That’s it. Who decided, when, why?
From Wikipedia: In 1939, an international conference recommended that the A above middle C be tuned to 440 Hz, now known as concert pitch. This standard was taken up by the International Organization for Standardization in 1955 (and was reaffirmed by them in 1975) as ISO 16.
There’s an extensive summary there of how pitch standards have varied over time, and the reasons for this.
Note that A=440 is by no means universal. See, for example, this discussion. This causes lots of hassles when orchestras travel (e.g. a piano has to be entirely re-tuned - a serious chore).
Bagpipe A is between 470 and 480Hz, which is higher than standard B-flat. (That would be specifically the Great Highland Bagpipe.)
Anyway, while GorillaMan gave a more comprehensive answer, I’ll point out that it has to be something, so why not 440?
I believe that in the 19th century it was generally closer to 425 or so. The audiences liked a “sharper” sound and so orchetras gradually increased their pitch. Sopranos and tenors are not amused by this, since they are asked to sing nearly a half tone higher than what the pieces were written for. S half tone above 425 is 450, but I have heard some European orchestras tune their A to 452.
Now? :dubious: A-440 was an informal standard years before it was an official one, at least in the band instrument world (which a lot of musicologists probably don’t pay much attention to). It was around at least as far back as the teens when it was known as Low Pitch, to differentiate it from High Pitch, another standard that put A at 456 or 457.
A while ago I read a fascinating article in the Wall Street Journal (can’t find it now) about “Temperament.” I suggest you do some Googling (the Wiki article isn’t very good).
In a nutshell, the theoretical frequency divisions in a standard scale don’t match up with reality. When you divide your frequencies up into a standard twelve-note scale (c; d flat/c sharp; d; e flat/d sharp; e; f; g flat/f sharp; g; a flat/g sharp; a; b flat/a sharp; b) based on a logarhythmic proportion, they don’t come out evenly. If you determine your scale based on perfect fifths (each note has a frequency ratio of exactly 3:2 to the fifth note previous), you don’t end up at a perfect octave when you get to your twelfth note.
So a “Temperament” is a set of frequencies determining what notes you WILL use for a given piece of music. Most composers will use some default temperament, but occasionally composers will design their own temperament, or even vary the temperament for a given piece.
You write a song, and change the temperament so that A equals whatever you want.
No, when you divide a scale into twelve parts based on a logarithmic proportion, they come out exactly even (by a ratio of the twelfth root of two); that’s what equal temperament is (twelve equal half steps per octave, based on a logarithmic scale).
You’re right that the whole number ratios don’t add up. An easy way to see this is to add up two major seconds (9/8), which yields a major third of 81/64, rather than 5/4 (the proper just-intoned third).
Thank you for stating it much more clearly than I did.
Of course dividing it up based on logarithmic proportion makes it even. But doing it this way skews the whole-number ratios, which skews the harmonies.
The WSJ article I mentioned discussed a composer (Bach?) who made a huge deal of temperaments, designing his own and so forth, in order to get his harmonies just the way he wanted. I wish I could find it.
I see what you were saying now.
Right, equal temperament is fundamentally out of tune. The advantage is that it’s equally out of tune in every key, as opposed to, say, mean tone temperament which is relatively (to equal temperament) in tune for C major, but gets progressively more out of tune the farther away from C you get (which is why you’ll rarely, outside of J.S Bach, see Baroque music in more than three or four flats). If you can get your hands on a programmable keyboard, set it to mean tone in C, then play an F-sharp major chord (or do the same in just-intonation. shudder).
Have you got more detailed information on this? I’m not going to hold up Wikipedia as a reliable source, but nor do I have access to a copy of Grove to fill in some of the gaps.
Regarding temperament: few instruments really do play in equal temperament as a matter of course. String instruments certainly don’t, even though they may not realise it. I’m often talking to pupils about making something ‘as minor as possible’, i.e. pushing minor 3rds, 6ths and dominant 7ths as low as possible, and leading notes the other way. Similarly making the 3rd degree of a major key as high as possible ‘without it sounding out of tune’. Out of context this can sound nonsensical, but not when the adjustments are being made, especially in an ensemble situation. I can’t speak with authority on wind or brass instruments, but I have talked with some players who say similar things happen to a lesser extent.
Of course, when you then come to play serial music, where each note of the chromatic scale takes equal importance, you have to readjust back into equal temperament again.
Randy, if you’re interested in the history of equal temperament and other tuning systems, I highly recommend this book. It explains the history and the math in lucid detail and should be required reading for any music theorist.
That’s fine and all, but I don’t see what temperament has to do with A being set to 440. You could have A440 in any temperament you want.
I had a conductor that said that many people were worried about the increased pressure the higher tunings put on the older instruments.
For example a Strad was designed when “A” was much more flat than it is today. The amount of additional pressure that tuning to today’s “A” puts against the body could start causing harm to these older instruments that were not designed to withstand those sort of pressures.
So, among other reasons, eventually the orchestras of the world decided to come together and stop trying to outdo each other and just decide that A = 440-445.
We all know A should really be 432, not 440 (or, God forbid, higher!). Here are some good reasons, from this luminary:
He directs us all to Jimi Furia’s Furthur Explanations, so you know he isn’t one of those LaRouche loonies on about “Verdi Tuning”.
Harry Partch and Wendy Carlos have both created their own tuning systems. If you’re interested in this kind of thing, their music is worth checking out.
My trusty old Yamaha DX7 had a couple of dozen tunings in it including (IIRC) a 24 note equal temperament tune which was amazing. I had a companion book with sheet music specially written for the tune.
Now I’m going to have to dig that out.
I think my DX11 has a 48 note equal temperament, and I imagine that the DX7 (which is a higher-end instrument) would as well.
My voice teacher once did an opera written in quarter tones. They had two rehearsal pianos tuned a quarter step apart. Apparently it was awful; it just sounded out-of-tune.
24-note equal temperament is more commonly known as quarter tones, and is not uncommon in modern classical music.
This is software which creates different intonations, although I’ve never got around to experimenting with it myself.
You must have the black DX7II - the originals brown ones didn’t have microtuning.
I remapped my TX81Z to reverse the keyboard - low notes to the right, high to the left. I got the idea from something Joe Zawinul did with an ARP 2600. Very cool effect!