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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
    
A frequency difference is what lies between most notes –  user10164 Apr 24 at 20:26

2 Answers 2

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
    
I'll add that the difference isn't only in pitch. Even in equal intonation, in which the pitches of A# and Bb are the same, you would use one or the other in certain contexts. You don't have a Bb in the F# major scale, except as an accidental, because it already has a B natural. Even as an accidental, it has a different meaning than an A#: it's a diminished 4th, not a major third (though they happen sound the same in equal intonation). This might not make sense to many amateur musicians, but when you start seeing music in terms of phrases and not just individual notes, it becomes important. –  Greg Jackson Apr 24 at 20:07

I think Answer #1 is more complex than the question asked. The direct answer is that no, A# and Bb are not the exact same notes. Though they are close, A# is slightly higher in pitch than Bb. It is possible to play both of these notes at their correct frequencies on some instruments, such as a violin or a singing voice, because the player can control the pitch of each note very precisely. However, the player has less precise control of note pitch on other instruments, such as guitars and pianos, and it would not be practical to add enough strings or frets to include all possible sharps and flats. As a compromise, guitars and pianos are tuned "temperately", meaning that they use the same note for both A# and Bb, and the frequency of that note is somewhere between the exact frequencies for A# and Bb. Most listeners do not notice that tempered notes are not precisely on pitch.

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This answer is misleading. In equal temperament, A# and Bb are different notes that are on precisely the same pitch (and so share a key on a piano, for example). It's not that they're "off" from their "correct frequencies", it's that equal temperament defines them to be identical pitches. Instead of thinking of just intonation as "right" and equal intonation as "wrong" or "nearly right", it's important to recognize that they're different systems of temperament that have specific purposes. –  Greg Jackson Apr 24 at 19:59
    
And it's not generally true that A♯ is higher than B♭. You're probably referring to a leading tone A♯ that's “gravitating” towards its B resolution. But apart from such leading notes, just-intonation actually tends to make sharps lower, compared to 12-edo tuning (because a sharp-note is more likely to be the third of a major chord). –  leftaroundabout Apr 24 at 22:58

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