IEC 61260-1: Base-2 vs Base-10 Frequency Ratio Systems
TL;DR
IEC 61260-1 permits two systems for calculating filter frequencies. The base-10 system (preferred) uses powers of 10: fm = fr × 10^(k/G) where G = 3b (b=1 for octave, 3 for 1/3 octave) and fr = 1000 Hz. The base-2 system uses powers of 2: fm = fr × 2^(k/b). The two systems produce slightly different centre frequencies — the maximum deviation is about 0.13% (0.011 dB), well within all class tolerances. Base-10 produces "rounder" frequencies at standardized values. Base-2 produces exactly-spaced octave intervals. Most modern instruments use base-10 per the IEC preference.
Base-10 System (Preferred)
The base-10 system derives centre frequencies from powers of 10:
fm = fr × 10^(k / G)
Where fr = 1000 Hz (reference frequency), G = 10 × b / 3 (G = 10/3 for 1/1 octave, G = 10 for 1/3 octave), and k is the band index. This system has the property that the octave ratio is 10^(3/10) = 1.99526... rather than exactly 2.
Advantages of base-10:
- Produces the standardized nominal frequency series (31.5, 63, 125, 250, 500, 1000...)
- Aligns with the preferred number series (ISO R10)
- Consistent with existing measurement standards and databases
Base-2 System
The base-2 system uses exact powers of 2:
fm = fr × 2^(k / b)
Where b is the bandwidth fraction. This produces exact octave ratios: the frequency doubles precisely for each octave step. The 1000 Hz reference frequency is shared, so both systems agree exactly at k=0.
Advantages of base-2:
- Mathematically cleaner — exact octave relationships
- Simpler for digital filter design using bilinear transform
- Band edge frequencies are exact 2^(1/2b) ratios
Practical Differences
The maximum frequency difference between the two systems occurs at bands far from the 1000 Hz reference:
| Nominal freq | Base-10 exact | Base-2 exact | Deviation |
|---|---|---|---|
| 31.5 Hz | 31.623 | 31.250 | 1.2% |
| 63 Hz | 63.096 | 62.500 | 0.95% |
| 125 Hz | 125.89 | 125.00 | 0.71% |
| 1000 Hz | 1000.0 | 1000.0 | 0% |
| 8000 Hz | 7943.3 | 8000.0 | 0.71% |
The deviation is largest at 31.5 Hz (1.2%) but this translates to only about 0.1 dB difference in measured band level — well within even Class 0 tolerances.
Which System to Use
IEC 61260-1 states the base-10 system is preferred. When in doubt, use base-10. The choice must be documented in measurement reports per ISO 3382-1 reporting requirements. In practice, most commercial analyzers use base-10 unless specifically configured otherwise.
Band Edge Calculation
Regardless of system, band edges are computed symmetrically around the centre frequency. For base-10: f₁ = fm × 10^(-1/(2G)), f₂ = fm × 10^(1/(2G)). For base-2: f₁ = fm × 2^(-1/(2b)), f₂ = fm × 2^(1/(2b)). See filter design for how these edges define the filter response.
SonaVyx Implementation
The RTA and SPL meter octave analysis use the base-10 system with IEC 61260-1 preferred centre frequencies. The FFT-based implementation sums power spectrum bins within each band's edge frequencies. See digital implementation for technical details.
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Last updated: March 19, 2026