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How could the Greek (Pythagoras et al.) measure the frequencies - as they didn't have a mobile app?

They didn't have a tuning fork or any other standardized measure. But even without standards they were able to find out the ratios: by measuring strings or weigh pieces of iron. But how could they count the frequencies?

Or - with other words - when was the first tune pitch defined as something about Hertz >400 and <450?

I am suspicious that they were really able to define the wavelength and frequencies and that the also could define the pitch of the tone G. But the longer I think about it the more I believe they had the abilities.

I will try out some tests myself and when I'll find the results I'll tell you here the answer.

Albrecht Hügli
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    My question may be related to this one: https://music.stackexchange.com/questions/66957/how-did-pythagoras-and-ptolemy-measure-the-relative-pitch-of-musical-notes – Albrecht Hügli Oct 12 '19 at 09:10
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    Why restrict it to just the Greeks? No-one had a mobile app for this until about 15 years ago! – JimM Oct 12 '19 at 12:04
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    But we didn't find wires of telephone lines on the archaeological excavations. So they might have had already wireless transmission, don't you think? – Albrecht Hügli Oct 12 '19 at 13:23
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    This can't be a serious question. – jjmusicnotes Oct 12 '19 at 14:18
  • This probably is better suited to hsm.SE (history of science and math) – Carl Witthoft Oct 12 '19 at 14:22
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    The first definition of "A" as being in that range was rather a couple thousand years after Pythagoras. – Carl Witthoft Oct 12 '19 at 14:23
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    @jjmusicnotes: this question is meant quite seriously (apart oft mobile joke! - that‘s only mentioned to make it more interesting and attraktive to the younger generation. – Albrecht Hügli Oct 12 '19 at 14:40
  • I don't see how this question is appreciably different from the one you link to in a comment, and I would answer this one with the same [answer](https://music.stackexchange.com/a/90042/2257) I wrote for [History of standardization of pitch and tuning: measuring waves](https://music.stackexchange.com/q/90025/2257). Why shouldn't this be closed as a duplicate of either? What distinguishes it from them? – phoog Oct 12 '19 at 15:19
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    ok, phoog, I have to admit there it is much different, but meanwhile I've been thinking a lot what I would have done if I had been an ancient Greek and I've also learnt more about the measures of time and length in China, Egypt, Greek and Roman. – Albrecht Hügli Oct 12 '19 at 15:47
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    Perhaps then you can share what you know about measurement if time, particularly with regard to precision. As far as I can see it was not possible between the middle ages and the invention of the pendulum to measure time precisely enough to have numerical measurement of frequency. I doubt ancient technology allowed sufficiently precise measurement of time, while precise measurement of length is relatively simple. – phoog Oct 12 '19 at 16:03
  • I've been thinking a lot about this problem. I agree that it was not necessary to define the pitch as 440 or to count the vibrations. But I had even ideas how they could have defined minutes and seconds ... if they had wanted... but this is not a question I meant to discuss here. Now I'm pretty sure that the tone C and a tone that we call as such today was possible. Of course not in Hertz. The logical question to my answer I would give will be: Were the ancient Greek the able to tune their instruments near +/- 10 Hertz of the pitch in the middle age or today? – Albrecht Hügli Nov 07 '19 at 21:23

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There is no historical evidence that the ancient Greeks ever measured the frequencies of sounds. They developed their theories of intervals using the relative lengths of strings or pipes, which are an equivalent way to relate intervals to geometrical ratios of lengths.

There is no obvious reason why the Greeks could not have invented the siren (see below), and by 300BC they already had reasonably accurate water-driven clocks, but in general they were more interested in philosophical discussion about how things ought to work, rather than scientific experimentation to find out how they actually worked.

The method of sound frequency measurement in Hz used by Helmholtz in "The Sensations of Tone" (first published 1863) was a siren, which is basically a rotating disk with a pattern of holes through which air is blown. It is easy to measure the rotational speed using a clock, and hence know the fundamental frequency of the sound produced.

I remember seeing a demonstration of exactly the same measurement system in high-school-level physics, back in the 1960s. Of course electronic frequency measurement was possible at that time, but (like modern tuning apps) it was a "magic black box" compared with a mechanical system whose working could be understood.

Helmholtz's other experimental method was to use sympathetic resonance to demonstrate the existence of a particular overtone in a sound, but that does not measure the frequency in Hz except by an independent calibration of the resonator itself.

Before Helmholtz, pitch standards (pipes, bells, tuning forks, etc) were simply compared with each other, and not with any absolute measurement. As a result, almost every geographical area in Europe had is own local pitch standard, though travelling professional musicians, and the practical range of human voices, tended to keep them more or less aligned with each other.

A mechanical strobe tuner is not a practical method of tuning musical instruments. The tuning fork was invented in 1711, and before that time the usual pitch standards were bells or reed pipes.

For church music, pipe organs provided a "standard" simply because they were impossible to retune quickly. Ironically the pitch of organ flue pipes (similar to a flute or recorder) is temperature dependent while the pitch of reed pipes is not, but in practice the reed pipes were (and still are) retuned to match the flues to compensate for temperature changes, because that is more practical.

guest
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  • Ummm, what do you mean 'a mechanical strobe tuner is not practical' ? Strobe usually implies strobed light, and the StroboConn was the tuning device in every school in the 60s and 70s. – Carl Witthoft Oct 12 '19 at 22:13
  • @CarlWitthoft Likely means "was", else the sentence doesn't really have anything to do with the question. – user45266 Oct 12 '19 at 22:18
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The earliest mechanisms which indicated or measured seconds weren’t constructed until the mid 1500’s. And, of course, they were not accurate until the discoveries and inventions of Galileo and Huygens (et.al.) in the next century. So there were no measurements or frequencies in anything per second (such as Hz) till after that. Before that, relative audio frequency tuning was done either by ear, or by sympathetic resonance against some other instrument or resonant tuning device in the local community. e.g. different places made instruments tuned to different local standards.

Various Western orchestras were tuning at a local frequency somewhere around 425 to 475 Hz in the 1800’s. (Possibly earlier to make it easier on traveling composers and musicians.) (And likely measured using mechanical strobe tuners.) According to Wikipedia, 440 wasn’t standardized in the U.S. until 1936. This was so that fixed tuning instrument makers didn’t need to make slightly different instruments for different major Western orchestras around the world.

Strobe tuners don’t count sound cycles directly. They use a clockwork-like mechanism capable of counting revolutions per second. And the tuner looks for synchronizing some visible display of the sound waveform against the revolving mechanical reference. (Or these days, a computer simulation of the same.)

hotpaw2
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  • Did you mean 1836? Helmholtz notes that the 440 Hz standard was established by a German standards body in the early 19th century, but I do not remember the exact year. Of course, it was not widely adopted until later, and I don't think it was ever universal. – phoog Oct 12 '19 at 15:59
  • Different European countries and cities used different tuning “standards” in the 1800’s. – hotpaw2 Oct 12 '19 at 16:02
  • So what precisely happened in 1936? Was it the first time an international standards body recognized the 440 Hz standard? Different orchestras use different pitch standards even today. Why does the adoption of a German national standard 100 years earlier not count as standardization? Can you link to the Wikipedia article that is the source of your claim, or at least identify it? – phoog Oct 12 '19 at 16:48
  • If you're talking about the article [440 Hz](https://en.wikipedia.org/wiki/A440_(pitch_standard)), it appears that the 1936 event was the adoption of 440 Hz by an American standards body. That has no more authority than the 1834 adoption by the German standards body, except inasmuch as it contributes to an increased consensus of national standards bodies. It's also unclear why you put "standards" in quotes. A national standard established in the nineteenth century is still a genuine standard. – phoog Oct 12 '19 at 16:53
  • Regarding your edit, why would standardization "in the US" contribute to "fixed tuning instrument makers [not needing] to make slightly different instruments for different major Western orchestras around the world"? I'm not being nitpicky for its own sake. Rather, I think this could be a great answer but in its current state it is not. – phoog Oct 12 '19 at 17:12
  • A good separate question would be where and when did mass production of musical instruments for International distribution and sale scale up. – hotpaw2 Oct 12 '19 at 17:14