I'm coding an algorithm for transpose chords, but I only have little knowledge of the Music theory.
Is it wrong F# include in key of Db instead of Gb? If the key with a flat all the enharmonic chords must replace with their flat notes?
Key C
G A B C D E F
when transpose to Key Db
Ab Bb C Db Eb F Gb
or Is this also correct according to music theory?
Ab Bb C C# Eb F F#
Is it wrong F# include in key of Db instead of Gb?
Usually, yes. The fourth degree of the D♭ scale is G♭, and it is incorrect to spell it as F♯.
However, F♯ is the raised third degree of the D♭ scale, and if your source is very chromatic, it might legitimately use the raised third degree, in which case the correct result in D♭ would be F♯. This is unlikely, but possible. To be clear, the source pitch would have to be one of the following:
| Key | Pitch |
|---|---|
| C | E♯ |
| D | F♯♯ |
| E♭ | G♯ |
| E | G♯♯ |
| F | A♯ |
| F♯ | A♯♯ |
| G♭ | B |
| G | B♯ |
| A♭ | C♯ |
| A | C♯♯ |
| B♭ | D♯ |
| B | D♯♯ |
As you might guess by the number of keys in which this pitch is something-double-sharp, it is not common.
There is a simple rule for this. When you transpose, two things must change identically for every note: the distance in letters and the distance in half steps. If you go from C to D, all the letters must increase by one (for G, this means changing to A) and all the pitches must move by two half steps. If you go from C to D♭, the letters are still increasing by one, but the pitches are increasing by only one half step.
Unfortunately, a lot of music notation software gets this wrong, or perhaps the people using it get it wrong. Regardless, you can find a lot of horribly misspelled scores out there on the internet. I was looking for a particularly chromatic passage from Mozart's Requiem a few weeks ago, and the first score of it that I found on YouTube was self-engraved by someone who didn't know what they were doing, and it was a disaster.
So make sure you're using reputable sources for your transpositions, and stick to the "letter first, then half steps" rule, and you should be fine.
Short answer: for a lot more than convenience's sake, each key will consist of each one of 7 letter-named notes, those being A-G. One main reason is to avoid having a ♯ and/or ♭ next to another same letter name, and thus having to write them on the same line/space. That would mean one or more letter names would not feature as well.
Generally, keys will have only sharps or only flats affecting notes - in major keys. This is reflected in their key signatures, which are there to tell which notes will not be naturals. That falls apart somewhat when minor keys are met: the leading note will mean in some keys with a flat in the key sig. will often have a sharpened note for that note. It doesn't mean the key sig. gets a sharp and a flat, but the notes involved in their scales will have flats and sharps, e.g. D (harmonic) minor - D E F G A B♭ C♯ D.
Whilst in 12tet, you idea of the G♭ sounding exactly like F♯, doing that will produce two notes with the 'G' name - not good, and where's F? Also two C names but lacking a D in your last version will also be confusing.
Best stick to sharps only when needed, and flats only when needed. So, we could (and do!) have a key of C♯ written differently from the key of D♭.But both sounding the same in 12tet.
