Terhard/Parncutt subharmonic matching

regarding the root of the chord, I"m sure you're all familiar with Richard Parncutt's 1987 paper "the root of a chord"? (It can be found on his website). Academic wise, I believe it's the most definitive take on this, ( though I'm coming up with a different theory to account for why the minor triad is so tonally strong yet does not appear in the harmonic series in a strong fashion (unless you invert it, etc)). cheers, Kelly
--- In tuning@yahoogroups.com, chrisvaisvil@... wrote:

It seems to me to be better ultilized as a guide to chord substitution under the proper musical circumstaces.

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The chord CEG implies A, because E corresponds the 3rd harmonic of A, and G corresponds to the 7th. CEG also implies F, of which C is the 3rd harmonic and G is the 9th. CEG also implies D, of which C is the 7th harmonic and E is the 9th. Repeating the same procedure
*

So why is the root of 5:6:9 the 5?

-Mike

On Dec 18, 2012, at 11:48 PM, kellyjohnson5001 <kellyjohnson5001@...>
wrote:

regarding the root of the chord, I"m sure you're all familiar with Richard
Parncutt's 1987 paper "the root of a chord"? (It can be found on his
website). Academic wise, I believe it's the most definitive take on this, (
though I'm coming up with a different theory to account for why the minor
triad is so tonally strong yet does not appear in the harmonic series in a
strong fashion (unless you invert it, etc)). cheers, Kelly

> So why is the root of 5:6:9 the 5?

Is it the 5? I use to play around with Parncutt's subharmonic matching routine from his 1987 paper, but I don't have my notes with me. You mean, why is it 5, instead of 4? Me too, I'm not sure his approach is valid, given the mutliple 'weighted' candidate roots it gives. I think a gestalt process is simpler: if you have a patter of 3rds (5-6-9), then it's natural to extend the pattern down, or up, to the other 3rds. There's such a fixation on the harmonic series pattern in studying chord perception...but the harmonic series itself is equally spaced before it reaches our ear. It's harmonicity is a partly a product of our logarithmic middle ear...a fun topic to ruminate over

-Kelly

>
> -Mike
>
> On Dec 18, 2012, at 11:48 PM, kellyjohnson5001 <kellyjohnson5001@...>
> wrote:
>
>
>
> regarding the root of the chord, I"m sure you're all familiar with Richard
> Parncutt's 1987 paper "the root of a chord"? (It can be found on his
> website). Academic wise, I believe it's the most definitive take on this, (
> though I'm coming up with a different theory to account for why the minor
> triad is so tonally strong yet does not appear in the harmonic series in a
> strong fashion (unless you invert it, etc)). cheers, Kelly
>