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I wrote a song in Db Major, but I could also notated that it would be equivalent to say C# Major as well. I am not well versed in musical theory and I think both are equivalent to each other and wonder if there are situations which there are preferences to say one over the other. If not why. I play guitar and bass so I would love to know.

What I am mainly writing for is guitar, bass, vocals, keys and drums. But there will be some translation from Keys to actual stringed instruments like Violins and Violas with possibly some oboe or clarinets. I have an EWI player too interested in subbing for those wind parts so I would want to make sure he is comfortable with the scale notations.

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    If you wrote it out as Db, but put 2 # for the key signature, it'd work in D. If you wrote it out in C#, but put no # or b at the beginning, it'll be in C. Is there a particular reason it has to be in C#/Db ? After your edit, I feel that either C or D has to be a more playable key.I appreciate that this doesn't directly answer your question, so it's a comment. – Tim Feb 10 '14 at 15:17
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    I am using the C#/Db scale because it is easier for the vocalist to sing the melody in. Plus it was exciting for me not to write in C or D as a guitar player as it forced me to think of different positions for chordal progressions. FYI. – tony.stack Feb 10 '14 at 17:12
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    For what it's worth, I know players, particularly horn players, who will sit out if they're handed a chart in C#. Yes, it's enharmonically equivalent, but in most contexts, Db is more commonly used, and a lot of folks aren't comfortable reading in C#. – kiprainey Feb 12 '14 at 4:58
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C♯ and D♭ are enharmonically the same. This means that they are played by the same key on a piano, but they have a different musical meaning and they actually should sound a tiny bit different (although the difference is minimal). However, string or woodwind instruments might be able to play them slightly differently and thus correctly.

In Pythagorean tuning, each semitone consists of 100 cents on average. C♯ and D♭ actually differ 41 cents from each other. This stems from the fact that the tuning is defined by going through the circle of fifths with a ratio of 3:2 (see table here).

The interested reader can refer to the fantastic book "Music: a Mathematical Offering" by Dave Benson, available for free here.

To answer your question in practice: usually the key with fewest signs is used :)

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    Good answer. It's tempting to think of everything in equal-temperament terms, but many instruments are capable of playing in just intonation. – Jonathan Van Matre Feb 11 '14 at 19:55
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    Sorry, buy this answer confuses me. What do you mean 'they actually should sound a tiny bit different'. Are they not the exact same scale? If so, they should sound identical – JohnandLyn Henry Jul 15 '16 at 14:30
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    I'm a little confused how you got 41 cents, by my calculation a Pythagorean perfect fifth is very close to 702 cents compared to 700 for 12TET, so if we stack 12 such fifths going from Db to C#, those differences would add to close to 24 cents (~23.46) which the Wikipedia article points out after the table you referenced. Wiki quote: "each augmented or diminished interval is exactly 12ε (≈ 23.460) cents narrower or wider than its enharmonic equivalent." – teletypist Sep 8 '17 at 1:36
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    @dorien I think you've been misled by that book. For one, Pythagorean tuning is rarely used these days. Notwithstanding that, even musicians using Pythagorean tuning are not going to make a distinction between C# and Db, at least not in a single piece of music or without retuning between two sections, because they'll still be playing in a 12-tone scale, and with only 12 tones C# and Db have to be the same pitch. Maaaybe someone experimenting with microtonal music would use different pitches for C# and Db, but that would be outside any general context of Western music theory. – Andy Sep 8 '17 at 17:28
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    @Andy (not sure what u meant by 'expiremental proof') Singers usually end up using a combination of 'just-intonation-style' pitch adjustment, and some tempered scale. It is actually a natural tendency to make such adjustments. It's harder to 'hear' equal-temperament. Remember, just intonation minimizes beating (warbling), because the harmonies are whole-number ratios. A singer will HEAR the warbling beat frequency, and will naturally try to eliminate it (although some REAL singers and musicians CAN hear 12-tet, and reproduce the same beating in harmonies that a 12-tet tuned-piano does). – Kenni Kuhlmann-Clark Sep 25 '17 at 4:02
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You're right that in most situations those are absolutely equivalent, so the distinction has more to do with what instruments will be playing it and what they're used to. If you're writing for piano, it really doesn't matter much at all, both are pretty common. All things being equal, I might slightly prefer to call it Db just because it has fewer accidentals in the signature. If string instruments will be playing it, I would first note that isn't a very resonant key for them and might be better if you transposed it. But I would lean toward C# maybe since—very generally—string players prefer sharps to flats. I would say the opposite is true for most wind instruments.

If you clarify what you're writing for, it would help, but the general answer is that it doesn't make a huge difference, and the default choice would probably be to use Db with it's five flats rather than C# with it's seven sharps (including notes like E# and B#, which tend to throw beginners off more than others).

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They are indeed equivalent, at least in Equal Temperament (which is the most widely used tuning system in western music). You might prefer one over the other depending on how things modulate.

If you're going to modulate to the parallel minor, use C#, since C# minor has 4 sharps, whereas Db minor doesn't really exist (it would have 8 flats--one for each note and then a second one for B, putting Bbb in the key signature).

If you're going to modulate to the dominant, use Db, since the dominant is Ab with 4 flats, whereas the dominant of C# would be G# with 8 sharps.

  • I think the context is probably the most important consideration in determining the key signature, as your example clearly shows. +1, and I think this is the best answer, FWIW. – user45266 May 21 at 4:27
  • They are equivalent in every twelve-tone temperament. – phoog May 23 at 5:21
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In just intonation there is a real difference between the two, in equal temperament not. For fixed pitch instruments there is no difference, but for other pitched instruments (including vocals) it should make a difference. That does not imply that a performer on a non-fixed pitch instrument will indeed make that difference heard, all the more so when that performer is playing together with fixed pitch instruments.

  • How would a string ensemble or vocal ensemble perform a piece differently in C sharp from how they would perform it in D flat? They absolutely would not. – phoog May 23 at 5:23
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I only just learned this, but it has to do with how the notes get named out. In a major scale, all notes A-G, no matter sharp or flat, are expected to appear exactly once.

So in your case, if we spell out the scales:

C# - D# - E# - F# - G# - A# - B# - C#

But the problem is that E# doesn't exist, it's F. Same with B#. And if we write it like that...

C# - D# - F - F# - G# - A# - C - C#

We have 2 Fs, 2 Cs, and no E or B. But if we examine Dd...

Dd - Ed - F - Gb - Ab - Bb - C - Db

All of the notes exist naturally and we see A-G exactly once!

So you are right that the notes are the same. As others have stated, Db has 5 accidentals, which is fewer than the 7 from C#. But we can see now that it's not just a matter of how many accidentals there are, but rather how the scale "fits" the notes.

However, this is only the "correct" answer as would be taught in a music theory class, to answer the question of "Is this scale C# or Db?".

The practicality of the players' comfort with reading sharp vs flat and other factors can be used to ultimately determine the notation, because in the end the players will be playing the same notes on their instruments.

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    E# does exits. – Dom Jul 15 '16 at 14:16
  • It's a bit confusing! – Tim Jul 15 '16 at 14:24
  • @Dom maybe I explained myself poorly. This question & answer provides good insight, and provides a similar answer to a similar question as this one. music.stackexchange.com/questions/23976/… – parker.sikand Jul 15 '16 at 18:45
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    @parker.sikand which is both my question and answer so I get that. Saying E# doesn't exist is the problem I'm having with this answer. – Dom Jul 15 '16 at 18:49
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    well feel free to edit or suggest an edit. I was just trying to offer the "alphabet rule" as I have seen it called, and none of the other answers on this question provided that, but I think it is relevant here to clarify when a major scale would be called C# vs Db. I actually didn't notice at first that the other question was yours, my mistake. And since you seem to know what you're talking about, maybe you could help clarify my answer, as quite honestly I don't know the proper way to explain it other than in the "laymans terms" I've used. – parker.sikand Jul 15 '16 at 19:47
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With no other context, the version of the key with fewer double sharps, double flats, and white key accidentals (e.g. E#, Cb) tends to be easier to read and therefore win out. For example, Db major is more readable than C# major, partially because their seventh scale degrees are C and B#, respectively.

If you're modulating from another key, though, the version of the key with more of the rare accidentals may win instead. For example, a piece that starts off in C# minor tends to involve C# major instead of Db major (e.g. the Toccata of Debussy's Pour le piano).

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In equal temperament, the keys are equivalent. But there are two things to consider...

First, the number of sharps or flats in the key signature. In general, Db would be preferred over C#, because your key signature will have five flats instead of seven sharps. You'd prefer B over Cb because the key signature will have five sharps instead of seven flats. The keys of F# vs Gb are a toss-up: you have six altered pitches either way.

But the second consideration is the one important to your question, because you mentioned clarinets - they're a transposing instrument.

If you're writing for only "C instruments" (which produce a C pitch for a written C, even if that pitch is in a different octave) there's no general preference. But not all instruments are C instruments.

French horns are "in F" - when a C is written, an F sounds from the instrument. As a consequence, French horn music will have one more sharp (or one less flat) in the key signature to sound the same as the C instruments.

Clarinets, trumpets, and tenor saxophones are "in Bb". When a C is written, Bb sounds - so they need two more sharps or two fewer flats. And the Eb instruments like alto sax or alto clarinet are going to need three more sharps, or three less flats.

So if you're writing a piece that could be in F# or Gb, and you're going to include an alto sax, they'll be looking at either three flats or nine sharps (yes, nine - double sharps on the F and G).

Flat keys are preferred for any piece that includes the transposing instruments. Nobody likes seeing double sharps in a key signature.

  • But enharmonic equivalent keys are perfectly normal for transposing instruments. That is, the transposition for B-flat instruments can be a diminished third rather than a major second. A piece in B major will have parts for the B-flat instruments in D flat. The concert-pitch players would be just as unhappy to have their parts in C flat as the B-flat players would be to have theirs in C sharp. – phoog May 23 at 5:30

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