A "neutral" triad between major and minor and its impact on consonance

Try the following chords (listed in order of consonance my ear interprets them
as)

1) 4:5:6 (major triad AKA 1/1, 5/4, 3/2)
2) 18:22:27 ("neutral" triad AKA 1/1, 11/9, 3/2...the 11/9 being almost
perfectly in between 5/4 and 6/5 on a logarithmic scale)
3) 10:12:15 (minor triad AKA 1/1, 6/5, 3/2)

I have a hunch that the ear prefers progression from larger to smaller
intervals in triads to the point that 18:22:26, despite being much higher limit
than even the minor triad, is still more consonant sounding than it, though less
consonant than the major triad. When you hear these chords...do you agree?

If so it also seems to beg the question...why not have scales where an
approximate 18:22:27 can (fairly well) substitute in for a major
chord...especially in scales with several near-11/9 intervals?

On Tue, Aug 17, 2010 at 4:47 PM, Michael <djtrancendance@...> wrote:
>
> Try the following chords (listed in order of consonance my ear interprets them as)
>
> 1)  4:5:6 (major triad AKA 1/1, 5/4, 3/2)
> 2)  18:22:27 ("neutral" triad AKA 1/1, 11/9, 3/2...the 11/9 being almost perfectly in between 5/4 and 6/5 on a logarithmic scale)
> 3)  10:12:15 (minor triad AKA 1/1, 6/5, 3/2)

At this point I have no idea which psychoacoustic percept we're
referring to when we say "consonance" anymore. So I'm going to go with
the minor triad, because A minor is on my TV right now. Never mind,
looks like it was just the vi chord, and it was in C major, so now I
like 4:5:6. So I'm going to plead the fifth and go with 6:7:9.

>    If so it also seems to beg the question...why not have scales where an approximate 18:22:27 can (fairly well) substitute in for a major chord...especially in scales with several near-11/9 intervals?

There are scales like that. Try messing around with 26-tet, or 33-tet,
or 40-tet, or 47-tet. Just mess around with the 7-note diatonic MOS
where the fifth is a super-flat meantone fifth and ignore that there
might be a better approximation to 5/4 somewhere else in the scale.
Either way, the major thirds there are like 350-360 cents, and still
are clearly recognizable as major thirds. And then try messing around
with 22-tet and 27-tet, where 9/7 substitutes for 5/4. Remember all of
those messages I just posted? They had a point! :)

-Mike

MikeB>"At this point I have no idea which psychoacoustic percept we're
referring to when we say "consonance" anymore."
Firstly I'm not referring to psychoacoustics...believe me if I was I would be
using the word concordance! :-S
Ugh, ok look...by consonance I meant sense of relaxation. Heck...I'm just
going to say resolvedness 100% of the time from now on. Because whenever I use
"consonance"... there's always someone going on off-topic about things like why
they, say, think I should be using the word "concordance". All the while, back
in reality, I'm actually avoiding that word on purpose to say "this interests me
because it seems to DEFY standard concordance theories to an extent".

>"Never mind, looks like it was just the vi chord, and it was in C major, so now
>I
like 4:5:6. So I'm going to plead the fifth and go with 6:7:9."
Now this is just getting useless...even if you completely missed my
intentional mention of consonance and not concordance I didn't mention a 6:7:9
once in my example...so what on earth are you talking about here?

>"Either way, the major thirds there are like 350-360 cents, and still are
>clearly recognizable as major thirds. And then try messing around with 22-tet
>and 27-tet, where 9/7 substitutes for 5/4"
Ah, ok. I knew you mentioned those tuning having such chords...I just didn't
think to categorize them as "halfway between major in minor...not just in math
but in feel as well." :-)

Although my general question is here is (again)...how many people on here
indeed think a triad with the second note between a major and minor third sounds
more relaxed than a minor triad but less tense than a major one?

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> Although my general question is here is (again)...how many people on here
> indeed think a triad with the second note between a major and minor third sounds
> more relaxed than a minor triad but less tense than a major one?
>

This question doesn't even make sense to me, since I don't accept the premises.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Try the following chords (listed in order of consonance my ear interprets them
> as)
>
> 1) 4:5:6 (major triad AKA 1/1, 5/4, 3/2)
> 2) 18:22:27 ("neutral" triad AKA 1/1, 11/9, 3/2...the 11/9 being almost
> perfectly in between 5/4 and 6/5 on a logarithmic scale)
> 3) 10:12:15 (minor triad AKA 1/1, 6/5, 3/2)
>
> I have a hunch that the ear prefers progression from larger to smaller
> intervals in triads to the point that 18:22:26, despite being much higher limit
> than even the minor triad, is still more consonant sounding than it, though less
> consonant than the major triad. When you hear these chords...do you agree?

Not remotely. The 18:22:27 comes in distinctly last. And y'know, I may actually put a 6:7:9 as more consonant than the 10:12:15. But maybe that's just my bad mood talking.

> If so it also seems to beg the question...why not have scales where an
> approximate 18:22:27 can (fairly well) substitute in for a major
> chord...especially in scales with several near-11/9 intervals?
>

You mean like the Mohajira scale you quite liked a while back?

Me>> If so it also seems to beg the question...why not have scales where an
>> approximate 18:22:27 can (fairly well) substitute in for a major
>> chord...especially in scales with several near-11/9 intervals?
>>
Igs>You mean like the Mohajira scale you quite liked a while back?
Right...although I wouldn't exactly call that type of scale common. Jacky
Ligon seems to use those sorts of things in his scales a whole lot to create
IMVHO very resolved-sounding chords.

Me>> 1) 4:5:6 (major triad AKA 1/1, 5/4, 3/2)
>> 2) 18:22:27 ("neutral" triad AKA 1/1, 11/9, 3/2...the 11/9 being almost
>> perfectly in between 5/4 and 6/5 on a logarithmic scale)
>> 3) 10:12:15 (minor triad AKA 1/1, 6/5, 3/2)
Igs>"Not remotely. The 18:22:27 comes in distinctly last."

Ha well...if that's the case across the board for most people beside myself I
suppose I'm going to have to give this hunch up. Far as the 6:7:9...funny
thing, it DOES sound more consonant than both the 10:12:15 and 18:22:27 to my
ears. That seems to say, even if order does matter...perhaps either it doesn't
matter as much as periodicity

Oddly enough though, when I tried an "inverse order 6:7:9" chord of 14:18:21,
it sounded considerably more resolved sounding. Then again, Igs...if you think
that example too fails this theory might have more to do with my tastes in
hearing than people's tastes in general.

On Wed, Aug 18, 2010 at 12:52 AM, Michael <djtrancendance@...> wrote:
>
> MikeB>"At this point I have no idea which psychoacoustic percept we're
> referring to when we say "consonance" anymore."
>   Firstly I'm not referring to psychoacoustics...believe me if I was I would be using the word concordance! :-S
>   Ugh, ok look...by consonance I meant sense of relaxation.  Heck...I'm just going to say resolvedness 100% of the time from now on.   Because whenever I use "consonance"...  there's always someone going on off-topic about things like why they, say, think I should be using the word "concordance".  All the while, back in reality, I'm actually avoiding that word on purpose to say "this interests me because it seems to DEFY standard concordance theories to an extent".

OK, in terms of relaxedness, all 3 of the chords really do differ
depending on my mood. There are some times when I find 4:5:6 more
relaxing, and some times when I find it too intense and 10:12:15 (or
more likely 16:19:24) is more what the doctor ordered. Dark and
soothing. And then there are times when 18:22:27 is also really
relaxing and "pastoral" sounding, and can be quite relaxing because it
hangs between the diatonic perception of being a major and a minor
chord, without actually being either. And if I'm tired of tonal
sounding stuff, 18:22:27 is about as relaxing as it gets.

6:7:9 is relaxing all of the time though.

> >"Never mind, looks like it was just the vi chord, and it was in C major, so now I
> like 4:5:6. So I'm going to plead the fifth and go with 6:7:9."
>   Now this is just getting useless...even if you completely missed my intentional mention of consonance and not concordance I didn't mention a 6:7:9 once in my example...so what on earth are you talking about here?

Just trying to inject some humor into this conversation :)

> >"Either way, the major thirds there are like 350-360 cents, and still are clearly recognizable as major thirds. And then try messing around with 22-tet and 27-tet, where 9/7 substitutes for 5/4"
>   Ah, ok.  I knew you mentioned those tuning having such chords...I just didn't think to categorize them as "halfway between major in minor...not just in math but in feel as well." :-)

Right, but that's my point. They still "feel" like major chords, even
though the fifths are definitely in neutral third territory. And the
9/7 supermajor chords of 22-tet or the wide-fifth superpyth scale of
your choice still "feel" like major chords. And like you, I also
prioritize feel over anything else, so the fact that JI ratios from
11/9 to 9/7 can all be used to evoke the same major chord "feeling"
that we're used to goes to show you just how relatively unimportant JI
is in the "feeling" produced.

When you process a chord, you tend not only hear what it "is," but
also what it "can do" - how it relates to other chords in its
vicinity, how "resolved" it sounds, etc. And the fact that we're
talking about "other chords" and "vicinity" goes to show you how
quickly we jump into to thinking, subconsciously, in terms of scales -
whether diatonic or chromatic or what not.

But if you make the fifth flat enough, you can make the major thirds
go all the way down into clear neutral territory, and if you make them
sharp enough, you can make them go into supermajor territory - and yet
they are still, very clearly, "major" chords on some level. What do
you think this means?

>    Although my general question is here is (again)...how many people on here indeed think a triad with the second note between a major and minor third sounds more relaxed than a minor triad but less tense than a major one?

Sometimes I could see that being the case, but go listen to Moonlight
Sonata and tell me that it would be more relaxing if the minor chords
were tuned up to neutral...

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Right, but that's my point. They still "feel" like major chords, even
> though the fifths are definitely in neutral third territory. And the
> 9/7 supermajor chords of 22-tet or the wide-fifth superpyth scale of
> your choice still "feel" like major chords. And like you, I also
> prioritize feel over anything else, so the fact that JI ratios from
> 11/9 to 9/7 can all be used to evoke the same major chord "feeling"
> that we're used to goes to show you just how relatively unimportant JI
> is in the "feeling" produced.

That's how it feels to you, but you keep assuming your feelings are universal. And I also think it depends a lot on the music, not just the listener. Maybe I'll try posting some examples.

>"And the 9/7 supermajor chords of 22-tet or the wide-fifth superpyth scale of
>your choice still "feel" like major chords. And like you, I also
prioritize feel over anything else, so the fact that JI ratios from11/9 to 9/7
can all be used to evoke the same major chord "feeling" that we're used to goes
to show you just how relatively unimportant JI is in the "feeling" produced."
Agreed. Though I'm wondering if certain chords are rated higher by people
over the average of several people's ratings IE "more relaxed sounding most of
the time".

>"6:7:9 is relaxing all of the time though."
I agree it is very very relaxing sounding...but I'm wondering why. It does
seem to throw in a bit of everything as far as mood...but I wish I knew how so I
could go and generate other chords with similar properties. The only thing that
stares at me at first glance is that there in one prime (7) and the root has
factors of both two and three....while meanwhile 4:5:6 has one prime (5) but the
last note has two factors (again 2 and 3). Maybe having more factors in the
root tone gives an advantage? Or...do you have any ideas "why 6:7:9 works"?

>"But if you make the fifth flat enough, you can make the major thirds go all the
>way down into clear neutral territory, and if you make them
sharp enough, you can make them go into supermajor territory - and yet they are
still, very clearly, "major" chords on some level. What do
you think this means?"

I am guessing the brain uses lowest and highest note in the chord to define a
scale to use to rate notes in-between. I'm a bit unclear though...are you
saying moving the fifth down while NOT having the third at all makes the third
sound lower?

If it does...I am wondering if the brain in fact gravitates its perception of
all notes toward the logarithmic center/midpoint of the highest and lowest note
of a chord.

Gene-replying-to-MikeB>"That's how it feels to you, but you keep assuming your
feelings are universal."

But I suspect, though people of course won't think chords "feel" the same,
that many will think relatively along similar lines. The most obvious example
being a major triad sounding more sweet than a minor one to many if not most
people...but I think the logic can extend to more complex chords.

You can also say minor sounds more relaxed in trance music than major or major
sounds more relaxed in pop music, for example. However (even in terms of just
the melody and not rhythm/tempo), I think you would be hard pressed to find
someone who would say trance music is less tense. I'd even go so far as too say
tense chords sound "relaxed" in tenser music and relaxed chords sound relaxed in
relaxed style music.

On Wed, Aug 18, 2010 at 1:52 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Right, but that's my point. They still "feel" like major chords, even
> > though the fifths are definitely in neutral third territory. And the
> > 9/7 supermajor chords of 22-tet or the wide-fifth superpyth scale of
> > your choice still "feel" like major chords. And like you, I also
> > prioritize feel over anything else, so the fact that JI ratios from
> > 11/9 to 9/7 can all be used to evoke the same major chord "feeling"
> > that we're used to goes to show you just how relatively unimportant JI
> > is in the "feeling" produced.
>
> That's how it feels to you, but you keep assuming your feelings are universal. And I also think it depends a lot on the music, not just the listener. Maybe I'll try posting some examples.

I'm not assuming anything. I said that in response to Michael here:

> Ah, ok. I knew you mentioned those tuning having such chords...I just didn't think to categorize them as "halfway between major in minor...not just in math but in feel as well." :-)

So let me ask you: when you play with 26's diatonic scale, is it
recognizable? How about 33, or 40, or 26 + 7n? Assuming we're mapping
the fifth to be some ultra-flat, 1/2-comma meantone and beyond-size
fifth, and a major 3rd is 4 of those.

-Mike

On Wed, Aug 18, 2010 at 1:56 PM, Michael <djtrancendance@...> wrote:
>
> >"And the 9/7 supermajor chords of 22-tet or the wide-fifth superpyth scale of your choice still "feel" like major chords. And like you, I also
> prioritize feel over anything else, so the fact that JI ratios from 11/9 to 9/7 can all be used to evoke the same major chord "feeling" that we're used to goes to show you just how relatively unimportant JI is in the "feeling" produced."
>   Agreed.  Though I'm wondering if certain chords are rated higher by people over the average of several people's ratings IE "more relaxed sounding most of the time".

I would imagine so. But then again, I would also imagine that has to
do with their current conditioning.

> >"6:7:9 is relaxing all of the time though."
>   I agree it is very very relaxing sounding...but I'm wondering why.  It does seem to throw in a bit of everything as far as mood...but I wish I knew how so I could go and generate other chords with similar properties.  The only thing that stares at me at first glance is that there in one prime (7) and the root has factors of both two and three....while meanwhile 4:5:6 has one prime (5) but the last note has two factors (again 2 and 3).  Maybe having more factors in the root tone gives an advantage?  Or...do you have any ideas "why 6:7:9 works"?

Well, it is the simplest triad, other than 4:5:6, that has a fifth on
the outside. 10:12:15 beats it in terms of the consonance of each
individual dyad, but 6:7:9 beats it in terms of the strength of the
fundamental produced. Furthermore, 6:7 and 7:9 refer to the same tone,
although 6:9 refers to 3. But for 10:12:15, all of the dyads refer to
different fundamentals.

Whether 6:7:9 is "more" consonant than 10:12:15 I can't really say.
I'm not sure that it is. I think it just reflects a different "type"
of consonance, or a different way of hearing, than 10:12:15. 6:7:9 is
very consonant as a triad, and 10:12:15 is not, but has 3 very
consonant dyads. And all of this is ignoring the diatonic template
stuff I mentioned earlier.

-Mike