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In guitar or generally in any musical instruments, what is the difference between sharp notes & flat notes?

For example : Are A♯ & B♭ the same? And are C♯ & D♭ the same? Does that make any difference in terms of the sound produced by instruments?

Any help appreciated :)

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We have several other questions related to this, definitely look at the one Sergio links and search out the others :) –  Matthew Read Aug 30 '13 at 16:38

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up vote 10 down vote accepted

Actually it depends on the instrument.
Some instruments can produce different notes for A# and Bb, others can not.

There are different ways to intonate. On one side you have a just or harmonic intonation which is built on harmonics scale (each tone has a a matemathical relation between the base tone), this makes each tonality have its own intonation; on the other side you have temperate intonation which makes a compromise between frequencies and different keys, dividing the interval octave in equally distance semi-tones, to make possible one instrument to play in different keys, always using the same notes.

Here is a good explanation about this. Alsto worth to read this.

In practical terms, to be able to fine tune a chord (just/harmonic intonation in the guitar or different instruments playing/singing together) you must raise or lower some tones. Often the third in the chord needs adjustment. For example the third in F# chord (A#) should be higher than a Bb. If your instrument can't play it (like a piano) you land on tempered intonation, if you can play it (or bend the tone guitar/harmonica/etc) then you can get a just/harmonic intonated chord.

Wheat Williams posted this very clear table on his answer to another question. Notice how the third in the chord is higher or lower depending on the intonation model you are using. (the A# in my example of the F# major chord).

enter image description here

About the mathematical relation between tones in the harmonic scale:
(source here)

enter image description here

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The explanation doesn't make sense. F chord third is A, there's no A# in it. Are you saying that A# and Bb may be slightly different notes, depending on the tuning of a particular instrument ? Pianos will be generally tuned in a temperate manner,so they will sound good in any key. –  Tim Aug 30 '13 at 8:06
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I meant F# (major), corrected the answer. And in this case I play A# on the violin, or singing, with a different intonation (higher) that I would play a temperate Bb. Pianos are limited instruments regarding intonation models (just intonation or temperate intonation). Piano sounds good on a temperate intonated ensemble, but not on a baroque ensemble using just intonation. –  Sergio Aug 30 '13 at 8:49
    
The piano wasn't around in the Baroque period, so it would be incongruous and anachronistic to play such music with a piano. –  Tim Aug 30 '13 at 10:47
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True, but even in other context the problem comes up. When I play with string quartet, or with vocal music, we often discuss if we play temperate or just. If a piano is with, then there is no discussion :) –  Sergio Aug 30 '13 at 11:22

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