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Psychoacoustics 2 - Perception of Loudness

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Visit https://alexisbaskind.net/teaching for a full interactive version of this course with sound and video material, as well as more courses and material.

Course series: Fundamentals of acoustics for sound engineers and music producers
Level: undergraduate (Bachelor)
Language: English
Revision: January 2020
To cite this course: Alexis Baskind, Psychoacoustics 2 - Perception of Loudness
course material, license: Creative Commons BY-NC-SA.


Course content:
1.Introduction
limits of the Weber-Fechner law
2.Absolute threshold of hearing
Definition of the threshold of hearing – effect of age
3.Equal-loudness contours
Introduction to phons and sones – Definition of the equal-loudness contours – the phon – isophones – loudness correction – Limitations of equal-loudness contours
4.Loudness – the Sone
Definition of the sone scale – mapping of volume faders
5.Loudness and duration
Effect of duration on loudness
6.Complex sounds – Simultaneous masking
Loudness summation – Critical Bands – Simultaneous Masking – consequence for mixing
7.Just-noticeable differences for loudness
Definition and order of magnitude of the just-noticeable difference for loudness
8.Estimating loudness
Frequency weighting – dBA, dBB, dBC

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Psychoacoustics 2 - Perception of Loudness

  1. 1. Alexis Baskind Psychoacoustics 2 Perception of loudness Alexis Baskind, https://alexisbaskind.net
  2. 2. Alexis Baskind Psychoacoustics 2 - Perception of loudness Course series Fundamentals of acoustics for sound engineers and music producers Level undergraduate (Bachelor) Language English Revision January 2020 To cite this course Alexis Baskind, Psychoacoustics 2 - Perception of loudness, course material, license: Creative Commons BY-NC-SA. Full interactive version of this course with sound and video material, as well as more courses and material on https://alexisbaskind.net/teaching. Psychoacoustics 2 - Perception of Loudness Except where otherwise noted, content of this course material is licensed under a Creative Commons Attribution- NonCommercial-ShareAlike 4.0 International License.
  3. 3. Alexis Baskind Outline 1. Introduction 2. Absolute threshold of hearing 3. Equal-loudness contours 4. Loudness – the Sone 5. Loudness and duration 6. Complex sounds - Simultaneous masking 7. Just-noticeable differences for loudness 8. Estimating loudness Psychoacoustics 2 - Perception of Loudness
  4. 4. Alexis Baskind Introduction • The Weber-Fechner law is a rough approximation of for all sensory impressions, but has to be corrected and/or fine-tuned for each of them • Perception of loudness is complex subjective frequency-dependent phenomenon, that depends among other on the following factors: – Frequency content, bandwidth of the sound – Duration of the sound – Masking from other sounds – Attention of the listener Psychoacoustics 2 - Perception of Loudness
  5. 5. Alexis Baskind Outline 1. Introduction 2. Absolute threshold of hearing 3. Equal-loudness contours 4. Loudness – the Sone 5. Loudness and duration 6. Complex sounds - Simultaneous masking 7. Just-noticeable differences for loudness 8. Estimating loudness Psychoacoustics 2 - Perception of Loudness
  6. 6. Alexis Baskind Absolute threshold of hearing • The threshold of hearing is the average level in dB SPL of the softest pure tone that humans can detect, for each frequency Psychoacoustics 2 - Perception of Loudness • Note the effect of age (20, 40, 60 years) on the threshold
  7. 7. Alexis Baskind Outline 1. Introduction 2. Absolute threshold of hearing 3. Equal-loudness contours 4. Loudness – the Sone 5. Loudness and duration 6. Complex sounds - Simultaneous masking 7. Just-noticeable differences for loudness 8. Estimating loudness Psychoacoustics 2 - Perception of Loudness
  8. 8. Alexis Baskind Loudness level is not loudness • Loudness level (unit: phons) is relative measure of the frequency dependency of the perceived loudness for pure tones compared to the 1 kHz- Reference. • The Sone (see later) is a psychoacoustical measure for Loudness that describes the absolute perceived loudness between pure tones. Psychoacoustics 2 - Perception of Loudness
  9. 9. Alexis Baskind Equal-loudness contours • The equal-loudness contours are measures of sound pressure in dB SPL for which a listener perceives a constant loudness when presented with pure steady tones Psychoacoustics 2 - Perception of Loudness Frequency (Hz) • The phon is a measure of the perceptual loudness level of a pure tone • Those contours are also called isophones • The phon-value at 1 kHz equals the sound pressure level in dB SPL
  10. 10. Alexis Baskind Equal-loudness contours Psychoacoustics 2 - Perception of Loudness Frequency (Hz) Music Speech Ultrasound Infrasound Threshold of pain
  11. 11. Alexis Baskind Loudness correction • Music is often mixed loud, i.e. between 75 and 85 dB SPL, to allow hearing to get all frequencies • … but music is often listened at a softer level !  Then the mix will sound different (not even considering the fact that the speakers and the room are indeed different)  In particular, some of the low- and high-frequency content will be missing • Loudness correction on a consumer’s amplifier aims at allowing a better listening experience at low levels by boosting low- and high-frequencies Psychoacoustics 2 - Perception of Loudness
  12. 12. Alexis Baskind Loudness correction Example: K&H ES-20 Stereo-Amplifier Psychoacoustics 2 - Perception of Loudness Frequency response of the loudness corrector (contour) of the ES-20 amplifier
  13. 13. Alexis Baskind Limitations of equal-loudness contours Psychoacoustics 2 - Perception of Loudness • The phon-scale corresponds to the dB-SPL-scale, therefore the relation to the perceived loudness is not linear: for instance, a doubling of the perceived loudness does not correspond to a doubling of the level in dB SPL (but rather to+10 dB) Limitations of the Weber-Fechner-law • The equal-loudness contours are in principle only relevant for pure tones, not for complex sounds • The sound duration is not taken into account  What is the loudness of complex, time-modulated sounds? • The equal loudness contours don‘t allow to know, how loud a sound will be perceived in a mix
  14. 14. Alexis Baskind Outline 1. Introduction 2. Absolute threshold of hearing 3. Equal-loudness contours 4. Loudness – the Sone 5. Loudness and duration 6. Complex sounds - Simultaneous masking 7. Just-noticeable differences for loudness 8. Estimating loudness Psychoacoustics 2 - Perception of Loudness
  15. 15. Alexis Baskind Loudness – the Sone • The phon scale describes more precisely the perceived loudness than the dBSPL scale since it takes its frequency dependency into account. However, it doesn’t map the perception linearly. • As a matter-of-fact, it is known that an increase of the sound pressure level of 10 dB corresponds ca. to a doubling of the perceived loudness (except for very soft sounds) • The sone scale was introduced because of this reason. It’s based on the phone scale and corrects it in order to approximate loudness more precisely • Like the phon scale, the sone scale is based on pure tones, therefore it’s still not sufficient to estimate the loudness of more complex sounds Psychoacoustics 2 - Perception of Loudness
  16. 16. Alexis Baskind Loudness – the Sone Music notation Phons Sones 120 256 110 128 fff 100 64 ff 90 32 f 80 16 mf, mp 70 8 p 60 4 pp 50 2 ppp 40 1 32 1/2 25 1/4 19 1/8 14 1/16 (Of course the objective loudness of a mf or a ppp is very subjective and depends on the context, but this table gives an order of magnitude) Psychoacoustics 2 - Perception of Loudness
  17. 17. Alexis Baskind Faders 1. A linear volume fader would be almost useless, since it does not allow to control the loudness in a linear way: Reference: x 1 Amplification => Loudness change Reference (+0 dB) x 1.3 ca. 1.2x louder (+2.3 dB) x 0 silence x 0,5 ca. 1.5x softer (-6 dB) x 0,25 ca. 2x softer (-12 dB) x 0,125 ca. 3.5x softer (-18 dB) x 0,06 ca. 5x softer (-24 dB) (the resolution for soft levels is much too coarse) Psychoacoustics 2 - Perception of Loudness
  18. 18. Alexis Baskind Faders 2. A pure dB-Fader would also be not optimal, since the lower half of it would be almost useless: Reference: 0 dB Amplification => Loudness change Reference silence -10 dB 2x softer -20 dB 4x softer -30 dB 8x softer -40 dB 16x softer -50 dB 32x softer -60 dB 64x softer +10 dB 2x lauter +20 dB 4x louder(the resolution in this range is too coarse: a few centimeters correspond to a difference of 20 dB -¥ Psychoacoustics 2 - Perception of Loudness
  19. 19. Alexis Baskind Faders 3. The standard for Faders is actually a very good compromise: Reference: 0 dB Amplification => Loudness change Reference silence -10 dB 2x softer -20 dB 4x softer -30 dB 8x softer -40 dB 16x softer -60 dB 32x softer +10 dB 2x louder -50 dB -¥ (in this region, the fader allows to control loudness almost in a linear way) Psychoacoustics 2 - Perception of Loudness
  20. 20. Alexis Baskind Outline 1. Introduction 2. Absolute threshold of hearing 3. Equal-loudness contours 4. Loudness – the Sone 5. Loudness and duration 6. Complex sounds - Simultaneous masking 7. Just-noticeable differences for loudness 8. Estimating loudness Psychoacoustics 2 - Perception of Loudness
  21. 21. Alexis Baskind Effect of sound duration • Below 200-300 ms, the longer the sound, the louder it will be perceived • This observation is used in audio level metering instruments like the VU-meter, which smoothing time is set to 300 ms. Psychoacoustics 2 - Perception of Loudness Loudness / max loudness Sound duration (s)
  22. 22. Alexis Baskind Outline 1. Introduction 2. Absolute threshold of hearing 3. Equal-loudness contours 4. Loudness – the Sone 5. Loudness and duration 6. Complex sounds - Simultaneous masking 7. Just-noticeable differences for loudness 8. Estimating loudness Psychoacoustics 2 - Perception of Loudness
  23. 23. Alexis Baskind Complex Sounds • In case of sounds more complex than pure steady tones, the same principle applies (i.e. hearing is less sensitive to low- and high-frequencies at soft levels) • But the equal-loudness curves don’t strictly apply, since: – Overtones and noisy parts of a sound, which are first separated from each other by the auditory system, are combined afterwards and perceived as a unique entity – This loudness summation is complex and depends on the so- called critical bands (see below) – Among others, the superposition of single pure tones implies masking
  24. 24. Alexis Baskind Critical bands • The first type of frequency grouping occurs in the midbrain: adjacent simultaneous frequency components are combined in frequency bands which are perceived as one entity • Those frequency bands are called critical bands • In many cases, they dictate the frequency resolution of hearing • On top of that, the loudness of a broadband sound does not correspond to the sum of the loudness of all single components: it depends on the energy in each frequency band => loudness summation
  25. 25. Alexis Baskind Critical bands The critical bandwidth depends on the center frequency: • Up to 500 Hz, it equals circa 100 Hz • Above 500 Hz, it increases proportionnaly to the center frequency: the relative bandwidth is more or less constant (between 1/6 octave and 1/3 octave) => This could explain why 1/3 octave filters are used everywhere inDies könnte erklären, warum Terzband- Filter in sound engineering! Psychoacoustics 2 - Perception of Loudness
  26. 26. Alexis Baskind Critical bands and loudness summation Image: Thomas Görne, “Tontechnik” (based on Feldtkeller and Zwicker) Bandwidth Spectral loudness summation: loudness level of noises centered at 1 kHz with variable bandwidth Horizontal axis = noise bandwidth Vertical axis = effective sound pressure level in dB SPL
  27. 27. Alexis Baskind Simultaneous masking Frequency (kHz) If two tones with similar (but not equal) frequencies are played together, the loudest tone masks the softest partially or totally: The hearing threshold is locally raised Psychoacoustics 2 - Perception of Loudness
  28. 28. Alexis Baskind Simultaneous masking • The louder the loudest tone, the bigger the bandwidth of the masking pattern • Moreover, the behavior is asymmetric on the frequency axis Psychoacoustics 2 - Perception of Loudness Example: Masking of a soft tone by a 1-kHz pure tone Increase of the threshold of hearing in presence of an interfering Signal (1 kHz pure tone) Threshold of hearing Source: Blauert/Wikipedia
  29. 29. Alexis Baskind Simultaneous masking “Generally speaking, a high-frequency sound can only mask a low-frequency sound if the frequency spacing is small. A low- frequency sound can only mask a high-frequency sound if the former is loud compared to the latter” (Michael Dickreiter) This means for mixing: If two sounds share common frequency ranges, components of the softest are quite often masked by the loudest. A classical example is masking of a bass drum by an electric bass or vice-versa: if the bass drum is louder than the bass, only overtones of the bass remain audible (which also can be themselves masked by other instruments) Psychoacoustics 2 - Perception of Loudness
  30. 30. Alexis Baskind Simultaneous masking How to solve/reduce masking in mixing – With different EQs, so that every instrument has a privileged space in a given frequency region. For this purpose it‘s not relevant if the soloed track sounds good or coloured, only the result in the mix counts. Actually it‘s even often counterproductive to try to optimize the sound of each instrument independently from the other ones! – With less or shorter reverb, a different sounding reverb, and/or with an EQ at the output of the reverb – With dynamic processing (potentially with external Side-chain): the bass drum could for instance dominate during its attack and right afterwards be made softer to make the resonance of the bass more audible – With panning (see later, „Cocktail-Party-Effekt“) Psychoacoustics 2 - Perception of Loudness
  31. 31. Alexis Baskind Outline 1. Introduction 2. Absolute threshold of hearing 3. Equal-loudness contours 4. Loudness – the Sone 5. Loudness and duration 6. Complex sounds - Simultaneous masking 7. Just-noticeable differences for loudness 8. Estimating loudness Psychoacoustics 2 - Perception of Loudness
  32. 32. Alexis Baskind Just-noticeable level difference • The just-noticeable difference (JND), describes (of for all sensory perceptions) the lower threshold of perception of a difference in the physical stimulus • For loudness, the just-noticeable difference is about 1 dB • The JND depends on absolute loudness: – it is closer to 2 or 3 dB at the threshold of hearing – it can drop to .3 or .5 dB for loud sounds • JND depends also on the ear training Psychoacoustics 2 - Perception of Loudness
  33. 33. Alexis Baskind Just-noticeable level difference Just-Noticeable Level Difference of a 1-kHz tone as a function of sound pressure level (From Fastl H., Zwicker E., “Psychoacoustics: Facts and Models”) Psychoacoustics 2 - Perception of Loudness
  34. 34. Alexis Baskind Outline 1. Introduction 2. Absolute threshold of hearing 3. Equal-loudness contours 4. Loudness – the Sone 5. Loudness and duration 6. Complex sounds - Simultaneous masking 7. Just-noticeable differences for loudness 8. Estimating loudness Psychoacoustics 2 - Perception of Loudness
  35. 35. Alexis Baskind Estimation of Loudness, Frequency Weighting • Based on the previous observations, it’s clear, that a precise estimation of loudness with electronic means is hardly possible • The standards for loudness estimation are restrained to a simple correction of the spectral content • Those so-called frequency-weighting curves consists in several filters, that have to be selected with respect to the absolute sound pressure level Psychoacoustics 2 - Perception of Loudness
  36. 36. Alexis Baskind Estimation of Loudness, Frequency Weighting • The A-weighting (Unit dB(A) ) is designed for very soft sounds (Loudness level around 40 phon, very soft) • The B-weighting ( dB(B) ) for ca. 60 phon • The C-weighting (dB(C) ) for ca. 80 phon Psychoacoustics 2 - Perception of Loudness
  37. 37. Alexis Baskind Estimation of Loudness, Frequency Weighting • The measurement process in a sound level meter consists in: 1. converting the sound pressure in voltage (with an omnidirectional microphone) 2. applying the A-, B-, or C-weighting filter 3. calculate the RMS in dB • In practice, the B-Weighting is not used at all, and C- Weighting quite rarely => dB(A) is de facto a general standard for estimating loudness, though it is only suitable for soft sounds. Filter: A-, B-, or C-weighting RMS dB(A), dB(B) or dB(C) Psychoacoustics 2 - Perception of Loudness

Visit https://alexisbaskind.net/teaching for a full interactive version of this course with sound and video material, as well as more courses and material. Course series: Fundamentals of acoustics for sound engineers and music producers Level: undergraduate (Bachelor) Language: English Revision: January 2020 To cite this course: Alexis Baskind, Psychoacoustics 2 - Perception of Loudness course material, license: Creative Commons BY-NC-SA. Course content: 1.Introduction limits of the Weber-Fechner law 2.Absolute threshold of hearing Definition of the threshold of hearing – effect of age 3.Equal-loudness contours Introduction to phons and sones – Definition of the equal-loudness contours – the phon – isophones – loudness correction – Limitations of equal-loudness contours 4.Loudness – the Sone Definition of the sone scale – mapping of volume faders 5.Loudness and duration Effect of duration on loudness 6.Complex sounds – Simultaneous masking Loudness summation – Critical Bands – Simultaneous Masking – consequence for mixing 7.Just-noticeable differences for loudness Definition and order of magnitude of the just-noticeable difference for loudness 8.Estimating loudness Frequency weighting – dBA, dBB, dBC

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