Question 1

What is the difference between 1/1 octave and 1/3 octave analysis?

Accepted Answer

A 1/1 octave analysis divides the audible spectrum into approximately 10 bands, each spanning one octave (a 2:1 frequency ratio). Standard centers: 31.5, 63, 125, 250, 500, 1000, 2000, 4000, 8000, 16000 Hz. A 1/3 octave analysis uses three times as many bands (about 30), each spanning one-third of an octave (a 1.26:1 ratio). One-third octave provides finer frequency detail and is the standard for: noise criteria (NC, RC curves), building acoustics (STC, Rw calculations), environmental noise assessment, and speaker specification. One octave analysis is sufficient for quick tonal balance checks and broad EQ decisions. SonaVyx supports both, with the octave bar overlay toggling between 1/1 and 1/3 octave resolution.

Question 2

What are the standard 1/3 octave band center frequencies?

Accepted Answer

The standard 1/3 octave band center frequencies (per ISO 266/IEC 61260) are: 20, 25, 31.5, 40, 50, 63, 80, 100, 125, 160, 200, 250, 315, 400, 500, 630, 800, 1000, 1250, 1600, 2000, 2500, 3150, 4000, 5000, 6300, 8000, 10000, 12500, 16000, 20000 Hz. These are based on preferred numbers (the R10 series), where each frequency is 10^(1/10) = 1.259 times the previous one. The bandwidth of each band equals approximately 23% of its center frequency. Most acoustic standards reference these frequencies. SonaVyx octave band analysis uses these exact center frequencies and computes band levels by summing the FFT power spectrum bins within each band.

Question 3

How are octave band levels calculated from an FFT?

Accepted Answer

The process is: compute the FFT magnitude spectrum, convert to power (|X(f)|²), identify which FFT bins fall within each octave band (between the lower and upper band edge frequencies), sum the power of all bins in each band, and convert back to dB. The band edges are: lower = center × 2^(-1/(2n)) and upper = center × 2^(1/(2n)), where n is the octave fraction (1 for full octave, 3 for 1/3 octave). For a 1/3 octave band centered at 1 kHz: lower = 891 Hz, upper = 1122 Hz. At 48 kHz sample rate with 4096-point FFT (11.7 Hz bins), this band contains about 20 bins. The sum of their power gives the band level. SonaVyx performs this calculation in the Rust WASM DSP engine for real-time performance.

Question 4

Why are low-frequency octave bands wider in Hz than high-frequency bands?

Accepted Answer

Octave bands are defined by a constant ratio, not a constant width. Each octave spans a 2:1 frequency range: the 125 Hz octave covers 88-177 Hz (89 Hz wide), while the 4 kHz octave covers 2828-5657 Hz (2829 Hz wide). This proportional bandwidth matches human frequency perception, which is also ratio-based. We perceive the interval from 100 to 200 Hz (one octave) as the same musical interval as 1000 to 2000 Hz (one octave), even though the latter spans ten times more Hz. This is why octave band analysis is displayed on a logarithmic frequency axis, where each band occupies the same visual width. The proportional bandwidth means low-frequency bands contain fewer FFT bins and may have less statistical averaging, which is why low-frequency measurements often show more variability.

Question 5

When should I use 1/6 or 1/12 octave analysis instead of 1/3 octave?

Accepted Answer

Use 1/6 octave when you need more detail than 1/3 but want to maintain a smooth, manageable display. It resolves moderate-width peaks and dips that 1/3 octave merges together, and is the standard smoothing for parametric EQ decisions. Use 1/12 octave when investigating specific narrow-band features: resolving closely spaced room modes, identifying comb filter patterns, or detecting tonal components in noise. Beyond 1/12 octave, the display becomes as complex as the raw FFT and is rarely needed for practical measurement. For reporting, 1/3 octave is the standard in most acoustic standards (ISO, IEC, ANSI). For system tuning, 1/6 octave shows the level of detail that parametric EQ can address. SonaVyx offers 1/1, 1/3, 1/6, 1/12, and 1/24 octave options.

Question 6

How do octave band measurements relate to overall SPL?

Accepted Answer

The overall SPL is the energy sum (not arithmetic sum) of all octave band levels. In dB: L_total = 10 × log10(sum of 10^(L_i/10)) for each band L_i. For example, if 1/3 octave bands from 20 Hz to 20 kHz are all at 70 dB, the overall level is 70 + 10 × log10(31 bands) = 70 + 14.9 = 84.9 dB. A single dominant band sets the overall level: if one band is at 80 dB and all others below 70 dB, the overall is approximately 80 dB. A-weighting applies a correction to each band before summing. The A-weighted overall (dBA) gives more weight to mid-frequency bands. SonaVyx computes overall SPL using A, C, and Z weightings from the octave band data and displays both the broadband level and per-band breakdown.

Question 7

What is the relationship between 1/3 octave bands and critical bands?

Accepted Answer

Critical bands (also called Bark bands or ERB — Equivalent Rectangular Bandwidth) represent the frequency resolution of the human auditory system. The cochlea acts as a bank of overlapping bandpass filters, each about 1/3 octave wide in the mid-frequency range. This is why 1/3 octave analysis correlates well with perceived loudness and masking effects. Below 500 Hz, critical bandwidth is approximately constant (about 100 Hz), narrower than 1/3 octave. Above 500 Hz, critical bandwidth is approximately proportional to frequency, matching 1/3 octave closely. Noise within a critical band is perceived differently from noise spread across multiple bands, even at the same total energy. This is the basis for psychoacoustic models used in audio coding (MP3, AAC) and perceived loudness calculations.

Question 8

How do I convert between 1/3 octave levels and 1/1 octave levels?

Accepted Answer

A full octave band level equals the energy sum of the three 1/3 octave bands within it. For example, the 1 kHz octave band level = 10 × log10(10^(L_800/10) + 10^(L_1000/10) + 10^(L_1250/10)), where L_800, L_1000, and L_1250 are the 1/3 octave band levels at 800, 1000, and 1250 Hz. If all three 1/3 octave bands have the same level L, the octave band level is L + 10×log10(3) = L + 4.8 dB. Going the other direction (from 1/1 to 1/3) is not exact because the three sub-bands may have different levels. If you only have 1/1 octave data and need 1/3 octave, a common approximation is to assume flat spectrum within each octave and subtract 4.8 dB from the octave level to estimate each 1/3 octave band. SonaVyx measures at full FFT resolution and derives both band widths accurately.

Octave Band Analysis: 1/1, 1/3, 1/6, and 1/12 Octave Explained

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