10

Say I want to write a statement like this, but in a more compact form:

E♯ is the enharmonic equivalent of F♮

What symbol could I use instead of "is the enharmonic equivalent of"?

It doesn't seem right to me to use the equals sign = because the left and right hand sides aren't equal. The symbol should represent a qualified equivalence.

Or is the convention to "just hold your nose and use =" even though it's not actually true in the mathematical sense?

Edit 1

It occurs to me that we already use the equal sign in non-mathematical ways in music notation. For instance, the tempo indication:

♩ = 120

or the metric modulation:

♩. = 𝅗𝅥

Perhaps it's OK after all to use a plain equals sign to denote enharmonic equivalence. The tacit assumption is that the human reader of the notation will know how to expand the compact notation back into an English sentence.

Edit 2

I came across the decorated equals sign: ≑ which (to me anyway) conveys the idea that the terms on its left and right are sort-of equal.

Thinking about it, E♯ and F♮ are two different notations for the same physical property i.e. pitch. In the same way you could say:

"one two three" ≑ "un deux trois"

Edit 3

The reason I asked the question originally was that I was experimenting with the notation of Theoretical Keys. We'd most of us be comfortable with the idea that

F♯ is the enharmonic equivalent of G♭

F♯ ≑ G♭

and so:

6 sharps ≑ 6 flats

But what follows from this is this sort of thing:

10 sharps ≑ 2 flats

and

12 sharps ≑ 0 flats

The use of an equal sign in these statements looked plain wrong to me.

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    Well, there is a "congruent" symbol in math, $\cong$ (oops no markdown at this site). It's an "=" sign with a tilde over it. – Carl Witthoft Mar 12 at 15:03
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    Well, so long as you are in a well-tempered system, from a wavelength point of view, these two are equal. So it sort of depends on your intended usage. – Carl Witthoft Mar 12 at 15:05
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    Relevant anecdote: a friend of mine (musician) spent a year on a fellowship at Princeton's Institute of Advanced Study. As Albert Einstein used to hang out there years ago, I suggested she put a sign on her door proclaiming: "E = F♭". Which she did. It apparently was quite the conversation piece. Anyhow -- yeah, the equals sign is commonly used for this. – Athanasius Mar 13 at 2:41
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    An observation - the two usages you bring up in the edit are more like assignment (like in programming) than equality, while enharmonic equivalence is a similarity relationship. I don't think that invalidates the point you make about conversion to English, but it does bring up an argument for introducing a different symbol for enharmonic equivalence since it has different semantics than the current usages. – crass_sandwich Mar 13 at 13:27
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    @CarlWitthoft Sometimes when you cannot have LaTeX, you can input the symbols directly (Unicode): , , , (let us see if it works). – Jeppe Stig Nielsen Mar 14 at 19:11
10

Use Parentheses?

E♯ is the enharmonic equivalent of F♮

I've seen the following in scores but written on the staff instead of using letters: E♯ (F♮)

| improve this answer | |
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    This approach is used commonly in staff notation, at least for singers. For example, if there's an E♯ before a key signature change followed by an A♭ after the change, the E♯ may be followed by an F♮ in parentheses to warn the singer that the interval is enharmonically a minor third. The F♮ will often be smaller, and it will typically be a solid notehead without a stem, to reduce the likelihood of rhythmic confusion. – phoog Mar 12 at 16:53
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    This is what I have seen in the wild, and what I have used myself in writing my scores when I used an equivalence like this to change keys. It helps the singer's ear to see what the note is in the new key for reference. – Heather S. Mar 12 at 17:58
9

I think the equals sign actually works perfectly well for this purpose. For starters, "enharmonic" itself is really a short way to say "enharmonically equivalent", so from a language perspective, = makes a lot of sense. In any context where it is important to note that two things are enharmonically equivalent, it will be obvious that the normal distinctions about enharmonicity not being entirely the same are implied. Plus, = is such a commonly understood shorthand that its meaning is immediately obvious to even beginners.

As an alternative, I think the similar (~) sign from geometry could also work really well, and it probably comes closer to the exact meaning of enharmonic. The congruent symbol takes this even further, but isn't localised on many keyboards.

The main argument I have against other symbols, like the ones mentioned in other answers from mathematics or logic, is that they aren't nearly as accessible as an equals sign. Just about everyone in the world knows what an equals sign generally represents, but lamentably the same cannot be said about the congruent symbol, for example.

I've seen scores sneak their way from C major to D♭ major, and when their G♯ note gets tied to A♭, the composers (or editors) sometimes write "G♯=A♭" above the notes.

If you're okay with shorthanding the enharmonic relationship with a symbol, you have to be okay with letting the technicalities of enharmonic relationships be implicit. Otherwise, you may as well just write it out.

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4

Several mathematical symbols come to mind, as I don't think there is an official musical symbol.

Triple bar means "identical to"
Approximately means "almost equal to"
~ Tilde means "similar"

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  • Or per my comment, maybe "congruent" ? OTOH, there is no musical symbol for "is NOT the same as" either :-) – Carl Witthoft Mar 12 at 15:05
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    Please don't try to do this as there other terms and symbols that overlap with mathematics. For example, musical set theory doesn't really overlap well with mathematical set theory and symbols like '+' are used to indicate augmented triads not add notes together. – Dom Mar 12 at 15:17
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    Each symbol actually seems inappropriate. Not identical, respelling changes scale degree. Not approximate, at least on a fix pitch instrument like a piano the pitch will be exactly the same. Similar is just too vague, C1~C2 is also a similarity. – Michael Curtis Mar 12 at 16:27
  • @Dom I think the triple bar symbol is actually suitable if the purpose is to indicate a certain tuning system, though saying "let E# = F" is probably simpler. – awe lotta Mar 13 at 19:07
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    @MichaelCurtis I think you're interpreting too literally the definitions that MeanGreen gave. In math, "identical", "almost equal" and "similar" have specific definitions, and the symbols themselves can be used in many fields for other particular definitions. For example, one could say that two numbers are equivalent under modular arithmetic with the triple bar, despite the numbers being written differently, so to say "identical" I think is a bit of a misnomer. I don't see why musical notes can't be talked about similarly, i.e. enharmonic spellings are identical under a certain system. – awe lotta Mar 14 at 5:20
4

In Kostka and Payne, Tonal Harmony the equal sign is used...

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...or...

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...or...

enter image description here

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3

As far as I know, there is no sign. Why should there be? That statement and other similar ones aren't commonplace, and whenever there's a need to use it, simply write the fact down.

There are, as Dom rightly states, many mathematical signs and symbols which actually mean completely different things musically. + and - and o come to mind. And = isn't going to be a true statement anyway. B♯ = C ? Not true!

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    B♯ = C is completely true in the 12-tone musical system. (On the other hand, if you're considering that the pitch required from an instrument with variable pitch might be different because of a different harmonic context, then C = C is also not true.) – phoog Mar 12 at 16:57
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    @phoog - it's not *completely * true. It sounds the same in 12tet, but it doesn't look anything like when it's written, does it? And when it's part of an interval, it's different too. It is enharmonic, but that's as far as it goes. Yes, I'm pedantic! – Tim Mar 12 at 17:14
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    I understood the expression B♯ = C to be shorthand for the statement "the pitch of B♯ is the same as the pitch of C," which certainly is true in the 12-tone system (and a good number of systems with more tones besides). That B♯ and C are not written the same is question begging (1.5 and 3/2 aren't written the same, but that doesn't stop them from being equal). I also do not see the relevance of whether the pitch is part of an interval or not. – phoog Mar 12 at 17:54
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F# - Gb or F#/Gb

(I know you use the slash to indicate a secondary dominant or any other degree of another degree).

https://www.theorie-musik.de/grundlagen/enharmonische-verwechslung/

Edit:

I agree that / is used to assign F/G = F chord above G. So how about back slash: F#\Gb

After reading the other answers here I think a good and clear solution will be euqal in parentheses: F# (=Gb)

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  • I typically see slashes in guitar chords, indicating that the bass note is different than the indicated chord. In that sense, / means "different" to me. – Eric Duminil Mar 12 at 23:49

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