# D-flat diminished vs. A7

I was figuring out how to play the chords of The Phantom of the Opera with my guitar. If the I-chord is eg. D minor, then when the song goes "the phantom of the opera is there", at that "there" the chord is, apparently, the rather strange but cool-sounding D-flat diminished (at least according to sources online).

I have never really learned the diminished chords on guitar, so I was trying to figure out how to play the Db dim. I knew from having studied it a bit that it's like Db minor, but with the fifth lowered to a fourth. Db minor would be first string free, second fret on second string, first fret on third string. But that last one would be the fifth from D, so we lower it one semitone, so the third string is also free.

Then I started thinking what the fourth string would be. Well, since E is in the chord, it would be the second fret. And indeed, it sounds like Db dim.

Then I suddenly realized... this finger pattern is actually awfully familiar. It's A7! Well, without the A on the fifth string, I suppose.

So I thought, what happens if I just play A7 instead of Db dim. It turns out it sounds pretty much exactly the same. Or at least same enough that you don't really hear the difference in the song.

This got me thinking: Wouldn't this work for any song in practice? Instead of playing a diminished chord, just play the 7 chord that's four semitones lower (eg. from Db to A)? At least on guitar that tends to be significantly easier.

(Although I suppose playing something like E7 instead of Ab dim might change the chord quite noticeably due to the highest note being an E, which doesn't belong in Ab dim...)

(Edit: I made a mistake above of calling the diminished fifth a "fourth". Shows how much I know about music theory... Still keeping it so that the responses below making the correction make sense.)

• What's for sure is that it would be C♯-diminished, not D♭-diminished, for a whole bunch of reasons. Jun 16 at 22:27
• What's the difference?
– Warp
Jun 16 at 22:48
• @Warp as far as the notes played there is no difference. But it has to do with conveying intent. The simplest way to explain it is that the chord acts as a vii chord in the piece, not as a flat i chord, therefore it should be denoted using the 7th root in D: C. Jun 16 at 23:41
• @Phoog: There's no F in C#dim, but rather E. C# E G (A#). Jun 17 at 5:53
• “it's like Db minor, but with the fifth lowered to a fourth.” This statement is incorrect, it is a 5th lowered a half step to a diminished 5th. A 5th to a 4th is a whole step down and would not be a diminished chord. Jun 17 at 9:05

EDIT! I hadn't bothered to actually listen to the tune. The bass is Bb, it's a Bb dim7 chord, not C#dim, let alone "Db dim". :/ Do not believe what you find on the internet, it is mis-heard, mis-transcribed, mis-spelled rubbish. Learn to keep your ears open and listen.

And now, the following is my original answer based on the assumption that what's played is actually C#dim. Why did I believe that, when I'm telling not to believe internet transcriptions?

Yes, A7 contains a C#dim chord. The more common tones two chords have, the more likely it is that they can work as substitutes of each other.

You've been able to identify a perfectly good musical pattern from just one example. That's a really good thing, that's how music should be learned! By playing example songs, worrying about theory later, if at all. I strongly recommend that before seeking "proper" theoretical legitimization on the internet, you try and test your newly found hypothesis or candidate pattern on more example songs. Do the replacement the other way around - when you see an A7 chord in a song that's in D minor, try replacing it with C#dim! Then try it in other keys. Try the replacement even regardless what the key is! Try everything. Play by ear! Don't look at ready-made sheet music, most of what you find on the internet or even published books is mis-heard, mis-transcribed, mis-spelled rubbish anyway. Lyrics, melodies, chords, all of it. Listen to the song and make up your own mind, what the chords should be. Maybe then look at how others had heard and written it, if you want to compare notes. :)

There's no single correct way to reason about harmony. Every approach is fine, if it helps you deal with musical situations in practice.

One real-world way to deal with accompaniment is to reduce everything to three chords per key: I, IV and V. Let's assume that you have to accompany a song by ear, and you only know three chords. Impossible? Far from impossible. Take a song that's in D minor, and you only know the chords Dm, Gm and A7. Chances are that for a lot of songs you'll be able to do just fine and nobody notices anything. Such a playing-by-ear folk musician would most probably play an A7 for the C#dim 10 times out of 10, because as you noticed, it's practically the same thing.

If you want theory words, the C# note is important for the tonic Dm, it's the so-called leading tone. Dm's dominant chord A7 contains the leading tone C# as its "third". The pair C#dim - Dm works as a good substitute for the A7 - Dm dominant-tonic motion. Only the V - I bass motion is missing, but it can be just nice for a change.

It's called C# instead of Db, because there's an assumed idea baked in the traditional language of Western music theory that at any given time there are seven pitch slots named with letters A to G, and each of them can be modified with "sharps" or "flats". If you say "Db", it implies that in your opinion, D has been flatted, so D couldn't be e.g. natural. But if you test this by playing notes over the A7 or C#dim chord, you'll agree that D natural is kind of fine there. But C natural is against the harmonic feeling. C has been sharpened, and that's why you call it C#.

The seven-pitches-per-octave way of thinking is not a law of nature or anything, it's just a traditional way of thinking that's prevalent in the Western music culture, even so much that it's hard-coded into the written and spoken language. Sometimes that thinking gets in the way, like when talking about eight-pitches-per-octave harmony and the diminished scale.

• I think your Bbdim7 chord is more likely a C#dim7 in 3rd inversion. Jun 18 at 1:08
• @ericw31415 Do you mean that I should have written it as C#dim7/Bb instead of Bbdim7, because Bbdim7 theoretically has Bb, Db, Fb and Abb? I don't think that's helpful anymore, more like ridiculous. Sometimes, using "proper" theory gets in the way instead of helping, and this is such a case. In my opinion. Jun 18 at 10:30
• Isn't Bb dim7 (at least on guitar) essentially the same as A7, except that on the fifth string it's on the first fret (ie. Bb) rather than free (ie. A)? It does sound very similar, except perhaps a bit more dissonant because of that lowest note (which I suppose is the idea).
– Warp
Jun 18 at 18:20
• @Warp That's what the question is about, isn't it? I tried to answer that question in this answer. Which other songs have you tried this on? Did you encounter similar feelings about swapping dim and 7 chords? Jun 19 at 10:37

You've also discovered how close 7♭9 chords are - and often are substituted, for diminished. The 7♭9 in your case is A7♭9 - where the root (A) on guitar has been changed to B♭. With that open version voicing, it becomes a diminished chord - which can actually be labelled in different ways.

Answers have alluded that your D♭ dim chord should be called C♯ dim. True, but on guitar, when you play notes, you don't particularly consider their names - that becomes more important when they're written down. Thus your D♭ would be written in the same space/line as your D(♮). Just a technical thing.

No you can't always substitute a dominant 7 chord that is 4 semi-tones lower for a diminished chord. But - there are a lot of instances where you can.

It all boils down to what purpose the chord plays in the song. In your specific example, the C# dim chord (D♭ dim as you called it) is the vii dim chord of D minor and its purpose is to create tension leading to a resolution back to Dm. This is because of the dissonance in the tri-tone in the C# dim chord (C# - G). If that sounds familiar it is because this is exactly what a V7 chord is used for. Effectively the vii dim chord is a root-less V7 chord in the first inversion.

So while not all dim chords can be replaced by dominant 7 chords 4 semi-tones lower, the vii dim chord can usually be replaced by the V7. The inclusion of the root tends to give the V7 chord a 'fuller' sound. The opposite effect can be achieved by replacing a V7 chord with a vii dim chord, which is an equally valid substitution.

Typically the diminished chord also has a diminished seventh note. In this case you would have C#, E, G, B♭. The only place to fit the B♭ is the third fret of the third string, and the G can then be played on the third fret of the first string. The fingering would be 3-2-3-2-x-x.

That said, the diminished chord has a similar function as the dominant seventh chord, in that both C#dim and A7 resolve to Dm. This is why "replacing" the diminished chord with a seventh chord four semitones lower will generally sound fine.

However, there is a catch. C#dim, Edim, Gdim and B♭dim are all enharmonic, so sometimes they might be written "wrong". For example if you see a Gdim resolving to Dm, most likely it should have been notated as C#dim, and you should replace it with A7 rather than Eb7. If you pick the one that isn't the most "appropriate" however it would not sound wrong at all, perhaps just a bit "jazzy".

You might even do the same replacement on purpose on a seventh chord. For example, try playing a A7-D cadence and then try C7-D, Eb7-D (that's the more common one, Eb7 is called the "tritone substitution" of A7) and F#7-D. None of them will feel completely out of place.

• Eb7 to Dm is standard "tritone substitution," known in classical circles as an augmented sixth chord with the D flat spelled as a C sharp (so it can sound Wagnerian or similar rather than jazzy). C7 to Dm wouldn't be so out of the ordinary, either. Only the remaining option, F#7 to Dm, fails to sound particularly cadential. Jun 17 at 10:05
• F#7 to Dm is definitely the weirdest of the bunch, but F#7 to D could be seen as an inversion of F#7 to Bm7. Jun 19 at 15:31

First let me point out a few things about the note names. The notes of the Dm triad are D, F, A. So D♭m is D♭, F♭, A♭. So there really is no E, it's just that E is enharmonic to F♭. Then to make it a diminished triad you have to flatten the fifth but not to a fourth as you said, but to the flat fifth (enharmonic to a sharp fourth, since the interval between the fourth and fifth is a whole step, not a half step). Flattening A♭ gives A♭♭ (enharmonic to G) so the chord is D♭, F♭, A♭♭.

But as was pointed out, it should be C# diminished because being an A7 without the root, it would be A, C#, E, G without the A, so C#, E, G. Also much easier to write than D♭, F♭, A♭♭.

Having said all that, I agree with what @Nigel is saying and I would add that it's more the case that the vii dim is a sub for the V7 than the V7 is a sub for the vii dim. This extends to the V9 as well where the half-diminished vii is a common sub for V and in classical circles is analyzed as "the incomplete dominant 9th" rather than "the half diminished vii". For example in the key of C the dominant 9th V chord is G, B, D, F, A, but B, D, F, A would be a common choice in four-part harmony.

Try this: compare the C9 chord on the guitar (the voicing is C E B♭ D G) with Em7♭5 (E B♭ D G, i.e. the same notes without the C root). (Em7♭5 is basically another way of saying E half diminished although maybe subtly dependent on context.

We'll note two things first:

• It's easier to spell the D♭ dim chord in "The Phantom of the Opera" as a C♯ dim chord, especially since this song is in D minor.
• The underlying chord at "there" (the C♯ dim chord) is not changed at the next word of the lyrics, "inside", which is sung with B flats.

This "The Phantom of the Opera" case is actually a case where substituting a diminished chord (e.g. C♯ dim) with a dominant 7th chord with its root 4 semitones lower (e.g. A7) is questionable. This is because the diminished chord is kept when a melody note plays that is 9 semitones (modulo 12) above the root of the diminished chord...or 1 semitone (or 13 semitones) modulo 12 above the root of the dominant 7th chord with its root 4 semitones lower. It does not matter that both the diminished chord with its root 1 semitone below the tonic (C♯ dim in our case) and the dominant 7th chord with its root 5 semitones below the tonic (A7 in our case) are both dominant-function chords and therefore normally can be substituted for each other - a minor second or minor 9th between the root and the melody note is often undesirably dissonant.

Using that dominant 7th chord (A7) at "there" and swapping to that diminished chord (C♯ dim) at "inside" is generally seen as undesirably going from more consonant to more dissonant at a point of tension in common practice period harmony, as combined with the B flat melody notes of "inside", this is actually a chord progression from A7 to C♯ dim7. The 7th of a viiᵒ7 chord (e.g. C♯ dim7) typically resolves downward to the root of a V7 chord (e.g. A7), and therefore, reversing a viiᵒ7-V7 chord progression to V7-viiᵒ7 is generally frowned upon in common practice period harmony. (Admittedly, the C♯-B♭ sung interval between "there" and "inside" is already disregarding common practice period harmony by refusing to properly resolve the C♯ leading tone...but we are still keeping dominant-function harmonies between both words, so this might be forgivable.)

You might want that crunchy minor 9th sound by keeping an A7 chord when the notes of "inside" are sung...but the fans, especially the observant fans, might not.

• Thanks to your answer, I went and listened to two versions of the tune: youtube.com/watch?v=tE6SRBnDHx8 and youtube.com/watch?v=tL25rbnvM4o ... and it's actually Bb dim 7 relative to a tonic Dm they would be playing in the first "verse". :/ Doh. Jun 17 at 22:37
• I wrote "D flat diminished" because it was the easiest way to try to figure out how to play that chord on guitar (using the idea that "a dim chord is like a minor chord except that the fifth is lowered by a half step") because it was easiest to think of the D minor "shape" on the first three strings, shifted one lower. I'm not versed enough in music theory to know that talking about C# (instead of Db) in the context of a song that's on Dm is the "proper" notation. But as the person above notes, apparently the song doesn't actually use C# dim but Bb dim7. Which is very similar but not identical
– Warp
Jun 18 at 18:31
• Honestly, I'd say those versions are still using C# dim7 in 3rd inversion, which has Bb at the bottom. I think the latest version I checked actually did used C# dim at "there". Jun 18 at 22:20
• @Warp What you call it reflects how you think about it. I do not care about the spellings of notes in dim7 chords, all I need is a root note to be able to play the chord and imagine alternative perspectives. Worrying about theoretical spellings does not help me do anything. It's a symmetric chord, and the traditional theory of there being a double-flatted seventh is weird rubbish that doesn't reflect the actual uses I have for the chord, IMHO. Some people like that theory though! It's subjective. Music theories are humanistic, cultural studies, not natural science. Jun 20 at 17:33

The two chords in question are the dominant seventh chord and the leading tone diminished seventh chord.

Both chords can function as types of dominant harmony. Both chords contain the leading tone and the subdominant scale degrees and that is the main reason why they can work the same way.

If you overlap the two chords - the dominant seventh chord and the leading tone diminished seventh chord - you get a dominant seventh flat nine chord. In harmony theory there is a concept that dominant harmony - not a specific chord, but several chords that all function the same way, that function as dominants - are portions of this larger dominant seventh flat nine chord.

You figured out that concept intuitively.

Wouldn't this work for any song in practice?

Broadly speaking, yes. But, like anything else, the devil is in the details. A comparison case that comes to mind is a passing diminished seventh chord versus a generic dominant chord. The passing chord example might be `C C#dim7 Dm` the chromatic half steps `C C# D` form the main passing motion, along with `Bb` stepping down to `A`, and it creates a certain sound, technically it creates a specific kind of voice leading. If you instead played `C A7 Dm` you will get a progression that is functionally the same, in a generic sense, but you will get a different voice leading. In some songs the passing chromatic steps may be a critical part of the song's identity, in which case swapping out the chord ruins the effect. A song like Ain't Misbehavin' is an example.

Side note: you mix up sharps and flats when "spelling" the leading tone and that make your question a bit hard to read. Your first example is in `D` minor, the dominant seventh chord being `A7`, the leading tone of the key being `C#`, and so the leading tone diminished seventh chord is `C#dim7` not `Dbdim7`. In the second example with `E7`, the key would be `A` (major or minor), the leading tone would be `G#`, the leading tone diminished seventh chord would be `G#dim7`.

Chord tones are spelled out in thirds `A C# E G Bb`, `E G# B D F`, etc. etc.

• "Bother [sic] chords contain the leading tone"? :) Jun 20 at 20:08
• @paulgarrett, thanks! Fix that and a few other typos. Jun 20 at 20:24
• Or maybe any chord containing a tritone should be called a "bother chord" :) Jun 20 at 21:21

First, look at 'Phantom'. It's B♭dim7, root note B♭. Adding A to that chord isn't an option.

So, if you wanted to talk about D♭dim being equivalent to A7, you picked a bad example!

But, sure, let's talk about that anyway.

Yes, D♭dim (Or it might make more sense to spell it as C♯dim in this conversation) shares three notes with A7. And it's quite likely it might be used as a dominant of D, perhaps in the sequence C, C♯dim, Dm7, G7, C.

And, IN THIS CASE, adding an A bass note to the C♯dim wouldn't mess up the function of the sequence. You might even feel it enhanced it.

BUT IT WOULDN'T BE THE SAME. That's important enough to shout about! The chord would have the same function, but it would have a different flavour. A composer is entitled to ask for one or the other, and expect you to obey.

You are, of course, also entitled to say 'I'm just using your song as a basis for my jazz improvisation and I'll make whatever chord substitutions I like!' Which is fine, as long as you don't lose sight of the fact that one dominant-function chord is not the same as any other. C♯dim has a different flavour to A7, even though they both lead you to D. That difference of flavour can be musically important. It certainly shouldn't be merely dismissed.

• And then there are those who don't use other chords for creating jazz versions, but because they don't know what they're hearing or reading, or can't tell the difference. "I'll make whatever chord substitutions I like, because I only know three chords." :) Jun 21 at 17:29
• @piiperiReinstateMonica Yes, that's pretty much where I fear the original questioner was coming from! Jun 22 at 18:50