Does a diminished first exist?

Question

Are there any instances where the first note in a scale/chord is "diminished"? For instance, could a Db occur in a D chord, where the context explicitly requires that this is a Db (diminished first) and not a C# (major seventh)?

One example of a chord where this could occur, is the chord consisting of Db-F#-A-C. I'd be inclined to call this a D chord with diminished first and minor seventh. However, due to the dissonance between Db and C, I don't think this chord is ever used.

Answer 1

Chord naming and interval naming are two pretty different things -- for example, your Db-F#-A-C chord's name would more likely focus on the F#, since you create a minor triad between F#-A-Db(C#). That's all highly contextual, and talking about prime or octave intervals in chord context is extremely rare.

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For the interval naming question, my understanding is as follows:

• 2nds, 3rds, 6ths, 7ths have major and minor variations with aug/dim at either extreme.
• 4ths, 5ths, primes, and octaves have a "perfect" variation, with aug/dim, again, to be used outside of this.

So looking at two notes -- D and Db. Depending on the register of each note, this interval is either going to be a prime or an octave of some flavor--both notes are some kind of D.

If the two notes are a half step away from one another, this interval is always called an augmented prime. The interval is one half step larger than a perfect prime, which is a distance of 0 half steps.

In the case that the two notes are in different octaves, suddenly the ordering dictates whether the interval is larger (augmented) or smaller (diminished) than a perfect octave:

• Db in lower octave, D in upper octave is an augmented octave, enharmonic to a minor 9th
• D in lower octave, Db in upper octave is a diminished octave, enharmonic to a major 7th

So to rehash the whole answer here: a "first" in chord talk necessarily is unmodified. If your chord is named X, even if that note in particular is only implied, any "variations" of that pitch would have a name of an upper chord member (9th or 7th). If the variated note truly was functioning as a chord root, then your chord is really bitonal and it never had anything to do with X in the first place.

In interval talk, you can't have a diminished prime because intervals can't have negative distance. You can instead have a diminished octave.

Answer 2

Dissonances as such aren't much of an issue – resolving a dissonant chord into a consonance to give that consonance a "finality" is one of the most important things in classical harmony. That's not the trouble.

Your chord has two other problems though:

1. What's dissonant? Well, as you've written it and intend the "diminished first" to work, the root would be in dissonance to all the other notes. However, if you render that chord on piano, the three lower notes won't sound dissonant at all, you'll likely perceive not an augmented third D♭-F♯ but a pure fourth C♯-F♯. Then, as NReilingh says, the lower three notes simply make up an inverted F♯-minor chord, though the high note would enharmonically have to be B♯ – that chord I'd interpret as a diminished-seventh chord B♯-D♯-F♯-A with a C♯ pedal point, resolving to C♯-major. Bach used that kind of effect a lot. But this has nothing to do with the "diminished first" effect, the C♯ would clearly just be a pure fourth up the implied G♯ root of that chord.
2. What should it resolve to? The diminished first, if it should make sense, should clearly resolve downwards. The F♯ should resolve upwards. That gives us the following options:
   • C and G. Simple enough, the chord would unambiguously be of C gender. But to complete it, you'd need to lead both upper voices a third up. That's an unusually large way to go (except in bass) when resolving a strong dissonance. Actually I really like the result if I go to c-minor, but it sure sounds quite foreign. The upper c would actually more "naturally" resolve downwards, but there's hardly options for that – only, it could stay on C or go to B♭. In both cases, you'd crave for an E to make a major tonic or dominant-seventh, but the alto voice has a hard time reaching an E.
   • C♭ and G or C and G♯ – if we interpret either this way we have much the same problem as in point 1.: an augmented fifth will be perceived as a minor sixth instead, unless we put it in the context of yet another crazy dissonance-resolution.
   • C♭ and G♯ – why, that's even more crazy!
   • Right then. András Hummer already brought up microtonality. The most relevant quarter-tone consonance is the eleventh harmonic, which is a kind of tritone. Unfortunately, it's a quarter-flat tritone, so by leading one voice a half step and the other a quarter we'd only get the inversion of this interval – that would certainly be too far-fetched to be perceived consonant. What we can do is step both in a quarter-tone. That brings us to an ordinary dissonant tritone, but that one can be used in an ordinary dominant-seventh purpose. And if I try that... Whoa! It works amazingly well.

Answer 3

Bit late, but didn't read any good comments. Chord naming aside. Yes you can get a Db-F#-A-C chord. Resolve for instance like Db-F#-A-C-Db, C-G-Bb-C-E, F-F-A-C-F All stepwise (except bass of course) as Db to E is an augmented second.

Wouldn't take that "quarter tone" example above serious. It sounds like a seriously out of tune version of C-E-G-C, C-F-A-C, Db-Gb-Bbb-C, C-Gb-Ab-Eb, Db-F-Ab-Db (which is why it "works well").