Talk:70:90:105:126

Name

This should be the subharmonic seventh chord, not 1/(7:6:5:4). 1/(7:6:5:4) is a half-diminished chord that doesn't even include a perfect fifth, and the term subharmonic alone isn't enough to signify that as the altering on the fifth should always be explicit. Also, the subharmonic ninth chord 1/(9:7:6:5:4) should extend the subharmonic seventh chord, so if 1/(7:6:5:4) is the subharmonic seventh chord, then 1/(9:7:6:5:4) can't be the subharmonic ninth chord. Finally, there's the neat symmetry that the harmonic sixth chord 6:7:9:10 inverts to the subharmonic seventh chord 1/(7:6:5:4) and the harmonic seventh chord 4:5:6:7 inverts to the subharmonic sixth chord 1/(12:10:8:7). —FloraC (talk) 08:58, 11 March 2026 (UTC)

Please see https://en.xen.wiki/w/Kite%27s_thoughts_on_harmonic_and_subharmonic_nomenclature. I believe it addresses all your objections. --TallKite (talk) 18:55, 20 March 2026 (UTC)

I think that's a good try. It's almost the best one can make out without awareness of the basics of inverting a chord in the practice of negative harmony. Unfortunately due to the lack of awareness, your nomenclature for seventh chords and onwards, as well as sixth chords, are all unnecessarily irregular.

In negative harmony practice, a chord is inverted not w.r.t the tonic but w.r.t. the midpoint of the tonic and fifth. The major triad inverts to the minor triad, but the dominant seventh chord inverts to the minor-major sixth chord. Since the minor seventh is a minor third above the fifth, inverting it makes it a minor third below the tonic, and octave-reducing it gives the major sixth.

Becuz you paired the dominant seventh chord with the minor seventh flat-fifth chord, your nomenclature shows several asymmetries:

• Your harmonic ninth chord is an extension of your harmonic seventh chord, but your "subharmonic ninth chord" isn't an extension of your "subharmonic seventh chord" up to octave reduction.
• Your harmonic eleventh chord corresponds to a common name, but your "subharmonic eleventh chord" doesn't.
• Your sixth chords are irregular special cases.

None of them is necessary. They are all fixed if you follow the negative harmony practice I laid out above, by pairing dominant seventh chords with minor-major sixth chords. From here, we further have dominant ninth chords with minor-major sixth added-eleventh chords, dominant added-eleventh chords with minor-major sixth-ninth chords, and dominant eleventh chords with minor-major sixth-eleventh chords. Assign 5/4, 7/4, and 11/4 to the appropriate diatonic categories and you'll sort all the JI chords out.

So in conclusion, I think I've made a good case for my initial request that 1/(9:7:6:5) is the subharmonic seventh chord, not 1/(7:6:5:4).

—FloraC (talk) 09:34, 21 March 2026 (UTC)