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Octave Frequency Calculator

This octave frequency calculator shifts 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

Hz
oct
−10 oct0+10 oct
Common reference frequencies

Result

Shifted frequency
Shift in octaves / semitones / cents
Nearest note
Nearest 1/1 octave band
Nearest 1/3 octave band
1/3 octave band edges (fc/21/6 to fc·21/6)
Formula
f′ = f · 2N
1/1 octave band edges: fc/√2 to fc·√2
1/3 octave band edges: fc/21/6 to fc·21/6
Frequency ruler (log scale, 16 Hz – 20 kHz; large ticks = 1/1 octave bands, small ticks = 1/3 octave bands)

Octave shifts from base frequency (±5)

ShiftFrequencyNearest note

ISO Preferred Octave Band Centers

1/1 Octave (Hz)1/3 Octave (Hz)
12.5, 16, 20, 25
31.531.5, 40
6350, 63, 80
125100, 125, 160
250200, 250, 315
500400, 500, 630
1000800, 1000, 1250
20001600, 2000, 2500
40003150, 4000, 5000
80006300, 8000, 10000
1600012500, 16000, 20000

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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. This octave doubling means any frequency produces a note that sounds "the same" but higher when doubled, and the same but lower when halved. The math is simple — f′ = f · 2N for N octaves — but the consequences ripple through audio engineering, room acoustics, and psychoacoustics. The log-scale frequency ruler above spans the full audible range, showing how audio frequency bands are arranged across the 10 standard octaves.

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. To see exact note frequencies at each octave, use the note to Hz converter with adjustable A4 reference.

Octaves in room acoustics and EQ

In room acoustics, octave-band measurements are essential for diagnosing room modes (standing waves), characterising reverberation time (RT60), and specifying sound absorption materials. A broadband noise floor is routinely broken into 1/1 or 1/3 octave bands for noise surveys and building acoustic ratings. On the signal-processing side, a typical 31-band graphic equalizer places its sliders at ISO 266 1/3-octave centres (20 Hz, 25 Hz, 31.5 Hz … 20 kHz), and parametric equalizer Q factors are often specified in octaves — e.g., Q = 1.41 corresponds to a bandwidth of approximately one octave (since bandwidth in octaves ≈ 1/Q × 2/ln(2) for gentle curves). Understanding octave math helps you set crossover frequencies, EQ points, and octave-smoothed FFT displays without guessing. The interval calculator extends this to arbitrary semitone intervals if you need finer resolution than a full octave.

Frequently Asked Questions

Why doubling a frequency sounds like the "same note"
The basilar membrane in the inner ear has a roughly logarithmic mapping from frequency to position. Doubling frequency shifts the peak of vibration by a fixed distance along the cochlea — the same physical "step" regardless of where you start. Plus, the harmonics of a tone at 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?
An octave (1/1) is a 2:1 ratio. A 1/3 octave is 21/3 ≈ 1.26:1 — three of them stack to make one octave. For acoustic measurement, 1/3 octave bands give finer spectral resolution (31 bands across the audible range vs. 10 for 1/1). EQ pedals and rack EQs are often 1/3 octave (31-band graphic EQs). FFT analyzers typically offer 1/1, 1/3, 1/6, 1/12, and 1/24 octave modes.
Why aren't the band centers exact powers of 2?
Because ISO 266 uses the R10 preferred-numbers series (geometric progression by 101/10, not 21/3). The exact 1/3 octave step would give 125 → 157.5 → 198.4 → 250... but ISO rounds to 125 → 160 → 200 → 250 (R10 numbers). Three R10 steps multiply to 1.995, very close to 2 but not exact. The benefit is memorable round numbers; the cost is a small (~0.5%) deviation from "true" octaves.
How many octaves does human hearing span?
From 20 Hz to 20 kHz is exactly 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?
Yes — the formula 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?
All three are logarithmic measures of ratios. Octave = factor of 2 in frequency. Cent = 1/1200 octave = factor of 21/1200 ≈ 1.000578 (pitch). dB = 20·log₁₀ of an amplitude ratio (intensity). Note that dB is base-10 log while octaves/cents are base-2 log: 1 octave ≈ 6.02 dB in amplitude terms (since 20·log₁₀(2) = 6.02). Useful conversion!
How do I convert an octave shift to semitones or cents?
Multiply by fixed conversion factors: 1 octave = 12 semitones = 1200 cents. So a shift of 0.5 octaves equals 6 semitones (a tritone in equal temperament) or 600 cents. A shift of 1/12 octave equals exactly 1 semitone. Going the other way: cents ÷ 1200 = octaves. These conversions are exact within 12-TET; in just intonation the ratios differ slightly. Most digital audio workstations use cents for fine-grained pitch correction and octaves for coarser transposition.
What is octave equivalence and why does it matter for audio engineering?
Octave equivalence is the psychoacoustic principle that tones separated by a 2:1 frequency ratio are perceived as "the same pitch class" — the note A at 110 Hz, 220 Hz, 440 Hz, and 880 Hz all sound like "A" despite being four distinct frequencies. In audio engineering, this matters because room modes often occur at octave multiples of the room's fundamental resonance: if the fundamental mode is at 40 Hz, related modes appear near 80 Hz, 160 Hz, and 320 Hz. Identifying the base frequency and using this octave shift tool to trace its harmonics helps target EQ cuts and bass trap placement.
How are 1/3 octave bands used to set graphic EQ crossover points?
A 31-band graphic equalizer places each fader at an ISO 266 1/3-octave centre frequency (20 Hz, 25 Hz, 31.5 Hz … up to 20 kHz). To find the crossover frequency between any two adjacent faders, compute the geometric mean: √(f₁ × f₂). For example, between the 1000 Hz and 1250 Hz bands the crossover is √(1000 × 1250) ≈ 1118 Hz. Knowing band edges (fc/21/6 to fc·21/6) also helps you set parametric EQ bandwidth to cover exactly one 1/3-octave band rather than spilling into neighbours.