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Why do musicians use concert A, the A above middle C, as the standard pitch reference for tuning? Various national and international standards define the frequency of this note. For example, ISO 16 specifies that musical instruments should be tuned such that A4 is 440 Hz. Other standards specify A4 as 415 Hz, 435 Hz, and various other values. Wikipedia does a good job of explaining why they chose the various frequencies, but why do they define that particular note as the tuning standard?

A few standards do use other reference pitches, like scientific pitch with C4 = 256 Hz, but the vast majority define A4. Likewise, some kinds of bands tune to other notes, like B♭ for wind bands, but again most use A. Why? Wikipedia suggests that it’s because all orchestral stringed instruments have an A string. Is that the whole reason, or are there other factors?

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Some remarks: While the "a" is somewhat fixed, the octave is not. A violoncello will use the "a" of a deeper octave. Brass bands use "b" instead, since this is the base tone for many of the instruments. –  guidot Jun 3 at 7:59
    
Speculation, but the sound of "A" is natural to sing, could possibly have something to do with it. –  Meaningful Username Jun 3 at 9:43
    
Also speculation: 440 is evenly divisible 3 times (220 - 110 - 55) making the octaves slightly easier to read down to that level, no fractional hertz. –  David Wilkins Jun 3 at 15:49
    
@MeaningfulUsername Funny you should mention that – one of the things that prompted this question is that I noticed that the repertoire for tenors goes roughly to A4, excluding solos. –  Bradd Szonye Jun 3 at 21:55
    
@guidot Do you have a reference for the brass band tuning? And is that concert B, or is that B as played on a B♭ instrument? –  Bradd Szonye Jun 3 at 22:11

2 Answers 2

up vote 17 down vote accepted

Had to do some digging for this one.

First off, some informed speculation:

A, of course, is the first letter in the alphabet, so its as good a place as any to define a standard. Plus, as you say, it is one of the open strings in common on all string instruments (along with D and G). The A above middle C is also a relatively centrally-located pitch, accessible to a range instruments. An octave lower would have been inaccessible to flutes and oboes (and not an open string).

To expand on this: String instruments are relatively easy to retune, but also relatively quick to go out of tune (especially when strung with gut strings), so they should tune to the more stable wind instruments. The oboe was one of the first wind instruments to be regularly added to the orchestra (in the Baroque period), and, for whatever reason, it is now used as the pitch standard (there's another good question to ask). Oboes can't hit G3, therefore, we have the following set of constraints:

  • Open string on violin: G3, D4, A4, E5
  • Also an open string on viola & cello(8vb): G3, D4, A4 (no high E string)
  • Also available on the oboe: D4, A4 (no low G)
  • In a "comfortable" range on the oboe: A4(*)

(*) I am not an oboist, but I'm sort of assuming here that, at least on early instruments, the D4, which was the second-to-lowest note on the oboe, might have been a bit harsh sounding. I found a quote from Berlioz' Treatise on Orchestration which agrees with this notion: "The lower notes of the oboe, which sound ugly when exposed, may be suitable in certain harmonies of an eerie and sorrowful character..."

At any rate, I think the answer to your question will lie in discovering why the oboe is used as the reference pitch. Presumably, at least in the early Baroque, it would have been the continuo harpsichord (or organ) providing this reference, so maybe this shift coincided with the disappearance of continuo in the Classical era?

Some additional historical information that may be relevant:

In the early 6th century, when Boethius lists all the note names by letter, he starts (unsurprisingly!) with A as the lowest pitch. This presumably set a precedent for using A as a reference pitch.

In 1711, British trumpeter John Shore invented the tuning fork which allowed accurate tuning to a reference pitch. He even gave one to Handel, with a pitch of C=512Hz, corresponding to your scientific pitch.

In 1834, Johann Heinrich Scheibler, a silk manufacturer and acoustics researcher, invented a "tonometer" for accurately measuring pitches, based on an array of fifty-two tuning forks, spanning a range of pitches fro A3 to A4. Why did he choose A? I don't know! But this device allowed him to study a range of tunings in use at the time. He describes his tonometer in detail in Der Physikalische Und Musikalische Tonmesser, which is apparently available on amazon, if you fancy original sources and can read German.

Based on his studies, he recommended A4=440 to the Congress of Physicists in Stuttgart in 1834, which they accepted. The Streicher piano company also adopted this standard, manufacturing pianos with "440" stamped on the label. This wasn't the first attempt at standardized pitch, but due to Scheibler's tonometer, it was likely the most accurately measured standard up to that point. Nor would it be the last word in tuning; the French government passed a law on Feb. 16, 1859 requiring A=435, or "Diapason Normal" which would become widely adopted internationally.

For more reading:

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I'm pretty sure that A4 was already well established as concert pitch by the time Scheibler developed his system. It looks like tuning forks were already converging on A as the main tuning pitch by the mid-1700s. Handel had an A fork by 1740. –  Bradd Szonye Jun 3 at 7:59
    
That seems quite possible. I don't know if there's any way to know this beyond it just made sense. One trouble I was running into was that, for the sake of comparison, historical tuning forks are often reported in terms of what A4 would be relative to them, even if they themselves aren't in A. Both of the "for more reading" links also refer to a source: Alexander Ellis' History of Musical Pitch which looks to be available here: books.google.com/… –  Caleb Hines Jun 3 at 12:49
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I suspect that orchestras were using A to tune even before the invention of tuning forks. I found the comment that brass bands use B instead very interesting. Perhaps that would help to track down the evolution of such practices? –  Bradd Szonye Jun 3 at 18:24
    
Interestingly, Baroque pre-valved brass parts often (but not exclusively) used natural trumpets in D and natural horns in F. Both of these harmonic series contain an A (as either the fifth or the third). –  Caleb Hines Jun 3 at 18:31

I think there are two questions here:

  1. Why A?
  2. Why A=440?

The first is reasonably answered - to tune a string instrument with no frets, the tuning note needs to be that of an open string, which limits it to G, D, A or E (violin). It is not suprising that A became the standard.

The A=440 question is far less easy to answer. I play early music (mainly recorders), and to cover all early music I would need a set of recorders at renaissance pitch (A=415), a set at baroque pitch (A=440) and a set at French Baroque pitch (A=466). Considering that at a minimum a set is 4 wooden instruments, the outlay is not insignificant.

Evidently the standard pitch of orchestras has been creeping upwards; A=446 is not unheard of. In the 1960s, brass bands were pitched about a quarter tone sharper than A=440 (as well as most instruments being Bb, so 3/4 of a tone below concert pitch). Most bands decided to lower their instruments to (B flat) concert pitch by adding extra tubing, but this ruined the tone of many good instruments. But I think all modern brass instruments are pitched at (B flat) concert pitch.

So why A=440?? I don't think there is a definitive answer.

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Why A=440Hz is covered here: en.wikipedia.org/wiki/… . One advantage mentioned is that 440Hz is not a prime number and is therefore easy to produce in a lab, but there are certainly easier numbers to use than this. Three octaves down we have A=55Hz, which is exactly halfway between Noth American (60Hz) and rest-of the world (50Hz) mains frequencies. –  steve verrill Jun 3 at 11:26
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Right, the 440Hz part of things is well documented. I'm actually interested in the first part of your answer. I realize that A is not surprising, but why that note and not D, E, or G? –  Bradd Szonye Jun 3 at 18:20
    
This is pure conjecture, but I suspect A was chosen since it is roughly in the middle of the treble instrument (violin) range. So tuning the E string against A is easy (E is in the A major chord). Tuning the D string is a bit more complex (A is in the D major chord), and tuning the G string is a tad harder again, but possible for most players. But I am not a string player - anyone care to differ? –  kiwiron Jun 4 at 8:19

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