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The diminished chords and the augmented chords do not fit into any standard key signature. What is the best way to specify the notes? Initially, let's assume that the key signature is C major. For the diminished, which is better: C - E♭ - F# - A, C - E♭ - G♭ - A, C - E♭ - G♭ - B♭♭, something else? Similarly for the augmented chord: C - E - G# or what? How about, the same chords based on other notes? E.g. one semitone up, is it better to use C# or D♭?

Would it make a difference if the piece is not intended to be in any clear key and the C major signature was just for convenience or neutrality?

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  • They might not fit into a standard key signature, but they certainly fit into standard scales. The minor scale contains both diminished and augmented triads, e.g. B D F Ab and Eb G B in C minor.
    – user19146
    Apr 20, 2017 at 17:20
  • @alephzero A good point so, at least when in a minor key, that makes the choice of notation easy.
    – badjohn
    Apr 20, 2017 at 17:34

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Diminished and augmented chords (along with major and minor chords) are aspects of what we call tertian harmony, which indicates that these harmonies are built in thirds. Thus when we spell them, we want to make sure we spell them in thirds.

For the diminished triad, the preferred spelling is C E♭ G♭, since C to E♭ is a third and E♭ to G♭ is a third. Putting F# on top creates a second between E♭ and F#, which is not ideal.

But the fully diminished seventh chords (your C E♭ G♭ B♭♭) and augmented triads (C E G#) are a different story, because they're symmetrical. The fully diminished seventh chord is a cycle of pitches each separated by three semitones, and the augmented triad is a cycle of pitches each separated by four semitones. As such, any of those pitches can be the root of the chord, so there are multiple acceptable spellings for each of those chords.

The augmented triad, for instance, can correctly be spelled C E G#, A♭ C E, or E G# B# (though this last one is rare).

As for the fully diminished seventh chord, just make sure they stack in thirds from the bottom: C E♭ G♭ B♭♭, A C E♭ G♭, F# A C E♭, and D# F# A C are all acceptable. However, something like C E♭ F# B♭♭ is not correct, since there is no way to stack that harmony in thirds.

One final issue with the fully diminished seventh chords: if it resolves as a viio7--I, you want to spell the chord such that the half step below tonic is the root. So if the chord resolves to B♭, you'll want to spell the first chord based on A; if it resolves to G, you'll want to spell the first chord based on F#; etc.

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  • I'd have thought, in key E, that E G#B# is the best way to spell E+. No rarer than any of the other 11?
    – Tim
    Apr 20, 2017 at 17:44
  • It depends on how it's resolving (I didn't include this because I thought it would make the answer too long). If it's resolving to A, it doesn't matter the key: E G# B# is the best spelling. But if it's just an upper neighbor on the fifth, E G# C would be the best spelling.
    – Richard ♦
    Apr 20, 2017 at 17:46
  • Not being (too) picky, but if C features, it isn't an aug5, maybe a m6?
    – Tim
    Apr 20, 2017 at 18:01
  • Well it also depends on how "vertically" someone is thinking. If we sustain E G# in the lower voices while the upper voice moves B--C--B, I view this as just an elaboration of an E major triad. But if someone insists on calling that middle entity a chord, it would be an augmented triad based on C. (Not that I espouse that at all!)
    – Richard ♦
    Apr 20, 2017 at 19:29
  • Some interesting ideas here but some clash. Consider a diminished chord built on C within G minor. Richard's approach would suggest C-E♭-G♭-B♭♭ but it seems a bit odd to have G♭ when the key is G. Alephzero's approach would suggest C-E♭-F#-A as three of them are in the key signature and the other is a common note in G minor.
    – badjohn
    Apr 21, 2017 at 7:20
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I assumed that diminished chords took their name from the lowest note played, making that the 'root' from which the other minor thirds emanated. Thus with C at the bottom, the next would be Eb (m3) then Gb (d5) and if the diminished 7 was there as well, it would be just that - Bbb (d7).

Now whether that would make the 'correct' spelling for Ao (still in C) A, C, Eb, Gb is the question. If A is the base note, then a m3 above is C, then Eb (d5) and Gb. Same chord, same vertical voicing, but different inversion? If so, the Bbb of the other is now called A, and indeed written as A. In key A, maybe, if F#o features, it could be written F#, A, C, Eb. All a little confusing!

With augmented, there's only three notes to contend with, and the mere title ought to help the naming. C+ = C, E, G#. E+ = E, G#, B#. G#+ = G#, B#, Dx.

Lots of music with dims and augs I read isn't party to these 'rules', and I have to say that I get confused when it's not written 'correctly', but, on the other hand, it's often easier to read, if I'm not mentally analysing it as I go. But to see a chord written in the dots with a Bbb, with the chord symbol of Ao above is somewhat unnerving.

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  • I don't recall seeing a Ao / B♭♭ conflict but I could see that it could be confusing. Occasionally, I am surprised by the guitar chord and I have to stop and think for a moment. Sometimes the explanation seems to be that it has been simplified: the piano has a more complex chord than the guitar.
    – badjohn
    Apr 21, 2017 at 7:24
  • @badjohn - just checked a big band arrangement of Meditation - in Bb. One part with Dbo, next part (same melody later) C#o. Appropriate bass notes, but why call the same chord different names? Escapes me!
    – Tim
    Apr 21, 2017 at 7:36
  • That's pretty odd. It would suggest that someone figured out the guitar chords without attention to the context; I get that impression often. Maybe there was a change in shift between the translation of the two chords. I used to play in a big band (long, long ago) but I would not have noticed this as I just had my sax or clarinet part.
    – badjohn
    Apr 21, 2017 at 7:55
  • @badjohn - the dots reflected the chord naming, same progression before and after. Just poor writing, I'd say.
    – Tim
    Apr 21, 2017 at 8:22
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A lot depends on the harmonic context, on what chord is being set up. I'd try and spell the chord so that the leading tones make sense with where you are going harmonically or whatever key you might be modulating to (even if the modulation is very temporary and not for long enough to change the key signature).

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For me, it's simpler to think of the diminished seventh chord as derived from the scale degrees of a diminished octatonic scale. The diminished octatonic scale is: 1 2 b3 4 b5 b6 6 7.

So instead of the diminished chord formula equaling 1 b3 b5 bb7, it would be 1 b3 b5 6. This translates more easily in my mind.

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