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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 '15 at 20:26
up vote 15 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 '15 at 20:07

Enharmonic notes are different, e.g. G# and A-flat, even though it is not always the case that instruments make different sounds for these different notes. These different note names are used to indicate differences in terms of the melodic or harmonic content of the music.

For example, in A minor, G# is frequently encountered as the "leading tone" back to the tonic. Notating this sound with an A-flat would mis-represent what is going on in the music. Similarly, writing an E major chord as E,A-flat,B does not correctly the harmonic relationship between the root of the chord and the third (or the fifth if it were indicated with a C-flat). This would just be a notational convention if it weren't the case that many instruments can and do express the differences between enharmonic notes in terms of the sounds that they make.

A key instrument in this regards is the voice: it is the most commonly encountered instrument with continuous pitch adjustment, and composing and analyzing vocal music was a key facet in the historical development of western music theory which is the context in which this question arises.

Going back to the leading tone in A-minor, a vocalist singing a capella will tend to raise the pitch of that note, relative to the corresponding piano note, a component of "expressive intonation". Slightly sharpening the note makes it's resolution to the tonic (A) more satisfying. Similar considerations apply in terms of harmonic content: an E-major chord is E,G#,B -- the G# indicating the note a third above the E; in a choral group, the people singing the G# will (usually) select there pitch to be consonant with the E's (which is different from the equal-tempered G# on a piano). These considerations apply to other continuous pitch instruments, in particular unfretted string instruments in an orchestra.

Going further would require delving into the historical aspects of tuning, temperament and intonation as well as overall description of functional harmony and melody...

Even though the keyboards and guitars that are the primary instruments used in popular music do not make different sounds for these different notes, accurately describing what is going on in the music, whether melodically or harmonically, requires differentiating between enharmonic notes.

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Adding onto Sergio's excellent answer: There are multiple ways in which enharmonic notes (notes of essentially the same pitch with different names, such as A# and Bb) come into play, as it were. One is with respect to different tunings. Sergio's answer cites a table that concerns two tunings, equal and just. There are in fact lots and lots of tunings, many of which involve different compromises between equal temperament and Platonic, "natural" tunings (based on integer ratios). And so you'll see various differences between enharmonic pitches, so that the F# that shows up in a D7 won't necessarily equate with the Gb that shows up in an Ab7 (even though C shows up in both chords). An instrument tuned to play the former chord may not be able to play the latter well, and vice versa.

That example highlights another way in which enharmonic notes make a difference: music theory. This has no intrinsic impact on how the note sounds; rather, they are differences in how the note is used or interpreted. A D7 chord consists of the notes D, F#, A, and C. If you were to "spell" it D, Gb, A, C, that would sound essentially the same, but it would be marked wrong on an exam, because that second pitch is not being used as a Gb, but as an F#. That D7 will typically resolve to a G chord—major or minor—and in either case, the pitch a half-step down from G is being used as the seventh or leading tone of that G scale.

This also explains some accidentals in actual music that typically mystify beginning students, such as double-sharps and double-flats. Why notate something Fx, when G sounds the same? Such a situation often arises when you have a secondary dominant: a dominant chord resolving to a chord other than the tonic. If you're writing something in B Major, say, and you have a D# Major (V/vi) resolving to g# minor (vi), that D# Major should be notated D#, Fx, A#—not D#, G, A#, even though those pitches happen to be the same, because the note that resolves to G# should be Fx, not G.

This also applies to variously altered chords. The sharp 9 and flat 13 of "the" altered dominant seventh chord (aka tritone substitution) are shifted from their natural position, so that for our good ol' D7 chord, the sharp 9 would be E#, not F, and the flat 13 would be Bb, not A#. And so on.

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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 '15 at 19:59
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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 '15 at 22:58
    
@leftaroundabout leading tones are also lower in just intonation; they are also usually the major third of a chord. – phoog Jan 12 at 18:12
    
@phoog: that's matter of considerable dispute. Pablo Casals used to insist that leading tones be rendered almost a quarter-tone higher than just intonation, to make it clear that you have not a harmonious third in a consonant chord, but rather an energic forerunner note, leaving the unrequiting dominant for the tonic. – leftaroundabout Jan 12 at 19:12
    
@leftaroundabout then Pablo Casals was not employing just intonation. – phoog Jan 14 at 1:04

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