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Is there any note naming system out there that uses the normal note names for non-accidental notes (A,B,C,D,E,F,G) but has one syllable unique names for the accidental notes?

I find it frustrating that all systems I’ve seen use the accidental system, which to me causes artificial problems (ex. You are in the key of F# major and need key change to a sharper key)

I get why this system exists due to it having theory information contained, and it was invented before the tempered tuning system, but nowadays it just gets in the way.

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    With enharmonic equivalence, changing to a sharper key than F sharp is simply going around the circle of fifths to a flatter key, as you no doubt already know. Is there any context without enharmonic equivalence in which one would be in F sharp (let alone need to modulate to a sharper key)?
    – phoog
    Oct 6 at 13:22
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    To what end? You'll just get more frustrated when you start learning microtonal music anyway. BTW, are you aware of the German system with B and H, among many others? Oct 6 at 14:23
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    @puzzleshark not to mention that G sharp major has F double sharp in it. Which is why nobody in their right mind uses G sharp major. Why is F sharp major to A flat major more of a context switch than F sharp major to G sharp major?
    – phoog
    Oct 6 at 17:49
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    @puzzleshark, G sharp major would be called a theoretical key, it would normally be called the enharmonic equivalent A flat major. Where have you actually encountered playing a piece of music in G sharp major? Oct 6 at 18:07
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    I added a big postscript to my answer to address the fact that: Yeah, all these systems have inherent difficulties. But for performance, especially improvisatory, we want to get to the place where we don't have to think about the notes' "names" at all. Oct 6 at 18:52
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The benefit of the "letter name" system is that it's easy to relate pitch-classes across octaves. The difficulty, as you point out, is that the naming is fixed and has no relationship to the key. As Tim suggests, moveable do solfege lets you modulate at will while still recognizing the unchanged structure of the melody. Yes, there are modifiers for raised or lowered pitches (see the table at the preceding wikipedia link), though they're less universally known and there's some disagreement about "me/ma" etc). And of course you run a risk of confusion since a fixed-do solfege system is used instead of letter names to identify pitches in much of the world.

It's a chordal rather than melodic solution, but I know a guitarist who recorded for decades in the famous Muscle Shoals studios, who says they preferred to read from chordal lead-sheet using roman numerals (I, vi, IV) instead of "C, Amin, G" etc., so that if a singer says "Hey, can we try it a half step lower," they can modulate at sight. One could adapt this approach to melodic material by simply referencing scale degrees, substituting numbers for solfege syllables.

Music theory analyzing 12-tone and some other post-tonal works uses a numerical system to count half steps, e.g. C is 0, C# is 1, D is 2, etc. Often, rather than using "10" and "11" for the last two pitches (0-indexed, so the twelfth pitch is 11), "A" and "B" will be substituted to avoid confusion between "10" and "1 0."

Ultimately you have to suit the system to the purpose. This "0123456789AB" system works well for representing linear "tone rows" across time. If you're analyzing pitch clusters in Stravinsky, you might instead count half steps vertically and index 0 to the lowest note. If you're analyzing rhythms or metric patterns in serial works, other systems would be better. If you're inventing some kind of midi-piano-roll style intabulation of specific pitches, you might want a system that includes not just pitch-class but register, e.g. middle C is 0, an octave lower is -12. (Though why reinvent the wheel; midi does have a designation for middle C, 60.)

But ultimately, moveable-do solfege comes closest to what you're looking for: a pre-existing, monosyllabic, more-or-less intuitive method for referring to melodic pitches with reference to the tonal center rather than a fixed pitch-class.

Footnote: In several comments you've clarified that your main purpose is to make on-the-fly modulation easier to think through in practice. Ultimately I'd advise you to pursue a performative fluency that transcends systems of signifiers. There's a story-form joke that I'll abbreviate:

The band was finally getting their big break. They'd rehearsed in the garage. They'd won the high school battle of the bands. They'd even played local clubs and developed a following. Now this was the night; they were opening for the big act in the big venue. They knew there were record label talent scouts in the audience. The set was going great and every member was starting to dream of the fame and fortune that awaited them. The lead singer thought:
"Oh man, I'm going to build a mansion in Beverly Hills that will make M.C. Hammer cry and put in a solid gold hot tub. I'm going to drive a Ferrari on Mondays, a Porsche on Tuesdays..."
Meanwhile, the drummer was thinking, "Heyyyy, I'm gonna get so many babes. And so much dope. I can finally quit my job at McDonalds!"
The keyboard player was thinking, "Should I get a vintage Moog first? Or a Hammond?"
And meanwhile, what was going through the bass player's head?...
"One. Four. Um, Five. One. One. Four. Four—Imeanfive..."

The point is: Yes, you can play a tune in C and represent it as "C C G G A A G." You can modulate to F# and call it "F# F# G# G# A# A# G#." You can call it "do do sol sol la la sol" in either key, or use numbers. But ultimately, you want to get fluent enough with your instrument, with the material, and with the language of scalar and arpeggiated movement, that you can just play without asking yourself what each note is as you play it.

I know, I know, that's just a final goal, and to get there you do have to go through the rough work of figuring out notes. But it's good to keep that final goal in sight. The pitch names are just that, names; they only represent music, just as words only represent ideas.

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    Chordal lead sheet is interesting but fails to meet the requirement for one-syllable names for five of the twelve tones of the twelve-tone scale.
    – phoog
    Oct 6 at 13:19
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    And of course the tone-row system has the bisyllable "seven," though I seem to have fuzzy recollections of some aural-skills classes singing serial music using "sev" for seven... Oct 6 at 13:22
  • Given the English habit of setting "heav'n" as one syllable, I've never had much trouble with "sev'n." It's a bit awkward sometimes, but manageable.
    – phoog
    Oct 6 at 13:27
  • Your 2nd para.: similar to NNS - and actually what I've used for decades!
    – Tim
    Oct 6 at 13:36
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    Small point: the mod12 system is not just used for analysis. It's the basis for composition systems as well.
    – Aaron
    Oct 6 at 16:48
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...why this system exists

If the music is essentially diatonic - like the past 1,000 years of western musical tradition - then the seven letters ABCDEFG (the gamut) represent the diatonic tones. The sharps and flats of key signatures then represent transpositions of the diatonic gamut. Accidentals represent what can be through of as momentary transpositions (secondary chords) or modal/chromatic alterations of the essential diatonic gamut, for example, the raised/lowered seventh scale degree in minor, or the "double" leading tone chromaticism of augmented sixth chords.

I find it frustrating that all systems I’ve seen use the accidental system

That's because so much music is essentially diatonic expanded with some elements of chromaticism.

You are in the key of F# major and need key change to a sharper key

Now you're getting into a specific situation.

If you are in a key signature with lots of sharps and flats, you can get accidentals of double sharps and double flats, or other spellings which can be hard to read. Some of that is connected to music history and convention. In the classical era key signatures tended to use less sharps/flats, and modulations were to "close" keys. That stuff isn't really hard to read. Later periods pushed into more distant keys and more chromaticism. Certain styles conventionally use simple keys. I sight read from hymnals, and even though some are from more recent times, they tend to use simple key signatures. You are not acknowledging that the standard notation system is easy to read for a huge amount of existing music.

My reading skills are not that great, but a big part of the issue is reading relative harmonic changes, and getting a sense for what the accidentals provide as harmonic queues to typical patterns. For example, if I see a sharp, I usually recognize it as a temporary leading tone and my hands move for some kind of V I movement which you technically might call tonicization or think of as a sort of localized transposition. So, if the music were in C major and I see a G♯, I think A minor and sort of shift my mental and hand orientation to A minor temporarily. Similarly, if I see a flat, I will probably assume the flat is on the seventh scale degree and the move is to the subdominant which would be like playing in C major, hitting a B♭, and moving to an F chord. The point being that C major, A minor, and F major are all diatonic, and the accidentals are both queues to (sort of) transpose and they are the points where the various keys "overlap".

I need to name the letter is the above example just to be clear, but in actual reading I'm not paying attention to each and every letter. Realtive changes and staff line distances are much more important. You can't avoid reading letters entirely, because you need some point of reference. It becomes more like this, when I get oriented to the A, let's say the second space on the treble clef staff, then when I see a on the line below, I don't really care that it's a G, the is really telling me the note below A is a half step below. Similarly, if the key were F♯ and I'm playing a note on the second line of the treble staff and the next note is on the space below with a double sharp x, I really try to not think "F double sharp" but recognize the note on the space below with x as "a half step below" the G♯ I'm playing.

Have you ever seen when someone has written the letter names on keyboard keys, or maybe even on a fretboard? That's a bad idea if you really want to handle chromatic harmony. The key someone might naively mark as G is really a G, or a Fx or an A♭♭.

None of that will make much sense or be do-able until one has practices all major and minor scales, along with various harmonic patterns (all the cadences, circle of fifth sequences, rule of the octave, etc.), in three inversions/positions, in all the major and minor keys. You have to practice that stuff until you are equally comfortable playing basic patterns in any key. You should be able to, for example, hit and resolve a French augmented sixth chord to the dominant, in all inversion, in any key, without hesitation.

It may seem contradictory to some of what I've written above, but when practicing patterns in all keys you do what to think of the pitch letters, because certain spelling make more sense in particular harmonic contexts. For example, go up three half steps from middle C. As a major key tonic, that will normally be E♭. If I play a major triad on that tone, I tend to always think of it as E♭ major, but this is wrong. If the key is E♭ major, then sure, the chord is E♭ major. But, if the key were G♯ minor, that same triad should be properly called D♯ major. So, when practicing in G♯ minor, I will be very careful to mentally recognize D# and not E♭. Similar thing for the leading tone in G♯ minor, it's Fx and not G♮.

...artificial problems (ex. You are in the key of F# major and need key change to a sharper key)

I'm not sure I see what the problem is. F♯ major is six sharps. "Sharper" I suppose is one more sharp in the key signature, C♯ major, seven sharps. You could enharmonically change that to D♭ major, 5 flats to keep things simpler. Theoretically you can keep adding sharps to the key signature. From C♯ major you could go to G♯ major, all seven letters sharped, but the F would be double sharp. That's theoretical, but a practical nightmare, so you enharmonically respell G♯ major to A♭ major. For all practical purposes the worst you have to deal with is key signatures of either seven sharps or seven flats. The dilemma for reading is getting used to reading double sharps and flats. I think the path to that skill is not reading discrete letter spellings, but relative changes where most of those accidentals are raised secondary leading tones or leading tones lowered to become subdominant degrees.

Is there any note naming system out there that uses the normal note names for non-accidental notes (A,B,C,D,E,F,G) but has one syllable unique names for the accidental notes?

There are chromatic solfege systems that do exactly that, give unique syllables to the 12 chromatic tones.

But those are not notation systems.

I could be wrong, but I suspect the real "problem" for you may be reading staff notation rather than the pitch naming system. A chromatic 12 syllable system won't resolve that problem.

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  • The issue is if I am playing a song in the key of C major, but it modulates briefly to other surrounding keys then this is fine, I just add the corresponding sharps and flats and all works out. However If I am playing that same song in the key of F# major I now have to start adding double sharps to some notes. I rarely practice in keys such as G# major, and so I will not be as comfortable. I could instead think in Ab but now I have to do a context switch in my mind where all notes change names, and if the modulation is short (as they often are) then I immediately switch the names back again Oct 6 at 17:11
  • I get why the accidental system exists, but there should be a separation of concerns. The theory does not need to enter the picture when you are actually just trying to perform, and I don't believe it helps you when you are performing. Oct 6 at 17:13
  • Also this system fails with even simple chords. D diminished 7th for example in the context of C major (which is pretty common) has an Ab/G# in it which isn't anymore Ab then it is G#, therefore in the context of that chord it doesn't make sense to call it Ab or G#. Oct 6 at 17:19
  • @puzzleshark Thanks, this helps clarify the context of how you're imagining using such a system: on-the-fly, maybe improvised, modulation of notated material. I'm going to edit my answer to suggest thinking in scale degrees as well. But ultimately, I think the practical answer will lie in getting comfortable enough with the material that you're not "decoding" it as you're playing it, whether you're reading someone else's notation or creating your own improvisation. Oct 6 at 17:20
  • @puzzleshark "...I rarely practice in keys such as..." as I say in my answer, this is actually a significant root of the problem. Oct 6 at 17:59
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0 .. 11 that's how computers do it :)

and piano roll notation uses some sort of graphics OF that 0 .. 11

but no other common use, really.

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