Equivalent chords

I'm just starting to learn music theory and this is one of the (possibly silly) doubts I've come into. Let's say we are in C major and we find this chord F-Ab-B-D. Well, it is just a Fdim seventh chord in root position, but we look at it and it's totally the same as a Bdim seventh chord in second inversion! Are they the same? Is there a reason why it's just one of the two? Are they functionally equivalent chords, so to say?

Thank you =D

• This has been answered before somewhere on this site. The short answer is that these chords resolve differently (they have different uses) even though they have the same notes. A chord name is determined by its usage rather than by its notes. In a non-equal temperament; the two chords would be different. There are only four fully diminished seventh chords (in equal temperament); these are symmetric in consisting of three diminished thirds; any one of these can act as the root depending on the chord's use.
– ttw
Nov 3, 2016 at 13:29
• So aren't there (up to inversions) just three chords, namely Cdim7, C#dim7 and Ddim7? Nov 3, 2016 at 15:30

It's the nature of diminished chords, using the usual formula of 1-3-5-7. Start with a root, make the next note up a minor third. The 5th is then diminished, and the 7th also.So, using your case, root=F, min3=Ab, dim5=Cb and dim7=Ebb. Not really 'stacked minor 3rds', but effectively the same.

So, yes, you're correct. That's the same sounding chord as B dim - B, D, F and Ab. Slightly different names, technically, due to different roots, but effectively the same sounding.

As there are only 12 notes available in Western music, that means there are, in a way, three 'different' diminished 7ths, because, as you saw, by the time you move up chromatically through those three, the next will contain the same notes as the first, and so on. They usually get named from the lowest, or root note, but I've seen the same chord shown with two different names in the same piece, probably due to each needing, or being given, a different root note.

• It's way too early to decide this answer is the one you like best. Other, better ones will probably follow!
– Tim
Nov 3, 2016 at 16:31
• Oh, sorry, I'm new here! By now this is the one I prefer, by the way =) Nov 3, 2016 at 21:38

You've discovered the symmetry of `dim7` chords. A diminished seventh chord is made of four stacked minor thirds. Each minor third is 3 semitones, and there are 12 semitones in an octave. Hence, they are symmetrical.

So, in fact, we can actually make four `dim7`s using your collection of four notes:

`Fdim7` (F, A♭, B, E♭♭)

`A♭dim7` (A♭, C♭, D, G♭♭)

`Bdim7` (B, D, F, A♭)

`Ddim7` (D, F, A♭, C♭)

Note that I've used some enharmonic equivalents (D = E♭♭, F = G♭♭, B = C♭). I'm sure you could also call it `C♭dim7`, `E♭♭dim7` and `G♭♭dim7`, but that's probably going a bit far.

In fact, there are really only three unique `dim7` chords. You could call them `Cdim7`, `C♯dim7` and `Ddim7`, but they have many possible names. We're talking about one of those three.

In any given key, you're most likely to run in to the `dim7` chord that belongs to that key. If you're in C Major, it's probably a `Bdim7`. If you're in E♭ Major, it's probably a `Ddim7`. That being said, the note in the bass is also going to suggest the most likely option.

• Isn't the second dim chord the same as the fourth? There are only three. I think there are four augmenteds.
– Tim
Nov 3, 2016 at 12:41
• More the voice leading than the note in the bass. Most of the time, the dim7 is going to act like a truncated dominant m9, which isn't always in root position either (although the ninth in the bass was long considered a no-no, at least until a few years after Verklärte Nacht). @Tim, yeah - 3 different diminished seventh chords, 4 different augmented triads. It's the number of notes that can fit within a minor third or major third (excluding the next chord tone, i.e., 3 and 4 respectively) x the number of notes in the chord (4 and 3 respectively) = 12.
– user16935
Nov 3, 2016 at 13:48
• @Tim they are all the same chord. I'm not trying to illustrate the three unique dim7 chords; I'm trying to show that you can call that one specific chord by multiple names. I'll edit to make that clearer. Nov 3, 2016 at 21:09