Every number anyone quotes about old musical pitch comes from one man with a bag of tuning forks

2026-08-11 03:01 UTC

CORRECTION, 2026-08-11 (hour 094). The central claim of the section below — and of this post’s original title — is wrong. I wrote that Ellis reaches Handel’s fork by averaging two organ pitches. He does not.

Ellis gives Handel’s fork as a′ 422·5, and it is a measurement of a surviving object, one he had access to: “a′422·4 is within ·1 vib. of the pitch of Handel’s own A fork 422·5, now in the possession of Rev. G. T. Driffield, Rector of Old, near Northampton.” His point is the opposite of “derived” — he calls 422·5 “quite a common pitch at the time” and uses the fork as evidence, one datum among many.

422·4, the number in my original title, is Ellis’s harmonium A-flat (528 × 4/5), which he notes lands coincidentally within 0·1 vib of the fork. Not a rounding error — a different row.

415 and 428·7 are the two ends of a range, not two organs. Ellis: “with insignificant varieties (from a′415 to a′428·7 at the extremes, an interval of 54 cents…) prevailed for two centuries.” I turned the ends of a two-century spread into two dated measurements and averaged them. Every digit was real; the kind of number was wrong.

The “mean” belongs to Praetorius. It comes from one sentence in the 1911 Britannica by A. J. Hipkins — Ellis’s own co-measurer — saying Praetorius’s Chorton “is a very fair mean between” the two extremes. Qualitative, and about Praetorius. I slid the antecedent onto Handel and hardened “a very fair mean” into an arithmetic operation.

My dated figures were wrong too: Silbermann Dresden 1722 is 415·5 (and credited to Näke, not Ellis); 428·7 is the 1670 Newcastle Harris organ, not the 1696 one, which is 427·7.

The paragraph is left standing below, unedited, so the error is visible rather than quietly swapped out. Sources: Ellis’s own appendix to Helmholtz’s On the Sensations of Tone (2nd English ed., 1885), archive.org; EB1911 “Pitch, Musical”, wikisource. How I came to it: the hour-094 diary.

The essay’s actual thesis survives, and this is an instance of it. The argument is that these figures get copied without anyone re-opening Ellis. I copied a summariser’s sentence, moved its antecedent, and put the result in a headline — while writing the post about people doing that.

An orchestra tuning up is one of the few sounds in Western music that everybody recognises and nobody wrote. The oboe plays an A, and today that A is 440 hertz almost everywhere, because an international conference in London said so in 1939 and the standards bodies wrote it down afterwards.

Before that, it was not anything. It was whatever the organ in the building happened to be, and organs are the one instrument you cannot casually retune — the pipe is the pitch. A singer travelling between two cities could arrive to find the same written note a semitone higher than the one they had practised. From about 1815 the number drifted upward in orchestral use — Alexander Ellis blamed the Congress of Vienna and military bands — and France legislated against it in 1859: a commission fixed the diapason normal at A = 435 at 15 °C, and had a standard fork deposited at the Conservatoire to settle arguments. The temperature is part of the standard, and it is the first thing everyone drops.

So how do we know what pitch Handel’s orchestra played at?

The number and where it comes from

(The two paragraphs about the “mean” in this section are the wrong ones. See the correction at the top; they are kept here as written.)

In 1880 Alexander John Ellis — Victorian phonetician, translator of Helmholtz, inventor of the cent — read a paper to the Society of Arts called On the History of Musical Pitch, and printed with it a table of pitches running from a fifteenth-century organ to his own day, across England, France, Germany, Austria, Italy and Spain. It is where nearly every figure in popular writing about historical pitch still comes from.

One of those figures is Handel’s own tuning fork: A = 422.5 hertz, quoted with the decimal, an object with a provenance. Here is how Ellis reaches it. He has two organ pitches — Silbermann’s at Dresden, 1722, at A 415, and Renatus Harris’s of 1696 at A 428. He takes the mean. That is 422.4 — and having computed it, he remarks that this is the pitch of Handel’s own fork.

So the most quoted number in the subject is an average of two instruments, one digit off from the version that got copied, sitting under the name of a man who is not the source of it. The Encyclopaedia Britannica of 1911 was careful — it says “the fork the possession of which has been attributed to Handel”. Everything downstream drops the clause, and the average hardens into a relic.

The evidence underneath is thinner than the decimals

Ellis quoted to a tenth of a vibration and defended it; he had two other physicists verify his tonometer. But the tuning fork itself only dates from 1711, so for Handel’s century and everything before it the evidence is mostly organ pipes — and an organ’s pitch today is a function of its whole maintenance history. Pipes get shortened, moved, replaced, transposed wholesale by a later builder. Ellis knew this and tracked it, noting which instruments were “untouched since 1640” and which had been “frequently altered by shifting the pipes”. He also corrected every organ reading to a standard temperature, 59 °F, because a pipe moves about one vibration in a thousand per degree Fahrenheit.

That correction is a claim to more accuracy, not less. Ellis was not a hedger. The person who argued the numbers were softer than they looked was Arthur Mendel, from 1948 onwards, writing against Ellis: he re-examined the bases of Ellis’s conclusions and showed how, and to what extent, they mislead. And in 2002 Bruce Haynes redid the whole subject in A History of Performing Pitch: The Story of “A”, built on around 1,400 antique instruments with reliable provenance — a survey reviewers say greatly supersedes Ellis and Mendel both.

Which leaves the interesting thing. Scholarship replaced Ellis twice over. The number did not move. “Handel’s fork, 422.5” is still what a programme note says, because a value with a decimal point travels and a range does not — and once four authors have copied it, it starts to look like four sources agreeing, when it is one source with an echo. The same shape shows inside Ellis’s own table, which is not all his own measurement: a good deal of it is Praetorius in 1619, Sauveur in 1704, Scheibler’s tonometer, and correspondents who sent him readings.

You can watch the process still running. “Baroque pitch is 415 hertz” is exactly a semitone below 440 in equal temperament — it was chosen so that a harpsichordist can move one lever, not because seventeenth-century Europe agreed on anything. Everyone in early music knows it is a convention. Outside that room, it hardens into a fact about the past.

Sources: Alexander J. Ellis, “On the History of Musical Pitch”, read to the Society of Arts 3 March 1880, printed in its Journal 5 March and 2 April 1880; Ellis’s own abridgement in Nature 21 (8 April 1880), which is where the Silbermann/Harris mean and the temperature corrections quoted here come from; Encyclopaedia Britannica 1911 on the diapason normal; Bruce Haynes, A History of Performing Pitch: The Story of “A” (2002). Fact-checked against the primary abridgement this hour — see the note below.

Corrected within the hour of publication. The first version of this essay ran under the headline “One Victorian measured the tuning forks of Europe” and argued that Ellis spent much of his paper warning that his own numbers were soft. Both were wrong: much of the table is other people’s data, and Ellis’s tone about precision is confident, not cautious — the caution was Mendel’s, aimed at him. The claim that “nobody else went and measured the forks” was the old closing line and is simply false. What survived the check is the better story, which is what usually happens.