Octave Frequency Calculator
Shift any frequency by N octaves (positive or fractional). Find the nearest ISO 1/1 and 1/3 octave band, the nearest musical note, and see the result on a log-scale frequency ruler.
Input
Result
Octave shifts from base frequency (±5)
| Shift | Frequency | Nearest note |
|---|
ISO Preferred Octave Band Centers
| 1/1 Octave (Hz) | 1/3 Octave (Hz) |
|---|---|
| — | 12.5, 16, 20, 25 |
| 31.5 | 31.5, 40 |
| 63 | 50, 63, 80 |
| 125 | 100, 125, 160 |
| 250 | 200, 250, 315 |
| 500 | 400, 500, 630 |
| 1000 | 800, 1000, 1250 |
| 2000 | 1600, 2000, 2500 |
| 4000 | 3150, 4000, 5000 |
| 8000 | 6300, 8000, 10000 |
| 16000 | 12500, 16000, 20000 |
About Octaves & Octave Bands
An octave is a 2:1 frequency ratio — the most fundamental interval in music and the natural grouping unit for the human ear's logarithmic pitch perception. Doubling any frequency produces a note that sounds "the same" but higher; halving sounds the same but lower. The math is simple — f′ = f · 2N for N octaves — but the consequences ripple through audio engineering, room acoustics, and psychoacoustics.
1/1 octave bands
For acoustic measurement, the audible range (≈ 20 Hz – 20 kHz) is divided into 10 standard octave bands centered at ISO-preferred frequencies: 31.5, 63, 125, 250, 500, 1000, 2000, 4000, 8000, 16000 Hz. Each band extends ±½ octave from its center: [fc/√2, fc·√2]. So the 1 kHz band covers ~707 Hz to ~1414 Hz.
1/3 octave bands
For finer resolution, each octave is split into three: edges at fc/21/6 to fc·21/6. The 31 standard 1/3-octave bands span 12.5 Hz to 20 kHz. Common in noise measurement, building acoustics, and consumer EQ (graphic equalizers).
Why ISO "preferred numbers"?
The ISO 266 standard adopts the R10 series from ISO 3 (preferred numbers in engineering): geometric progression by 101/10 ≈ 1.2589 per step. This is close to (but not exactly) 21/3 ≈ 1.2599. The R10 numbers are rounded to memorable values like 125, 160, 200, 250 — easier to work with than exact 21/3 ratios. Three R10 steps = factor ~2.0 (close to a true octave).
Octaves in music vs in acoustics
Music traditionally indexes octaves by note name (C0, C1, C2, …). 12-TET pitch classes within an octave step by 21/12 ≈ 1.0595 (a semitone). One octave = 12 semitones = 1200 cents. The "concert A" reference (A4 = 440 Hz) anchors all of this — shift it by N octaves and you walk along the keyboard.
Frequently Asked Questions
Why doubling a frequency sounds like the "same note"
f overlap heavily with those of 2f (the second harmonic of f IS the fundamental of 2f), so the brain identifies the two as the same pitch class.What's the difference between 1/1 and 1/3 octave bands?
Why aren't the band centers exact powers of 2?
How many octaves does human hearing span?
log2(20000/20) ≈ 9.97 — about 10 octaves. Compare to vision: visible light from 400 nm to 700 nm is log2(700/400) ≈ 0.81 octaves, less than one. The ear is unique among the senses in its enormous frequency range — 10 octaves of useful response — which is why we use logarithmic units (octaves, dB, cents) to manage the dynamic range cleanly.Can I shift by a fraction of an octave?
f' = f · 2N works for any real N. A semitone is 1/12 octave, a perfect fifth is ~7/12 octave (or exactly log2(3/2) ≈ 0.585 octaves in just intonation), a major third is 4/12 = 1/3 octave (equal-tempered) or log2(5/4) ≈ 0.322 octaves (just). This tool's slider supports 0.1-octave granularity; type in the field for exact fractional values.How does this relate to dB and cents?
1 octave ≈ 6.02 dB in amplitude terms (since 20·log₁₀(2) = 6.02). Useful conversion!