minor thirds

Using WAVmaker, I made a 44KHz WAV file of sine waveswith simple envelopes
with the following:

1. Dyads, lower tone always 440 Hz.
(a) 6:5
(b) 19:16
(c) 32:27
(d) 13:11
(e) 7:6
2. Triads, composed of the above dyads with an added upper tone of 660 Hz.
3. Triads, composed of the above dyads with an added lower tone having the
frequency of the difference between the two upper tones.

I also listened to the whole several times at the half-speed.

Here are some very tentative and entirely subjective observations:

(1) It was unnecessary to do the third set, as the difference tones were
very clear with the dyads alone. With the second set, the added tone masked
the difference tone considerably.

(2) The dyads grouped themselves into three sets: (a), (b,c,d), and (e) in
that I had a real sense of what I hear as root motion when I went from a
dyad in one set to any in another set, but this was not present within the
set (b,c,d).

(3) The greatest qualitative difference is between the 7:6 and all of the
others, then follows the difference between the 6:5 and the rest. The 7:6
is really in another interval category while the others all are
identifiably 'minor thirds' in terms of familar musical syntax.

(4) I find the 6:5 to be the smoothest of the triads but it is not
necessarily the triad familiar from tonal music, but the 6:5 dyad's clear
difference tone creates a Major chord that conflicts with the minor
interpretation.

(5) The dyads b,c,d are still qualitatively distinct from one another. I
find 19:16 as a dyad to be the most familiar of the three, but 32:27 the
better third in the ordinary triad. This changes a bit with the added
difference tones, suggesting perhaps that 19:16 is the better tuning for
the minor triad in 6-4 position due to the consonance of the difference
tone. 13:11 is the least clear of all _in terms of minor third syntax_, but
the added support of the difference tone seems to bring out a melancholic
quality that might be useful in a compositional context where the 13:11 is
projected explicitly.

I'd be curious to hear what others hear in similar tests.

I'm curious Dan why did you Dyad with 440?

Daniel Wolf wrote:

> From: Daniel Wolf <DJWOLF_MATERIAL@compuserve.com>
>
> Using WAVmaker, I made a 44KHz WAV file of sine waveswith simple envelopes
> with the following:
>
> 1. Dyads, lower tone always 440 Hz.
> (a) 6:5
> (b) 19:16
> (c) 32:27
> (d) 13:11
> (e) 7:6
> 2. Triads, composed of the above dyads with an added upper tone of 660 Hz.
> 3. Triads, composed of the above dyads with an added lower tone having the
> frequency of the difference between the two upper tones.
>
> I also listened to the whole several times at the half-speed.
>
> Here are some very tentative and entirely subjective observations:
>
> (1) It was unnecessary to do the third set, as the difference tones were
> very clear with the dyads alone. With the second set, the added tone masked
> the difference tone considerably.
>
> (2) The dyads grouped themselves into three sets: (a), (b,c,d), and (e) in
> that I had a real sense of what I hear as root motion when I went from a
> dyad in one set to any in another set, but this was not present within the
> set (b,c,d).
>
> (3) The greatest qualitative difference is between the 7:6 and all of the
> others, then follows the difference between the 6:5 and the rest. The 7:6
> is really in another interval category while the others all are
> identifiably 'minor thirds' in terms of familar musical syntax.
>
> (4) I find the 6:5 to be the smoothest of the triads but it is not
> necessarily the triad familiar from tonal music, but the 6:5 dyad's clear
> difference tone creates a Major chord that conflicts with the minor
> interpretation.
>
> (5) The dyads b,c,d are still qualitatively distinct from one another. I
> find 19:16 as a dyad to be the most familiar of the three, but 32:27 the
> better third in the ordinary triad. This changes a bit with the added
> difference tones, suggesting perhaps that 19:16 is the better tuning for
> the minor triad in 6-4 position due to the consonance of the difference
> tone. 13:11 is the least clear of all _in terms of minor third syntax_, but
> the added support of the difference tone seems to bring out a melancholic
> quality that might be useful in a compositional context where the 13:11 is
> projected explicitly.
>
> I'd be curious to hear what others hear in similar tests.
>
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Message text written by INTERNET:tuning@onelist.com
>From: Patrick Pagano <ppagano@bellsouth.net>

I'm curious Dan (sic) why did you Dyad with 440?<

440 was an arbitrary frequency within the range where the difference tones
would be, for me, singable. As reported, I also tried the whole thing an
octave lower.

Many thanks Daniel, for reporting your sine-tone experiments with various minor thirds/augmented tones. Perhaps you would be so kind as to expand the menagerie to the following, and give us your taxonomic groupings of distinctness as before.

ratio cents difference pitch class (31-tET)
from previous of difference tone
(cents) when lower tone is A
6/5 315.6 F
31/26 304.5 11.1 Fb
25/21 301.9 2.6 Fb
19/16 297.5 4.4 E
32/27 294.1 3.4 E
sqrt(7/5) 291.3 2.8 Fbb/Dx
13/11 289.2 2.1 Fbb/Dx
20/17 281.4 7.8 D#
27/23 277.6 3.8 D#
7/6 266.9 10.7 D

Is it possible for you to do the test blind? i.e. Have someone rename the files randomly from 1 to 10 but keep a record for you to look up afterwards (and don't look at the file creation times).

I also propose the following modification in order to minimise the distinction afforded by mere pitch change. For the dyads, instead of moving the upper tone, move both tones by equal contrary motion, or perhaps just move the lower tone (since raising the lower tone lowers the difference tone (by 5 to 6 times as much)).
-- Dave Keenan
http://dkeenan.com

Message text written by INTERNET:tuning@onelist.com
>Many thanks Daniel, for reporting your sine-tone experiments with various
minor thirds/augmented tones. Perhaps you would be so kind as to expand the
menagerie to the following, and give us your taxonomic groupings of
distinctness as before.<

Maybe someone else would like to do this -- I was able to it while I had
some extra time last week during recovery from knee surgery, and now want
to get back to composing where I'm not likely to use 27/23 or 31/26 (let
alone the sqrt of 7/5) in the immediate future.

Yes, I listened to it in random order (I used a wav player with a shuffle
function which is great for ear training).

One important thing I forgot to mention was that each dyad or chord was 5
seconds long. The 6/5 and 7/6 I recognized almost immediately, the others
took a few seconds to sort out among the group 19/16, 32/27, 13/11. I've
been tuning sine wave oscillators by hand for a long time (since '77), so
my results should be considered in that context. I'd like to hear from
someone relatively new to this.