Questions on Carl's Hypothesis of Major & Minor

Hi Carl,
I've been trying to keep up with the rapid-fire discourse between you and Mike, but I can't do it. I missed the part where your hypothesis of minorness was laid out. Is it the case that you hypothesize that minor chords get their "quality" by having low tonalness and low roughness, while major chords get their quality by having high tonalness and low roughness?

Is "tonalness" a measure of how strongly a chord produces a single VF?

If tonalness vs. non-tonalness determines major vs. minor for chords of low roughness, what effect does varying roughness have on chord quality? What would quality would you predict that a chord with high tonalness and high roughness would have? Presumably, a chord with low tonalness and high roughness would just sound like gibberish, right?

But what about 6:7:9 vs. 14:18:21? Apologies if you already covered this with Mike, but the former is more tonal and less rough than the latter, right? The former would produce difference tones of 1, 2, and 3, while the latter would produce difference tones of 3, 4, and 7. So, shouldn't 6:7:9 sound more "major"?

-Igs

Hi Igs,

> I missed the part where your hypothesis of minorness was
> laid out. Is it the case that you hypothesize that minor
> chords get their "quality" by having low tonalness and low
> roughness, while major chords get their quality by having
> high tonalness and low roughness?

Yes.

> Is "tonalness" a measure of how strongly a chord produces
> a single VF?

Yes.

> If tonalness vs. non-tonalness determines major vs. minor
> for chords of low roughness, what effect does varying
> roughness have on chord quality?

It makes the chords discordant.

> What would quality would you predict that a chord with high
> tonalness and high roughness would have?

Impossible. Roughness ruins the signal -- it is the failure
of the cochlea to resolve the spectrum you are hearing.

> But what about 6:7:9 vs. 14:18:21? Apologies if you already
> covered this with Mike, but the former is more tonal and less
> rough than the latter, right?

The roughness should be the same, since they have the same
intervals (modulo some minor differences due to absolute
frequency effects). I would say 6:7:9 is more tonal and
happier, yes. It depends somewhat on whether the chord is
being heard as 2:something:3 or (4):6:7:9. The latter is
more likely if the chord is registered at C5 or above.
We can also try priming. Try playing 10:12:15, then
6:7:9 (6=10), then 4:6:7:9 (6=6) and then 6:7:9 (6=6) again.
Does it become happier? Or you might try simply
3:6:7:9 -> 6:7:9 vs 4:6:7:9 -> 6:7:9

Cheers,

-Carl

(I haven't been able to keep up with your correspondence
with Mike either)

Igs> What would quality would you predict that a chord with high
> tonalness and high roughness would have?

Carl>"Impossible. Roughness ruins the signal -- it is the failure
of the cochlea to resolve the spectrum you are hearing."

Finally something I completely agree with Carl on! :-D

Now a further question, where do neutral intervals fits between major and minor
in all of this
A) Do they have in-between levels of tonality/VF-ness compared to major (higher)
and minor (lower)?
B) Overall...is it fair to say that something with high roughness is likely to
have less directed emotion (unless the desired emotion is chaos/indecisiveness)
than something with low roughness? And, if so, how do neutral/major/minor
intervals likely weigh in on this scale?

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
> A) Do they have in-between levels of tonality/VF-ness compared to major (higher)
> and minor (lower)?

I'd think neutral chords would have lower levels of tonality. What's the lowest you can go in the harmonic series to get a neutral third between a 3/2? 18:22:27? Yeah, you'd get difference tones of 4, 5, and 9...not quite a clear VF. At least with 10:12:15, you get 2, 3, and 5 as difference tones...maybe ever so slightly more tonal.

Let's see...a super-major of 14:18:21 gives 3, 4, and 7. Perhaps this means that a neutral triad is less tonal even than a super-major? I don't know, I don't quite get how to calculate "tonalness" yet, but I do know that straight otonal chords (like 4:5:6:7) give difference tones of 1 between each adjacent pair, and difference tones of 2 between evens and odds, suggesting a strong single VF. So my guess about how "tonalness" works is that a chord will sound tonal when most of its intervals produce the same difference-tone frequency.

> B) Overall...is it fair to say that something with high roughness is likely to
> have less directed emotion (unless the desired emotion is chaos/indecisiveness)
> than something with low roughness? And, if so, how do neutral/major/minor
> intervals likely weigh in on this scale?

My guess would be yes, and that high roughness is necessarily low tonalness as well. Neutral chords are slightly tonal and somewhat rough in comparison to major and minor chords. It's interesting that in some ways, neutral chords feel "between" major and minor, and in other ways they feel completely outside of that distinction. They are strange creatures, indeed!

-Igs
>