[itsme]

I admit I have not completely understood what "letter offset" is good for. It seems that this is complicating things as E - F is a distance of one semitone, F - G is a distance of two semitones. The consequence is that transposing needs to be specified with two values like (-1 -2). Does that really work as intended for all chords in a song?

Assumption: we are in the world of "well-tempered" music where e.g. f# and gb are considered the same tone.

By now in any case I came across, one "distance" value specifies transposing (Finale, MuseScore, EasyABC, MobileSheets, ChordPro Reference Implementation). There's transposing "by key" or "by semitone". Both can be thought of being based on a closed circle with 12 positions like a clock. "by key" uses the circle of fifths. "by semitone" uses c c# d d# e f f# g g# a a# b (or its equivalent written with flats). Transposing goes the same number of steps to the left or to the right for every key or note. Both approaches lead to the same result.

Open question: shall the tone or key be written using flats or sharps.
There are conventions if flats or sharps shall be used. That's for better readybility. Music theory, music notation, personal preferences - these three might be slightly different. Keys and chords are seen as "flat" or "sharp" by most musicians, based on the main scale of the base tone. Ab is "flat", G# is "sharp". It is common to avoid mixing sharps and flat and it is common to write the bass tone of slash chords so that it matches the chord, e.g. A/C# is the normal way, A/Db is very unusual as A is a "sharp" chord a c# e, being the tonic of the key A with three sharps, the IV of key E with 4 sharps or the V of key D with 2 sharps.

There's a limitation of the current UI: the flat / sharp buttons allow specifying to use flats or sharps only for the whole song. This is sufficient for a lot of (most?) cases. I meet the limitations sometimes with songs in minor keys when I want to write down bass notes. 
Example: a simple I IV V I in minor Am Dm E7 Am. I add a bass run Am/E Dm/F E7/G# Am/A
Transposing results are not nice (only) for certain keys:
Dm/A Gm/Bb A7/Db Dm/D should better be Dm/A Gm/Bb A7/C# Dm/D
Gm/D Cm/Eb D7/Gb Gm/G should better be Gm/D Cm/Eb D7/F# Gm/G
This is a constructed example, "Yesterday" by the Beatles as mentioned before is another one.

In my practical use songs where I need a destination key to which I cannot transpose nicely happen rarely. In these cases I would use a workaround: make a copy, transpose it in the text editor (supposed the reported issues are fixed) and edit manually what I want to be different.

[itsme]

The chords of "Yesterday" as they are written down in Realbook 6th Edition.
I can transpose it to all 12 keys and everything looks fine - not too bad, I think.

[erhe]

erhe - the one thing I'm unsure about is what you are proposing from a UI perspective here. All of your examples and the script are taking two inputs for every chord you have transposed, but does that mean the UI should be asking for two separate inputs as well? Your algorithm asks for a letter offset as well as a semitone offset - does that mean I would then be applying those same offsets to every chord in the entire song? Is that what most users would expect when using a transpose feature?

It's all here in the Transpose dialog, nothing more is needed:

   

The musical interval can be calculated from the two key centers that the user specifies in the Transpose dialog. Because the key centers are specified as letter-named pitches, it is possible to get a full musical interval. For example from G to E it's either a minor third down (-2, -3), or a major sixth up (+5, +9).

If someone specifically wants to transpose by a named musical interval, like for example in the Sibelius notation software, there could be an alternative way to say, say, "minor 3rd down", but I don't think most MobileSheets users need that.

[erhe]

I admit I have not completely understood what "letter offset" is good for. 

Letter names come from a culture where there are thought to be seven notes per octave in a harmonic context at any given time. That's not the only possible musical culture, but it is very common, and because of the prevalence of that culture, we use letter names for communicating musical ideas. There are cultures like guitar-fretboard-oriented players, some of whom do not know the letter-name thinking at all, and the resulting music can reflect the difference in thinking.

In the culture from which the letter name oriented way of thinking comes from, musical intervals are defined by the letter name difference of two pitches. Assuming intervals below one octave, an interval from C anything to D anything is called a "second". For example, the interval from C to D# is called an augmented second. In a harmonic context where a musician is thinking about the set of seven possible pitches as being B - C - D# - E - F# - G - A, the jump from C to D# would be called an augmented second. The width of a minor third is the same number of semitones, but calling an interval a third implies that there could be a note in between.

In the same culture, it is very common to think of chordal harmony in terms of stacks of thirds. A seven-note chord rooted on C would start from C and use every other letter name. C, E something, G something, B something, D something, F something, A something. For example, a chord called "C 13 #9", if constructed systematically, would have the notes C, E, G, Bb, D#, F, A.

Letter-based naming is a way for letter-name-thinkers to communicate ideas to other letter-name-thinkers. Sometimes, letter names may not be a good tool for reasoning at all. For diminished harmony that has eight notes per octave, or for thinking about enharmonic re-interpretations, letter names can hide or obfuscate what a musician is thinking.

[sciurius]

The main difference is that @ehre is transposing keys, while we are transposing intervals.

When transposing intervals, the result of D one interval down is ambiguous, it can be Db or C#.

Using the transposition rules for keys, the result of D when transposing from F to E is non-ambiguous: C#.

The result of D transposing from C# to C, also one interval down, would then be Db.

We would need to apply enharmonic equivalents, otherwise Ab transposing from C# to C would become Abb. In the real of well-tempered tunings we call this G,

[Skip]

It looks, to me, like a comparison of apples/oranges (equal temperament/non-equal temperment). Being an equal temperament, hobbiest type, I would be unhappy with getting a transposition to double sharps/flats. Users of other temperments will probably feel differently.

https://www.cmuse.org/well-tempered-vs-equal-tempered/

[erhe]

I am not transposing keys, I am transposing letter-named pitches by intervals. The transposition interval is derived as the difference between the base pitches of a "from key" and "to key", but it can be set perfectly fine without any keys at all. Atonal pieces can be transposed with the exact same method, and there does not have to be a key.

I think you mean "semitone".

[erhe]

It looks, to me, like a comparison of apples/oranges (equal temperament/non-equal temperment). Being an equal temperament, hobbiest type, I would be unhappy with getting a transposition to double sharps/flats. Users of other temperments will probably feel differently.

This has absolutely nothing at all to do with temperament. Double-sharps do not exist because of temperament.

In a B+5 chord there are the notes B, D# and F##.

The notes of a Cdim7 chord are: C, Eb, Gb, Bbb. 

It has nothing to do with temperament.

[Skip]

I think you and I pretty much agree but are using different words, and I don't know enough to keep up with you and the others. 

And I would erase the F## and replace it with a G to make it easier for me to read. It's just a different way of naming a note to me. I learned it as G, not F##. If I were further down the road musically that could change, maybe. I would do the same if it was called an Abb, if that's possible. 

[erhe]

The situations where you would actually get a double-sharp or double-flat in pop chord charts, even if you're pedantic about spelling, are few and far in between. But to protect the innocent and the unprepared, maybe there could be a feature that shows those as simpler enharmonic equivalents.

Anyway. Why I started this thread, I was rehearsing a song with a singer, and she asked if we could do the song a bit lower. "No problem, I'll use the transposition feature in MobileSheets," I thought. But then it showed me things like A/Db, which took me by surprise in the middle of the song. I had written the chart myself and I thought, what the actual heck have I done here, until I realized it was the transposing feature.

[Skip]

Surprises are a bxxxxx, aren't they?