Curious Disconnect in Heaton's History of Pitch Article

[Matt_DeMeritt]

Hello,

I've been doing some research and stumbled upon an interesting disconnect, or call it what you will--a historical discrepancy perhaps. I do have a theory to account for this, but I would like to set that aside for now as I am still trying to gather as much information as possible. It's a simple matter, and allow me to illustrate it with the following quote from Barrie Heaton's article on the History of Pitch, found here:
http://www.piano-tuners.org/history/pitch.html

"Pythagorus used a pitch of 256Hz on his monochord. The study of mathematics was known as philosophy in the time of Plato.

Modern science began to measure pitch accuracy in cps or cycles per second around 1834 when a group of distinguished German physicists using a mechanical stroboscopic device found that the pitch of the tuning fork that they were testing was at A440 cps. It was only later that the frequency was expressed in Hz."

Ok, so if science didn't know how to accurately measure pitch until around 1834, how did Pythagoras use a pitch of 256Hz?

A logical question, is it not? Or am I missing something here? If so, I would certainly like to get your thoughts on exactly what.
You see, the claim that Pythagorus tuned to 256Hz is rather prevalent among those who write about such matters, but few if any stop to question how he achieved such a precicely enumerated pitch. Is there any evidence to point to Pythagoras using 256Hz? Such evidence should explain HOW this was acheived at such an early age. Thank you kindly in advance for your input!

Matt

[Bill Kibby]

We'll have to leave that to Barrie to answer, I confess I don't spend a lot of time wandering around this site, so I want to thank you for pointing out the idea of a mechanical strobe, it goes some way to answering a question I have often raised, about how Victorians measured frequency. This was presumably a follow-up to Stampfer's stroboscope of 1832?

However, there are many references to particular frequencies used at earlier dates. Some were achieved by measurement in retrospect, on an old organ or tuning fork etc., but not all can be explained satisfactorily in this way, and some quote decimals of 1Hz.

Isn't it also a bit much to expect that a randomly-made tuning fork just happened to have a pitch of such a round figure as 440? May we know the source of that idea?

The American Music Industry adopted Pitch A440 in 1925, I can't recall any earlier use of it, but I will check.

C=256 is known as "Philosophical Pitch", and certainly in an arbitrary area like pitch, this is the only one with a solid logic, so it surprises me that it was not adopted. It is based on a theoretical pitch where a "note" C has a frequency of ONE. Doubling the octaves, we arrive at Pitch C being 512Hz. I have never heard of any connection between this and the ancient Greeks.

Hz is, as you say, a modern term for frequency, following the trend towards honouring famous scientists by naming units after them, and I don't think anyone is suggesting that Pythagoras used it! I had a debate with OFCOM engineers about the appalling electrical interference we suffer here, and they couldn't understand how I knew that the ticking was not 6Hz. Sometimes, in this high-tech age, we lose sight of the way people coped without electronics, perhaps there was a simple, practical way of starting with a long string vibrating once a second, and dividing the length to get the octaves, or simply plucking the harmonics.

[vernon]

pitch is one of many disputatious subjects.Academic heres there is no confidence that Pythagoras ever existed.
There are plenty of learned books on the history of the subject so it need not be rehearsed here in detail.
Bill rightly observes that historic pitches have largely been determined by refernce to ancient organs and antique tuning forks.
The huge historical variation brings into the equation the question of "key".
Without getting mired in "temperament " common sense requires that we observe "key" as a very floppy subject as pieces were composed in the past mostly at different pitches.Today's pitch can be a tone or two adrift from say,Mozart's pitch,depending on not only which Country he was playing in but even the City!
Some Cties had two pitches--one for the Duke and one for the church.

[Bill Kibby]

My mistake, 1834 was when Scheibler recommended A440.

[Matt_DeMeritt]

Thank you very much for the replies. Bill, the idea of taking a very long string vibrating once per second and working from there, that is somewhat along the lines of what I was thinking. One of the pieces of the puzzle that I was able to uncover in my research is that the second of time originated, to a very, very high degree of accuracy, in ancient Sumeria. To make a long story short, the second of time is how long it takes for a pendulum with a string length of one Sumerian kush to make a swing, with a deviation of only 3 milliseconds. So we have a metronome basically, then what else is needed?

There would need to have been an understanding by the ancients that pitch is vibrational. Secondly, there would need to have been a basic understanding of beat frequencies. Also, musical ratios. Take all of these components together, and all you need is a little math and a little trial and error to obtain a precise frequency. Now this only works with the lower frequencies (or I should say it works far, far better), like for example 32Hz and 36Hz. Sounded together, these two tones produce beats at a frequency of 4Hz. They also represent the ratio of 9:8.

So 4Hz beat frequency, 9:8 interval...follow? There is only one pair of frequencies that will match this criteria, 32Hz and 36Hz. No other pair of frequencies will work, and by this method, I surmise, the ancients could have measured frequency. Their 256 cycles per 'Sumerian kush' would thus be very close to our own measured 256Hz.

Pythagoras spend time in captivity in Babylonia, where we have learned that the so-called 'Pythagorean temperament' or intonation really originated from. It is also known that these ancient cultures had some stringed instruments that were very large, with string lengths even taller than a man's height.

Considering the precision of the Sumerian timekeeping system, the almost implicit reflection therein of musical ratios and frequencies relating to a tuning system based on 3:2 and 256Hz, and the taken-for-granted assertion that Pythagoras tuned to 256Hz, the only thing missing that would really make a lot more sense out of this was an ancient method for obtaining frequency. So I worked backwards to put this solution together. What do you think?

[Bill Kibby]

The first rule is to never underestimate Pythagoras. He is said to have worked on tuning and temperament, according to my college notes of 1963! I would have imagined that only Stephen Fry would know what a Sumerian kush is. I don't think it is practical to work audibly in such low frequencies. I would think more in terms of the fact that (assuming we know seconds) it is very easy for a musician or a piano tuner to estimate 8 beats a second, by tapping once a second, then doubling and redoubling. A string could be tuned to that rhythm, and then the 8th harmonic could be sounded to give 64Hz, a more recognisable note. Another string could be tuned to this, and its 4th harmonic would give us 256Hz.

I have no idea what the accuracy would be!