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This article suggests that accurate measurement of pitch wasn't possible until around 1870. Another source suggested that is was possible around the time of J.S. Bach. Does anyone have more info on this please?

EDIT: I am asking about the measurement of absolute pitch, in some kind of standardized unit such as Hertz.

Robin Andrews
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    Including a couple of relevant quotes from the articles would be helpful so that answerers don't have to read it/them in their entirety. – Aaron Mar 03 '22 at 20:46
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    It depends on what you mean by "measure accurately." Do you mean absolute or relative measurements? It was certainly not possible to quantify frequency in absolute terms before it was possible to measure seconds, so some time after the invention of the pendulum clock. But Savart's activities in 1834 certainly sound to me like the accurate measure of pitch. – phoog Mar 03 '22 at 20:51
  • This is a fascinating question, and the link makes a nice initial, non-scholarly, broad-overview first step into the topic. But agreed; for us to answer meaningfully, we have to nail down a bit more what "measure" means and what "accurately" means. Pythagoras *measured* the relationships of intervals—say, A vs D—quite mathematically, but it didn't matter to that discussion whether his A was 440 Hz. *Are* we talking about pitch standardization? Even then, John Shore's tuning fork helps you compare A to A, down to the cent, even if you're not actually counting cents... – Andy Bonner Mar 03 '22 at 21:47
  • I would propose that measure = produce an arbitrary reference pitch or report the pitch of a sounded tone, and accurately = within the tolerances of human perception. Although less accurate attempts would likely be worth mentioning too, if they preceded an "accurate" measurement. – Edward Mar 04 '22 at 00:03
  • @Edward the problem remains: how would you define accuracy? How/when can you define if a definition of pi is accurate? Even the most precise person would agree that, in some situations, 3 could be a valid assumption. – musicamante Mar 04 '22 at 05:35
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    About definition of accuracy: https://en.wikipedia.org/wiki/Accuracy_and_precision – ojs Mar 04 '22 at 09:22
  • Given 440Hz and 415Hz A and the mysticism around 432Hz, I'd say that at least 3 significant digits could be assumed – ojs Mar 04 '22 at 09:24
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    Instead of "accurately" you might re-word this questions as something like "measured in hertz" if that's what you really mean. Otherwise, explain what you mean by "accurate." – Michael Curtis Mar 04 '22 at 19:45
  • "Within the tolerances of human perception." By that, I mean that a 440Hz tone is accurate if it sounds just like an ideal 440Hz tone. That's all you could ever need in a musical context. – Edward Mar 04 '22 at 21:55
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    An early unit was "feet" for an organ pipe, as in "8 foot pitch". Of course it depends on the length of the foot and the exact construction of the pipe, but it gave a way to use measurable length to specify a pitch. – Mark Lutton Mar 04 '22 at 22:52
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    @MarkLutton excellent point. The pitch of an organ pipe also depends, of course, on atmospheric conditions, if you're looking for precision, but it's far less variable than a string. Pythagorean pitch theory uses length as its dimension of measurement but eliminates the need for absolute measurement of that dimension by dealing in ratios. There are too many properties affecting the pitch of a vibrating string for it to be a useful standard. – phoog Mar 05 '22 at 09:05
  • @Edward "a 440Hz tone is accurate if it sounds just like an ideal 440Hz tone": most people can't tell you whether a tone heard in isolation is 440 Hz or 441 hz. But anyone can hear the difference between a 440 Hz tone and a 441 Hz tone if they are played along with a second tone known to be 440 Hz. With two tones sounding simultaneously, you can detect even smaller differences in frequency if the tones are sounded for a long enough time. – phoog Mar 05 '22 at 09:10

2 Answers2

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In the article you linked...

By 1834 the Frenchman Félix Savart (1791-1841) was building giant brass wheels 82cm across, with 720 teeth. Savart’s contribution was a mechanical tachometer connected to the axis of the toothed wheel. He calibrated a rotational scale with the tooth rate, and for the first time demonstrated that specific tones were associated with specific frequencies.

...italics added for emphasis.

How does that not answer your question?

Michael Curtis
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  • Because it is a single source and others may disagree? Like I said, I heard that accurate measurement was possible in Bach's time, but I can't remember where. – Robin Andrews Mar 04 '22 at 21:21
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    @RobinAndrews, this is a Q&A forum, not a place to receive exhaustive research and bibliography. Look up Savart, frequency, pitch, etc. That lead me to search 'savart wheel' in Google Books and found confirming info. – Michael Curtis Mar 04 '22 at 22:12
  • Demonstrating that specific tones are associated with specific frequencies does not necessarily imply that it was possible to quantify the frequency. – phoog Mar 05 '22 at 09:14
  • Further to @phoog's point, European scientists had figured out that there was a direct correspondence between frequency and pitch as early as the 17th century. The trick was to make an absolute measurement of the frequency. [More details in my answer here.](https://music.stackexchange.com/questions/51265/at-what-point-in-history-did-the-relationship-between-pitch-and-frequency-become/) – Michael Seifert Mar 05 '22 at 15:34
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Looking at this page, history of sound waves, I would conclude that Fouriers work was a precondition for any abstract measurement.

Savart produced sound waves with a chosable frequency, but a comparison via a human ear and correction (tuning?) iterations were required, which I would consider as sort of an indirect or relative measurement. Similar other references for comparison existed earlier, but were not adjustable, like the tuning fork invented around 1711.

So I would be surprised, to find a measurement deserving that name in time of Bach.

Mechanical frequency meters can be imagined (stack of resonators with step-wise resonance frequency, measurement by checking which one vibrates most) but I have seen real world examples only for very small frequency ranges as for alternating current here and its not clear, how to adjust the principle to undirected and poorly selectable wave as sound.

guidot
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  • If Savart could quantify the rate of revolution (a question whose answer I haven't been able to find) then he would have been able to quantify frequency. I would also argue that measuring relative pitch by comparison to a known reference frequency should not be discounted, since that can yield very precise results. – phoog Mar 04 '22 at 15:38
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    At Savart's time marine chronometers were accurate to 0.5 seconds per day, which means five significant digits. – ojs Mar 04 '22 at 20:28
  • @ojs I thought we were still in the 15-seconds-per-day era then. Do you have a reference? Regardless, is there any evidence that Savart measured (or could measure) r.p.m. with that degree of precision? – phoog Mar 05 '22 at 09:12
  • @phoog I'm not sure why this is important to you, but for one example you could check the Kingston trip under https://en.wikipedia.org/wiki/John_Harrison#H4. Note that this happened in 18th century, which is 100 years before 1800s. – ojs Mar 05 '22 at 10:36