ET triads

I've been listening to 4-5-6 chords in various ET's. This is what I came
up with for usable ones up to 53, ranked from worst to best...

15
12

22
19
31
41

53

I posted a long time ago that the first ET with a better 4-5-6 than 12 was
31, but I've changed my mind.

The spaces indicate the largest changes of character. 15 and 12 sound
similar to me, except that 15 has an extra beating that's pretty loud. It
gets on my nerves, but it isn't messy.

19 and 22 sound more alike than any in the bunch. 19 sounds a tiny bit
better, maybe because of its one just interval. 41 sounds better than 31,
but not as good as I thought it would. When you hit 53, you just love it.
It is pretty much indistinguishable from just, at least under the
conditions I was using...

Midi Relay and a soundblaster live with the reed organ patch. This patch
has proven very good for comparing intervals. I compared the tunings with
the 4 fixed to middle C, all in root position.

C.

I miss 34 with just this chord.
But then again, that's just based on theory :-)

Kees

-----Original Message-----
From: Carl Lumma <clumma@nni.com>
To: tuning@onelist.com <tuning@onelist.com>
Date: Monday, March 15, 1999 7:00 AM
Subject: [tuning] ET triads

>From: Carl Lumma <clumma@nni.com>
>
>I've been listening to 4-5-6 chords in various ET's. This is what I came
>up with for usable ones up to 53, ranked from worst to best...
>
>15
>12
>
>22
>19
>31
>41
>
>53
>
>I posted a long time ago that the first ET with a better 4-5-6 than 12 was
>31, but I've changed my mind.
>
>The spaces indicate the largest changes of character. 15 and 12 sound
>similar to me, except that 15 has an extra beating that's pretty loud. It
>gets on my nerves, but it isn't messy.
>
>19 and 22 sound more alike than any in the bunch. 19 sounds a tiny bit
>better, maybe because of its one just interval. 41 sounds better than 31,
>but not as good as I thought it would. When you hit 53, you just love it.
>It is pretty much indistinguishable from just, at least under the
>conditions I was using...
>
>Midi Relay and a soundblaster live with the reed organ patch. This patch
>has proven very good for comparing intervals. I compared the tunings with
>the 4 fixed to middle C, all in root position.
>
>C.
>
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On Mon, 15 Mar 1999 10:01:04 -0500, Carl Lumma <clumma@nni.com> wrote:

>The spaces indicate the largest changes of character. 15 and 12 sound
>similar to me, except that 15 has an extra beating that's pretty loud. It
>gets on my nerves, but it isn't messy.
>
>19 and 22 sound more alike than any in the bunch. 19 sounds a tiny bit
>better, maybe because of its one just interval. 41 sounds better than 31,
>but not as good as I thought it would. When you hit 53, you just love it.
>It is pretty much indistinguishable from just, at least under the
>conditions I was using...

I did a similar comparison once, using Cool Edit to generate sawtooth waves
of precise frequency (within the limits of the software, which seem to be
accurate enough for this test). 53 has just an extra bit of "animation"
that is lacking in the just chord (but I prefer even a bit more detuning;
41 is about perfect, and even though 31 has noticeable beating, it isn't at
all objectionable to me). I didn't specifically do a 19 vs. 22 comparison,
but I've used them both and find their triads quite pleasant. 29-equal is
another tuning with good triads, IIRC.

12 at first doesn't sound so bad, because we're used to hearing it, but
once you hear 41 or 53, and go back to 12, ugh! Of course, I've been using
16-equal a lot lately, which is worse than 12 by far in the major triad
comparison, but it has an interesting character of its own that makes up
for its faults, and it can be "tamed" with suitable timbres.

--
see my music page ---> +--<http://www.io.com/~hmiller/music/music.html>--
Thryomanes /"If all Printers were determin'd not to print any
(Herman Miller) / thing till they were sure it would offend no body,
moc.oi @ rellimh <-/ there would be very little printed." -Ben Franklin

Carl Lumma wrote,

>I've been listening to 4-5-6 chords in various ET's. This is what I
came
>up with for usable ones up to 53, ranked from worst to best...

>15
>12

>22
>19
>31
>41

>53

Surely you're leaving some out! Even restricting ourselves to 5-limit
consistent ETs under 53, the rms error gives the following ranking (and
accuracy values for 1% std. dev.):

53: 99.8%
34: 98.7%
46: 97.9%
50: 97.0%
31: 96.6%
41: 96.0%
19,38: 94.3%
49: 94.3%
43: 93.9%
22,44: 89.2%
37: 88.6%
48: 88.5%
47: 86.8%
45: 86.5%
39: 85.4%
27: 85.0%
42: 82.7%
35: 80.2%
29: 78.6%
12,24,36: 78.5%
26: 78.3%
28: 75.4%
15,30: 74.4%