A440 vs A432: converting the audiophile debate into an actual cents number
A friend deeply invested in the 'A432 sounds more natural' online debate asked me exactly how far off that tuning actually is from standard A440 — working through the logarithmic cents formula gave a concrete, less mysti
We write the way we argue on the bench: exact factor, one sharp trap, one worked example you can re-check.
A friend deeply invested in the 'A432 sounds more natural' online debate asked me exactly how far off that tuning actually is from standard A440 — working through the logarithmic cents formula gave a concrete, less mystical answer than the online forums.
Start with the exact relationship. Everything else is just arithmetic and knowing when to round.
The factor that settles arguments
This is the relationship our converters use. Screenshot it if you have to — just stop re-deriving it from a half-remembered blog post.
Cents = 1200 × log2(432 ÷ 440) — a logarithmic relationship applied to the two competing tuning standards
Write that line once at the top of your notes. Every later arithmetic step should point back to it instead of inventing a friendlier number mid-stream.
The mistake that keeps showing up
Assuming the difference between A440 and A432 is negligible just because 8 Hz sounds small, without converting to cents to see the actual perceptual gap — nearly a third of a semitone is clearly audible to trained musicians.
I still write the unit next to every intermediate value. It looks pedantic until it catches the one swap that would have shipped wrong.
- Write down the known value in A432 (Hz).
- Confirm the target unit is really cents relative to A440, not a similar-looking one.
- Apply the factor: Cents = 1200 × log2(432 ÷ 440) — a logarithmic relationship applied to the two competing tuning standards.
- Round only at the end, to the precision your tool or spec supports.
Worked example
You want to know exactly how far A432 tuning deviates from standard A440 concert pitch, in cents.
1200 × log2(432 ÷ 440) = 1200 × log2(0.9818) ≈ −31.8 cents.
That's about 31.8 cents flat relative to A440 — noticeably out of tune to most trained ears, though smaller than a full semitone (100 cents).
If you want a second check, invert the conversion and see whether you recover the original quantity within normal rounding.
Quick reference table
| A432 (Hz) | Calculation | cents relative to A440 |
|---|---|---|
| 1 | 1 × — | — |
| 2 | 2 × — | — |
| 5 | 5 × — | — |
| 10 | 10 × — | — |
Use the table for speed once you trust the factor. Do not use it as a substitute for understanding which definition of the unit you are on.
Why the exact number matters
Understanding the real cents gap between competing tuning standards separates genuine acoustic discussion from tuning myths — 31.8 cents is a real, audible, measurable difference, not a rounding error.
Precision is not about showing off decimals. It is about making sure the shopping list, the machine setting, and the acceptance check are all describing the same physical quantity.
Pocket recap
Run the actual logarithmic cents formula rather than judging by the raw Hz difference — 432 Hz is about 31.8 cents flat of 440 Hz, a real but sub-semitone gap.
Keep the converter link nearby for the next time the same debate shows up in a group chat. Re-typing the factor from memory is how the wrong cousin of a unit sneaks back in.
Try the converters mentioned in this article
FAQ
What is the exact A432 (Hz) to cents relative to A440 factor here?+
Cents = 1200 × log2(432 ÷ 440) — a logarithmic relationship applied to the two competing tuning standards
Should I round partway through the calculation?+
No — carry full precision through the multiplication and round only the final answer, to the precision your tool, gauge, or spec actually supports.
What's the single biggest mistake people make with this conversion?+
Assuming the difference between A440 and A432 is negligible just because 8 Hz sounds small, without converting to cents to see the actual perceptual gap — nearly a third of a semitone is clearly audible to trained musicians.
This article was written by The Turbo Unit Converter engineering desk (Applied units & field metrology) and last reviewed on 2026-07-18 against NIST SP 811 and the BIPM SI Brochure. Read our full editorial policy.