Speech Intelligibility Index

The Speech Intelligibility Index predicts how much of a speech signal is audible, and therefore intelligible, to a listener in a given noise and hearing condition. It reduces a speech spectrum, a noise spectrum and a hearing threshold to a single number in [0, 1]: 0 when nothing useful reaches the listener, 1 when the whole speech-bearing spectrum is audible. This page covers the one-third-octave-band method of ANSI S3.5-1997 (R2017): 18 bands from 160 Hz to 8000 Hz.

Note

SII vs STI. The SII predicts intelligibility from audibility (how much of the speech spectrum clears the noise and the hearing threshold at the listener’s ear) while the STI characterises a transmission channel: how much of the speech modulation a room or sound system preserves. For the latter, see the Speech Transmission Index guide.

1. Inputs and the band-importance function

All three inputs are equivalent spectrum levels (ANSI S3.5-1997 clauses 3.11 and 3.55) sampled at the 18 one-third-octave band centres: the speech spectrum level $E_i^{\prime }$, the noise spectrum level $N_i^{\prime }$ (both in dB SPL) and the hearing threshold $T_i^{\prime }$ (in dB HL). Each band $i$ contributes to intelligibility in proportion to its band-importance function $I_i$ (ANSI S3.5-1997 Table 3, average speech material), which sums to one across the 18 bands.

from phonometry import hearing

# The standard normal-effort speech spectrum (Table 3) in quiet, normal hearing.
result = hearing.speech_intelligibility_index("normal")
print(round(result.sii, 3))          # 0.996  (nearly everything audible)
print(round(hearing.sii.BAND_IMPORTANCE.sum(), 6))   # 1.0

result.plot()   # per-band audibility and its weighted contribution (needs matplotlib)

With no noise and a normal hearing threshold the standard speech spectrum is almost fully audible, so the index is close to one; the small deficit is the listener’s own self-speech masking.

The importance function is where the perceptual knowledge of the standard lives. It descends from the articulation experiments behind French and Steinberg’s articulation index: listeners scored nonsense syllables heard through filters that removed one part of the spectrum at a time, and the drop in score measures how much intelligibility each band carries. The outcome is strikingly unequal, and unrelated to where the speech energy sits: the five bands from 1250 Hz to 3150 Hz carry about 43 % of intelligibility (the place and manner cues of consonants live there), while the five lowest bands, 160 Hz to 400 Hz, carry about 11 % even though they hold nearly half of the speech power. Ii from Table 3 is the average-speech compromise; the standard’s Annex B tabulates alternative importance functions for specific test materials (nonsense syllables, monosyllabic word lists, short passages), which shift weight according to how much redundancy the material offers.

2. Masking and the band-audibility function

The procedure (ANSI S3.5-1997 clause 5) turns the inputs into a per-band audibility. Speech masks itself downward from each band ($V_i=E_i^{\prime }-24$); the larger of that and the external noise, $B_i$, spreads upward in frequency with a level-dependent slope to give the equivalent masking spectrum level $Z_i$ (clause 5.4):

$$Z_i=10{\log }_{10}\left(10^{0.1N_i^{\prime }}+\sum _{k<i}10^{0.1\left(B_k+3.32C_k{\log }_{10}(0.89f_i/f_k)\right)}\right).$$

The masking is combined with the equivalent internal noise ($X_i^{\prime }=X_i+T_i^{\prime }$, the reference internal noise shifted by the hearing loss) into the equivalent disturbance $D_i$ (clause 5.6), and the band-audibility function is the speech-to-disturbance ratio scaled into $[0,1]$ (clause 5.8):

$$A_i=\mathrm{clip}\left(\frac{E_i^{\prime }-D_i+15}{30},0,1\right).$$

At speech levels well above normal effort a level-distortion factor of clause 5.7 (unity for the standard spectra used on this page) reduces $A_i$ further; phonometry applies it automatically.

3. The index in noise

The Speech Intelligibility Index is the band-importance-weighted sum of the band audibilities (ANSI S3.5-1997 clause 6):

$$\text{SII}=\sum _i{I}_i{A}_i.$$

import numpy as np
from phonometry import hearing

speech = hearing.standard_speech_spectrum("normal")
# A descending broadband masking noise (an office/ventilation-like spectrum).
noise = np.array([38.0, 37.0, 36.0, 34.0, 32.0, 30.0, 28.0, 26.0, 24.0,
                  22.0, 20.0, 18.0, 16.0, 14.0, 12.0, 10.0, 8.0, 6.0])

result = hearing.speech_intelligibility_index(speech, noise)
print(round(result.sii, 2))                # 0.46
print(result.band_audibility.round(2))     # per-band Ai

result.plot()   # the figure below: Ai and the weighted contribution per band

Show the code for this figure

import numpy as np
import matplotlib.pyplot as plt
from phonometry import hearing

speech = hearing.standard_speech_spectrum("normal")
noise = np.array([38.0, 37.0, 36.0, 34.0, 32.0, 30.0, 28.0, 26.0, 24.0,
                  22.0, 20.0, 18.0, 16.0, 14.0, 12.0, 10.0, 8.0, 6.0])
result = hearing.speech_intelligibility_index(speech, noise)

# One line:
result.plot()
plt.show()

# By hand, mirroring what SIIResult.plot() draws:
pos = np.arange(result.frequencies.size)
weighted = result.band_audibility * result.band_importance
fig, ax = plt.subplots()
ax.bar(pos, result.band_audibility, color="#c6dbef", label=r"Band audibility $A_i$")
ax.bar(pos, weighted / weighted.max(), width=0.5, color="#1f77b4",
       label=r"Importance-weighted $I_i A_i$ (scaled)")
ax.set_xticks(pos)
ax.set_xticklabels([f"{f:g}" for f in result.frequencies], rotation=45, ha="right")
ax.set_xlabel("One-third-octave band [Hz]")
ax.set_ylabel("Band audibility")
ax.set_title(f"SII = {result.sii:.2f}")
ax.legend()
plt.show()

A raised hearing threshold (threshold=) lifts the equivalent internal noise and lowers the index, exactly as added masking noise does. The SIIResult also carries the per-band masking $Z_i$, disturbance $D_i$, audibility $A_i$ and importance $I_i$, and its .plot() renders the figure above.

The same speech and noise heard by a listener with a sloping high-frequency loss shows what that costs, band by band:

Show the code for this figure

import numpy as np
import matplotlib.pyplot as plt
from phonometry import hearing

# The same speech and office noise as above, heard through a sloping
# high-frequency loss (hearing threshold levels at the 18 band centres).
speech = hearing.standard_speech_spectrum("normal")
noise = np.array([38.0, 37.0, 36.0, 34.0, 32.0, 30.0, 28.0, 26.0, 24.0,
                  22.0, 20.0, 18.0, 16.0, 14.0, 12.0, 10.0, 8.0, 6.0])
threshold = np.array([5.0, 5.0, 5.0, 5.0, 8.0, 10.0, 12.0, 15.0, 18.0,
                      22.0, 28.0, 35.0, 42.0, 48.0, 55.0, 60.0, 65.0, 70.0])
res = hearing.speech_intelligibility_index(speech, noise, threshold=threshold)
print(round(res.sii, 3))       # 0.358  (0.458 with normal hearing)

# One line: the same audibility bars, now limited by the hearing threshold.
res.plot()
plt.show()

The loss removes the bands that carry the consonant cues, which is why the index falls by a fifth while the level of the speech has not changed at all. This is the practical use of the SII in audiology and in noise control for occupied spaces: a target index can be met either by lowering the noise or by restoring audibility (amplification), and the band profile says which bands the effort has to go into. The age-related thresholds of ISO 7029 make a convenient population input, see the hearing-threshold guide.

4. Vocal effort

Talkers raise their voice in noise, and the standard gives four standard speech spectra for the vocal efforts normal, raised, loud and shout (ANSI S3.5-1997 Table 3). Passing the effort name selects the corresponding spectrum; speaking louder lifts the whole spectrum and, in a fixed noise, raises the index.

import numpy as np
from phonometry import hearing

# The same broadband noise, four vocal efforts.
noise = np.array([48.0, 47.0, 46.0, 44.0, 42.0, 40.0, 38.0, 36.0, 34.0,
                  32.0, 30.0, 28.0, 26.0, 24.0, 22.0, 20.0, 18.0, 16.0])
for effort in hearing.sii.VOCAL_EFFORTS:
    print(effort, round(hearing.speech_intelligibility_index(effort, noise).sii, 2))
# normal 0.12 | raised 0.36 | loud 0.59 | shout 0.79

print(hearing.standard_speech_spectrum("loud")[8])  # 42.16 dB SPL at 1 kHz

The four spectra are also available as one plottable result: standard_speech_spectra() returns a StandardSpeechSpectrum carrying the band centre frequencies and the per-effort band levels, and its .plot() draws them as one labelled family on the one-third-octave band axis.

Show the code for this figure

import numpy as np
import matplotlib.pyplot as plt
from phonometry import hearing

# One line: the whole ANSI S3.5-1997 Table 3 family.
hearing.standard_speech_spectra().plot()
plt.show()

# By hand, mirroring what StandardSpeechSpectrum.plot() draws:
res = hearing.standard_speech_spectra()
pos = np.arange(res.frequencies.size)
fig, ax = plt.subplots()
for effort, levels in zip(res.vocal_efforts, res.levels):
    ax.plot(pos, levels, "o-", label=effort.capitalize())
ax.set_xticks(pos)
ax.set_xticklabels([f"{f:g}" for f in res.frequencies], rotation=45, ha="right")
ax.set_xlabel("One-third-octave band [Hz]")
ax.set_ylabel("Speech spectrum level [dB SPL]")
ax.legend()
plt.show()

The same four spectra feed the index: in a fixed broadband noise, each higher vocal effort lifts the speech spectrum and raises the SII.

Show the code for this figure

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.ticker import NullFormatter
from phonometry import hearing

# The four ANSI S3.5-1997 Table 3 spectra and the fixed broadband noise above.
noise = np.array([48.0, 47.0, 46.0, 44.0, 42.0, 40.0, 38.0, 36.0, 34.0,
                  32.0, 30.0, 28.0, 26.0, 24.0, 22.0, 20.0, 18.0, 16.0])
efforts = hearing.sii.VOCAL_EFFORTS         # ("normal", "raised", "loud", "shout")
freqs = hearing.sii.BAND_CENTERS            # the 18 one-third-octave band centres

fig, (ax_s, ax_i) = plt.subplots(1, 2, figsize=(12, 5))

# Left: each higher vocal effort lifts the whole speech spectrum.
for effort in efforts:
    ax_s.plot(freqs, hearing.standard_speech_spectrum(effort), "o-",
              label=effort.capitalize())
ax_s.set_xscale("log")
ax_s.set_xticks(list(freqs))
ax_s.set_xticklabels([f"{f:g}" for f in freqs], rotation=45, ha="right")
ax_s.xaxis.set_minor_formatter(NullFormatter())
ax_s.set_xlabel("One-third-octave band [Hz]")
ax_s.set_ylabel("Speech spectrum level [dB SPL]")
ax_s.legend()

# Right: the SII each spectrum reaches in the fixed noise.
sii = [hearing.speech_intelligibility_index(e, noise).sii for e in efforts]
pos = np.arange(len(efforts))
ax_i.bar(pos, sii)
ax_i.set_xticks(pos)
ax_i.set_xticklabels([e.capitalize() for e in efforts])
ax_i.set_ylim(0.0, 1.0)
ax_i.set_ylabel("Speech Intelligibility Index")
plt.show()

The vocal-effort names work anywhere a speech spectrum is expected, including as the first argument to speech_intelligibility_index.

5. SII or STI?

The two speech metrics answer different questions from different measurements, and each is blind to what the other captures:

	SII (ANSI S3.5)	STI (IEC 60268-16)
Question answered	Is enough of the speech spectrum audible at the listener’s ear?	How much of the speech envelope does the transmission channel preserve?
Inputs	Speech, noise and hearing-threshold spectra (18 one-third-octave equivalent spectrum levels)	An impulse response (indirect) or a STIPA recording through the channel (direct)
Band machinery	Band-importance weighting Ii applied to the band audibility Ai	Modulation transfer function m(F) per octave band, converted to an effective SNR
Captures	Steady noise, upward spread of masking, hearing loss, vocal effort, level distortion	Reverberation, echoes, noise and (measured directly) non-linear processing
Blind to	Reverberation and any time-domain smearing: a fully audible but hopelessly reverberant channel still scores high	Individual hearing status: hearing-impaired listeners need specific corrections
Typical use	Audiology, hearing aids and protectors, noise-control targets at a listener position	PA systems, intercoms and rooms: rating a transmission channel end to end

The same space can pass one and fail the other. A quiet, highly reverberant atrium is an SII near 1 with a poor STI; a dry office flooded by ventilation noise can rate an acceptable STI from its impulse response while the SII (and the noise-aware STI, via snr= or level=) reveals that little of the speech spectrum clears the noise. When both mechanisms are in play, compute both; the inputs are cheap once the room and the noise have been measured. See the Speech Transmission Index guide for the STI side.

6. ANSI S3.5-1997 report (.report())

SIIResult.report(path) renders a one-page PDF fiche laid out like a speech-audibility report: a standard-basis line, an optional metadata header block, a per-one-third-octave-band table of the equivalent speech spectrum $E_i^{\prime }$, the Table 3 band-importance function $I_i$ and the band-audibility function $A_i$ beside the audibility and importance-weighted contribution bars (the result’s own .plot()), the boxed SII = X single number, an optional verdict row and a footer with the fixed disclaimer. It uses the same ReportMetadata container and rendering engine as the ISO 717 insulation fiche; a supplied requirement is read as the minimum required SII (a higher SII passes). verbose=True adds the equivalent disturbance spectrum level $D_i$ column. Rendering needs reportlab (pip install phonometry[report]); only engine="reportlab" is supported. Pass language="es" for a Spanish fiche.

from phonometry import hearing, ReportMetadata

res = hearing.speech_intelligibility_index(speech, noise, threshold=threshold)
res.report(
    "sii_fiche.pdf",
    metadata=ReportMetadata(
        specimen="Conversational speech in low-frequency ambient noise",
        measurement_standard="ANSI S3.5-1997",
        laboratory="Phonometry Reference Laboratory",
        requirement=0.75,            # minimum required SII (a higher SII passes)
    ),
)

The example fiche is regenerated with make reports and kept rendered in the repository; click the preview to open the PDF.

One-page speech-intelligibility-index fiche: a metadata header, a one-third-octave-band table of the equivalent speech spectrum, band importance and band audibility, the audibility bars, the boxed SII = 0.851 single-number result and a PASS verdict against a 0.75 minimum.

Download the report (PDF)

Speech intelligibility index fiche (SIIResult.report), the SII with its per-band audibility.

What this guide covers

Covered. ANSI S3.5-1997 (R2017)‘s one-third-octave-band method (18 bands, 160 Hz to 8000 Hz): the equivalent speech, noise and hearing-threshold spectrum levels, the Table 3 band-importance function and standard speech spectra by vocal effort, the self-speech masking, upward spread of masking, level-distortion factor and band-audibility function of clause 5, and the index of clause 6. speech_intelligibility_index, standard_speech_spectrum and standard_speech_spectra implement these, and SIIResult.report(path) renders the ANSI S3.5-1997 fiche.

Not covered. The standard’s own title is plural (“Methods for the Calculation of the Speech Intelligibility Index”): phonometry implements only the one-third-octave-band procedure, not the standard’s other band-resolution methods. The band-importance function used is always Table 3’s average-speech compromise; Annex B’s alternative importance functions for specific test materials (nonsense syllables, monosyllabic word lists, short passages) are not implemented. The Speech Transmission Index, a different metric for a transmission channel rather than listener audibility, is covered separately in the Speech Transmission Index guide.

See also

• Speech Transmission Index: the STI/STIPA transmission index that the SII complements.
• Loudness and Sound Quality Metrics: loudness, sharpness and the perception metrics of what the listener hears.
• Filter Banks: the one-third-octave bands the SII is evaluated on.
• Levels: the spectrum and band levels behind the equivalent spectrum-level inputs.
• API reference: hearing.sii.

Quick answers

Which frequency bands matter most for speech intelligibility?

In the one-third-octave-band method of ANSI S3.5-1997, the band-importance function $I_i$ (Table 3, average speech material) sums to one across 18 bands from 160 Hz to 8000 Hz. The five bands from 1250 Hz to 3150 Hz carry about 43 % of intelligibility (the consonant cues), while the five lowest bands, 160 Hz to 400 Hz, carry about 11 % despite holding nearly half of the speech power.

How is the Speech Intelligibility Index calculated?

The SII of ANSI S3.5-1997 clause 6 is the band-importance-weighted sum of the band audibilities, $\text{SII}={\sum }_i{I}_i{A}_i$, over 18 one-third-octave bands. Each band audibility is $A_i=\mathrm{clip}\left((E_i^{\prime }-D_i+15)/30,0,1\right)$ (clause 5.8), where $E_i^{\prime }$ is the equivalent speech spectrum level and $D_i$ the equivalent disturbance combining external noise, upward spread of masking and the equivalent internal noise. The index lies in $[0,1]$.

When should I use the SII instead of the STI?

Use the SII (ANSI S3.5) when the question is whether enough of the speech spectrum is audible at the listener’s ear: it captures steady noise, upward spread of masking, hearing loss and vocal effort, but it is blind to reverberation. The STI (IEC 60268-16) rates a transmission channel, how much of the speech modulation a room or sound system preserves. When both mechanisms are in play, compute both.

References

• American National Standards Institute. (1997). American National Standard Methods for the Calculation of the Speech Intelligibility Index (ANSI S3.5-1997 (R2017)). Acoustical Society of America. The one-third-octave-band method (18 bands): the band-importance function (Table 3), the standard speech spectrum level and reference internal noise (Table 3), the masking, disturbance and band-audibility procedure (clause 5) and the index (clause 6).
• French, N. R., & Steinberg, J. C. (1947). Factors governing the intelligibility of speech sounds. The Journal of the Acoustical Society of America, 19(1), 90-119. https://doi.org/10.1121/1.1916407The articulation-band experiments that the band-importance function of section 1 descends from.