Talk:Rootminor triad/WikispacesArchive

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future developments

I think that this triad is a much better analysis of the quality of "minorness," and that this interpretation has the most psychoacoustic weight behind it.

In brief, there's a few ways to hear a minor chord: if the imagined root is something like (1):10:12:15, it doesn't sound "sad" at all. But if you hear the root of it as being something like (1):16:19:24, it does indeed sound "sad" and "minor."

This interpretation would suggest that the "sad" and "rooted" view is because you're hearing something like 16:19:24, which is more complex and hence more dissonant and hence "sad."

If the tuning list ever comes back to life and can arrive at some kind of consensus on it, this should just be changed to "minor triad." Until then, I'll leave the less controversial "rootminor" name up.

- mbattaglia1 September 18, 2011, 10:11:51 AM UTC-0700


You are never going to get a consensus on that.

- genewardsmith September 18, 2011, 10:38:05 AM UTC-0700


I was trying to be polite, but what I really meant to say was that

1) the tuning list isn't up to date on our modern understanding of pitch perception

2) I posted a thread about this to start the discussion and contribute some things I've learned recently

3) This thread will either end in a flamewar or it won't get a response and the tuning list will continue to die

4) I don't think I'll get consensus either, but not because of a carefully-planned rebuttal to this idea, but because of one of the above things

- mbattaglia1 September 18, 2011, 11:00:36 AM UTC-0700


I was thinking about it for decades, and finally I experimented with 16:19:24 using csound. And yes, it sounds reasonable - but how can I really believe it's because 19/16 is the "true minor third", if I'm so over-familiar with the 12edo third (3\12), which is only 2.5 cents from it?

BTW: It obviously breaks the theory of stacked thirds ("Terzschichtung" in German)

- xenwolf September 19, 2011, 12:34:33 AM UTC-0700


I don't think that it's necessarily that 16:19:24 is "the true minor chord" or anything like that. I think that's an oversimplification. Actually, my definition for "rootminor" chord is that it's an essentially-tempered mixture of 10:12:15 and 16:19:24, not just one of them.

You might want to take a look at some of the other essentially tempered dyadic chords on the wiki. For example, take a look at the "magical seventh" chord, which is 3 6/5's with a 7/4 on the outside. And take a look at the "sensamagic chord," which is two 9/7's that sum to 5/3 on the outside. Both of these chords can be heard in more than one way, which is characteristic of all the essentially tempered dyadic chords on this page.

For example, the magical seventh chord sounds "diminished," but because of the 7/4 on the outside it sounds "otonal" and "rooted." This chord blends those two sounds together in that way.

Likewise, the two 9/7's can evoke the feeling of there being a root 7/1 below the lowest note, kind of like (1:)7:9:(junk) - and, if you focus on the outer dyad as 5/3, they can also evoke the feeling of there being a root that's a 3/1 below the lowest note, kind of like (1:)3:(junk):5.

There may be other ways to hear these chords as well, those are just the most prominent for me.

Also, in the perception of the minor chord, let's say C-Eb-G, there's more than one way to hear it, depending on which root you pick:

C as root: sounds "minor" and "sad"

Ab as root: sounds like a maj7 chord and not sad

Eb as root: sounds like a maj6 chord in inversion with no 5th

It's been known for a while that the perceived "sadness" of the chord has to do with its perceived root - if you imagine it as part of a maj7 chord it doesn't sound as sad anymore. It's been proposed that the "sad" version of C minor comes from its being heard as 3/2 + "junk" - that the minor third is completely ignored by the ear as inharmonic. I've never seen any real proof for this, nor have any other 3/2 + "junk" chords been proposed as xenharmonic minor chords.

However, the other essentially tempered dyadic chords on this wiki are other chords that suggest a dual harmonic interpretation, much like the minor chord. Also, I note that despite that 10:12:15 is simpler than 16:19:24, 1:2:4:8:16:19:24 is simpler than 5:10:20:40:80:96:120. This is why I suggest that the fact that this chord can function in more than one way denotes that it's an essentially-96/95 tempered 10:12:15 chord.

- mbattaglia1 September 19, 2011, 01:03:30 AM UTC-0700


1:2:4:8:16:19:24 is simpler than 5:10:20:40:80:96:120. Indeed - nothing against 16:19:24 for minor chords :-)

Maybe I expressed it misunderstandable - I only wished to point on 3\12 and problems with the theory of de:"Terzschichtung".

...and finally I believe that we have not a high-precision perception of real frequencies, but we can deal very well with ambiguities (of each kind).

- xenwolf September 19, 2011, 01:40:39 AM UTC-0700