Is a note that is enharmonic to a diatonic note of some diatonic scale, also diatonic in regards to that scale?

Question

I'm learning some music theory from a book, and encountered some question in my head that I can't seem to answer.

The question is in the title:

• Is a note that is enharmonic to a diatonic note of some diatonic scale, also diatonic in regards to that scale?

An example:

• Let's take the C major scale. I know the note D is diatonic to this scale (it is the II degree of the scale). What about Ebb? Is it also said to be diatonic to the C major scale?

• It is the same pitch.

• I understand a piece would be better to just use D and not Ebb 99% of the time, but we're talking theory here.

Answer 1

No, notes enharmonic to a diatonic scale are not diatonic in regards to that scale.

An easier example to envision for this purpose is whether D♭ is a diatonic note in A major since the enharmonic C♯ is. ...No, that D♭ is almost always a misspelling of a perfectly good diatonic note instead.

If sung, the enharmonic note should be more likely to be made slightly out of tune compared to its diatonic spelling (i.e. the C♯ should be sung in tune in that A major song, but the D♭ won't necessarily be sung in tune).

Answer 2

I understand a piece would be better to just use D and not Ebb [in the key of C major] 99% of the time, but we're talking theory here.

Then let's talk theory. Theory should explain "why" it would be used or not used.

What does it mean to be diatonic? It isn't just a collection of frequencies, it's a collection of named pitches using the gamut of letters ABCDEFG, which creates the important sense of steps between scale degrees. When everything is spelled correctly the scale degrees are separated by steps and those steps then have functional, tonal, and modal identities within the scale.

When you use accidentals the diatonic purpose is to either change the tonal center - the tonic, even if it's just implied - or the mode, and that changes the function of the changed tone.

If we take away the specifics and just ask "what do flat type accidentals do?" We can say they normally lower tones to create new subdominants or change major mode to minor. In the specific case of a double flat, we can also say the tone being lowered must already be some kind of flat.

So, with an E double flat we are starting from something that would already be a flat, an E flat, and then we have lowered it to become either a subdominant or a minor mediant. E flat is the subdominant of B flat major, so E double flat is the subdominant of B double flat major. E flat is the minor mediant of C minor, so E double flat is the minor mediant of C flat minor.

In either case, it would obviously be easier to not use theoretical key signatures and spell our tone as D natural to be the subdominant of A major, or the minor mediant of B minor.

The interesting thing is the E double flat/D natural in those two cases isn't the only accidental involved with the changes. A G sharp would be important for the change to A major, and an A sharp would be important for the change to B minor. Both of those involve black keys on the piano, and in C major would require accidentals. It's hard to imagine what would prompt someone to then notate that white key above middle C as an E double flat!

The only reason I can think of for such odd enharmonic spellings is hypothetically using an accidental without a sense of functional reason, or not understanding key signatures and spelling chords in thirds.

I suspect the question arises, because in the specific case of E double flat in C major, the enharmonic is to a natural tone, a white key on the piano, and those white key sort of always seem diatonic. If the scenario were, for example G sharp, in F sharp major, respelled as A flat, I wonder if there would be the same sense of A flat is diatonic to F sharp major?

Bottom line: if you have introduced an accidental, you are not in the same place you started. You have either changed mode or tonic, and that resets the notion of what is diatonic.

Enharmonic equivalents will both be diatonic somewhere, but not in the same place.

Answer 3

Diatonic notes are those belonging to major or minor keys.It means the opposite to chromatic.

So the names of notes pertinent to a particular scale/key have specific names. That in itself means note D is diatonic to key C, whereas E♭♭ isn't - it's a different note name - and possibly even a different pitch in anything other than 12tet.

It's not even the case where a simpler C♯ is diatonic to key D, whereas D♭ is not. There won't be two different 'D' notes in a key.

Looking from a different angle, say key C, and slight modulation may include something like E♭♭ (can't bring one to mind though !!), but at that point, it would have to in fact be E♭♭, and not D♮, rendering it absolutely non-diatonic.

Answer 4

No. The concept of 'diatonic' is all tied up with the concept of 'spelling it right'. You could have picked a much simpler example - the seventh note of C major scale is B, not C♭.

Don't get too hung up on being diatonic. The scale of the key or mode you're currently in is a framework, not a restriction. It's absolutely fine to take that B and suddenly put an A♭ minor chord around it. Then it would make sense to spell it as C♭, and this wouldn't necessarily imply a shift away from C major!

Answer 5

There is a difference in describing the frequencies you hear and attribute to the scale versus the letter names and their convention.

All diatonic scales derive their letter names from the sequence

{A, B, C, D, E, F, G, A, B, C, D, ... etc}

As is, these are all "natural notes", meaning that they are in the key of C. Consecutive notes are a step apart except for {B, C} and {E, F} which are 1/2 steps.

So, the degrees of the D major scale have the names {D, E, F, G, A, B, C, D}, i.e. some type of F is the third of D. To make this a major scale you need to include the accidentals that make the sequence of steps (w-w-h)-w-(w-w-h). For the sequence of letters to describe the D maj scale we need {D, E, F#, G, A, B, C#, D}.

Enharmonic tones, as you know, are two different names corresponding to the same sound, like A# and Bb, or B# and C. However, as many answers point out, even though Gb is the "same" note as F#, Gb will never be the major 3rd of D by our naming convention.

It is also worth mentioning that this phenomenon is present on the piano, guitar, other fretted instruments, and some horns, because they are constructed to have equal tempered tuning. In other tuning systems A# may not be the same frequency as Bb in any key.