# Historical tuning standards?



## CMayo

Pop musician here, new to the forums. I watched a YouTube video about the Baroque lute today and learned about Baroque tuning, given as A=415hz. A bit of Googling turned up info on different tuning standards through the years and I found references to A4 ranging from 392hz to 465hz 

I can understand how tuning standards varied, but how did the guy making the tuning forks 500 years ago make a perfect A415 or A440 fork without instrumentation of some sort, i.e. strobotuner, digital tuner, etc.?


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## mbhaub

Here's one method: they would take a long strip of paper and coat it with carbon. Then attach a fine needle or quill to a tuning fork. Clocks were reasonable accurate. Put the tip of the needle on the carbon paper, move the paper at a constant speed, strike the tuning fork. Tiny (very tiny) waveforms are engraved on the paper. Count up the number of waves over a certain period and lo and behold! you can calculate the cycles per second! It's a nice physics lab experiment. 

Then there's this method: if you know the length of a string, theoretically you can figure out the frequency it vibrates at. It's a bit more complicated since the thickness of the string, the tension and other factors like density make a difference. Back then, steel wound strings were years off, and animal intestines were the source of strings. At least they were somewhat consistent.

It's an interesting question that few musicians ever think about. I still marvel at someone like Bach whose ear was so acute that he could tune a harpsichord octave into twelve equal partitions without any electronic assist.


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## CMayo

mbhaub said:


> Here's one method: they would take a long strip of paper and coat it with carbon. Then attach a fine needle or quill to a tuning fork. Clocks were reasonable accurate. Put the tip of the needle on the carbon paper, move the paper at a constant speed, strike the tuning fork. Tiny (very tiny) waveforms are engraved on the paper. Count up the number of waves over a certain period and lo and behold! you can calculate the cycles per second! It's a nice physics lab experiment.
> 
> Then there's this method: if you know the length of a string, theoretically you can figure out the frequency it vibrates at. It's a bit more complicated since the thickness of the string, the tension and other factors like density make a difference. Back then, steel wound strings were years off, and animal intestines were the source of strings. At least they were somewhat consistent.


Fascinating. Thanks for your reply!


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## Enthalpy

Suggestion: there were very few founders of church bells in a country. They could agree among themselves over a tune, and then all bells could serve as a secondary pitch standard. Stable over time, consistent over all locations, available in every town at every hour or better.

As an engineer, I'd like to comment that explaining now how people did centuries ago is extremely presuming. Activities took decades or centuries to mature by dozens of skilled and creative people. Then in 2021, someone who ignores the technology available then, doesn't have the skills, isn't more clever than people then, is alone and spends between 5min and 20years, has about zero dot nothing chance to reinvent the ancient method.

The usual result is "We didn't understand how they did". Which, unfortunately, some commentators translate with "It was impossible", and this is horribly wrong. We ignore how the pyramids were built, but they're here.

About accuracy: in 1761, John Harrison built a marine chronometer accurate to 24 seconds over 9 days, that is, 1/30 000, or 30ppm.
John_Harrison#H4​and, err, I dunno even how they checked the accuracy of said chronometer back then. But it's badly better than what we need to tune a music instrument.

Just a siren could convert an accurate slow mechanical rotation into a sound.


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## CMayo

*Solved!*

I used the Library of Congress's "Ask A Librarian" feature a couple of days ago, and this reply arrived this morning. And... I've looked up The Story of A before; even the e-book is $130.00!

Before tuning forks, instruments that were not fixed in pitch, such as stringed instruments, were tuned to the pitch of the instruments that were fixed in pitch, such as recorders, oboes, pipe organs, etc. A fixed-pitch instrument is tuned mathematically. The resonating chamber is measured and the measurements tell the maker what pitch is produced in that size resonating chamber. Because of the potential variations in fixed-pitch instruments caused by extreme weather changes, and other factors, pitch standards varied wildly from country to country and sometimes from town to town. If you would like to know more about the subject, there is a terrific book by music historian Bruce Haynes called "The History of Performing Pitch: The Story of A." You can use the Worldcat database to find the book in a nearby library. The link to the book's Worldcat record is here. http://www.worldcat.org/oclc/925740829


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