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.
- Becuz you paired the dominant seventh chord with the minor seventh flat-fifth chord, your nomenclature shows several asymmetries:
- 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).
- Before we debate our disagreements, can we start with saying what we agree with? 1) I agree that the negative harmony approach of melodically inverting the chord and then moving the root down a fifth is a reasonable approach. BTW it's not true that I wasn't aware of it. I'm just not convinced it's the best approach. 2) Do you agree that "7th chord" can refer to not just the dom7 chord but also the min7, dim7, etc.? And the same for 6th chord, 9th chord, etc.? 3) Of all the chord names I have listed on my "Kite's Thoughts" page, which ones are the same as your names? --TallKite (talk) 19:48, 22 March 2026 (UTC)
- Right, I think the negative harmony practice is the best practice since it minimizes asymmetries. I agree on your (2). However, I don't see a need to assign harmonic/subharmonic-based names to all common JI chords, so I simply don't try. For example, 8:10:12:15 doesn't need a harmonic-based name, since it's 5-limit. Same with 10:12:15:18. I think you agree, as you said: "Often the resulting terms are rather useless, because it duplicates a much more widespread term." The chords that do need such terms are those that mix intervals of multiple primes, like 4:5:6:7.
- As for (3), my nomenclature is the same as yours for harmonic chords from seventh to thirteenth, as well as harmonic and subharmonic sixth chords. The subharmonic seventh chord is obviously different, and the subharmonic ninth chord I'm not super sure of. I don't really assign simple subharmonic eleventh or thirteenth chords as they are not very notable/useful to begin with. The useful ones are extensions of the subharmonic sixth chord: the subharmonic sixth added-eleventh chord 1/(24:20:16:14:9), the subharmonic sixth-ninth chord 1/(24:20:16:14:11), and the subharmonic sixth-eleventh chord 1/(24:20:16:14:11:9).
- Yes, I agree 5-limit chords like 8:10:12:15 don't need a harmonic name. But I do sort of like "harmonic third" for 5/4, since "major 3rd" includes 81/64, 4\12, etc.
- The "glue" that holds subharmonic chords together is the simplicity of the intervals between individual notes. This simplicity only occurs in certain voicings. 24:20:16:14:11:9 is a very dissonant voicing. 11:9:7:6:5:4 is much better. Because it has much simpler ratios. Surely we can agree that 9/4, 9/5 and 3/2 sound better than 16/9, 20/9 and 8/3? And likewise that 7/4, 7/5 and 7/6 sound better than 8/7, 10/7 and 12/7? And 11/4, 11/5 and 11/6 sound better than 16/11, 20/11 and 24/11?
- So what to call 11:9:7:6:5:4? Is it a sixth-ninth-eleventh chord with the 6th, 9th and 11th voiced below the root? Or is it simply an eleventh chord in root position, in the obvious voicing, a close voicing of stacked 3rds? The latter is much more straightforward. This is why the 11th subharmonic makes much more sense as a root than the 3rd subharmonic.
- Same with 24:20:16:14:11 vs. 11:7:6:5:4. Same for 24:20:16:14:9 vs. 9:7:6:5:4, but here the 9th subharmonic is the obvious root.