A century-old reflex

Chapter 3 of Volume 10 introduced the Lombard effect. This chapter looks at two situations in singing, loud accompaniment and ear plugs or in-ear monitors, because they change the inputs to the loop of Chapter 5.

Two paths, one cochlea

Singers hear their own voices by two paths: air conduction, as sound leaves the lips and travels round the cheeks into the ear canal, and bone conduction, as vibration of the folds passes through the skull and soft tissues straight to the inner ear.

A physical fact is often overlooked here: air- and bone-conducted versions of one’s own voice add up in the same cochlea. The accompaniment reaches the same cochlea by air and masks both parts of one’s own voice at once. “Hearing yourself by bone” is therefore not an independent channel that escapes masking. What ear plugs and in-ear monitors really change is the proportion: they attenuate outside sound together with the air-conducted own voice but let the bone-conducted own voice through (and amplify it at low frequencies).

The program below does the accounting band by band: the air- and bone-conducted components of the own voice, the accompaniment, the isolation and occlusion effect of ear plugs or in-ear monitors, and the gain at which the own voice is mixed into the monitors. The own-voice-to-accompaniment ratio in each band sets the precision of pitch resolution in that band, the bands are combined by inverse variance, and the result is fused with a less precise somatosensory channel that noise does not affect (steady-state Kalman weights). All levels are illustrative assumptions.

# Hearing yourself through air and bone in loud accompaniment, band by band
# (illustrative). Air- (AC) and bone-conducted (BC) own voice add up in the SAME cochlea;
# outside noise masks both. Plugs cut AC voice and band by 20 dB and boost BC at low
# frequencies (occlusion); in-ear monitors isolate 25 dB and add the own voice back at mix
# gain m dB. Band pitch sd = 6 cents x (1 + 10^(-SNR/10)), combined by inverse variance,
# then fused with a noise-free laryngeal/vibrotactile sense (sd 25 cents, assumed).
import math

BANDS = (250, 500, 1000, 2000, 4000)
VOICE_AC = (78, 82, 80, 74, 66)            # own voice by air, open ear
# bone path relative to air (BC dominant at 1-2 kHz)
BC_RE_AC = (-6, -3, 2, 3, -10)
OCCL = (15, 10, 3, 0, 0)                   # occlusion boost of the bone path, ear shut
ORCH = (92, 94, 90, 82, 74)                # loud band at the singer's ear
SD_SOMA = 25.0
db_sum = lambda *ls: 10 * math.log10(sum(10 ** (v / 10) for v in ls))

def condition(kind, mix=0.0):
    rows = []
    for i in range(len(BANDS)):
        ac, bc, noise = VOICE_AC[i], VOICE_AC[i] + BC_RE_AC[i], ORCH[i]
        if kind == "quiet":
            noise = 30.0
        elif kind in ("plugs", "iem"):
            cut = 20 if kind == "plugs" else 25
            ac, noise, bc = ac - cut, noise - cut, bc + OCCL[i]
            if kind == "iem":
                ac = db_sum(ac, VOICE_AC[i] + mix)         # monitor feed of the own voice
        rows.append((db_sum(ac, bc) - noise, 1 / (1 + 10 ** ((bc - ac) / 10))))
    sds = [6.0 * (1 + 10 ** (-snr / 10)) for snr, _ in rows]
    sd_aud = 1 / math.sqrt(sum(1 / s ** 2 for s in sds))
    prec = 1 / sd_aud ** 2 + 1 / SD_SOMA ** 2
    return rows, sd_aud, (1 / sd_aud ** 2) / prec, 1 / math.sqrt(prec)

print("SNR = own voice minus accompaniment at the cochlea (dB, 250 / 1k / 4k Hz);")
print("air = share of own voice arriving by air; sd in cents; w = weight on hearing")
print("condition             |  250    1k    4k  | air  | hear  |  w   | fused")
CASES = (("quiet room", "quiet", 0), ("open ears, loud band", "open", 0),
         ("foam ear plugs", "plugs", 0), ("in-ear monitor -10 dB", "iem", -10),
         ("in-ear monitor +0 dB", "iem", 0), ("in-ear monitor +6 dB", "iem", 6))
for name, kind, mix in CASES:
    rows, sd_aud, w, sd_f = condition(kind, mix)
    snrs = " ".join(f"{rows[i][0]:+5.1f}" for i in (0, 2, 4))
    air = sum(a for _, a in rows) / len(rows)
    print(f"{name:22s}| {snrs} | {air:4.0%} | {sd_aud:5.1f} | {w:.2f} | {sd_f:5.1f}")
# SNR = own voice minus accompaniment at the cochlea (dB, 250 / 1k / 4k Hz);
# air = share of own voice arriving by air; sd in cents; w = weight on hearing
# condition             |  250    1k    4k  | air  | hear  |  w   | fused
# quiet room            | +49.0 +54.1 +36.4 |  62% |   2.7 | 0.99 |   2.7
# open ears, loud band  | -13.0  -5.9  -7.6 |  62% |  14.2 | 0.76 |  12.4
# foam ear plugs        | +15.0 +15.0  +2.4 |   2% |   2.9 | 0.99 |   2.9
# in-ear monitor -10 dB | +20.1 +20.1 +10.1 |  12% |   2.8 | 0.99 |   2.7
# in-ear monitor +0 dB  | +20.5 +21.2 +17.4 |  35% |   2.7 | 0.99 |   2.7
# in-ear monitor +6 dB  | +21.8 +23.5 +23.1 |  60% |   2.7 | 0.99 |   2.7

The results can be read as four situations.

A quiet room: the own voice is 36–54 dB above the noise, the auditory estimate has a standard deviation of about 2.7 cents, and about 62 % of the own voice arrives by air.

Open ears, loud band: the own voice is 6–13 dB below the accompaniment in the bands shown, and the standard deviation of the auditory estimate rises to 14.2 cents; after fusion the somatosensory channel receives about a quarter of the weight (auditory weight 0.76), and the combined standard deviation is 12.4 cents. This is what Chapter 5’s hypothesis of “more somatosensory weight under masking” looks like in the model.

Foam ear plugs: the accompaniment and the air-conducted own voice are both cut by 20 dB, but the bone-conducted own voice is amplified at low frequencies by the occlusion effect, so the own-voice-to-accompaniment ratio returns to about +15 dB in the low and middle bands (about +2 dB at 4 kHz), and auditory precision recovers to 2.9 cents. The price is that only about 2 % of the own voice reaching the cochlea now comes by air: the singer hears almost entirely a bone-conducted voice, boosted in the bass and weak in the treble, very different from what the audience hears.

In-ear monitors: isolation is better, and the microphone signal of the own voice is mixed back into the earpieces. Raising the mix gain from −10 to +6 dB brings the air-conducted share back from 12 % to 60 %, close to the 62 % of open ears, while keeping the signal-to-noise ratio around +20 dB in the low and middle bands. The point of the monitor mix is thus not only to be “louder” but to restore the natural proportion of air and bone conduction in the own voice.

Hear differently, sing differently

If singers regulate their level by ear, changing what they hear changes what they sing. The program below uses two assumed slopes (0.5 dB per dB each for the Lombard and sidetone effects) to estimate the vocal level under four monitoring conditions, and the resulting voice-to-band ratio reaching the audience.

# Lombard and sidetone effects with open ears, plugs and in-ear monitors (illustrative
# regulation model, not fitted). Vocal level V (dB re open ears in quiet):
#   V = sL * max(0, N_heard - N0) - sS * (self_heard - self_open),  sL = sS = 0.5 ASSUMED
# The audience hears the singer by air only: plugs change what the singer hears, not the
# hall.
import math

# band at the ear (dB), Lombard onset, slopes
N_BAND, N0, SL, SS = 94.0, 45.0, 0.5, 0.5
# own voice at the cochlea by path, open ear (dB)
AIR, BONE = 85.0, 83.0
db_sum = lambda *ls: 10 * math.log10(sum(10 ** (v / 10) for v in ls))
SELF_OPEN = db_sum(AIR, BONE)

# 20 / 25 dB isolation; occlusion +8 dB on bone
def voice_level(kind, mix=0.0):
    n, s = {"open": (N_BAND, SELF_OPEN),
            "plugs": (N_BAND - 20, db_sum(AIR - 20, BONE + 8)),
            "iem": (N_BAND - 25, db_sum(AIR - 25, BONE + 8, AIR + mix))}[kind]
    return SL * max(0.0, n - N0) - SS * (s - SELF_OPEN), n, s

print(f"accompaniment {N_BAND:.0f} dB at the ear; slopes sL = sS = {SL} dB/dB (assumed)")
print("condition            | band heard | own voice heard | vocal level | to the hall*")
v_open = voice_level("open")[0]
CASES = (("open ears", "open", 0), ("foam ear plugs", "plugs", 0),
         ("in-ear, own mix -6 dB", "iem", -6), ("in-ear, own mix +6 dB", "iem", 6))
for name, kind, mix in CASES:
    v, n, s = voice_level(kind, mix)
    print(f"{name:21s}|  {n:5.1f} dB  |   {s - SELF_OPEN:+5.1f} dB      |  {v:+5.1f} dB  "
          f"  | {v - v_open:+5.1f} dB")
print("* change in the singer-to-band ratio in the hall, relative to open ears")
print(f"in a quiet room (30 dB) the model predicts no Lombard rise "
      f"({SL * max(0.0, 30 - N0):+.1f} dB)")
# accompaniment 94 dB at the ear; slopes sL = sS = 0.5 dB/dB (assumed)
# condition            | band heard | own voice heard | vocal level | to the hall*
# open ears            |   94.0 dB  |    +0.0 dB      |  +24.5 dB    |  +0.0 dB
# foam ear plugs       |   74.0 dB  |    +3.9 dB      |  +12.6 dB    | -11.9 dB
# in-ear, own mix -6 dB|   69.0 dB  |    +4.1 dB      |   +9.9 dB    | -14.6 dB
# in-ear, own mix +6 dB|   69.0 dB  |    +6.9 dB      |   +8.6 dB    | -15.9 dB
# * change in the singer-to-band ratio in the hall, relative to open ears
# in a quiet room (30 dB) the model predicts no Lombard rise (+0.0 dB)

Singing with open ears against 94 dB of accompaniment, the model predicts a rise in vocal level of about 24.5 dB over singing in quiet, a vocal load to be wary of. With foam ear plugs the band heard drops to 74 dB, and the singer hears themselves louder because of the occlusion effect (+3.9 dB), so the vocal level rises by only 12.6 dB; but the audience is not wearing ear plugs, and the voice-to-band ratio reaching the audience falls by about 12 dB. With in-ear monitors it falls by about 15–16 dB at the two mix settings. The direction of this result, that isolation and occlusion make singers sing more softly, agrees with the sidetone effect and with Garnier and colleagues’ observations; its size depends entirely on the assumed slopes and should not be taken as a prediction.

The trade-off is practical: isolation protects hearing, lightens the vocal load and makes pitch easier to hear, but the singer then needs other cues (the sound engineer, recordings, deliberate calibration) to know how they sound in the hall.

Chapter summary

The Lombard effect is a robust, nearly automatic reflex: the louder the noise, the louder the voice, and the louder one hears oneself, the softer; instructions alone hardly suppress it, and feedback training is needed. A singer’s own voice reaches the same cochlea by air and by bone (bone dominating at 1–2 kHz), and outside noise masks both. The illustrative calculation shows that with open ears in a loud band the own voice is 6–13 dB below the accompaniment, pitch estimation worsens and somatosensory weight rises; ear plugs restore the signal-to-noise ratio but leave the own voice heard almost entirely by bone; a monitor mix can restore the natural proportion of air and bone conduction. Isolation also makes singers sing more softly, lowering the voice-to-band ratio reaching the audience, a reliable direction whose size depends on assumptions. The next chapter leaves measurement behind to read some classical writing on singing and listening.