6:7:9 vs 10:12:15

This is a response to an experiment Carl asked me to try, but I can't find the original post.
I tried priming myself by playing 4:5:6:7:9, then dropping the 5 and then the 4 to see if I could get myself to hear 6:7:9 as "major". No dice! The second I even dropped the 5, I no longer had the impression of hearing a major chord, even with the 4 still playing. I heard a minor 7th chord, plain as day. Nothing "happy" or "bright" or major about the chord whatsoever. Just for kicks, I replaced the 5th harmonic with a 7/6 above the 4th harmonic, making a subminor 7th chord, and noticed no change in emotional quality over the 4:6:7:9 chord. The 9th harmonic did beat notably with the 7/6, though. However, dropping the 7/6 and adding the 5th harmonic back in pulled the chord back toward a major feel (although a slightly complicated major feeling due to the 7th and 9th harmonics).

I then played it as 3:6:7:9 and noticed no real change except that the chord sounded "thinner"; playing the 4 really thickens up the sound in a way that no octave-doubling of any other note in the chord does.

I then compared 6:7:9 with 10:12:15 (where 10 is the same pitch as 6, and 15 the same pitch as 9). I noticed that sure enough, the 10:12:15 sounded somewhat rougher, and also "thinner", which I presume means there was less of a VF being heard. The 10:12:15 was less "restful" than the 6:7:9 as well, and a little bit brighter. I would not call it more "major", and I *certainly* would not call it more minor...I might say that the emotional quality was the same between the two, but the smoothness of 6:7:9 made it a little "darker" or "rounder" sounding.

Also, with the 6:7:9 chord, I noticed that if you *don't* play the 4th harmonic, it really isn't all that obvious that the 6th harmonic isn't the root. It's painfully obvious when you *do* play the 4th harmonic that that's the real root, but if you never had that contrast, you'd probably never notice.

I also noticed an interesting phenomenon with harmonics 4:5:6: they "turn into" harmonics 12:15:18 if you play a note a 3/2 below the 4th harmonic. Interesting how adding or subtracting one note can change the VF of the entire chord.

Lastly, I noticed that the more harmonics I added to a chord, the stronger the VF became but the less "major" it sounded. IOW, 4:5:6:7 sounds less major than 4:5:6, 4:5:6:7:9 barely sounds major at all, and 4:5:6:7:9:11 doesn't sound even the least bit major to me. Aren't these higher-harmonic chords more tonal than the bare 4:5:6?

So, Carl, what do you make of this? If I still hear 6:7:9 as minor, even when played as 4:6:7:9, and if I hear it as less rough but no less minor than 10:12:15, does that mean a) that I'm just a non-ideal listener, or b) that tonalness is not the ideal indicator of minorness?

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> So, Carl, what do you make of this? If I still hear 6:7:9 as minor, even when played as 4:6:7:9, and if I hear it as less rough but no less minor than 10:12:15, does that mean a) that I'm just a non-ideal listener, or b) that tonalness is not the ideal indicator of minorness?

I hear 6:7:9 as both otonal and minor; as you say, a kind of dark, smooth minor.

Gene wrote:

> I hear 6:7:9 as both otonal and minor; as you say, a kind of dark,
> smooth minor.

Did you try these:

> 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?
>
> And you might try simply 3:6:7:9 -> 6:7:9 vs 4:6:7:9 -> 6:7:9.

?

-Carl

On Sat, Sep 18, 2010 at 6:39 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> > So, Carl, what do you make of this? If I still hear 6:7:9 as minor, even when played as 4:6:7:9, and if I hear it as less rough but no less minor than 10:12:15, does that mean a) that I'm just a non-ideal listener, or b) that tonalness is not the ideal indicator of minorness?
>
> I hear 6:7:9 as both otonal and minor; as you say, a kind of dark, smooth minor.

Indeed, smooth. I hear 6:7:9 as smoother than 10:12:15. 10:12:15 is a
bit "sadder" too, I think. In comparison, I also hear 20:26:30 as
smoother than 14:18:21, and equally less emotionally pungent.

-Mike

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

> Indeed, smooth. I hear 6:7:9 as smoother than 10:12:15. 10:12:15 is a
> bit "sadder" too, I think. In comparison, I also hear 20:26:30 as
> smoother than 14:18:21, and equally less emotionally pungent.

Huh, 6:7:9 sounds rougher than 10:12:16 to me... certainly this
would be expected from the Plomp/Levelt/Sethares perspective.

-Carl

Mike wrote:

> I also hear 20:26:30 as
> smoother than 14:18:21, and equally less emotionally pungent.

You mean 10:13:15. -C.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Gene wrote:
>
> > I hear 6:7:9 as both otonal and minor; as you say, a kind of dark,
> > smooth minor.
>
> Did you try these:

Nope.

One thought:

6:7:9 has the dyads 3/2, 7/6, 9/7 in it
10:12:15 has the dyads 6/5,5/4,3/2 in it

Thus, far as dyadic "limit-based periodicity" goes, 10:12:15 seems
superior...though so far as "triadic limit-based periodicity" goes 6:7:9 seems
the obvious winner as it is in lower numbered form as a triad .

Meanwhile 6:7:9 has the closest dyad in it (7/6) far as root-tone
roughness...but it also has 9/7, which obviously is further apart and thus has
less root-tone roughness than 10:12:15's largest "consecutive" dyad of 5/4.

Comparisons such as these seem to say neither chord ha a clear advantage, but
simply different kinds of consonance. And actually deciding which types of
consonance are more important, I'm guessing, could only truly be determined by a
listening test among many people.

-Michael

Michael wrote:

> 6:7:9 has the dyads 3/2, 7/6, 9/7 in it
> 10:12:15 has the dyads 6/5,5/4,3/2 in it
>
> Thus, far as dyadic "limit-based periodicity" goes,

Dyadic analysis isn't used for periodicity.

-Carl

Yes, but 10:12:15 is more "biting" in a different way than 10:12:15.
And 0-333-702 cents slightly even more so. The same happens if you
approach 5 in 4:5:6 from the other direction as well - 14:18:21 is
more biting than 10:13:15.

And if we're dealing with 4:5:6:7, and you detune 7 similarly, the
same pattern continues, I find. Detune both 5 and 7 and you get an
even "sadder" tetrad that can happen to coincide with the 7-limit
utonality if you bring them both down.

As a side note, I find the optimal amount to detune these is somewhere
around the "divergent unison" HE max at around 50 to 70 cents, as
George Secor noticed works spectacularly well for 17 equal.

Harmonic entropy strikes again!

On 9/18/10, Carl Lumma <carl@...> wrote:
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
>> Indeed, smooth. I hear 6:7:9 as smoother than 10:12:15. 10:12:15 is a
>> bit "sadder" too, I think. In comparison, I also hear 20:26:30 as
>> smoother than 14:18:21, and equally less emotionally pungent.
>
> Huh, 6:7:9 sounds rougher than 10:12:16 to me... certainly this
> would be expected from the Plomp/Levelt/Sethares perspective.
>
> -Carl
>
>

--
-Mike

On Sat, Sep 18, 2010 at 9:28 PM, Mike Battaglia <battaglia01@...> wrote:
>
> And if we're dealing with 4:5:6:7, and you detune 7 similarly, the
> same pattern continues, I find. Detune both 5 and 7 and you get an
> even "sadder" tetrad that can happen to coincide with the 7-limit
> utonality if you bring them both down.

And if you detune 6, of course, it gets worse. Bring it down, and you
get a diminished tetrad, bring it up, and it's still pretty scary
anyway.

Do the same with 4:5:6:7:9. Sharpen the 9 and you get something like
the Hendrix chord, which has its own feeling, flatten it, and you get
this kind of slightly mystical sound that sounds somewhat "minor" and
more emotional when put in a musical context. You'll note that the
effect predictably decreases as you alter higher and thus less
significant harmonics. In fact, if you keep 4:5 the same and alter
6:7:9:... (alter 8 if you want), there comes a point where the sadness
will "equal" that of the minor triad, or at least approach it. If we
take the b and # symbols to mean lowering and sharpening by this
divergent interval, then 4:5:6b:7#:9 is a good example of that, or
maybe 4:5:6b:7#:9#. Feel free to find nearby JI intervals so that the
whole thing isn't "rough" if you want, which if you think of this as
an extension of regular mapping in which "#" is a "prime," would be a
type of temperament.

This assumes you are playing both 1 and 2, or at least 2, in the bass below 4.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Huh, 6:7:9 sounds rougher than 10:12:16 to me... certainly this
> would be expected from the Plomp/Levelt/Sethares perspective.

You mean 10:12:15, I presume. What sort of timbre are you using to compare? I used a sawtooth wave. I think with numbers this low, periodicity might be more of a factor than the critical band. FWIW, this is not the result I was expecting. I had to play the two back to back several times to make sure my ears weren't playing tricks on me.

-Igs

Igs wrote:

> > Huh, 6:7:9 sounds rougher than 10:12:16 to me... certainly this
> > would be expected from the Plomp/Levelt/Sethares perspective.
>
> You mean 10:12:15, I presume.

Sorry.

> What sort of timbre are you using to compare?

Typical musical timbres.

> I used a sawtooth wave.

Not a typical musical timbre...

> I think with numbers this low, periodicity might be more of
> a factor than the critical band.

I agree. But somebody said "smooth", which is usually a term
used to discuss critical band effects.

-Carl

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> You mean 10:12:15, I presume. What sort of timbre are you using to compare? I used a sawtooth wave. I think with numbers this low, periodicity might be more of a factor than the critical band. FWIW, this is not the result I was expecting. I had to play the two back to back several times to make sure my ears weren't playing tricks on me.

It's not a straightforward comparison, as the chords have s different character, probably due to one winning in terms of critical band and the other in terms of periodicity.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> I agree. But somebody said "smooth", which is usually a term
> used to discuss critical band effects.

10:12:15 is harmonious but a little chaotic. 6:7:9 is darker but more coherent. Of course, if you don't give yourself time to listen they sound very similar.

<Me> Thus, far as dyadic "limit-based periodicity" goes,
Carl>"Dyadic analysis isn't used for periodicity."

...but you'd better believe it matters in this example no matter what the
formalities! Lower-limit = less complexity, stronger "dyadic limit
periodicity"...or whatever you want to call it.

I refuse to stab myself in the foot about the definition of periodicity. You
(Carl) seem to have a bizarre definition of periodicity that you refuse to
define in specifics. I've asked two PHD geophysicists about it and both have
given me an answer you said was wrong.

Plus you said the definition of periodicity "varies given different
circumstances". Due to this vagueness no wonder I'm confused. I'd say sine
waves of 100,200,400 hz have a "period" of 0.01 seconds because that's the time
of the GCD where all cycles of the wave intersect...given period = 1/frequency.
100hz does 1 cycle, 200 does 2 cycles, 400 does 4 cycles...within that time
frame. And that time frame in the above example is 1/100 (period for one cycle
of 100hz) = 0.01 seconds.

Yes, that's in mathematical specifics. Yes, considering two PHDs backed it up
and it's purely mathematical and not subjective...I'm sticking with that unless
not just you but several people tell me otherwise and give specific mathematical
examples.

For the record, the reason I said "limit-based periodicity" and not
"periodicity" is that I have given up trying to find your definition of
periodicity, but realize "periodicity" and "odd-limit" are about the closest
concepts I can think of to what I'm describing.

Regardless...on this list Igs, myself, and several others have related
dyads with low-numbered denominators. That's my point. Call it whatever you
want...but I wish we could just concentrate on solving the problem rather than
playing a guessing game of what we call each phenomenon. I'd call it a "level
of complexity" with regard to low-limit fractions having less complexity than
higher ones (as the Tonalsoft microtonal dictionary says)...but I'm pretty sure
you'd complain about that too.

So...what's your answer as to why "dyadic analysis isn't periodicity"...not
to mention a clean-cut version of your definition of periodicity? I can't read
your mind....no one can....so please don't expect me to.

Michael wrote:

> Plus you said the definition of periodicity "varies given
> different circumstances".

No I didn't.

> I'd say sine waves of 100,200,400 hz have a "period" of 0.01
> seconds

Yup.

> For the record, the reason I said "limit-based periodicity"
> and not "periodicity" is that I have given up trying to find
> your definition of periodicity, but realize "periodicity" and
> "odd-limit" are about the closest concepts I can think of to
> what I'm describing.

You seem to understand that the period of a waveform is the
time it takes to repeat. "Periodicity" is a notion from
psychoacoustics. Here is a high-ranking google result:

http://www.ncbi.nlm.nih.gov/pubmed/10714267

I don't know what "limit-based periodicity" is.

-Carl

Getting caught up here

Igs wrote:
>This is a response to an experiment Carl asked me to try, but I
>can't find the original post.

I summarized it here:
/tuning/topicId_92969.html#92974

> I tried priming myself by playing 4:5:6:7:9, then dropping the
> 5 and then the 4 to see if I could get myself to hear 6:7:9 as
> "major". No dice! The second I even dropped the 5, I no longer
> had the impression of hearing a major chord, even with the 4
> still playing. I heard a minor 7th chord, plain as day.

4:6:7:9 sounds like a minor 7th chord to you?

> I then played it as 3:6:7:9 and noticed no real change except
> that the chord sounded "thinner"; playing the 4 really thickens
> up the sound in a way that no octave-doubling of any other note
> in the chord does.

The experiment is whether 6:7:9 sounds any different after
being framed with either 4: or 3:.

> I noticed that sure enough, the 10:12:15 sounded somewhat
> rougher,

Boy, I don't get that.

> and also "thinner",

10:12:15 does sound thinner to me.

> Aren't these higher-harmonic chords more tonal than the
> bare 4:5:6?

I wouldn't say that.

> a) that I'm just a non-ideal listener, or b) that tonalness
> is not the ideal indicator of minorness?

or c) you used sawtooths and have to start over?

-Carl

On Sun, Sep 19, 2010 at 1:16 AM, Michael <djtrancendance@...> wrote:
>
> <Me> Thus, far as dyadic "limit-based periodicity" goes,
> Carl>"Dyadic analysis isn't used for periodicity."
>
> ...but you'd better believe it matters in this example no matter what the
> formalities!  Lower-limit = less complexity, stronger "dyadic limit
> periodicity"...or whatever you want to call it.

There is, however, a synergy that emerges when more than two notes are
played together, and which can't be ignored. The periodicities of each
individual dyad in 10:12:15 are simpler than those in 6:7:9, but 6:7:9
is more concordant overall. Then again, if you hear 6 as the root,
then the triadic concordance isn't quite happening for you.

Michael, try this:

5:6:7 by itself

vs

1.25:2.5:5:6:7

You will note that the first one is a nice, pleasant, smooth
microtonal sonority, that sounds slightly diminished unless you focus
on the virtual 1 popping out (which may be a habit that is partially
learned). The second one forces a perception of the 5 as the root and
is considerably more discordant. Dyadic analysis isn't quite as useful
here.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> > I tried priming myself by playing 4:5:6:7:9, then dropping the
> > 5 and then the 4 to see if I could get myself to hear 6:7:9 as
> > "major". No dice! The second I even dropped the 5, I no longer
> > had the impression of hearing a major chord, even with the 4
> > still playing. I heard a minor 7th chord, plain as day.
>
> 4:6:7:9 sounds like a minor 7th chord to you?

Well, I suppose it's more like "feels like". But it does indeed feel minor, and no less so with the 4th harmonic. Adding the 5th harmonic brings it back in a major direction, but as long as the 9th harmonic is sounding, that minor feeling is there.

> The experiment is whether 6:7:9 sounds any different after
> being framed with either 4: or 3:.

No, it doesn't.

> > I noticed that sure enough, the 10:12:15 sounded somewhat
> > rougher,

> Boy, I don't get that.

Okay, I probably used the term "roughness" wrong. I should have said "less concordant".

> > Aren't these higher-harmonic chords more tonal than the
> > bare 4:5:6?
>
> I wouldn't say that.

Can you define "tonal" then?

> > a) that I'm just a non-ideal listener, or b) that tonalness
> > is not the ideal indicator of minorness?
>
> or c) you used sawtooths and have to start over?

I anticipated that comment, so last night I tried: piano, acoustic guitar, and "distorted guitar" patches. No change.

-Igs

Igs wrote:

> > 4:6:7:9 sounds like a minor 7th chord to you?
>
> Well, I suppose it's more like "feels like". But it does
> indeed feel minor, and no less so with the 4th harmonic.
> Adding the 5th harmonic brings it back in a major direction,
> but as long as the 9th harmonic is sounding, that minor feeling
> is there.
[snip]
> > The experiment is whether 6:7:9 sounds any different after
> > being framed with either 4: or 3:.
>
> No, it doesn't.

Noted.

> > > I noticed that sure enough, the 10:12:15 sounded somewhat
> > > rougher,
>
> > Boy, I don't get that.
>
> Okay, I probably used the term "roughness" wrong. I should
> have said "less concordant".

Yes, ok.

> > > Aren't these higher-harmonic chords more tonal than the
> > > bare 4:5:6?
> >
> > I wouldn't say that.
>
> Can you define "tonal" then?

Tenney height may be one way to measure it partially-kindof.
In that case, 4:5:6 has slightly more tonalness
than 4:5:6:7:9etc.

Note I said tonalness. Unfortunately tonal has other
meanings... aargh.

-Carl

>"The periodicities of each individual dyad in 10:12:15 are simpler than those in
>6:7:9, but 6:7:9
is more concordant overall. "
Hmm...are you saying that in all (or "just" most) cases triadic periodicity
trumps dyadic periodicity?

Here's another perhaps more extreme example: 9:11:13 vs. 10:12:15.

Michael, try this:
5:6:7 by itself
vs
1.25:2.5:5:6:7

Bizarre...I hear very little difference...and what little difference I hear
I figure could easily be attributed to mere presence of the extra overtones. I
can kind of hear what you mean (if I'm following correctly) by 5:6:7 pointing to
a root at 1/1 and 1.25:2.5:5:6:7 pointing to a root at 5...but, mood wise, I
don't feel a huge jump.

On Sun, Sep 19, 2010 at 12:54 PM, Michael <djtrancendance@...> wrote:
>
> >"The periodicities of each individual dyad in 10:12:15 are simpler than those in 6:7:9, but 6:7:9
> is more concordant overall. "
>   Hmm...are you saying that in all (or "just" most) cases triadic periodicity trumps dyadic periodicity?
> Here's another perhaps more extreme example: 9:11:13 vs. 10:12:15.

If you play 9:11:13 by itself, it will probably sound more concordant
than 10:12:15. If you take the 9 and double it an octave or two below,
as in 2.25:4.5:9:11:13, and also do the same for 10:12:15, thus making
2.5:5:10:12:15, the 10:12:15 with octaves will be more concordant.

I have a theory of minorness that is related to Carl's, but differs
somewhat. My theory is that detuning the harmonic series slightly
causes not too much of a perceptual problem, but that detuning it
significantly can make it so discordant that it becomes painful, and
you want to just shut it off - unless you detune it to the extent that
it becomes another part of the harmonic series. As an initial test,
let's pick the global maximum of HE, around 60-70 cents, as the
interval to detune things by, since it maximally confuses your brain
between hearing this interval as a unison and something else. This
isn't a hard and fast rule, just use it as a guideline and find the
nearest most discordant sonorites possible.

Let's first see the pattern. So I'm going to denote an alteration by
this interval downward as "b" and upward as "#" respectively, just to
give you an intuitive grasp on what I mean. Again, in each case, don't
treat the 63 cents as a hard and fast rule, but rather an opportunity
to explore and find the nearest "maximally discordant" interval. Play
1 and 2 below all of these intervals. If you're in Scala, put the main
dyad first and the octave equivalent notes afterward, so 1:2:3 becomes
2:3:1, so you hear things in the right register. Let's see what
happens:

2:3:1 - concordant
2:3b:1 - discordant, ambiguous, slightly unpleasant unless you're used to it
2:3#:1 - also somewhat discordant, perhaps not as much as 1:2:3b
though. This is good if the 2:3 is about 2:3.1

I'm not going to write the octave equivalent notes anymore, just when
you play these sonorities, note that you should double the lowest note
by two octaves below:
4:5 - concordant
4:5b - sounds minor, perhaps "sad" is the word you'd use for this.
Note that 4:5b is about 5:6, so this sonority is about 1.25:2.5:5:6

4:5:6 - concordant
4:5b:6 - sounds minor, perhaps "sad" again
4:5b:6b - even more discordant, slightly more pain being added, this
is "diminished". If 6 is about 5.7 it works well here.
4:5:6b - we're keeping 5 unaltered but changing the less significant
6, this may sound "bright" or "exciting," but certainly slightly more
perceptually "painful" than 4:5:6 by itself. Perhaps not enough that
you'd use the descriptive word "painful", but the underlying concept
remains similar nonetheless.

Anyway, I'll spare you the rest of them, but this pattern continues
all up the series to present xenharmonic minor chords as well. I'll
just present next the "series of negativity," which you should hear as
intervals that are increasingly "negative" in an intuitive sense. They
may sound sad, then despairing, then frightening, then "turn this the
hell off." Here's the series:

4:5b:6 - you can make this 1/1 - 6/5 - 3/2, which is minor.
4:5b:6:7# - you can make this # even sharper than 60 cents for maximum
effect, presumably because of tetradic interactions I'm not aware of.
Try 1/1 - 6/5 - 3/2 - 27/18. (Note that if you do 4:5b:6:7b, you get
something like the 7-limit utonality, which is often perceived as an
"extension" of minor).
4:5b:6:7#:9# - make the 9# something like 37/16 or 14/6, and play
around by ear to get the "worst" note.
4:5b:6:7#:9#:11# - make the 11# something like 23:16, or play by ear
to get the "worst" note.
4:5b:6:7#:9#:11#:13# - make the 13# something like 53:16, or play by
ear to get the "worst" note. Again, you've had fun creating maximum
concordance, now try to create maximum discordance.
4:5b:6:7#:9#:11#:13#:15b - make the 15b something like 11:3.
4:5b:6b:7#:9#:11#:13#:15b - We just changed 6 to 6b. Make it 10:7

This should sound pretty unpleasant, and a clear extension of the
"minor" sound into ever increasingly frightening sonorities. I
recommend NOT turning the volume down as it gets worse to experience
the negativity full blast. The first two have been used in 12-tet for
a long time under the guise of the minor chord and the minor/maj7
chord. Sharpening the D doesn't really do much in 12-tet, because you
just get an octave doubling of the minor third, but chords like
C-Eb-G-B-D-F# or C-Eb-G-A-D-F# are often used to sound even more
hopeless than min/maj7 chords - note the F# is, itself, a sharpened
11:4.

Or, more intuitively, C-E-G is major, C-Eb-G is minor, and C-Eb-Gb is
diminished. Unless you can imagine the diminished chord in a more
positive context (e.g. as part of the otonal 5:6:7, it won't work too
well).

OK, let's have some more fun. Take that ridiculous sonority that we
just had, 4:5b:6b:7#:9#:11#:13#:15b. Then let's start resolving some
of the harmonics back:

4:5b:6:7#:9#:11:13:15 - resolve 6, 11, 13, and 15 back. Should sound
like it's "relaxing" a bit, I really like the resolution here.
4:5b:6:7:9:11:13:15 - resolve everything back but 5. Should sound like
it's relaxing more, and chilling out.
4:5:6:7:9:11:13:15 - whee!

Have fun with it. Your perception will no doubt differ from mine in
the exact labels used, or additional musical context you might imagine
chords in that might make them not seem "as bad" as me - but the
concept is accurate enough on some level to warrant continuing to
follow - right? :)

> Michael, try this:
> 5:6:7 by itself
> vs
> 1.25:2.5:5:6:7
>
>      Bizarre...I hear very little difference...and what little difference I hear I figure could easily be attributed to mere presence of the extra overtones.  I can kind of hear what you mean (if I'm following correctly) by 5:6:7 pointing to a root at 1/1 and 1.25:2.5:5:6:7 pointing to a root at 5...but, mood wise, I don't feel a huge jump.

Try 5:6:7:9:11 and 1.25:5:6:7:9:11 then. Then again, if you've always
heard 5:6:7 as having a root of 5, because you aren't conditioned to
listen for the VF at 1, then this experiment may not work on you. You
might want to take a break between the two chords to avoid priming
effects.

-Mike

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

> Try 5:6:7:9:11 and 1.25:5:6:7:9:11 then. Then again, if you've always
> heard 5:6:7 as having a root of 5, because you aren't conditioned to
> listen for the VF at 1, then this experiment may not work on you. You
> might want to take a break between the two chords to avoid priming
> effects.

The "register" is also important; that VF at 1 is a whole lot lower than the lowest note at 5, so if you're playing at or around middle C, it may be too low to hear. If you play a few octaves up, the VF might be more audible.

-Igs

On Sun, Sep 19, 2010 at 6:30 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Try 5:6:7:9:11 and 1.25:5:6:7:9:11 then. Then again, if you've always
> > heard 5:6:7 as having a root of 5, because you aren't conditioned to
> > listen for the VF at 1, then this experiment may not work on you. You
> > might want to take a break between the two chords to avoid priming
> > effects.
>
> The "register" is also important; that VF at 1 is a whole lot lower than the lowest note at 5, so if you're playing at or around middle C, it may be too low to hear. If you play a few octaves up, the VF might be more audible.

Igs: I'm glad you're saying this, because I think this is a direct
consequence of the critical bandwidth being larger in lower registers.
I'm working on a formulation of Harmonic Entropy that starts with a
filterbank of comb filters with a rolloff, and I'm trying to figure
out how to "spread" the harmonics out so as to encapsulate the
surrounding region. It occured to me that giving them a width that's
proportional to the critical bandwidth might be the best way to go. If
you factor in that the critical bandwidth is larger in lower
frequencies, it explains why the extent to which you detune things
matters less in lower registers (save for beating).

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Igs: I'm glad you're saying this, because I think this is a direct
> consequence of the critical bandwidth being larger in lower registers.
> I'm working on a formulation of Harmonic Entropy that starts with a
> filterbank of comb filters with a rolloff, and I'm trying to figure
> out how to "spread" the harmonics out so as to encapsulate the
> surrounding region. It occured to me that giving them a width that's
> proportional to the critical bandwidth might be the best way to go. If
> you factor in that the critical bandwidth is larger in lower
> frequencies, it explains why the extent to which you detune things
> matters less in lower registers (save for beating).

Y'know, I never quite understood the claim that tuning matters less in lower registers. Why is it that even pure JI chords like 4:5:6 sound like garbage when you get into the contrabass register?

-Igs