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Quoting the Wikipedia article:

The notes C♯ and D♭ are enharmonic (or enharmonically equivalent) notes. Namely, they are the same key on a keyboard, and thus they are identical in pitch, although they have different names and different role in harmony and chord progressions.

The paragraph above strikes me as a paradox, I fail to see how anything other than pitch defines a note, ergo if the pitches are identical there is nothing more to say.

I have a decent basic understanding of melody and scales, but not harmony and chords. Can someone please explain how naming a note C♯ instead of D♭ would have any consequences at all?

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5 Answers 5

up vote 11 down vote accepted

The primary answer to your question is that although pitch defines the basic frequency of the note, there is—at least in common-practice tonal music, and many other styles too—an entire other trait called function. A C# and a Db are the same pitch (at least on the piano, these will often have slightly different tunings when played by unfretted string instruments or sung by vocalists etc.), but the C# is implying a need to resolve up to D while Db implies a need to resolve down to C. Not every composer or notater is as careful to maintain this distinction, but it's definitely the default.

As others have pointed out, different keys have different expectations for the diatonic pitches. One would expect to see C# in, say, A Major, but Db in Ab Major. In the rare case that a Db happens in A Major, it will be there specifically to imply a chromatic resolution to the (otherwise foreign to the key) C natural.

One of the great beauties of this particular notation system is that composers can indicate more than simply which buttons to press, or fingers to put down or notes to sing. Composers and arrangers can also show specific function of each and every note just what enharmonic choices they make. One sweet side effect of this is that a composer can imply one kind of movement or resolution, but then frustrate the tendency for dramatic effect while still easily informing the performer about how to interpret the notes.

Here's an example from the literature of an enharmonic change being used by the composer to signal a modulation. It's from m. 133 of the first movement of Beethoven's Grande Sonate Pathétique.

m. 133, Beethoven Pathétique, enharmonic modulation

Please note that, although the key signature is C minor, this particular excerpt is firmly in G minor, as can be seen by all of the Bbs, F#s, and A naturals. Compare the second and third measures of this excerpt. In measure 2 Beethoven writes an F# fully diminished seventh chord (F#, A, C, and Eb). There's a voice exchange as it moves to the final 32nd note chord—that is, the Eb in the bass moves down to C while the C in the soprano moves up to Eb—but the harmony is the same. This is a viio7 chord in G minor, and it resolves normally to i with the G minor triad on beat 4 (well, technically, the resolution was on beat three, but the upper voices hold suspensions and retardations until beat 4). Now look at the third measure. It begins with the same F#dim7 as the previous measure, but the last 32nd note chord and the following quarter note are different. They are now a D#dim7 (D#, F#, A, and C), but—except for a slight rhythmic change in the bass—these two measures would still sound exactly the same to a listener until the final beat. That's because a D#dim7 and an F#dim7 are enharmonically equivalent, one just has a D# where the other had an Eb. However, the function of these two chords is completely different: whereas the F#dim7 wants to move to Gm including a downward resolution of the 7th, Eb, to D, the D#dim7 wants to move to Em including an upward resolution of the root, D#, to E. In fact, the entire next section of the piece is in the key of E minor, which is quite distant from both G minor and the original key of C minor.

The listener doesn't know about the change until the new unexpected resolution on beat 4, but the pianist is alerted to the change early via the enharmonic shift in the notation. More importantly, Beethoven would have learned about distant resolutions such as this from teachers (potentially Haydn?), method books, or other composer's music specifically in terms of the types of modulations made available by enharmonic respellings like this: using diminished seventh chords, German augmented sixths, pure melodic resolutions, etc.

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Are you saying it's because, as well as renaming the given note, other notes in the scale are renamed to fit the scheme of sharps/flats, but given that the note is in being used a different key it's distance from the tonic gives it a relative pitch which functions differently and coincidentally indicates a different relationship-by-name to other notes? –  spraff Sep 7 at 7:59
    
@spraff Really good question, but no, that's not what I'm driving at. (Although it is definitely true that instruments without fixed pitches can and do play enharmonic notes with different tunings when the situation warrants.) I'm saying that C# vs. Db is somewhat analogous to pair vs. pear in the English language—they generally sound exactly the same, but nevertheless have different meanings. Further, much like in a pun, I can exploit the tension between how it sounds and how it functions. –  Pat Muchmore Sep 7 at 11:37
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It might also make sense to compare "pear" and "pyrus". They refer to the same thing, but which you use in a given utterance says something about what you're trying to say. Or "Clark Kent" and "Superman"; the individual is the same, so what difference does it make which term is used? Quite a lot, actually. –  Joshua Taylor Sep 7 at 20:51
    
Thanks a lot, Pat, but do you think you could point to a couple of extracts of music which demonstrate this? –  spraff Sep 19 at 11:25
    
@spraff I added an example by Beethoven, as well as an explanation, to my answer. Let me know if it makes any sense. –  Pat Muchmore Sep 19 at 13:38

On many non-keyboard instruments performers will play slightly different notes; these slight differences reflect/determine how these notes behave in a given harmonic and melodic context. In at least some cases, these differences are related to (approximations of) just intonation; in other cases there are ideas of expressive intonation, which again result in the performer playing these notes slightly differently. Even in the context of fixed pitch, equal temperament instruments, using the different alternate notes indicates which of these behaviours are implied.

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To the existing answers, I'll add that it isn't only enharmonic notes which have this issue of different functions. Let's say you're in the key of C, and you want to play an 'A'. That A could function as (among other possibilities) the root of an A minor chord (a minor 3rd below C), the third of an F major chord (a major 3rd above a perfect 4th above C), or the fifth of a D minor chord (a perfect 5th above a major 2nd above C). In just tuning, the first two would imply a frequency ratio of 5/3 (or ~1.667), while the later might (depending on how the 2nd is defined) imply a frequency ratio of 27/16 (or ~1.688). In equal temperament, as on a modern piano, these end up being rounded to the same pitch, 2^(9/12) (or ~1.681), but the ear/mind attempts to round them to the correct pure interval.

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Here is a very simple example of how those two notes are different.

In any key, you would have 7 notes one of each letter. If you are in the key of D major, you would have notes D, E, F#, G, A, B, and C#. It would not make any sense to call the last note a Db because you already have a D in your scale as the root.

Another example is that chords are built in thirds. A third pretty much is a skip in letter name. So if you take an A major chord you would have the notes A, C#, and E make up the chord. Calling the C# a Db would not make sense because A to Db is not a third, but a fourth.

I'll list a few more examples later. It is hard to answer on a phone.

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A to C# and A to Db are both thirds, aren't they? The fourth of A is D natural. C# and Db are enharmonically equivalent so any intervals involving them should be interchangeable. I was under the impression it is just convention that we say C# in A major rather than Db, but they are both technically correct. –  Charles Sep 7 at 0:00
    
@Charles intervals are named based on the letter name. Any A to any C will be a third. Any A to any D will be a fourth. An A to a C# specifically is a major third while an A to a Db is a diminished fourth. These are different intervals. It's a little confusing at first, but this is important especially when sight reading sheet music. –  Dom Sep 7 at 0:10
    
Ah, diminished fourth makes all the difference. Thanks. –  Charles Sep 7 at 0:16

They may sound the same, but when written down on the staves, they take on different personas.If one has any education in music, one will expect the appropriate note to be written. As in, when in the key of, say E major/ C#minor, one would expect a C#, not a Db, which just doesn't feature in that key. Likewise, in say, Db, one wouldn't expect a C# note to be there. Technicalities, more than anything. start a sentence in English without a capital letter - it's just not right. A surgeon wouldn't ask for ' a wotsiname' in the middle of an operation. Things are given names for specific reasons.

With only 7 letters, there are going to be plenty of times when a particular note will have to be an A rather than a B. That is when we need to know if it's an A# or a Bb, and it's often dependent on the key we're in. If it's a key with sharps, it's more likely to be called A#, and vice versa.

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