A tone is a sound composed of a single frequency component. Sounds we hear can be either pure tones (e.g. a whistle in a quiet background), or a combination of numerous tones with comparable amplitudes, what we call “complex” sounds (e.g. fan noise). However, even if their frequency content is significant, some complex sounds may be dominated by a specific frequency component (e.g. the blade passing frequency of a fan in the broadband flow noise). In this case, the noise is characterized as “tonal” since it is perceived as a tone. Tonality is a metric expressing the relative weight of the tonal components in a given noise spectrum. Its calculation is based on a comparison between the amplitude of the tonal component and the amplitude of the noise at the neighboring frequencies. The Tone-to-Noise Ratio (TNR) and the Prominence Ratio (PR) are two very close metrics quantifying how much a tone is distinguishable by the human ear in dB. However, their calculation depends on the spectral resolution and doesn’t take into account the frequency-sensitivity of the human ear’s level perception. To better match the human perception, a psychoacoustic version of tonality has emerged taking account the loudness value of each frequency component.
ECMA-74 : 2019 annex G describes the psychoacoustic tonality based on a human hearing model and given in t.u.HMS (Hearing Model by Sottek). It has been developed to match the human perception of pitch and tonality and thus incorporates several psychoacoustic aspects :
- the bark scale defines the critical frequency bands,
- loudness is used to compare the tone to the background for each critical band,
- the threshold of human hearing and masking effect are taken into account.
The loudness of each audible frequency component is compared to the background’s loudness within each critical band, incorporating the possible masking effects. The amount of tonality of each component are then summed up to compute the global tonality value in t.u HMS. As a result, the global tonality calculated is theoretically unlimited and is more realistic as shown on this perception scale:
Psychoacoustic tonality also presents other advantages :
- it shows how much tones occur in each critical band
- it indicates at what frequency each tone is occurring, and in what proportion thanks to the frequency information given by the loudness treatment
Electric motor sound can exhibit strong tonalities under electromagnetic excitations. The two following sounds from EOMYS e-NVH benchmark have been recorded at 2270 and 2330 RPM, in the exact same conditions. However, there is a strong difference between these two sounds: the first one sounds very rough while the other one sounds more tonal.
Low tonality noise, testbench at 2270 RPM
High tonality noise, testbench at 2330 RPM
The testbench is a Permanent Magnet Synchronous Machines with 12 slots and 10 poles. The slotting harmonics of such a motor occur at ten times the mechanical frequency (H10) and multiples. Moreover the testbench has a high level of eccentricity, producing many additional harmonics. At 2270 RPM, the main harmonics (around H20) have almost the same level (see blue spectrum below). The harmonics frequencies being close enough to be part of the same critical band, they are not considered as tonal and a sensation of roughness is created. On the other hand, when one of the harmonics excites a structural mode of the e-motor, creating a resonance, the noise level radiated at this specific frequency becomes dominant. A feeling of tonality is then produced.
The plot below shows the difference in tonality according to the Prominence Ratio:
- at 2770 RPM, there is only one prominent tonal component around 400 Hz, and calculated roughness is 0.55 asper,
- at 2330 RPM, there are two high tonal components, including one around H20, but the roughness only reaches 0.09 asper.
This example shows that calculated tonality correctly reflects auditory perception. It also demonstrates that it is not straightforward to improve e-motor sound quality: a slight change in the operating conditions can improve one psychoacoustic aspect but also degrade another one.
Application to Manatee
Sound quality metrics are available as a standard output of Manatee e-NVH software. This way, the tonality of different electric motors or switching strategies can be easily compared.
- What is psychoacoustics ?
- What is masking effect ?
- What is loudness ?
- What is tonality ?
- What is modulation effect (roughness / fluctuation strength) ?