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I'm writing a piano app for a high school class I teach and I'm trying to figure out the best algorithm to name chords related to a specific key. I'll use C major as the example for this question.

I've figured out how to name some of the chords that exist in neighbouring/related keys. For example, the chord D major is borrowed from the key of G acting as a V of V. What's the connection for a chord like Db major (the bII chord)? Or a chord that begins on F# (or Gb)?

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Hmm, interesting question. I assume you're using uppercase and lowercase Roman numerals to distinguish chord quality? If so, I see two options.

Accidentals and Roman Numerals

D major, as you've correctly said, is best shown as V/V and not II. But F♯ wouldn't be V/vii°, because that doesn't exist. But it would be silly to write it as V/V/iii, which sometimes does happen. Instead, this suggestion would be to write F♯ as ♯IV. If this F♯ chord were diminished, however, you could show it as vii°/V (not ♯iv°). D♭ would be ♭II, D♭ minor would be ♭ii, and so on.

This approach follows in the tradition of Heinrich Schenker; you can find his use of these Roman numerals in scholarly discussions of "secondary" and "double" mixture.


But that leads me to wonder how helpful that would be for high school students. (Maybe this is unfair of me to say, since I don't know the class or the students.) I wonder if throwing in all possible chords is that helpful? Are you really intending to use chords like ♯vi and ♭iii? Which leads me to my second recommendation:

Stick With Chords That Actually Occur in Music

By doing this, you could get rid of the nonsensical chords like ♭iii that either don't really happen, or aren't encountered until much later in one's music theory training. By doing this, it seems you could stick to the following chords in a major key:

  • I, ii, iii, IV, V, vi, vii° (and any sevenths you want)
  • Applied chords to ii, iii, IV, V, and vi (with sevenths as you like)
  • Modal mixture of ♭III, ♭VI, and ♭VII.
  • (You decide whether to include ii°, iv, and vii°7.)
  • The Neapolitan ♭II.

This latter option, in my opinion, seems to mimic real musical practice, and therefore the actual music theory that they'll be using.

  • I completely agree Richard. Those are precisely the chords I was trying to handle. The odd one out seemed to be the Neapolitan bII chord. The Modal mixture chords can be determined through the tonic minor. The issue with writing an app is that you have to determine rules that work in every situation hopefully in an elegant way. – 02fentym Jun 6 '18 at 4:24
  • @02fentym ♭II is a very common way of notating the Neapolitan, if that's what you're asking. – Richard Jun 6 '18 at 4:27
  • No, that's not what I'm asking. I'm reading note data from a MIDI file which is just a series of numbers essentially. Middle C is 60 for example. If they are playing in the key of B, then BD#F# should read B major, but if they're playing in the key of Cb, then it should read CbEbGb. The issue I'm having is how to identify chords that aren't as "cookie cutter".My strategy has been to match chords that exist in related keys. For the key of C, I'm using G, F, Em (rel min or G), Dm (rel min of F), Am and Cm (tonic min). None of those contain the Db chord so I'm trying to figure out the connection. – 02fentym Jun 6 '18 at 4:31
  • In key C, wouldn't V/V/V be Amaj rather than F#? Although I agree dom of dom of dom isn't helpful. – Tim Jun 6 '18 at 6:33
  • Can you actually have a dominant of a diminished (V/viio), as to me dominants usually lead to M or m? Genuine question! – Tim Jun 6 '18 at 7:32
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In C, Db is the Neapolitan chord. Normally it occurs in first inversion and gets the symbol N6. F# is often called vii0/V analogous to II being V/V.

However, the sound and effects of these chords is far more importan than their names.

  • Thanks for the reply. I understand what the Neapolitan chord is, but I'm wondering where it's derived from? Is there a key that it is borrowed from that relates to the key of C like the examples I listed above? – 02fentym Jun 6 '18 at 4:03
  • Some theory books claim the Neapolitan is borrowed from the parallel minor but the Db isn't diatonic to c-minor either. I prefer to think of the Neapolitan along with the Augmented Sixths as just modified sub-dominants. In one sense, they are "diatonic" to the key of C major (or minor) in that their use need not signal a modulation. (Of course, they can also be used to modulate.) – ttw Jun 6 '18 at 8:29
  • One way to understand augmented and Neapolitan chords is as a way to resolve a tritone. In key C, the common resolution of G7 is for the augmented 4th F-B to "expand" into the 6th E-C. But in equal temperament, the diminished 5th B-F is equivalent to an augmented 4th B-E# which would "expand" into the 6th A#-F#. So G7 will resolve onto an F# major chord, just as well as onto C major. You can also replace the F# chord with a 6/4 5/3 progression to get G7 B/F# F#. Now resolve Db7 the same way in key C and then omit the 7th, and/or re-spell the chord to get the various augmented 6ths. – user19146 Jun 6 '18 at 10:50
  • In C, and for the last 100 years or so, Db is quite likely to be most usefully analysed as a b5 substitution for the dominant. This isn't 'jazz harmony' as opposed to 'classical harmony'. It's quite mainstream. – Laurence Payne Jun 6 '18 at 14:46
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Sounds like a fun project, but it would be a mistake to give your students the impression that you can compute the proper, key-relative notation of a chord based only on the notes that comprise it.

For example, in the key of C major, consider a chord containing C, D, F#, and A. This could be a V of V in 42 position, or it could be a common tone chord written as I4+2. The chord has to be interpreted for its function in context. There are many other examples like this, especially if you're going to be looking at certain periods, e.g. the dissonant tonalism of the impressionists like Debussy often add minor sevenths and major sixths to chords, and telling which chord is which is sometimes pretty hard-- intervallically, they are identical. For example, a computer would have difficulty distinguishing an Am7 from a C with an added 6th.

Perhaps the program could work as an introduction to the concept, and then you could use the program to show how it isn't always correct. That would be a good lesson!

  • You're right, however, I would take the more common naming, which is V of V. The app should name it as a D/C chord essentially. And like you said, the app is an introduction to the concept. It's not going to handle everything. A key is always given in the MIDI file so all of the chords should be related to the given key. There's no need to go any further than that. – 02fentym Jun 6 '18 at 4:26
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    Minor sevenths aren't intervallically identical to major sixths. Diminished sevenths are. – Dekkadeci Jun 6 '18 at 5:51
  • @Dekkadeci An Am with a minor 7th is identical to a C major with an added 6th. Try analyzing the first few bars of Claire de Lune and you'll see what I mean. – John Wu Jun 6 '18 at 7:30
  • Am7 does have the same notational makeup as C6, although the way you phrased the penultimate para. doesn't make that clear. C6 isn't the same as Cm7. Hence Dekkadeci's comment. – Tim Jun 6 '18 at 7:36
  • In your comment the word "notational" is not very clear. It sounds like you are saying the notation is the same, which is untrue. YW – John Wu Jun 6 '18 at 7:39
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I suggest you name chords as what they ARE - a non-judgemental 'bVII' or 'II7' - let the student (and the context) decide what they DO. Sometimes it's a 'cycle of 5ths', dominants of dominants thing. Very often it isn't. For instance, in a C major song it's very common to find a Bb chord. It MIGHT be acting as 'subdominant of the subdominant' (The Beatles 'Get Back'). It may just be a pleasant-sounding 'chord next to C' with no functional reason whatsoever. Don't leap on the 'IV of IV' possibility with a 'Good! That's given THAT one a reason to exist!' attitude.

Chords don't have to be justified as 'borrowed'. Where did that idea come from? A chromatic chord MIGHT be a gateway to another key. But it equally likely might not. Call II 'V of V' if that's what happens. But not if it doesn't.

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It seems like you really have two questions here. The first, what do I name these "out of key chords" for the app. The other, what relation do these chords have to the key, or what purpose do they serve. As for the the first question it seems that you have a lot of good advice. I think you want to stick to classical music theory and harmony theory,especially if this is for educational purposes.

As to the second point we often use "out of key chords" in progressions. This could be due to a modulation in key (see Max Reger). It could be a classic chromatic plagal cadence (like IV to iv (minor IV) to I). Here the minor IV is out of key but serves a purpose. Chord substitutions, especially tri-tone. Hence you may see ii --> bii^o --> I6 (or I Maj7) or something similar. For your app stick to the advice of your top answer but it would be cool if, in a future version, the app could identify these patterns in a chord chart or music. These oddities have a specific function in music. Just an idea.

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