Yahoo Tuning Groups Ultimate Backup tuning Minor chords and 16:19:24

I've gone back through the tuning archives and looked for discussion
on the psychoacoustic basis of the minor chord. These are the four
options I've seen most widely suggested

1) Minor chords are utonal 4:5:6 chords, hence assuming utonality is
something that's recognized by the ear
2) Minor chords are 10:12:15 chords, which may or may not mean the
same thing as the above
3) Minor chords are 16:19:24 chords, because they're rooted
4) Minor chords are 6:7:9 chords, because they're the chord in the
vicinity with the least complexity
5) Minor chords are heard as fundamentally inharmonic, save for the
outer 3/2 dyad

I've never really been satisfied with any of these in isolation,
because I think that the logic behind each one is flawed. I'm not
going to go into why I think it's flawed, however, unless specifically
asked, because otherwise this message will get long. I want to advance
a sixth option, which is

6) Minor chords are essentially 96/95-tempered, which means they're
both 16:19:24 and 10:12:15 at the same time.

Has anyone considered this possibility before?

-Mike

🔗Mike Battaglia <battaglia01@...>

Might as well give a bit more explanation. All of this stems from the
recent time I've put in listening to these essentially-tempered
"dyadic chords," things like (245/243-tempered) 1/1-9/7-5/3, or
(875/864-tempered) 1/1-6/5-36/25-7/4.

These chords are truly magical, and their characteristic nature is
that they imply more than one VF, and different ones can be brought
out via what you're look for. Since "musical context" is a nice
systematic way to make you look for something, these chords are
goldmines in that they have more than one interpretation which can be
brought out contextually. For any VF that you hear in one of these
chords, the other incompatible notes are generally heard the same way
that you hear the major 6th in a major 6 chord - it's like 4:5:6 with
some nice vaguely pseudo-harmonic junk on top.

Another chord that fits this description perfectly is the minor chord,
which likewise has a few different choices of VF (and/or "root"),
which are selected by musical context. I think that there are a few
different ways to perceive minor triads:

(1:)10:12:15 - how pleasant, a major 7 chord! (fully resolved)
(1:)(junk:)4:5 - when you hear it as a major 6 chord in 2nd inversion
(1:)16:19:24 - the familiar "sad" version

So this postulates that when we hear minor triads as being "rooted"
and hence "sad," the "sadness" comes from that we're biasing virtual
pitch perception into hearing them akin to (1:)16:19:24, which is more
complex and hence more dissonant and hence "sad." I believe that Petr
mentioned that we didn't always hear minor chords as "sad but rooted
chords" but in the early Renaissance were treated like "unresolved
acoustic cloudiness", which I also think is noteworthy.

In short, I think that 96/95 might be a fundamental comma in the
perception of western music.

-Mike

On Sun, Sep 18, 2011 at 10:42 AM, Mike Battaglia <battaglia01@...> wrote:
> I've gone back through the tuning archives and looked for discussion
> on the psychoacoustic basis of the minor chord. These are the four
> options I've seen most widely suggested
>
> 1) Minor chords are utonal 4:5:6 chords, hence assuming utonality is
> something that's recognized by the ear
> 2) Minor chords are 10:12:15 chords, which may or may not mean the
> same thing as the above
> 3) Minor chords are 16:19:24 chords, because they're rooted
> 4) Minor chords are 6:7:9 chords, because they're the chord in the
> vicinity with the least complexity
> 5) Minor chords are heard as fundamentally inharmonic, save for the
> outer 3/2 dyad
>
> I've never really been satisfied with any of these in isolation,
> because I think that the logic behind each one is flawed. I'm not
> going to go into why I think it's flawed, however, unless specifically
> asked, because otherwise this message will get long. I want to advance
> a sixth option, which is
>
> 6) Minor chords are essentially 96/95-tempered, which means they're
> both 16:19:24 and 10:12:15 at the same time.
>
> Has anyone considered this possibility before?
>
> -Mike
>

🔗Kalle Aho <kalleaho@...>

With steady tones I hear 10:12:15:17 as more concordant than
1/1:6/5:3/2:12/7 even when the 2:3 determines the root.
1/1:6/5:3/2:12/7 has more concordant dyads so shouldn't it be more
concordant when the virtual pitch of 10:12:15:17 is not heard at 1?
But it is not.

I also hear 10:12:15:17 as more concordant than 16:19:24:27 (which is
nice too).

This suggests to me that there is something to being low in the
harmonic series even when the numbers don't align with the heard
strongest virtual pitch.

Kalle

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I've gone back through the tuning archives and looked for discussion
> on the psychoacoustic basis of the minor chord. These are the four
> options I've seen most widely suggested
>
> 1) Minor chords are utonal 4:5:6 chords, hence assuming utonality is
> something that's recognized by the ear
> 2) Minor chords are 10:12:15 chords, which may or may not mean the
> same thing as the above
> 3) Minor chords are 16:19:24 chords, because they're rooted
> 4) Minor chords are 6:7:9 chords, because they're the chord in the
> vicinity with the least complexity
> 5) Minor chords are heard as fundamentally inharmonic, save for the
> outer 3/2 dyad
>
> I've never really been satisfied with any of these in isolation,
> because I think that the logic behind each one is flawed. I'm not
> going to go into why I think it's flawed, however, unless specifically
> asked, because otherwise this message will get long. I want to advance
> a sixth option, which is
>
> 6) Minor chords are essentially 96/95-tempered, which means they're
> both 16:19:24 and 10:12:15 at the same time.
>
> Has anyone considered this possibility before?
>
> -Mike
>

🔗Mike Battaglia <battaglia01@...>

On Mon, Sep 19, 2011 at 12:48 PM, Kalle Aho <kalleaho@...> wrote:
>
> With steady tones I hear 10:12:15:17 as more concordant than
> 1/1:6/5:3/2:12/7 even when the 2:3 determines the root.
> 1/1:6/5:3/2:12/7 has more concordant dyads so shouldn't it be more
> concordant when the virtual pitch of 10:12:15:17 is not heard at 1?
> But it is not.

There are two sensations generally created when a "concordant"
sonority is played. Which one are we talking about? You have

1) the generation of a strong virtual pitch
2) the generation of periodicity/isoharmonicity buzz

From the standpoint of harmonic entropy, the word "concordant" simply
denotes how predominant a single virtual pitch is in the probability
distribution for the dyad or chord. If you're playing a chord in which
the dyads are internally concordant, but which all point to different
virtual pitches, then the resulting mass itself won't imply a single
strong virtual pitch.

> I also hear 10:12:15:17 as more concordant than 16:19:24:27 (which is
> nice too).

I hear 10:12:15:17 as generating stronger periodicity buzz than
16:19:24:27. But what about 6:7:9 or 6:7:9:10? I hear 3:6:12:24:28:36
as generating strong periodicity buzz, but I'm not sure it generates a
stronger virtual pitch than the above - if anything, something like
3:6:7:9 now generates a weaker, alternate virtual pitch that's
(1):3:6:7:9, whereas for it to really sound "subminor" I need to be
focusing on the 3.

I think it's mighty interesting that we have this concept of playing a
low note in the bass to establish the "root" of a chord.

> This suggests to me that there is something to being low in the
> harmonic series even when the numbers don't align with the heard
> strongest virtual pitch.

And that something is called "periodicity buzz," that's what.

-Mike

🔗Mark N <nowitzky@...>

Hi Mike,

I think of a minor chord (e.g., A minor) as a 5:6 (A:C) on the bottom and 4:5 (C:E) on the top. So you have three harmonic intervals (A:C, C:E, and A:E).

But I'm not talking about your option 1. I don't really think our ears recognize "utonality".

--Mark

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "Mark N" <nowitzky@...> wrote:
> I think of a minor chord (e.g., A minor) as a 5:6 (A:C) on the bottom and 4:5 (C:E) on the top. So you have three harmonic intervals (A:C, C:E, and A:E).
>
> But I'm not talking about your option 1. I don't really think our ears recognize "utonality".

This is pretty much how I would describe my thoughts on the minor chord too. It's a chord made of three very simple, identifiable intervals. Who cares if they're stacked in a way that doesn't jive with the harmonic series?

I don't have much of a rebuttal to the tempering-out-96/95 idea except this:

What if I said that, instead of 96/95 being tempered out (so that 10:12:15 is identified with 16:19:24), it's REALLY 385/384 being tempered out, so that it's really 64:77:96 being identified with 10:12:15? Could you prove me wrong?

Keenan

🔗Mike Battaglia <battaglia01@...>

On Mon, Sep 19, 2011 at 10:55 PM, Keenan Pepper <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "Mark N" <nowitzky@...> wrote:
> > I think of a minor chord (e.g., A minor) as a 5:6 (A:C) on the bottom and 4:5 (C:E) on the top. So you have three harmonic intervals (A:C, C:E, and A:E).
> >
> > But I'm not talking about your option 1. I don't really think our ears recognize "utonality".
>
> This is pretty much how I would describe my thoughts on the minor chord too. It's a chord made of three very simple, identifiable intervals. Who cares if they're stacked in a way that doesn't jive with the harmonic series?

This assumes that they don't jive. My proposal is that they may jive,
at least if the chord is heard as being rooted.

> I don't have much of a rebuttal to the tempering-out-96/95 idea except this:
>
> What if I said that, instead of 96/95 being tempered out (so that 10:12:15 is identified with 16:19:24), it's REALLY 385/384 being tempered out, so that it's really 64:77:96 being identified with 10:12:15? Could you prove me wrong?

No, obviously I can't. I also can't prove that 16:19:24 is right
either, nor can you prove that it's wrong. In fact, we won't be able
to prove any of this until we can do some kind of MEG like they did
with the subjects here:

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2565400/

However, we can throw around some educated ideas just for fun. In this
case, my idea was a simple proposal that's worth adding to the list of
possible explanations for "minorness," and hence also to the list of
ways to generalize it to hunt around for new minor chords.

16:19:24 becomes a decent candidate if you assume the following

1) Virtual pitch integration occurs over the entire spectrum, meaning
the notes in the bass count as well
2) In western music assuming octave equivalence, the lowest note is
doubled down a few octaves, which means that 16:19:24 is more like
1:2:4:8:16:19:24 or something.
3) 1:2:4:8:16:19:24 is simpler than 5:10:20:40:80:96:120 (10:12:15 on
top), and also simpler than 4:8:16:32:64:77:96 (your chord), so
inasmuch as harmonic entropy means anything, it's going to be a more
likely choice.

I think that these are decent assumptions to make, so I'm proposing
it. Also, the fact that you can hear minor chords as being relative
minors of major chords (or maj6omit5 chords in inversion) would
suggest that this could be well analyzed as an essentially
96/95-tempered chord. I obviously have no proof for this, but I think
it's worth an exploration for anyone interested in the line of
research of how to come up with new xenharmonic minor chords. I'm
personally interested in it because whereas I find major is easy
enough to generalize (moar otonality!), minor has been far more
difficult.

The other essentially-tempered chords also generalize the multiplicity
of perceptions inherent in the minor chord, and I note particularly
that the 875/864 tempered "magical seventh" chord sounds like a
diminished seventh in which the outer 7/4 "roots" it - kind of a
similar feeling to what minor does to my ears. They do mix random JI
chord "qualities" together in interesting and novel ways. The
245/243-tempered stack of two 9/7's likewise has this dual perception
as 9/7 + junk on top, or 5/3 + junk in the middle, and I like that
quite a bit. I suggest that they may be a good starting point for
designing "sad" chords if you want - just construct an
essentially-tempered chord in which one of the possible
interpretations involves higher complexity and more dissonance, and
see what you can get.

-Mike