Decibels and phons

Compare sound pressure level and perceived loudness in the equal-loudness diagram: drag tones, change the level, read phon and sone.

Explanation Tasks

Equal-loudness contours (ISO 226)

Drag the tones; a click on an empty spot moves the selected tone there. Dotted contour sections lie outside the range of the standard.

Heard EQ at a different listening level heard change compensation EQ

Balanced at Played back at

at the selected tone
heard change
compensation EQ

A mix that sounds balanced at reference 1 is played back quieter or louder by the difference. The filled curve shows by how many phon each frequency then seems quieter or louder than 1 kHz; the dashed curve shows the EQ that restores the sound of reference 1.

Loudness: phon → sone

Tone	Frequency	dB SPL	phon	sone	dB(A)
1
2
3

As loud as 1 kHz at
Total level (energetic)
Total level A-weighted
Total level C-weighted

* outside the range of ISO 226 (20–90 phon, above 4 kHz up to 80 phon), extrapolated. The total levels are sums of sound power; the loudness of several tones cannot be added this way.

Speed

Glide with

constant dB SPL constant phon

Tones

Number

1 2 3

Selected (play, click)

Tone 1 Tone 2 Tone 3

Frequency Sound pressure level

Listening Volume control (all tones)

Show weighting curve

off A C

Presets

Keyboard: Space = play/pause, F = presentation mode, M = sound on/off

What is happening?

Same level, different loudness

Play a deep bass tone and a bright whistle tone through the same system at exactly the same sound pressure level: the level meter reads the same both times, but you hear a present whistle and a thin, quiet bass tone. The ear is not a measuring instrument with a flat frequency response.

Sound pressure level L is a physical quantity: L = 20 · log₁₀(p / p₀) with the sound pressure p (RMS value in Pa) and the reference sound pressure p₀ = 20 µPa, roughly the threshold of hearing at 1 kHz. 1 Pa gives 20 · log₁₀(50 000) ≈ 94 dB SPL – the level of the calibration tone in the settings menu (gear icon). How loud we perceive a tone, this number only tells reliably at one fixed frequency.

Try it: choose “3 tones at equal sound pressure”. All three tones have 70 dB SPL. According to the table the 1 kHz tone has 70 phon and 8 sone, the 8 kHz tone about 58 phon and 3.6 sone, the 63 Hz tone only about 35 phon and 0.73 sone – it sounds around eleven times quieter. Listen: turn the sound on and set “Number” from 1 to 2 – the 63 Hz tone is added but hardly stands out.

Phon: as loud as 1 kHz

The 1 kHz tone serves as the yardstick: a tone has a loudness level of L phon if it is perceived as loud as a 1 kHz tone at L dB SPL. At 1 kHz, phon and dB SPL are therefore equal by definition. This is determined in listening tests with sine tones, frontal in a free field, with young listeners with normal hearing. The curves are averages; individual people deviate considerably.

All equally loud tones together form an equal-loudness contour (isophone). In the diagram “Equal-loudness contours” they are drawn in grey from 10 to 90 phon. The contour through the selected tone is highlighted thickly in its colour, and a ring on the 1 kHz line marks the equally loud reference tone – “As loud as 1 kHz at” gives the same value.

Try it: choose “1 kHz at 60 dB”, set “Glide with” to “constant phon” and start “Let the frequency glide”. The tone glides up to 12.5 kHz, jumps to 20 Hz and always follows the 60 phon contour: around 3 kHz less than 57 dB SPL is enough, at 20 Hz it needs about 109 dB. With “constant dB SPL”, by contrast, the level stays fixed and the phon value changes.

Threshold of hearing and pain

The thick dashed curve is the threshold of hearing; anything below it (grey, “inaudible”) is not perceived by an average young ear. It lies at about 2.4 dB SPL at 1 kHz, 26.5 dB at 100 Hz, 44 dB at 50 Hz and 78.5 dB at 20 Hz. The ear is most sensitive around 3 to 4 kHz at about −6 dB SPL.

The reason is mechanical: the ear canal is a tube about 2.5 cm long, closed at the eardrum. Its quarter-wave resonance lies at the frequency f ≈ c / (4 · l), with the speed of sound c and the tube length l: f ≈ 343 m/s / (4 · 0.025 m) ≈ 3.4 kHz. It raises the sound pressure at the eardrum there. The middle ear transmits low frequencies less well, so the threshold rises steeply there.

At the top, “Threshold of pain (approx.)” marks about 120 dB SPL. But hearing damage is already a risk with long exposure to considerably lower levels. Try it: set a tone to 50 Hz and 50 dB and lower the level – below 44 dB the table shows “inaudible”.

The contours bunch up in the bass

Compare the spacing of the contours: at 1 kHz, 20 and 90 phon are exactly 70 dB apart, at 63 Hz only 46 dB, at 31.5 Hz just under 39 dB. Because the curves are squeezed together in the bass, the same level change alters loudness much more there than in the mids.

Worked example: a 50 Hz tone at 90 dB SPL and a 1 kHz tone at 60 dB SPL both have 60 phon. For 70 phon the 1 kHz tone needs +10 dB, the 50 Hz tone only +5.9 dB (90.0 → 95.9 dB SPL).

Try it: choose “3 tones at 80 phon” (63 Hz at 98.4 dB, 1 kHz at 80 dB, 8 kHz at 91.4 dB) and pull the “Volume control (all tones)” down to −30 dB. All points slide down by exactly 30 dB, but 1 kHz and 8 kHz end up at about 50 phon (2 sone), 63 Hz at only about 33 phon (0.61 sone). The bass now sounds only about a third as loud as the mids – on the same path it has crossed many more contours.

Heard EQ at another listening level

A mix that sounds balanced at one listening level sounds different at another – without anything changing in the signal. The diagram “Heard EQ at a different listening level” shows this for all frequencies: the mix is balanced at “Balanced at” and is played back quieter or louder by the difference to “Played back at”. The filled curve (“heard change”) shows by how many phon each frequency then seems quieter or louder than 1 kHz, the dashed one (“compensation EQ”) the EQ in dB that restores the original sound.

Worked example with “Studio 83 → home 60 phon”: the mix plays 23 dB quieter. 100 Hz then seems about 10 phon quieter than 1 kHz, 63 Hz 13.7 phon, 31.5 Hz almost 20 phon; at 8 kHz hardly anything changes. The compensation EQ boosts 63 Hz by about 8.7 dB – fewer dB than phon, because in the bass a few dB make a lot of loudness. Swap the values (60 → 83 phon): now the bass seems louder and the compensation EQ cuts it.

Common misconception: “At home the bass is missing, so the mix is thin.” Often only the listening level is lower. Mixing very loud, you mix the bass too low. A fixed reference level of about 79 to 85 dB SPL has proven itself, with occasional checks at low and high level. The loudness button on a hi-fi amplifier compensates only roughly: it knows the position of its control, not the level at the ear.

From phon to sone

Phon tells which tones are equally loud, but not how much louder one sounds than another. For that there is loudness N in sone: 1 sone is the loudness of a 1 kHz tone at 40 dB SPL. From 40 phon upwards we perceive roughly +10 phon as twice as loud, so N = 2^((L_N − 40) / 10) sone, where L_N is the loudness level in phon.

Worked example: 60 phon gives 2² = 4 sone, 80 phon 2⁴ = 16 sone – four times as loud. Below 40 phon the model approximates loudness with (L_N / 40)^2.642; 30 phon gives about 0.47 sone. In the diagram “Loudness: phon → sone” the sone axis is logarithmic, which is why the curve is a straight line from 40 phon on (“+10 phon ≈ twice as loud”).

Common misconception: “Double the power sounds twice as loud.” Double the power is only +3 dB; twice the loudness needs +10 dB at 1 kHz, i.e. ten times the power. In the bass less is enough: about +6.9 dB at 100 Hz, just under 6 dB at 50 Hz. And the sone values of several tones cannot simply be added, as the footnote below the table stresses.

Measuring with dB(A) and dB(C)

A sound level meter imitates the ear with a fixed weighting filter. A-weighting resembles an inverted contour at about 40 phon and strongly attenuates low frequencies (63 Hz: −26.2 dB), C-weighting is almost flat (63 Hz: −0.8 dB); at 1 kHz both are 0 dB. Below the table are the total levels – energetic, A- and C-weighted. Levels add as powers: from the individual levels Lᵢ the total level is L = 10 · log₁₀(Σ 10^(Lᵢ / 10)); two tones at 60 dB each give 63 dB.

The catch: the filter does not know the level. Try it: set a 63 Hz tone to 73.1 dB SPL (40 phon) and choose A under “Show weighting curve”. The curve is inverted and placed through the loudness level of the selected tone, so you can compare it with its contour. Hearing “subtracts” 33.1 dB here, A-weighting 26.2 dB – the A curve goes back to older measurements. At 90 phon (about 104.5 dB SPL) hearing subtracts only 14.5 dB, A-weighting still 26.2 dB: dB(A) underestimates loud bass by more than 10 dB.

That is why concerts are also measured in dB(C). DIN 15905-5 limits the rating level over 30 minutes at the loudest audience position to LAr ≤ 99 dB(A) and the peak level to LCpeak ≤ 135 dB(C).

Limits of the model

The model uses ISO 226:2003, interpolated over the logarithm of frequency (log f) between the frequencies of the standard; the 2023 edition differs by 1 to 2 dB at some frequencies. The standard covers 20 to 90 phon, above 4 kHz up to 80 phon; outside this range the curves are dotted and only extrapolated, and the table marks such values with *. Below 40 phon the sone conversion uses an approximation, and the threshold of pain is only drawn approximately.

The contours apply to single sine tones. Music and speech require loudness models that account for masking and bandwidth (e.g. after Zwicker, ISO 532), or in broadcasting loudness in LUFS according to ITU-R BS.1770.

When listening, the level ratios are always right, the absolute dB SPL values only after calibration in the settings menu. Headphones have their own frequency responses, and no tone is played louder than the reference for 0 dBFS. Look after your hearing: high levels only briefly.

Tasks

Practice questions

Questions from studio, stage and mastering – to think about, discuss and check with the module.

1. At what level should a mix be monitored, and why does it often sound different when played quietly at home than in the studio?

Show answer

Because the contours depend on level, the perceived tonal balance depends on the monitoring level. Mixing very loud, you hear a lot of bass and mix it too low; mixing very quietly, you add too much bass and treble. A fixed reference level of about 79 to 85 dB SPL has proven itself (depending on room size; in cinemas 85 dB C-weighted per channel), where the contours are relatively flat. In between you should check quietly and loudly. A constant level also protects your hearing and keeps decisions comparable over hours.
2. What does the loudness button on a hi-fi amplifier do, and why does it often only work approximately?

Show answer

It boosts the bass (and partly the treble) at low volume settings to compensate for the loss from task 4: with 30 dB less level, 63 Hz loses about 17 phon compared with 1 kHz. But the amplifier only knows the position of its control, not the actual level at the ear – that depends on speaker sensitivity, room, distance and recording level. Modern devices with a calibrated reference level (dynamic loudness compensation) therefore correct depending on the distance from the reference level.
3. The level at a concert is to be monitored. Why are dB(A) and dB(C) measured, and which limits does DIN 15905-5 specify?

Show answer

DIN 15905-5 limits the rating level over 30 minutes at the loudest audience position to LAr ≤ 99 dB(A) and the peak level to LCpeak ≤ 135 dB(C). A-weighting reflects the hearing risk in the middle frequency range well, but largely ignores low frequencies. With bass-heavy music the level in dB(C) can be 10 to 20 dB higher – and as task 5 shows, bass at high levels sounds much louder than dB(A) suggests. Mixing to dB(A) alone therefore easily leads to extreme bass levels; an additional dB(C) display makes this visible.

Tasks

Predict first, then try it out, then open the solution. “Load starting point” sets the matching initial values.

1. Same level, different loudness

A 1 kHz tone and a 100 Hz tone both have 60 dB SPL. Read the loudness level and loudness of both tones. How loud must the 100 Hz tone be to sound as loud as the 1 kHz tone?

Load starting point

Show solution

The 1 kHz tone has 60 phon (4 sone), the 100 Hz tone only about 34 phon (around 0.66 sone) – so it sounds only about one sixth as loud. For 60 phon the 100 Hz tone needs about 78.7 dB SPL, almost 19 dB more. Drag it onto the 60 phon contour in the diagram.
2. The threshold of hearing

A 50 Hz tone at 50 dB SPL. Lower the level until the tone becomes inaudible. Then change the frequency: where is the threshold at 20 Hz, 100 Hz and 1 kHz, and where is the ear most sensitive?

Load starting point

Show solution

At 50 Hz the threshold is about 44 dB SPL, at 20 Hz about 78.5 dB, at 100 Hz about 26.5 dB and at 1 kHz about 2.4 dB. The ear is most sensitive around 3 to 4 kHz at about −6 dB SPL – due to the resonance of the ear canal. So there are about 85 dB of difference in sensitivity between 20 Hz and 3 kHz.
3. Twice as loud in the bass

Both tones – 1 kHz at 60 dB and 50 Hz at 90 dB – sound equally loud (60 phon). Raise both to 70 phon. By how many dB do you have to increase each, and how does the loudness in sone change?

Load starting point

Show solution

At 1 kHz +10 dB are needed (60 → 70 dB). At 50 Hz about +5.9 dB are enough (90.0 → 95.9 dB), because the contours lie close together in the bass. In both cases the loudness doubles from 4 to 8 sone. At low frequencies every level change therefore acts almost twice as strongly – one reason why the bass stands out with level changes.
4. Listening more quietly

Three tones (63 Hz, 1 kHz, 8 kHz) are set to 80 phon, i.e. equally loud. Turn the volume control to −20 dB and then to −30 dB. How loud are the tones now in comparison? In the EQ view, set reference 1 to 80 and reference 2 to 50 phon.

Load starting point

Show solution

All tones become quieter by the same level, but not by the same loudness. At −20 dB: 1 kHz 60 phon (4 sone), 8 kHz about 59.8 phon, 63 Hz only about 48 phon (1.75 sone). At −30 dB: 1 kHz 50 phon (2 sone), 63 Hz about 33 phon (0.61 sone) – the bass now sounds only about a third as loud as the mids. Played back quietly, the same mix sounds thin in the bass; the loudness button on an amplifier compensates for this. The EQ view shows this for all frequencies at once (80 → 50 phon): 63 Hz seems about 17 phon quieter than 1 kHz, 31.5 Hz about 24 phon; a compensation EQ would have to boost 63 Hz by just over 11 dB.
5. dB(A) and phon in the bass

A 63 Hz tone at 73.1 dB SPL, with A-weighting shown. Compare phon, dB(A) and dB(C). Then raise the tone to 90 phon and compare again.

Load starting point

Show solution

At 73.1 dB SPL the tone has 40 phon; the meter shows 46.9 dB(A) and 72.3 dB(C). For 90 phon it needs about 104.5 dB SPL: that is 78.3 dB(A) and 103.7 dB(C). A-weighting always subtracts 26.2 dB at 63 Hz – but hearing “subtracts” 33 dB at 40 phon and only 14.5 dB at 90 phon. dB(A) therefore underestimates loud bass by more than 10 dB; that is why loud music is additionally measured in dB(C). When listening: the sound output only reaches the calibration reference in the settings menu (100 dB SPL by default); louder tones sound as loud as that reference, not louder.

Settings

Sound

Level calibration (dB SPL)

MIDI keyboard

Decibels and phons