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I've always considered a diminished chord to be a stack of minor thirds.

But when I think about this, it causes me problems when I try to name the notes.

For instance in a C# diminished chord, we have C#, E natural, G natural and Bb

The intervals between each pair of notes is a proper minor third. So far so good.

But—a minor third up from the top note, Bb, is Db, which although it is enharmonically the same pitch as C#, isn't a C#

Is my initial premise about the structure of diminished chords correct? And is there a way of naming the notes that doesn't involve enharmonic equivalent note names, or lots of double flats?

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Let's consider this

  • Every interval of a "third" is a step over one note name, for example from C something to E something. The somethings can be e.g. natural, flat or sharp
  • In a diminished chord you have three notes and TWO such steps
  • In a fully diminished seventh chord you have four notes and THREE such steps

C fully diminished seventh should be

  • C something
  • E something
  • G something
  • B something

If all the steps are minor thirds, then I get the following solution for the somethings:

  • C natural
  • E flat
  • G flat
  • B double-flat

If you want to voice the chord with doubled notes in the next octave you're left with the interval from B double-flat to the next octave's C. Because it's from B something to C something, it must be some kind of a second. So is that an augmented second then?

Following this same logic, let's see what kind of a solution we get for C# fully diminished. Remember, because they're thirds, it has to be C something, E something, G something, B something.

  • C sharp
  • E natural
  • G natural
  • B flat

At the end of the day, I see the whole thing as a theoretical kludge, trying to shoehorn music to fit into theory. Fully diminished chords fit the diminished eight-note scales nicely (unless you think about the note names), but the note naming scheme is based on having seven note names. In tunings we have commas, and in note naming we have this. Sometimes you'll find bits of theory that seem to describe music in a meaningful way, sometimes not.

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  • Those are significant points about the conflict between eight-note and seven-note scales, and about how the intervals within the diminished chord must be thee minor thirds and some sort of second, rather than four minor thirds.
    – Brian THOMAS
    Feb 13, 2021 at 10:37
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    @BrianTHOMAS Yes, the seven-note way of thinking and eight-note way of thinking are a bit like different languages. If your thinking is fixed to the seven-note idea - and our note naming system is based on that assumption! - then having more notes per octave and these weird diminished seventh chords feel like the rules of nature are being bent. It's like in Japanese, you have past tense forms of adjectives, so there are separate words for "currently yellow" and "yellow in the past". You need to use a different structure to translate that, because a single word won't work.
    – piiperi Reinstate Monica
    Feb 14, 2021 at 12:03
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The intervals are minor thirds. But the naming convention comes from a formula using the degrees of the major scale.

(1, b3, b5, bb7)

So, the letter names must match this convention to provide the expected spelling of the chord. In your example, E#, G#, and B# are the 3rd, 5th, and 7th degree of C# maj. Hence their appearance in the spelling. You are now using Bb as the starting point to jump a minor 3rd (which is okay) but then using its 3rd in the spelling (which breaks the standard spelling convention). As a side note this might be different in Just tuning rather than 12TET.

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The seventh of any chord is a second away from the octave.

The issue at hand is not unique to diminished (seventh) chords. The basic interpretation of all seventh chords are stacks of major and/or minor thirds. A C# dominant seventh, for example, is (from bottom to top) is C#-E#-G#-B (M3-m3-m3). The seventh, B, is a (major) second away from the octave, C#, not a third.

In the diminished seventh case, the seventh is an augmented second from the octave.

As Michael Curtis points out, the third above the seventh is the ninth, rather than the octave. It's just that in a diminished seventh chord, the octave and the (diminished) ninth happen to be enharmonically equivalent.

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I think part of the problem is how you called the chord generically a "diminished" chord instead of specifically "diminished seventh" or "diminished ninth" chord. As you stack up the thirds you need to keep those extensions in mind.

But—a minor third up from the top note, Bb, is Db

This introduces the same problem. You are now talking about some kind of ninth chord. If you disregard the sharps and flats and just look at letters C E G B D you can see it's some kind of ninth chord.

C# E G B♭ makes the first part specifically a diminished seventh chord.

Now just add on the ninth, lets use octave numbers to make the ninth clear, C#4 D♭5. You want to call that an octave, because the notes are enharmonically equivalent to an octave, but your spelling is a diminished ninth.

C# E G B♭ D♭ is a diminished ninth chord.

Of course it is enharmonically equal to a plain diminished seventh chord, but if you want to spell it with a diminished ninth, then name it with a diminished ninth.

And is there a way of naming the notes that doesn't involve enharmonic equivalent note names, or lots of double flats?

Let's do it again but with a root of C natural.

Start with letters C E G B D

Apply flats to make a diminished ninth chord C E♭ G♭ B♭♭ D♭♭

The way to avoid it is either:

  • don't bother with the diminished ninth, spell it a just a diminished seventh chord C E♭ G♭ B♭♭ C
  • use a different root to avoid double flats C E♭ G♭ A C, now it is an A diminished seventh chord.

You probably should not switch around the root to avoid double flats at the expense of clear harmonic function. C diminished seventh should resolve to a tonic of D♭ an A diminished seventh chord should resolve to B♭. Use the spelling that make the function clear.

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Within tuning differences, I'd say your idea of a diminished chord as a stack of minor 3rds is correct.

There are differences between diminished chords and the diminished 7th chords you mention in all but name - regular diminished chords have no 7th and consist of only 3 pitch classes (e.g. C♯-E-G).

There are ways to name some diminished 7th chords that don't involve enharmonic equivalent note names or lots of double flats - just start with sharps instead. (If you're lucky, you can get away with starting with naturals.) Your initial C♯-E-G-B♭ is on the right track. So are D♯-F♯-A-C and B-D-F-A♭. Just don't try looping them back onto themselves.

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Whilst a diminished chord appears to be stacked m3s, it actually isn't - quite. It's better to look at it from the more usual 1,3,5,7 aspect.

Thus, C diminished seventh will have letter names C E G and B. The root stays as such. The third is a minor 3, the 5th is a diminished 5, and the 7 is a diminished 7. So, the 3 is called E♭. The 5 is called G♭. The 7 is called B♭♭.

All that if the root is C. What if, with the same chord, the root is E♭? m3 is G♭. 5 is B♭♭. 7 is D♭♭. Slight change, and getting a little technical. No wonder a lot would write the B♭♭ as A! Having said that, I, along with I suspect many others, don't necessarily play the root as the lowest note. The whole chord goes round and round, and I often feel that the quoted 'root' is there either to fulfil some technicallity, or because that's what the writer decided it was going to be at that moment. Each to his own.

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