ౣ౗౮ :5824

‫ݖ‬ҧ୫ୟ୶ ൌᇱሺ݅ሻ‫ݖ‬௧ ሺ݅ሻ ‫୲ܰ ڄ‬୭୬ୟ୪σ௜‫א‬஼ೕౣ౗౮σ௜‫א‬஼ೕ

ౣ౗౮ᇱሺ݅ሻܰ୲୭୬ୟ୪

(5)

The corresponding index for this average band number can be calculated as݅୫ୟ୶ ൌ ‫ݖʹہ‬ҧ୫ୟ୶ ‫ۀ‬ǡ

(6)

where the ‫ہ‬ή‫ ۀ‬operator denotes rounding to the nearest integer. This index is used to add the tonal
loudness of the tonal component to ܰ୲୭୬ୟ୪େ୭୫୮ ሺ݅ሻ:ᇱሺ݅ሻ ‫ڄ‬ᶭ ‫ݖ‬ǡܰ୲୭୬ୟ୪େ୭୫୮ ሺ݅ሻ ՜ ܰ୲୭୬ୟ୪େ୭୫୮ ሺ݅ሻ ൅ ෍ ܰ୲୭୬ୟ୪

(7)௜‫א‬஼ೕ

where the ՜ operator describes the assignment of the right side to the left side variable. Accordingly,
the assignmentᇱᇱሺ݅ሻ െ ܰ୲୭୬ୟ୪
ሺ݅ሻቁ ‫ڄ‬ᶭ ‫ݖ‬ܰ୬୭୧ୱୣେ୭୫୮ ሺ݅ሻ ՜ ܰ୬୭୧ୱୣେ୭୫୮ ሺ݅ሻ ൅ ෍ ቀܰୱ୧୥୬ୟ୪

(8)௜‫א‬஼ೕ

is made. The next iteration starts by assigning a new set, of indices ‫ ܫ‬without the indices of ‫ܥ‬௝ౣ౗౮‫ ܫ‬՜ ‫ܥ ך ܫ‬௝ౣ౗౮ Ǥ(9)With this set of indices, the iteration starts again with Equation (1). The iterative process is stopped
once the condition described in Equation (2) is not fulfilled. The frequency ݂஼௢௠௣ ሺ݅ሻ (correspondingto ‫ݖ‬ҧ୫ୟ୶) is saved as the frequency of the maximum component assigned to ݅ during all iterations forfurther analyses (see section 4.2).
3.4 Calculation of Tonality
The mapping of tonal loudness to tonality is done by SNR-dependent scaling of the tonal loudness.
The scaling factor ‫ݍ‬ሺ݅ሻ is calculated using the same sigmoid functionͳ െ ି஺ήሺୗ୒ୖሺ௜ሻି஻ሻ ǡ ି஺ήሺୗ୒ୖሺ௜ሻି஻ሻ ൏ ͳ‫ݍ‬ሺ݅ሻ ൌ ൜Ͳି஺ήሺୗ୒ୖሺ௜ሻି஻ሻ ൒ ͳ(10)

as in ECMA-74. However, the SNR is calculated differently and consequentially the parameters ‫ܣ‬and ‫ ܤ‬need to be adjusted. The SNR is calculated in dependency of the index ݅ of the critical band:ܰ୲୭୬ୟ୪େ୭୫୮ ሺ݅ሻሺ݅ሻ ൌ(11)ܰ୬୭୧ୱୣେ୭୫୮ ሺ݅ሻand the parameters are set to ‫ ܣ‬ൌ ͵ and ‫ ܤ‬ൌ ͲǤʹͶ. The tonality of each tonal component is thencalculated asܶେ୭୫୮ ሺ݅ሻ ൌ ‫ݍ‬ሺ݅ሻ ή ܰ୲୭୬ୟ୪େ୭୫୮ ሺ݅ሻǤ
(12)
A calibration factor as described in ECMA-74 is not necessary. ܶେ୭୫୮ ሺ݅ሻ is actually dependent on
the time index ݈ and the critical band index ݅ or the critical band ‫ݖ‬. For consistency with ECMA-74,
it is denoted ܶେ୭୫୮ ሺ݈ǡ ‫ݖ‬ሻ. The time-dependent tonality ܶሺ݈ሻ can be calculated by taking the maximumof ܶେ୭୫୮ ሺ݈ǡ ‫ݖ‬ሻ over all critical bands ‫ݖ‬. This calculation procedure is based on the assumption thatthe perception of tonality is defined by the most dominant tonal component. The single value tonality
ܶ is calculated from the time-dependent tonality as explained in ECMA-74.
The unit of the tonality calculated by the Psychoacoustic Tonality method is given in tu HMS (tonality
units according to the hearing model of Sottek). The tonality of a 1 kHz tone with a sound pressurelevel of 40 dB is 1 tu HMS by design of the algorithm.

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4. RESULTS
4.1 Effect of revised Outer/Middle Ear Filter
The outer and middle ear filtering was revised because the ECMA -74 tonality often overestimates
tonality of low-frequent tonal components. To validate this effect and to design the new filters,
listening tests were conducted, which were published in [10]. In these listening tests, the equal
loudness contours of the tonal loudness of sinusoids with frequencies below 1 kHz were determined.

Figure 5 – Equal loudness contour (50 phon) of the tonal loudness for sinusoids below 1 kHz
Figure 5 shows the result for the 50 phon contour. The results of the listening test are close to the
ELCs of ISO 226:2003. Since the outer and middle ear filtering in ECMA -74 was designed aiming
for the ELCs of ISO 226:1987, the results of ECMA-74 follow this contour closely. This behavior
results in the overestimation of the tonality. With the new filter of the revised tonality calculation, theELCs follow the ISO 226:2003 contour and are thus much closer to the result of the listening test.
4.2 Effect of higher resolution and identification of components
The saved frequency ݂஼௢௠௣ ሺ݅ሻ of the tonal component (see section 3.4) achieved by the revised
tonality algorithm provides much clearer results. Figure 6 shows the effect on two synthetic signals.

Figure 6 – Left: Results of ECMA-74 tonality, Right: Result of revised tonality algorithm. Top to bottom:
Sinusoid (1000 kHz, 65 dB SPL) in pink noise (60 dB SPL), narrowband noise (950-1050 Hz, 65 dB SPL)
in pink noise (60 dB SPL)

5826

The result of the sinusoid helps to illustrate how much the resolution is improved. The result of
the narrowband noise shows how the improved resolution helps in understanding the character of a
tonal sound. The ECMA-74 result could occur from a narrowband noise or from a pure tone withfluctuating frequency and amplitude. With the higher resolution, it is clear that the tonality comesfrom different frequencies and thus originates from a narrowband noise.

Figure 7 – Engine starter with tonal component. Left: Results of ECMA-74 tonality, Right: Result ofrevised tonality algorithm.
Figure 7 shows the results of an engine starter which produces a tonal sound. The results show thatthe amplitude of the tonality is rather consistent for the two calculation methods, while the frequency
resolution is improved in the revised algorithm.

5. CONCLUSIONSIn this paper, modifications to the ECMA-74 tonality calculation are presented. Modifications to
the outer and middle ear filtering improve the results for low frequencies. Additionally, the new
definition of the filter allows different calculations depending on the sound field. The newly
introduced grouping of tonal components results in a much higher frequency resolution of thecalculated tonalities. Additionally, it inherently suppresses noise and the estimated tonal components
can be used for further processing in the future.
The presented modifications will likely be included in a future version of the EMCA -74 standard.

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Acustica, 97(3), pp. 355-363, 2011.
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