"corrected" evaluation...

12-11-00

I did another listening session of the new dyadic Tenney rankings.
The tetradic geometric mean list seems, on the overall, to do a
better job with the rankings.

My major concern was tetrads that seemed more *concordant* than they
should be in the new dyadic Tenney rankings.

First off… I have a retraction. The "stacked fourths" chord
0__492__980__1472 really does sound incredibly concordant. The #2
ranking on the new dyadic Tenney listing really reflects this. It
was unranked on the tetradic geometric mean list (not JI).

I thought tetrad #6-7: 0__502__1002__1390 should be more concordant
than #6-7. However, it was ranked #10 on the tetradic geometric
mean, so *neither* list seemed to make it as concordant as I wanted
it to be!

Tetrad #8-9: 0__388__702__970 should be near the most concordant in
my listening experience. As 4:5:6:7, it is ranked at the TOP of the
tetradic geometric mean list, so that listing does a better job with
it!

Tetrad #11-12: 0__498__702__886 should be ranked a *bit* more
concordant. It was #3 on the tetradic geometric mean list, so that
list did a better job with it.

Tetrad #15-16: 0__302__502__1004 seemed like it should be ranked a
*bit* more concordant. This one is not JI, so it is "unranked" on
the tetradic geometric mean list.

Tetrad #17-18: 0__204__702__1088 should be ranked as more
concordant. It is #5 on the tetradic geometric mean list, which does
a better job…

Tetrad #20-21: 0__318__816__1020 should be ranked *MUCH* more
concordant than this. (It's the 5:6:8:9). The tetradic geo list was
*MUCH* better with this one… it was #2.

Tetrad #27-28: 0__502__1002__1320 should be ranked more concordant.
It's exactly the same on the tetradic geo list, #28, so *neither* is
so satisfactory to me…

Tetrad #31-32: 0__388__776__1090 should be ranked more concordant.
It's #17 tetradic geo, so that list did a better job, to my ear.

Tetrad #33: 0__388__886__1274 should be ranked more concordant.
It's #13 on the tetradic geo list, so the geo list did a better job on
that one….

_____________ ___ __ _
Joseph Pehrson

>Tetrad #8-9: 0__388__702__970 should be near the most concordant in
>my listening experience. As 4:5:6:7, it is ranked at the TOP of the
>tetradic geometric mean list, so that listing does a better job with
>it!

How about its partner, 1/7:1/6:1/5:1/4, relative to some of the other utonal
chords on the list (remember, the DYADIC evaluation should be pretty
accurate when comparing utonal chords, since there's no otonal synergy to
worry about)?

>Tetrad #15-16: 0__302__502__1004 seemed like it should be ranked a
>*bit* more concordant. This one is not JI, so it is "unranked" on
>the tetradic geometric mean list.

Again, it is almost certain to get a _poor_ rating by a tetradic model.
However, it appears even the DYADIC model didn't make this consonanct enough
for you. How about its partner, 0_502_702_1004?

>Tetrad #27-28: 0__502__1002__1320 should be ranked more concordant.
>It's exactly the same on the tetradic geo list, #28, so *neither* is
>so satisfactory to me...

Hmm . . . this is an important jazz chord, so we indeed have an interesting
case here . . . its partner, 0_318_818_1320, seems a little more "weird"
even though it's simpler from an otonal (TETRADIC geometric mean)
perspective . . . would you agree? Oddly, TRIADIC considerations would seem
to support an opposite conclusion, since 0_502_1002_1320 contains a _minor_
triad, while 0_318_818_1320 contains a _major_ triad. Perhaps it's really a
question of familiarity?

So, other than this one chord, and the 0__502__1002__1390 chord, all the
chords you evaluated seem to be amenable to an interpretation involving
_both_ rankings, suitably combined. What about the chords you _didn't_
evaluate?

I wrote,

>So, other than this one chord, and the 0__502__1002__1390 chord, all the
>chords you evaluated seem to be amenable to an interpretation involving
>_both_ rankings, suitably combined.

Hmm . . . oops, there was also the 0__302__502__1004 which you thought was
too consonant for its place on both lists.

I have an idea for a better dyadic ranking . . . I'll increase the exponent
but decrease the standard deviation . . .

--- In harmonic_entropy@egroups.com, "Paul H. Erlich" <PERLICH@A...>
wrote:

http://www.egroups.com/message/harmonic_entropy/311

> >Tetrad #8-9: 0__388__702__970 should be near the most concordant in
> >my listening experience. As 4:5:6:7, it is ranked at the TOP of
the tetradic geometric mean list, so that listing does a better job
with it!
>
> How about its partner, 1/7:1/6:1/5:1/4, relative to some of the
other utonal chords on the list (remember, the DYADIC evaluation
should be pretty accurate when comparing utonal chords, since there's
no otonal synergy to worry about)?
>

Curiously enough, I listened quite carefully to the "pairs," but
many of them really did not seem similar to me. The chords I didn't
mention seemed pretty much in the right places... only the member of
the pairs that I thought was "more concordant than it was listed" I
felt should be moved. This happened with many of the pairs... (??)

And, I listened to the pairs carefully... thinking they SHOULD be
relatively the same... but they weren't (!!)

> >Tetrad #15-16: 0__302__502__1004 seemed like it should be ranked
a *bit* more concordant. This one is not JI, so it is "unranked" on
> >the tetradic geometric mean list.
>
> Again, it is almost certain to get a _poor_ rating by a tetradic
model. However, it appears even the DYADIC model didn't make this
consonanct enough for you. How about its partner, 0_502_702_1004?
>

So, at #15-16... 0__302__502__1004 is really doing "better" with the
Tenney ranking... Curiously enough, again, the "partner"
0___502___702___1004 was ok...

> >Tetrad #27-28: 0__502__1002__1320 should be ranked more
concordant. It's exactly the same on the tetradic geo list, #28, so
*neither* is so satisfactory to me...
>

> Hmm . . . this is an important jazz chord, so we indeed have an
interesting case here . . . its partner, 0_318_818_1320, seems a
little more "weird" even though it's simpler from an otonal (TETRADIC
geometric mean) perspective . . . would you agree?

Well, I'll have to listen to it again... but the "partner" seemed to
be in about the right place...

Oddly, TRIADIC considerations would seem to support an opposite
conclusion, since 0_502_1002_1320 contains a _minor_ triad, while
0_318_818_1320 contains a _major_ triad. Perhaps it's really a
question of familiarity?
>

Yet, 0___318__818__1320 is LOWER in the tetradic geometric mean
ranking... and that seems to be what I'm hearing. I only wanted the
OTHER one to move up (!!)

> So, other than this one chord, and the 0__502__1002__1390 chord,
all the chords you evaluated seem to be amenable to an interpretation
involving _both_ rankings, suitably combined. What about the chords
you _didn't_ evaluate?

I'm not sure, now that I got the charts right, that I would say
that... They STILL seem to follow the tetradic geometric mean chart
pretty well... better than either of the diadic charts, EXCEPT there
are a FEW that are much better like the 0___318___816__1020... in the
new diadic chart...

All the other chords seemed pretty appropriately ranked on the new
Tenney list... so I guess from THAT standpoint the ranking is about
as good as the tetradic geometric mean one...

Although, the chords that I mentioned REALLY seemed out of place...

__________ ___ __
Joseph Pehrson

>Curiously enough, again, the "partner"
>0___502___702___1004 was ok...

So you're saying you find 0__302__502__1004 considerable more concordant
than 0___502___702___1004? Hmm....

>I'm not sure, now that I got the charts right, that I would say
>that... They STILL seem to follow the tetradic geometric mean chart
>pretty well...

Except for the two chords above and the stack-of-fourths chord?

>> Hmm . . . this is an important jazz chord, so we indeed have an
>>interesting case here . . . its partner, 0_318_818_1320, seems a
>>little more "weird" even though it's simpler from an otonal (TETRADIC
>>geometric mean) perspective . . . would you agree?

>Yet, 0___318__818__1320 is LOWER in the tetradic geometric mean
>ranking... and that seems to be what I'm hearing. I only wanted the
>OTHER one to move up (!!)

Joseph, you must be reading something wrong, since 0_318_818_1320 is
15:18:24:32, while 0_502_1002_1320 is 45:60:80:96, so the former should be
HIGHER in the tetradic geometric mean ranking . . . if by HIGHER we mean
more concordant . . . right?

>All the other chords seemed pretty appropriately ranked on the new
>Tenney list... so I guess from THAT standpoint the ranking is about
>as good as the tetradic geometric mean one...

JOSEPH, Joseph, joseph -- Once again, the idea is not to compare the two
rankings against one another, but to try to understand that TETRADIC
harmonic entropy and DYADIC discordances are two separate phenomena
contributing to the overall sonance sensation. It is not productive to try
to focus on whether one ranking works better than the other, because each is
clearly way off in a number of cases (the TETRADIC one is way off for the
fourths-based chords mentioned above, and for chords like 9:11:13:15 which
Monz made a sound file of; the DYADIC one is way off for simple otonal
chords like 4:5:6:7, 5:6:8:9, and 6:8:9:10), and no amount of tinkering with
the specifics of the formulas is going to change that . . . What improvement
the latest version of the dyadic rankings may provide should be evaluated in
the context of being a _complement_ to the tetradic rankings, not as an
_alternative_ or _competing_ ranking . . .

--- In harmonic_entropy@egroups.com, "Paul H. Erlich" <PERLICH@A...>
wrote:

http://www.egroups.com/message/harmonic_entropy/317

>
> So you're saying you find 0__302__502__1004 considerable more
concordant
> than 0___502___702___1004? Hmm....

I realize that these tetrads were the subject of discussion before...
We had concluded that 0___502___702___1004, approximately expresssed
as 18:24:27:32, SHOULD be more concordant than 0__302___502___1004,
approximately expressed as 27:32:36:48... although they're only a few
chords different on the tetradic chart...

Well, I will listen to the #15-16 pair again... I am intrigued!

>
> >I'm not sure, now that I got the charts right, that I would say
> >that... They STILL seem to follow the tetradic geometric mean
chart pretty well...
>
> Except for the two chords above and the stack-of-fourths chord?
>

Right... The chord that I felt much better expressed by the diadic
Tenney was the stacked fourths:

0___492___980___1472

and the chord we were mentioning:

0___302___502___1004

And, there were several chords that I felt *NEITHER* list ranked
concordant enough:

0___502___1002___1390,

and

0___502___1002____1320

Other than that, my "anomolous" ones in the Tenney diadic listing,
followed the "better" or more concordant placement in the tetradic
geometric listing...

> >> Hmm . . . this is an important jazz chord, so we indeed have an
> >>interesting case here . . . its partner, 0_318_818_1320, seems a
> >>little more "weird" even though it's simpler from an otonal
(TETRADIC geometric mean) perspective . . . would you agree?
>

I'm going to listen to this #27-28 set and report back again... just
on a "listening" basis, without thinking too much about the chords...

> >Yet, 0___318__818__1320 is LOWER in the tetradic geometric mean
> >ranking... and that seems to be what I'm hearing. I only wanted
the OTHER one to move up (!!)
>
> Joseph, you must be reading something wrong, since 0_318_818_1320 is
> 15:18:24:32, while 0_502_1002_1320 is 45:60:80:96, so the former
should be HIGHER in the tetradic geometric mean ranking . . . if by
HIGHER we mean more concordant . . . right?
>

I was thinking of "lower" as being "more concordant" since the otonal
numbers were lower.... That's where THAT confusion came from...

> >All the other chords seemed pretty appropriately ranked on the new
> >Tenney list... so I guess from THAT standpoint the ranking is about
> >as good as the tetradic geometric mean one...
>

> JOSEPH, Joseph, joseph -- Once again, the idea is not to compare
the two rankings against one another,

OK... I won't try *THAT* again!

but to try to understand that TETRADIC harmonic entropy and DYADIC
discordances are two separate phenomena contributing to the overall
sonance sensation. It is not productive to try to focus on whether
one ranking works better than the other, because each is clearly way
off in a number of cases (the TETRADIC one is way off for the
fourths-based chords mentioned above, and for chords like 9:11:13:15
which Monz made a sound file of; the DYADIC one is way off for simple
otonal chords like 4:5:6:7, 5:6:8:9, and 6:8:9:10), and no amount of
tinkering with the specifics of the formulas is going to change that
.
. . What improvement the latest version of the dyadic rankings may
provide should be evaluated in the context of being a _complement_ to
the tetradic rankings, not as an _alternative_ or _competing_ ranking
. . .

Oh! Well, that's the first time I've really thoroughly started to
understand this! So it's a bit like a hologram... where there is an
ILLUSION of an image from different directions, but the total
corporeal effect isn't fully there...(??)
__________ ___ __ __
Joseph Pehrson

Joseph Pehrson wrote,

>I realize that these tetrads were the subject of discussion before...
>We had concluded that 0___502___702___1004, approximately expresssed
>as 18:24:27:32, SHOULD be more concordant than 0__302___502___1004,
>approximately expressed as 27:32:36:48... although they're only a few
>chords different on the tetradic chart...

Are you sure? I thought we had put these chords at the bottom of the geo
ranking, since they are essentially tempered: 0___502___702___1004 is no
more 18:24:27:32 than it is 20:27:30:36, and 0__302___502___1004 is no more
27:32:36:48 than it is 15:18:20:27.

>> JOSEPH, Joseph, joseph -- Once again, the idea is not to compare
>>the two rankings against one another,

>Oh! Well, that's the first time I've really thoroughly started to
>understand this!

Well, I kept harping on this point yesterday, which is why I got a little
frustrated that you seemed to continue in that vein today, so sorry for the
little rap on the knuckles there! But yes, this point is really basic to the
whole point of these experiments and the point of this list . . .

. . . and on that point, I have to say the tetradic problem is hopelessly
complicated. Not to mention the tetrads we're using here were not at all
designed for the purpose which Joseph ended up getting us to use them (with
many thanks to Joseph for the opportunities for interesting discussion).
What we should do is go back to dyads, and then tackle triads, which I have
some hope of being able to calculate chordal harmonic entropy for someday
(unlike tetrads).

--- In harmonic_entropy@egroups.com, "Paul H. Erlich" <PERLICH@A...>
wrote:

http://www.egroups.com/message/harmonic_entropy/324

> Joseph Pehrson wrote,
>
> >I realize that these tetrads were the subject of discussion
before... We had concluded that 0___502___702___1004, approximately
expresssed as 18:24:27:32, SHOULD be more concordant than
0__302___502___1004, approximately expressed as 27:32:36:48...
although they're only a few chords different on the tetradic chart...
>

> Are you sure? I thought we had put these chords at the bottom of
the geo ranking, since they are essentially tempered:
0___502___702___1004 is no more 18:24:27:32 than it is 20:27:30:36,
and0__302___502___1004 is no more 27:32:36:48 than it is 15:18:20:27.
>

Well, YES, we DID put them at the bottom of the ranking, but then we
tried to "squeeze" them in higher (more consonant) rankings by
invoking the ratios listed above.... Dunno why. Maybe it was a
mistake to do that (??) That's what I have in my notes, though...

> >> JOSEPH, Joseph, joseph -- Once again, the idea is not to compare
> >>the two rankings against one another,
>
> >Oh! Well, that's the first time I've really thoroughly started to
> >understand this!
>
> Well, I kept harping on this point yesterday, which is why I got a
little frustrated that you seemed to continue in that vein today, so
sorry for the little rap on the knuckles there!

No problem... It obviously wasn't totally "sinking in" and, although
I "heard" what you said, I obviously hadn't "ingested" it fully, so
went back to "comparing" things!

But yes, this point is really basic to the whole point of these
experiments and the point of this list . . .
>
> . . . and on that point, I have to say the tetradic problem is
hopelessly complicated. Not to mention the tetrads we're using here
were not at all designed for the purpose which Joseph ended up
getting us to use them (with many thanks to Joseph for the
opportunities for interesting discussion).

> What we should do is go back to dyads, and then tackle triads,
which I have some hope of being able to calculate chordal harmonic
entropy for someday(unlike tetrads).

Well, that would be more "focused" listening... more like first or
second "species" counterpoint! (Well, only diadic HARMONY). I'm all
for it. I thought the tetrads were really hard to hear and evaluate
anyway... If you notice, some people even "gave up" doing it, when
they had to rank them from "scratch." It was a wonder that David
Finnamore was able to do it like that!

I'm all for starting "simple." It would be an interesting listening
experience. If you manage to generate the diadic .mp3's I would be
more than happy to put them up on the Tuning Lab listening site.
Please, though, only send .mp3's this time!

_______ ___ __ _ _
Joseph

>Well, YES, we DID put them at the bottom of the ranking, but then we
>tried to "squeeze" them in higher (more consonant) rankings by
>invoking the ratios listed above.... Dunno why. Maybe it was a
>mistake to do that (??) That's what I have in my notes, though...

Do you have a message # to refer to here?

>Please, though, only send .mp3's this time!

You got it . . . perhaps 36 _random_ dyads, and I'll make it a _blind_ test
this time . . . what do you guys think?

--- In harmonic_entropy@egroups.com, "Paul H. Erlich" <PERLICH@A...>
wrote:

http://www.egroups.com/message/harmonic_entropy/327

> >Well, YES, we DID put them at the bottom of the ranking, but then
we tried to "squeeze" them in higher (more consonant) rankings by
> >invoking the ratios listed above.... Dunno why. Maybe it was a
> >mistake to do that (??) That's what I have in my notes, though...
>
> Do you have a message # to refer to here?
>

Unfortunately, I wrote those notes in pencil on a page with no
message
listing... In the future I will try to print directly from the
e-mail
message, rather than from some other documents I have copied messages
to! Or, at least, I will always include the #s!

> >Please, though, only send .mp3's this time!
>
> You got it . . . perhaps 36 _random_ dyads, and I'll make it a
_blind_ test this time . . . what do you guys think?

For me, that would work well... It seems quite easy to "prejudice"
judgements in any of this...

_____________
Joseph

Paul H. Erlich wrote:

> You got it . . . perhaps 36 _random_ dyads, and I'll make it a _blind_ test
> this time . . . what do you guys think?

:-)

--
David J. Finnamore
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--