What does this sharp sign with an arrow mean?

I've seen this symbol (that looks like a sharp sign with an arrow sticking out of it) in some meme videos, but I don't know what it means:

2 Answers

It's an indication for a three-quarter-tone sharp.

Another common symbol for the same thing is what looks like a regular sharp sign with three vertical strokes.

(Image source: MuseScore 4)

A single quarter-tone sharp, using the same convention as the symbol in the OP, uses a downward arrow extending from the left-hand vertical stroke. Alternatively, a sharp-like symbol with a single strike can be used for the same thing.

A whole variety of additional quarter-tone accidental symbols can be found in

The symbols for microtonal accidentals generally, and quarter-tones specifically, are not standardized.

• The answer by @ElEctric is more correct as the symbol with the arrow has a specific meaning in that system (to adjust a Pythagorean semitone by a comma). Commented Oct 11, 2023 at 13:32
• @Theodore the symbol is not unique to that system. H-E is the exception rather than the rule. Commented Oct 11, 2023 at 15:24
• I thought the one with the arrow attached was exclusive to HE system because I'd never encountered it anywhere else, including the other questions linked in your answer (though one has a separate arrow above or below). Do you remember where you might have seen it for some other 3/4-ish tone? Commented Oct 11, 2023 at 16:59
• @Theodore The links I included were for related symbols, not the symbol in this post. I'll see if I can find a good example of the arrow symbol in a score Commented Oct 11, 2023 at 19:28

In extended Helmholtz–Ellis just intonation (HEJI) notation, this symbol means "sharp, raised by one syntonic comma". In other words, multiply the frequency of the note by 177147/163840, which is 2187/2048 (a Pythagorean chromatic semitone) multiplied by 81/80 (the syntonic comma). In HEJI normal notes are Pythagorean intervals (3-limit), the regular sharps and flats raise and lower by 2187/2048, and the arrows and other accidentals are used to get intervals with other primes in them (5, 7, and beyond).

In equal temperament tunings where sharps raise by three or more steps, you will need to attach arrows to sharps and flats in order to notate the full gamut. Here, a sharp-up means "sharp, raised by one step".

In 53-TET, for example, a sharp raises by five steps, so:

• Natural: Root note
• Natural-up: Raise by 1 step
• Natural-double-up: Raise by 2 steps
• Sharp-double-down: Raise by 3 steps (sharp lowered by 2 steps)
• Sharp-down: Raise by 4 steps (sharp lowered by 1 step)
• Sharp: Raise by 5 steps (one chromatic semitone)
• Sharp-up: Raise by 6 steps (sharp raised by 1 step)
• Sharp-double-up: Raise by 7 steps (sharp raised by 2 steps)
• Double-sharp-double-down: Raise by 8 steps (double sharp lowered by 2 steps)
• Double-sharp-down: Raise by 9 steps (double sharp lowered by 1 step)
• Double-sharp: Raise by 10 steps (2 chromatic semitones)
• Double-sharp-up: Raise by 11 steps (double sharp raised by 1 step)
• Double-sharp-double-up: Raise by 12 steps (double sharp raised by 2 steps)

53-TET's flat side is notated in the same way, just in the opposite order:

• Natural: Root note
• Natural-down: Lower by 1 step
• Natural-double-down: Lower by 2 steps
• Flat-double-up: Lower by 3 steps (flat raised by 2 steps)
• Flat-up: Lower by 4 steps (flat raised by 1 step)
• Flat: Lower by 5 steps (one chromatic semitone)
• Flat-down: Lower by 6 steps (flat lowered by 1 step)
• Flat-double-down: Lower by 7 steps (flat lowered by 2 steps)
• Double-flat-double-up: Lower by 8 steps (double flat raised by 2 steps)
• Double-flat-up: Lower by 9 steps (double flat raised by 1 step)
• Double-flat: Lower by 10 steps (2 chromatic semitones)
• Double-flat-down: Lower by 11 steps (double flat lowered by 1 step)
• Double-flat-double-down: Lower by 12 steps (double flat lowered by 2 steps)

If the sharps or flats raise by 7 or 8 steps, you'll need stacks of three arrows (or more), giving you accidentals such as a sharp-triple-up (double sharp, then raise by 3 additional steps) or sharp-triple-down.

• This article includes a reference to the full Extended Helmholtz-Ellis notation system: The Extended Helmholtz-Ellis JI Pitch Notation. See p. 18. Maybe worth adding to your answer that the standard accidental symbols (with no extra marks) are used specifically to reference Pythagorean (3-limit just) tuning. Commented Oct 11, 2023 at 13:29