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Can you explain me the relation between note frequency and wire tuning? I see, for tuning violin, 440 hz is used and called an A4, while a 432 hz can also be used and that too called an A4. But, don't each note in an octave have a particular fixed frequency? What I am implying is, for example, if frequency of C in an octave (taking fouth octave) is X hz, be it I tune the wire to 432 hz or 440 hz, should the C's frequency still be fixed at X hz?

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    They're generally called strings rather than wires (in English)! – Tim Aug 25 '18 at 16:36
  • I misunderstood 'wire' as an English word. – NEWTONINSPIRED Aug 26 '18 at 17:09
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The frequency of C will always be relative to your chosen A. Depending on your tuning system, it will be somewhere around 1.2 times the frequency, a ratio of 6:5. A justly-tuned minor third has exactly that ratio, while the ratio of an equal-tempered minor third is the fourth root of two, which is about 1.1892. A Pythagorean minor third is 32:27, or about 1.1852.

We can easily calculate the frequency of these three definitions of C for any frequency of A:

| Frequency of A   | Pythagorean C  | Equal-tempered C  | Just C
|------------------|----------------|-------------------|-------
| 432.00           | 512.00         | 513.74            | 518.40
| 440.00           | 521.48         | 523.25            | 528.00

The violin has infinitely variable pitch. The point at which you stop the string for C will vary depending on which of these Cs you want. This in turn will depend on the harmonic and melodic context. But because the ratios are the same, the point at which you stop the string will be the same regardless of the frequency of the open string.

That is, wherever you put your finger to play the 528 Hz note when the string is tuned to 440 Hz, that will be the same place where you'll put it to play the 518 Hz note when the string is tuned to 432 Hz.

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A = 440Hz has become close to a standard tuning pitch throughout several parts of the world. However, A, historically, has been several other pitches in different parts of the world, and is still not exactly 440Hz when one considers various orchestras' tuning in various locations.

However - as long as everyone who is playing together in a particular ensemble all uses the same datum point of A = xxxHz, then it will sound fine. Once that has been established, all other notes, C3, F4, G5 etc., will be automatically in tune with a properly tuned instrument.

I could, for example, tune my guitar down (or up) a bit or a lot, and as long as each string is in tune with the others, playing it in isolation , it'll sound in tune with itself. Should someone else want to play along as well, they would have to use the tuning that my guitar was in, otherwise it's going to sound awful ! This was one of the reasons A = 440Hz was chosen. It could have been 437, 448, and as long as everyone adheres, there's no problem

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