A4 = 440 Hz: What Your Tuner's Reference Does

One note holds up the whole system

Musical pitch is relative. An octave is a doubling of frequency, a fifth is close to a ratio of three to two, and a semitone in equal temperament is a step of about 5.95 percent, but every one of those is a relationship between two notes, not a fact about either one. Ratios alone will tell you how far apart two notes are and never where they sit.

So the system needs one note nailed down by decree. That note is A4, and the decree is 440 Hz. From there everything else is arithmetic: A5 is 880, A3 is 220, and the twelve semitones in between each multiply by the twelfth root of two. Middle C works out at about 261.63 Hz not because anyone chose that number but because it is what falls out of the maths once A is fixed.

Which is why your tuner has the setting. Move the peg and everything moves with it, in formation. That is the crucial part to internalise: changing the reference does not put you out of tune with yourself, it puts you out of tune with anyone who did not change theirs.

The number has not always been 440

Standard pitch is a surprisingly recent piece of infrastructure. Before the nineteenth century there was no standard at all; pitch varied by city, by decade, and by whether you were in a church with an organ or a theatre with a band, ranging over something like a whole tone from end to end. Music was written to be transposed as necessary, because it had to be.

Through the 1800s pitch crept upward, driven partly by orchestras chasing brilliance and partly by the plain fact that higher-tuned instruments cut through more. Singers complained, loudly and reasonably, because the top of a written range does not move when the pitch does. France legislated a diapason normal of A = 435 Hz in 1859 in response. International agreement on 440 arrived in the twentieth century and was formalised as an ISO standard, which is where the number you see today comes from.

The takeaway for a practicing musician is not the history but the attitude it implies: 440 is a convention that works because everyone agreed to it, not a law of nature. It can be departed from, deliberately, when there is a reason.

The three reasons to change it

• Your ensemble tunes somewhere else.Many European orchestras sit at 442 or 443 Hz for a brighter sound. Individual orchestras have their own house pitch, and it is a question you ask before the first rehearsal rather than discover during it. Being “correctly” at 440 in a room tuned to 443 makes you the one who is out.
• You are playing baroque repertoire on period instruments. A = 415 Hz is the modern working standard for early music, and it is almost exactly a semitone below 440, which is convenient, because it lets a harpsichord be shifted and lets modern players read the notes as written. Some ensembles go further, to 392 for French baroque or 466 for certain German repertoire.
• The recording you are playing along to is not at 440. This is the one that catches people out. Older records, tape-mastered releases and anything speed-adjusted before release can sit meaningfully off concert pitch. If every string reads perfectly green and the track still fights you, stop retuning and check the track.

What to do about an off-pitch recording

You have two options and they are not equally cheap.

You can retune your instrument to the recording. Set the tuner's reference until the recording's pitch agrees, then tune to that. This is correct, it is what session players did for decades, and on a guitar or violin it takes a couple of minutes. On a piano it is not an option at all.

Finding the number is the part nobody explains. No tuner detects a recording's reference pitch for you. You find it by ear in about a minute. Play a held note from the track out loud into the tuner, ideally a sustained bass note or the root of a ringing chord, and read the cents. If it sits a few cents sharp of a note name, walk the reference up from 440 until the cents settle on zero; a few cents flat, walk it down. The scale above tells you where you are going to land: 8 cents is 442, and anything near 100 means the whole track is a semitone off rather than mistuned.

Or you can shift the recording. Pitch-shifting playback by a fraction of a semitone leaves your instrument alone and takes about a second, and unless the shift is large it is inaudible as processing. If the recording is a long way out (say it was recorded a whole semitone low), this is also how you play along in the written key without transposing on the fly. The details are in changing the key of a video.

Rule of thumb: retune the instrument if you are going to spend a week with the piece. Shift the recording if you are going to spend twenty minutes.

About 432 Hz

You will meet the claim that 432 Hz is a natural or healing frequency and that 440 was imposed for suspect reasons. The historical parts of that story do not hold up (pitch standardisation was a long, dull, international process driven by orchestras and instrument makers), and the physical claims have no evidence behind them.

The musically honest version is simpler. 432 Hz is about 31 cents below 440, roughly a third of a semitone. Any music tuned down slightly sounds marginally darker, slacker and mellower, and some people prefer that. That preference is a real, legitimate reason to use it. It just is not the same claim as the one usually being made, and if you play with anyone else you will need them to come with you.

Cents, and how far out is far

A cent is one hundredth of a semitone, and it is the unit worth thinking in because it is proportional: 440 to 442 Hz is about 8 cents, and so is 880 to 883.5, even though the second gap is twice as many Hz.

• Under about 5 cents: inaudible to nearly everyone in nearly every context.
• 5 to 15 cents: audible as a slight sourness in sustained chords, especially on thirds. This is where an out-of-tune string starts to make a chord churn.
• Over about 15 cents: everybody hears it, including people who say they are not musical.
• 100 cents: a semitone, or one fret.

For scale: 440 versus 442 is 8 cents, 440 versus 432 is 31, and 440 versus 415 is 101, an entire semitone. That last one is why baroque pitch is a different world and the other two are refinements.

The fastest way to develop a feel for these sizes is to listen to them against a sustained note, where small errors turn into an audible wobble rather than an abstract number. That method is practicing with a drone, and it is the single most useful intonation habit there is.

Then forget about it

For almost everyone, almost always, 440 is the right answer and the setting should never be touched. Its value is in the three cases where nothing else explains why you sound wrong, and for those three, nothing else will fix it. When a recording refuses to agree with a perfectly tuned instrument, the recording is allowed to be the thing that is wrong.

Every string of twenty-odd instruments, with note, octave and frequency at A = 440, is in the tuning reference.