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Commonly used scales such as the major and minor heptatonic scales contain only two different intervals between their neighbouring notes: the major second (whole tone) and the minor second (semitone). The common major scale has the semitones between its 3rd and 4th step, and 7th and 8th step, whereas the minor between 2nd and 3rd and 5th and 6th.

To create a trichord we take any note from the scale as a base note and and 2nd next and 4th next notes starting from the base one. The intervals between the base and 2nd and 2nd and 4th are always major or minor thirds (if we're using the scales mentioned above). These four combinations of major and minor thirds are all possible tertian trichords and their naming is well documented (e.g. C, Cm, Caug, Cdim).

Now, if we instead take a scale that contains different intervals between its neighbouring notes (semitones, whole tones, a whole tone plus a semitone), we can end up with different intervals between a base note and its 2nd next and between the 2nd next and 4th next: we could have a chord made out of a major second and major third.

In other words, the three notes have 2 and 4 semitones between the chord's notes.

How do we name such non-tertial chords? Are there rules for naming secundal-tertian or other hybrid (tertian-quartal?) chords?

  • You're considering natural minor. Don't forget melodic, and also the commonly used harmonic, with a tone and a half between 6 and 7. – Tim Aug 23 '16 at 12:09
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Chord names and symbols themselves are tertian ideas as they grew out of functional harmony. There are some chord symbols that kind of convey quartal or quintal ideas like the 7sus4 and the 6/9 chords, but how they are names still reflects looking at them as tertian. If I understand you correctly and you would have a C, D, and E for example I would be tempted to call it a Cadd9 as the only note missing in this is the 5th which is implied by the root.

There are ways to look a chord that may make more sense then relying on tertian ideas. One is pitch class set where all notes are enumerated from 0 to 11 for that repeat each octave. this you can look for similar relationships between sets. The 0 can be any starting note that makes sense, but to keep with the traditional ideas C is typically 0.

In a pitch class set a C major chord would be represented as [0, 4, 7] and any major chord in any inversion would reduce to this as its prime form which is just smallest way to represented the chord in an enumerated fashion like this. You can even extend these ideas to any system with a set number of pitches like 24 equal temperament if desired, just the numbering change. In the example above, you would just look at it as [0, 2, 4] which could make much more sense than the Cadd9 chord symbol.

This site gives a good list of possible pitch class sets and what they would be in traditional music and as you'll see a good chunk of them are not tertian in nature.

  • Thanks for your extensive answer! I have a follow-up: The chord with a major second (whole tone) and a major third (two whole tones) interval would be C-D-F#. It is a secundal-tertian hybrid. Does it have a name? – hvth Aug 23 '16 at 14:26
  • Honestly, I'd look at it as D7 in third inversion without a 5th. You typically don't look at multiple systems in the same chord as it screws with the goals of each different type of harmony – Dom Aug 23 '16 at 14:40
  • I've never understood why C,D,E should be called Cadd9, when the 9 is actually a 2. I'd go with C,D,F# as 3rd inversion of D7 too. - D7/C. – Tim Aug 23 '16 at 14:42
  • I found it in the table you linked: it is a 0-2-6 and is called Incomplete Dominant-seventh Chord.1/Italian-sixth, it seems. – hvth Aug 23 '16 at 14:46
  • @Tim chord symbols are never meant to show voicings, only what notes make up the harmony. It could be it is C, D, E, in closed position or the D could be a 9th away from the C. – Dom Aug 23 '16 at 14:53

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