Thanks to Dave Keenan

> [Gerald Eskelin, TD 518.20]
>>Welcome, Dave. It's about time someone introduced some good old fashioned
>>honest pessimism here.
> ...
>>Actually, Dave, I've been milking the hell out of sustaining dramatic
>>suspense. However, we have been dwelling too long on mere conflict. Your
>>contribution is most timely in that it provides a desperately needed element
>>of CRISIS.
>
> Hee hee! Thanks for a good chuckle, Jerry.

Glad you enjoyed it, Dave. Thanks for being a great "straight man."
>
>>> My money
>>> is on that they are not making any significant shift when the fifth is
>>> introduced (say less than 2 cents), it just sounds that way.
>>
>>Perhaps. We have considered that the effect may be a perceptual illusion.
>>Just in case, however, how much money did you have in mind?
>
> The conversion of such a small amount between Australian and US dollars
> would be a pain. But I promise to be real nice to you if I'm wrong. Like
> explain some microtonal mathematics of your choice, in detail with coloured
> diagrams. :-)

Thanks much, but I plan to beat it out of here just as soon as I have taken
advantage of the wisdom packed into this place to help solve the mystery of
the "high third" The more I learn here the more I tend to become addicted,
and I really can't allow that to happen. I need to get back to my writing
and publishing, and dropping in here everyday for the last month has really
cut into that. I do plan to stay in touch with folks by means of web sites
and email, however. And when I get to Australia (we've been trying for
years) I'll expect you to throw another shrimp on the barbie.
>
> [Gerald Eskelin, TD 518.22]
>>Wow! What a great contribution, Dave. I've been referring to the 6:7 third
>>in my music theory classes as the "dinky third," and that really has no
>>class at all. The term "subminor third" will allow me to regain my dignity
>>as a very cool professor of music. Many thanks.
>
> Wow! A chance to influence a real professor of music.

No big deal. My freshman students do that everyday. They don't know it but
they teach me much more than I teach them. One reason I'm reluctant to
retire is that they are my source of "raw" input--hence my intention to
"use" them next week for the "high third" demo.

> Then you need the
> following list. It's essentially a translation and extension of the system
> of a Dutch guy named Adriaan D. Fokker who, by the way, also coauthored a
> paper on Relativity with Albert Einstein.

Wow! Now _that's_ what I call name dropping.
>
> Ratio Name
> ----------------------------
> 11:12 narrow neutral second
> 10:11 neutral second
> 9:10 narrow major second
> 8:9 major second
> 7:8 supermajor second
> 6:7 subminor third
> 5:6 minor third
> 9:11 neutral third
> 4:5 major third
> 7:9 supermajor third
> 3:4 perfect fourth
> 8:11 super fourth
> 5:7 augmented fourth
> 7:10 diminished fifth

Aren't these last two backward? The 5:7 tritone is smaller than the 7:10
tritone, thus the 5:7 "contracts" (E-Bb) in resolution (diminished fifth)
and the 7:10 (E-A#) expands in resolution (augmented fourth). Remember, Paul
and Joe hold that "context is everything." (You don't suppose Mr. Fokker
would reconsider these, do you? Too late, you say? Okay. Do you suppose he'd
mind if we messed with it a bit?)

But then I suppose he was considering that the 5:7 ratio is mathematically
closer to the 3:4 ratio--thus a variety of "fourth." (I guess he never read
Piston.) It is comforting at times to note that even the smartest among us
don't know everything--except for Paul, of course. :-)

> 2:3 perfect fifth
> 7:11 subminor sixth
> 5:8 minor sixth
> 8:13 neutral sixth
> 3:5 major sixth
> 7:12 supermajor sixth
> 4:7 subminor seventh
> 5:9 wide minor seventh
> 6:11 neutral seventh
> 1:2 perfect octave
> 5:11 neutral ninth
> 4:9 major ninth
> 3:7 subminor tenth
> 5:12 minor tenth
> 2:5 major tenth
> 3:8 perfect eleventh
> 4:11 super eleventh
>
> See http://dkeenan.com/Music/IntervalNaming.htm for more
> explanation (than you probably want).

I really could have used this info when I wrote "Lies My Music Teacher Told
Me." Perhaps when we do the next [ fifth :-) ] printing I can do some
editing.

Thanks again for your "ass whipping" and for this very helpful terminology.

Jerry