Most musicians know that middle C is 220 Hz and frequencies change logarithmically, doubling for every octave. That’s simple enough to set with our current technology, but what about centuries ago? I’m guessing there wasn’t a 220 Hz standard, but how were musicians in sync with each other? Did they hear other musicians enough that they developed an ear for certain notes? Was there an official tuning fork that travelled the land, or did they manage to make many identical tuning forks? I’m guessing the latter was the case for the 1700’s and later, but before then?
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The A above middle C is 440 Hz. 220 Hz would be the A an octave below that, not middle C.
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The 440 Hz standard only dates to the 1950’s. Before that, all bets are off. Typicall in an old church, everyone else would tune their instruments to the organ, since the organ can’t easily change its pitch. String quartets and the like just tune to each other. If you look back to the 19th centurty and earlier, you’ll find all sorts of pitch pipes and tuning forks, and most of the time they don’t match each other at all.
In the 19th century the “standard” pitch rose quite a bit. “A” would have been a lot lower than 440 Hz before this time, probably somewhere around 380 Hz (and again, would vary quite a bit).
According to the printing on the side of my old tuning fork, it was the official pitch of the “A. F. of M” in 1917, and adopted by the US Gov’t in 1920.
I did some poking on the net, and it seems that the current ISO standard dates to 1955. However, the US apparently did adopt it as a standard in 1920, so you are correct. There was also an international conference of some sort in 1938 which also settled on 440 Hz. There was an earlier standard of 435 Hz by the American Federation of Musicians (which I’m assuming is the A.F. of M on your tuning fork), and I found one web site which referenced 440 Hz as the “higher german pitch” as compared to the earlier 435 Hz standard.
France standardized on 435 hz in 1859. One web site claimed that this was the first attempt to create a standard pitch.
I didn’t find any reference online indicating when or even if the A.F. of M. switched from 435 to 440. Does yours specifically say it is 440 or could it possibly be 435?
I should be more clear. This is a “C” fork, at 523.25, which is the C corresponding to A440. I assume that the A=440 pitch is being referred to.
I thought that the scale wasn’t completely predictable, because of the “tempering” of the chromatic scale? That is, on the keyboard instruments particularly, with their great range of notes, they aren’t tuned with precisely the same value of tones & semi-tones throughout, to create a more melodious effect? Hence Bach’s collection of pieces, “The Well-Tempered Clavier”?
(Course, it’s all just theoretical to me - pipers just have 9 notes to play with. Much simpler. 
)
Depends what you mean by “predictable”.
In just intonation, the octave is still a double, but the notes in between aren’t the same as the pitches you would get constructing scales in other keys. Just intonation means that a scale is a given set of rational ratios of the root, for instance, 3/2 for a fifth. Equal temperament refers to dividing the octave into equal steps (12 in the western scale, with frequencies forming a geometric progression multiplying by the twelfth root of two for each step). This allows you to play in any particular key with intonation slightly off in each one, and off in the same way. So called “just intonation” means that a major third should be a ratio of 5/4, for instance - (twelfth root of two) ** 4 is not quite this ratio.
This Wikipedia article has a good writeup on the subject:
Note the table of ratios for just intonation.
Comparison of today’s pitches with the pitches of pipes on old church organs going back to the 18th century show that pitch has risen over the centuries. Which is funny, when you think about it. You know how a band might play a song in the same key for three verses, and then move it up a key in the last verse, to keep it interesting? We’ve apparently been doing the same thing to all of musicdom.
Well that answers my question quite well.
I’ve extensively researched the subject, and 380 Hz is a bit low for 19th century tuning forks. Maybe 17th or perhaps the 18th century, but not the 19th. Let me see if I could dig up some references.
Here’s one site. As you can say, tuning forks varied greatly over the years, going from as low as A309 to as high as A455+. I know that certain organs were tuned as high as A480. But, in general, they seem to have averages well in the 400s, closer to 420 or 430 than 380.
Orchestral pitch has shown a steady increase over the years. but it is fairly subtle. But the mid-1800s, something around A435 was a pretty standard concert pitch. It wasn’t until 1955, as mentioned, that A440 became an ISO standard, although many orchestras have already been tuning to this for at least a decade or two.
Even today, some orchestras (especially European ones) tune slightly sharp, with A444 being relatively common.
Northern Piper—equal temperament is exactly what makes the frequencies mathematically predictable, to use your word. The logarithmic ratio between two notes of the same interval are the same across the scale.
Bach’s Well-Tempered Clavier is another story, as most historians seem to agree that this work wasn’t meant for today’s equal temperament, but rather one of several possible temperaments during Bach’s time which allowed a keyboard instrument to be played in all keys, although each key would have a different character to it because the ratios between intervals would slightly chance depending on the key.
That’s what they taught in my “Physics of Music” class – that a piano tuned to the precise notes sounds “wrong.”
It only sounds “wrong” if you play the wrong notes. 
The musical intervals we know and love today were discovered by the ancient Greeks (Pythagoras in particular) who noticed that whole number ratios of frequencies (or lengths of string, for the geometers) generated the best sounds.
Pythagooras was especially fond of the octave (2:1), the perfect fifth (3:2) and the perfect fourth (4:3). There are a bunch of other ratios to make 12 tones in an octave, but let’s stick with those three for a minute.
Let’s say you want to tune your piano. You start with middle C, which we will arbitrarily set at 400Hz for the sake of convenience. A fourth above middle C is F. The ratio is 4:3 (or a factor of 1.333…), so we’ll set that to roughly 533Hz. A fifth above middle C is G. The ratio is 3:2 (or a factor of 1.5), so we’ll set that to exactly 600Hz. Finally, an octave above middle C is the next C, a ratio of 2:1, or 800Hz.
Good so far, right? But now we run into a problem. Let’s say we want to tune the next octave of F, G and C. That F should be a perfect fourth above the 800Hz C, and it should also be an octave above the 533Hz F. So let’s see what we get:
533Hz x 2 = 1066Hz
800Hz x 1.333 = 1066.4Hz
Gasp! There’s a slight difference. If we tune it to 1066 exactly, then playing an F-to-F octave will sound delightful. But playing a C-to-F fourth will sound terrible. Similarly, if we tune it to 1066.4, we can play that high fourth, but not the octave. Naturally, the more octaves you try to tune, the worse the differences get. If you wanted to play a piece in a different key, you had to re-tune your piano so those intervals would be correct, which would throw the other stuff out of alignment. And if you were a composer, you’d better make sure that the instrument you were writing for could support all your intervals correctly simultaneously.
Equal temperament solved this problem by retaining the exact 2:1 ratio for the octave, and spacing the 12 tones inside equally instead of by their interval ratios. (Take the frequency of a note, multiply it by the 12th root of two, and that’s the next note.) The notes are very slightly off from their true ratios, and the intervals sound very good. Even better, the error is exactly the same in every octave, instead of getting worse the further out you go. Finally, you can transpose any song and it will have exactly the same intervals in a different key.
Some musicians say equal temperament is a bastardization, especially if they’re playing older music that was written for one of the more difficult systems. But most, I think, accept it as a compromise that more than makes up for its flaws.
My college wind ensemble always tuned slightly higher than 440 to match the mallet instruments which happened to be a little high. (We used an electronic tuner instead of a tuning fork).
Are there samples anywhere on the web that would have a piece of music played on an equal-tempered keyboard, and the same piece played on a non-equal-tempered keyboard, so that we could hear the difference?
Late 19th and early 20th century wind instruments often had crooks to change from “low pitch” to “high pitch”, depending which standard was used.
Woodwinds also frequently had multiple middle sections to conform, as well. (Crooks generally apply only to brass, I suppose. Maybe bassoon?)
I think you’re right. I should have said brass instruments. I guess a crook would be a curved piece of tubing. I don’t know what they called them on woodwinds.