Yahoo Tuning Groups Ultimate Backup tuning LISTENING EXPERIMENT #3: THE MINOR TRIAD

With Carl Lumma's help, I've posted 9 different versions of a minor triad.
I'd like to hear people's (esp. Jerry's) reactions to these triads (ears
only please), and eventually I will reveal their true nature.

"Paul H. Erlich" wrote:
>
> From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
>
> With Carl Lumma's help, I've posted 9 different versions of a minor triad.
> I'd like to hear people's (esp. Jerry's) reactions to these triads (ears
> only please), and eventually I will reveal their true nature.

3 seconds a chord isn't very much to work with.

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On Tue, 29 Feb 2000 12:43:39 -0500, "Paul H. Erlich"
<PERLICH@ACADIAN-ASSET.COM> wrote:

>From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
>
>With Carl Lumma's help, I've posted 9 different versions of a minor triad.
>I'd like to hear people's (esp. Jerry's) reactions to these triads (ears
>only please), and eventually I will reveal their true nature.
>
>http://lumma.org/erlich/minor0.wav

This one has a distinct, subminor quality (1:7/6:3/2?). It certainly
doesn't seem to be in the same category as the others.

>http://lumma.org/erlich/minor2.wav

Just a bit flattish, but still has a minor rather than subminor quality.

>http://lumma.org/erlich/minor3.wav
>
>http://lumma.org/erlich/minor4.wav
>
>http://lumma.org/erlich/minor5.wav

These three sound pretty much like 12-TET. I'm guessing that one is
probably 19/16 and another might be 13/11, but there's not much difference
in the way they sound.

>http://lumma.org/erlich/minor6.wav

This one has a noticeable but not entirely unpleasant roughness.

>http://lumma.org/erlich/minor8.wav

This one sounds the smoothest. 1/(6:5:4)?

>http://lumma.org/erlich/minor11.wav
>
>http://lumma.org/erlich/minor12.wav

The last two are just a bit sharp to sound like minor thirds, but I guess
it would depend on the context.

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OK, at this point I figure everyone who wanted to has had a chance to check
these out, except for Joe Monzo who's on the road. Joe, or anyone else who'd
still like to listen to these, if you're reading this, stop now so as not to
bias your eventual responses.

I'll start by saying _all_ the examples had a just 2:3 perfect fifth
(701.9550�). Furthermore, they were all in just intonation; I wanted to
include some tempered examples to fill some of the "gaps" but I couldn't
compress them (due to the non-repeating waveform of irrational intervals) so
I didn't send them to Carl.

http://lumma.org/erlich/minor0.wav

Carl Lumma:
>7/6

Gerald Eskelin:
>third too low

Herman Miller:
>This one has a distinct, subminor quality (1:7/6:3/2?). It certainly
>doesn't seem to be in the same category as the others.

Carl and Herman are correct -- this was a 6:7:9.
Minor third = 266.8709�

http://lumma.org/erlich/minor2.wav

Carl Lumma:
>0 with mistuned 5th?
>diff. tone 3/2 below root - 3rd of minor triad sounds like 7/4

Gerald Eskelin:
>third too low; not pleasant by itself, but when I sing the
>"suggested" fundamental it sounds just fine. I suspect it is a
>6:7:9.

Herman Miller:
>Just a bit flattish, but still has a minor rather than subminor quality.

Carl and Jerry both imagined a fundamental suggesting (at least in part) a
6:7:9, but actually this was a 34:40:51, with the third almost 15� higher
than a 6:7.
Minor third = 281.3583�

http://lumma.org/erlich/minor3.wav

Carl Lumma:
>mistuned 2
>3rd seems to sharpen vs. 2, but doesn't

Gerald Eskelin:
>third too low, but does not lock to the fundamental suggested
>by minor2

Herman Miller:
>...pretty much like 12-TET...might be 13/11...[see below]

This was a 28:33:42, with third only 3� higher than that of "minor2".
Minor third = 284.4470�

http://lumma.org/erlich/minor4.wav

Carl Lumma:
[]

Gerald Eskelin:
>does not lock to "my" minor third, but is close. Hold it! Is
>the fifth flat?

Herman Miller:
>>...pretty much like 12-TET...19/16 [or] 13/11...[see below]

This was 22:26:33 (minor third = 11:13). Herman was on the right track.
Minor third = 289.2097�

http://lumma.org/erlich/minor5.wav

Carl Lumma:
>mistuned 4?
>3rd seems to sharpen

Gerald Eskelin:
>very pleasant. I suspect this has a 5:6 lower third and a 4:5
>upper third wrapped in a nice 2:3 fifth.

Herman Miller:
>These [last] three [examples] sound pretty much like 12-TET. I'm guessing
that >one is
>probably 19/16 and another might be 13/11, but there's not much difference
>in the way they sound.

This was a 38:45:57, with third 23� lower than a 5:6.
Minor third = 292.7107�

http://lumma.org/erlich/minor6.wav

Carl Lumma:
[]

Gerald Eskelin:
>similar to minor5, but there is something slightly different.
>If pressed to say what it is, I'd guess the third is a smidge higher.

Herman Miller:
>This one has a noticeable but not entirely unpleasant roughness.

This was 16:19:24, which Xavier P. Charles (?) recently said he used on his
violin for classical repertoire due to its difference tones agreeing with
the fundamental.
Minor third = 297.5130�

http://lumma.org/erlich/minor8.wav

Carl Lumma:
>11 limit!

Gerald Eskelin:
>third is unpleasantly high

Herman Miller:
>This one sounds the smoothest. 1/(6:5:4)?

Herman was right -- this is the classic just minor triad (aka 10:12:15) that
Gerald _thought_ he would like.
Minor third = 315.6413�

http://lumma.org/erlich/minor11.wav

Carl Lumma:
>mistuned 12

Gerald Eskelin:
>third is almost a semitone high

Herman Miller:
>The last two are just a bit sharp to sound like minor thirds, but I guess
it would depend on the context.

This was 38:46:57, third is 15� higher than 5:6 and less than 31� higher
than 2^(3/12).
Minor third = 330.7613�

http://lumma.org/erlich/minor12.wav

Carl Lumma:
>two diff. tones = root and 2nd of apparent minor triad
>aug. fifth present? major??

Gerald Eskelin:
>third even higher than minor11; nearly a major triad

Herman Miller:
>The last two are just a bit sharp to sound like minor thirds, but I guess
>it would depend on the context.

This was 14:17:21, third is 50� lower than 5:4 and 64� lower than 2^(4/12).
Carl may have been hearing the difference tone created by the per
Minor third = 336.1295�

Thanks to all the participants for their honest reactions!

Oops -- I forgot to finish this line:

http://lumma.org/erlich/minor12.wav

Carl Lumma:
>two diff. tones = root and 2nd of apparent minor triad

...

Carl may have been hearing the difference tones created by the outer perfect
fifth and the upper major third, which would have been 1/1 and 8/7 relative
to the root of the "minor" triad.

On Thu, 2 Mar 2000 14:56:26 -0500 , "Paul H. Erlich"
<PERLICH@ACADIAN-ASSET.COM> wrote:

>http://lumma.org/erlich/minor6.wav
>
>Carl Lumma:
>[]
>
>Gerald Eskelin:
>>similar to minor5, but there is something slightly different.
>>If pressed to say what it is, I'd guess the third is a smidge higher.
>
>Herman Miller:
>>This one has a noticeable but not entirely unpleasant roughness.
>
>This was 16:19:24, which Xavier P. Charles (?) recently said he used on his
>violin for classical repertoire due to its difference tones agreeing with
>the fundamental.
>Minor third = 297.5130�

Interesting! In hindsight it makes sense that the 16:19:24 has such a
unique sound, due to the periodic repetition of the waveform at a frequency
just a bit too low to perceive as a pitch. I'm sure that must be the
"roughness" I heard.

Herman Miller wrote,

>Interesting! In hindsight it makes sense that the 16:19:24 has such a
>unique sound, due to the periodic repetition of the waveform at a frequency
>just a bit too low to perceive as a pitch.

How do you figure that it was too low? And how does this differ from, say,
the 14:17:21 and 22:26:33 examples?

>I'm sure that must be the
>"roughness" I heard.

Well, roughness is roughness, but I find that in a clear rooted
overtone-based chord like 16:19:24, the roughness can dissolve into a nice
"periodicity buzz".

Herman Miller wrote,

>>Interesting! In hindsight it makes sense that the 16:19:24 has such a
>>unique sound, due to the periodic repetition of the waveform at a
frequency
>>just a bit too low to perceive as a pitch.

I wrote,

>How do you figure that it was too low? And how does this differ from, say,
the 14:17:21 >and 22:26:33 examples?

The repetition frequency of the 16:19:24 example is 18.7 Hz; that of the
14:17:21 example is 21.4 Hz, and that of the 22:26:33 example is 13.6 Hz.
Anyway, I'm not sure what being just below audibility amounts to; I think
16:19:24 would have sounded a lot more "unique" if I put the minor triads in
a higher register, so as to make the missing fundamental an audible pitch.

On Fri, 3 Mar 2000 13:25:16 -0500 , "Paul H. Erlich"
<PERLICH@ACADIAN-ASSET.COM> wrote:

>How do you figure that it was too low? And how does this differ from, say,
>the 14:17:21 and 22:26:33 examples?

Well, the low pitch is somewhere around the D or E-flat above middle C,
which would put the "fundamental" at around 18-19 Hz. I don't know why I
didn't perceive this effect in the 14:17:21 or 22:26:33. I'll have to
experiment with some brighter timbres (sawtooth is usually nice for these
kinds of experiments).

>>I'm sure that must be the
>>"roughness" I heard.
>
>Well, roughness is roughness, but I find that in a clear rooted
>overtone-based chord like 16:19:24, the roughness can dissolve into a nice
>"periodicity buzz".

Yes, that's what I would have expected too. I should emphasize that what
I'm calling "roughness" here isn't the roughness that comes from the
beating of sine waves in the critical band (a distinctly UNpleasant sound),
but I can't think of a better word for it.

Herman Miller wrote,

>Yes, that's what I would have expected too. I should emphasize that what
>I'm calling "roughness" here isn't the roughness that comes from the
>beating of sine waves in the critical band (a distinctly UNpleasant sound),
>but I can't think of a better word for it.

It's the very fast rhythm created by all beat rates being multiples of the
fundamental frequency. This can happen even if the fundamental frequency is
in the bottom of the audible range, ~20-30 Hz.

LISTENING EXPERIMENT #3: THE MINOR TRIAD

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗David Beardsley <xouoxno@virtulink.com>

🔗Herman Miller <hmiller@IO.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Herman Miller <hmiller@IO.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Herman Miller <hmiller@IO.COM>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>