Whoever tried to send me a .wav file . .

Please don't do that! I got in big trouble for crashing the company's mail
server, and I can't play .wav files anyway. Please let me know if you want
to send me something, and I'll figure out another way for it do be done.
Thanks!


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Gary informs be that his example was in JI, not 88CET. He performed the
following comparison:

* Here's a traditional diminished triad (play 6:5 stack).
* Here's another way to tune that - more or less - same chord (play 5:6:7
chord). Notice that it's less dischordant.

And yet in some sense he perceives 5:6:7 is more discordant than 25:30:36
(the "6:5 stack"). Another example of this phenomenon is to compare 4:6:9
with 2:3:5. There is a sense in which the first chord is "purer" than the
second. More examples:

8:10:12:15 vs. 4:5:6:7
16:20:24:36:45:54 vs. 4:5:6:9:11:13

I think I know exactly what you mean. When the smaller constituent
intervals, which are the ones that contribute most to potential roughness,
are all simple, the chord can't help being smooth in a certain sense. It's
kind of the same reason 10:12:15 minor chords are more consonant than 6:7:9
chords (in a certain sense, of course).


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PAULE sez:
> Gary informs be that his example was in JI, not 88CET.

Ooop, it looks like I once again performed that "common mistake" I suspected
Pat M. of doing: Sending a reply "to sender only" when I intended to go to the
whole list. Here's that message:

---------------------------------------------------------


> 88CET does not have a good approximation to 6:5; do you mean 352 cents?

That's a logical question. That portion of the demo was rendered in JI, not
in 88CET. I was motivating 88CET's nontraditional thirds in the traditional
way: by its JI approximations. The general gist is:
* Here's a traditional diminished triad (play 6:5 stack).
* Here's another way to tune that - more or less - same chord (play 5:6:7
chord). Notice that it's less dischordant.
* That upper interval is one of 88CET's nontraditional thirds.
* The gap left between that subminor third and the fifth (9:7) is another one
of 88CET's nontraditional thirds.
* And it also has neutral third that splits the fifth right down the middle.


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