recent Keenan and Erlich posts

>>7:9:11, 8:10:13, 12:15:19
>>
>>I think they are all more consonant than the augmented triad of 12tET.
>
>Blech. The 12tET augmented triad might have less tonalness (more harmonic
>entropy), but with most timbres the lower roughness more than compensates.

Lower roughness of the tempered version?

>Also, I daresay I think you've trained yourself to like JI and dislike
>temperament.

Dah!

>In any case, the relevant point is not whether they fill ratio space, but
>whether they fill ratio space with only unison vectors mapping one diamond
>to a neigboring one.

Right. And they won't do that.

>>How do I do either of these things? (I'm using Microsoft Outlook
>>Express.)
>
>It took me a long time to find it (I use Eudora). See the menu:
>Tools/Accounts/Mail/Properties. I'm not sure if the duplication thing will
>work with Outlook. But the idea is to find the folder that Outlook is in,
>and duplicate the whole folder. Then rename the new copy of the Outlook
>application to "Paul's Outlook", and/or make a shortcut to it with that
>name and put it on the desktop.

Ouch! Certainly outlook e. supports multiple users.

>>It would be good to get diverse opinions on these questions.
>
>Ok folks. Start sending 'em in.

Well, I haven't been following, so I won't presume to answer anything in
particular. I'll just say that I find RMS to be good enough conceptually
and empirically for most purposes. (Can you site a counter-example, Dave?)

The only thing I noticed is: The distribution of (the same RMS) error
across a chord can change the sound of the chord. In particular, it may be
better, when the RMS error is in a certain range, to keep one interval(s)
just and heap all the error onto the other(s) than to spread the error out.

I haven't had time to test this, but it could make sense -- the just
interval(s) help lock down the periodicity of the chord. For 5-limit
triads, I think all 3 intervals can be weighted equally in this context.
Larger chords get tricky because of the abundance of intervals, and also
because the odd limit of these intervals goes up (the 7/5, for example,
shouldn't matter as much as the 7/4 in the 4:5:6:7 tetrad).

Then there is the question of what range the RMS error has to be in for
this to work. If the errors are small enough that they aren't perceptable
(say, less than a cent) when broken up, then it won't work. It also fails
if the one large error moves the interval that gets it out of its entropy
minima.

It is so small a deal that I don't think it's worth it to figure out. Just
thought I'd bring it up.

>>-Sea.
>
>Ocean?

Phononym.

Carl Lumma wrote,

>>>7:9:11, 8:10:13, 12:15:19
>>>
>>>I think they are all more consonant than the augmented triad of 12tET.

I wrote,

>>Blech. The 12tET augmented triad might have less tonalness (more harmonic
>>entropy), but with most timbres the lower roughness more than compensates.

Carl Lumma wrote,

>Lower roughness of the tempered version?

You bet.

>>Lower roughness of the tempered version?
>
>You bet.

How do you figure? I can see no reason why the tempered chord would be
less rough. I spent over 30 minutes listening to various augmented triads
not long ago and found the three I listed less rough than the 12tET chord.

-C.

I wrote...

>How do you figure? I can see no reason why the tempered chord would be
less >rough. I spent over 30 minutes listening to various augmented triads
not long >ago and found the three I listed less rough than the 12tET chord.

Well, roughness is actually something I don't have a good feeling for
measuring by ear, especially in triads. I leave it that I found the chords
I list more consonant than the tempered one. But, buy all means explain
your idea. I'd sure like to see the actual sensory dissonance surface for
the augmented triad...

-C.