silver linings in Hell

Two Fridays ago I was groping around for a 3:30 AM snack when I
halfheartedly settled on an old bag of stale trail mix. And while I
was sleepily trying to chew into what felt like a very hard raisin or
date, one of my teeth shattered. In a panic I spit out the half-mawed
remains of the trail mix and what used to be my tooth (which now
consisted of one big whiteish hunk and a bunch of old filling stuff -
it looked an awful lot like welding slag). When I stumbled into the
bathroom and looked into the mirror I only saw what my tongue had
already told me; all that remained was some truly hideous needle-like
stalagtite... I took three sleeping pills and hit the sack in the
hopes that it would all go away. It didn't all go away.

However, by the grace of some divine intervention it also didn't fully
expose a nerve, and today I'm (at least as far as I know) not much
worse for wear. Of course at this point any sane or reasonably
sensible person would probably wonder why the Hell I didn't, or don't,
go
to the dentist... they just wouldn't understand.

The fact is that I haven't been to a dentist in some thirteen plus
years, and while this is tied into the perpetual lack of coins (which
in this case means no health or dental insurance), that's not quite
the whole story (as I have at various interment times had dental
insurance)...

When I was twenty-two years old or so, my mothers live in auto
mechanic boyfriend Duke (AKA, Dave) arranged a deal with one of his
customers who was a dentist: he (Duke) would fix his (AKA, Dr. Mike)
Harley Davidson in
exchange for a mouthful of dental work on his girlfriends (AKA, my
mother) inept son (AKA, me).

So one Sunday morning, me, Duke, Dr. Mike and what I'm all but sure
was his one night stand from the previous evening, all illegally sneak
into the dentist office
that (for reasons unfathomable to me) employs Dr. Mike. Whatever else
might have occurred over the course of the next three hours, only two
things remain clear... 1) me valiantly struggling not to swallow my
tongue while Dr. Mike valiantly struggled to wedge my mouth open with
something that resembled and old doorstop, and 2) Dr. Mike's
"assistant" -- his booze-breathed female companion (whom I'm imagining
along with Dr. Mike is still up from the night before) -- distortedly
leering in at my prolonged near death experience.

It took about three days for the swelling to recede to the point where
I was no longer mistaking myself for The Lady in The Radiator...

They say, "what doesn't kill you makes you stronger." I don't know, I
guess what didn't kill me didn't kill me, but I sure as Hell don't see
that as any guarantee that it won't next time!

While I was on the phone and in the middle of blabbing away on this
story with my friend Pete, I was simultaneously scribbling away on the
back of an envelope when I suddenly noticed that when you take an
overtone sequence as say n...2n-1, the undertone sequence, i.e.,
2n-1...n, will also be the superparticular ratios in the guise of a
consecutive integer sequence where their sum is e, i.e., n-EDO. So
where n = 4 for instance, 4:5:6:7 becomes the 7, 13, 18, and 22 in 22e
where 7/22 = 5/4, 6/22 = 6/5, 5/22 = 7/6, and 4/22 = 8/7...

Ah well, as always, your beleaguered colleague in life,
Dan

p.s. "The Lady in The Radiator" was a reference to the exaggeratedly
puffy-cheeked lady in David Lynch's ERASERHEAD. Ray Wolfe has a nice
page on the movie in which he sort of symbolically sums it all up for
me (well as I'm seeing it today anyway) pretty well... "One of the
best scenes in the entire film is when Mary leaves Henry. She walks
over to the bed (while Henry is in it) and starts pulling at the
footboard. She looks like she is behind bars or in prison trying to
get out. After what seems like an eternity, we find that she was
simply trying to get the suitcase out from under the bed."

Hi Dan.

This morning I had a dream that I lost a tooth. Very strange . . .

>I suddenly noticed that when you take an
>overtone sequence as say n...2n-1, the undertone sequence, i.e.,
>2n-1...n, will also be the superparticular ratios in the guise of a
>consecutive integer sequence where their sum is e, i.e., n-EDO.

You mean e-EDO?

>So
>where n = 4 for instance, 4:5:6:7 becomes the 7, 13, 18, and 22 in 22e
>where 7/22 = 5/4, 6/22 = 6/5, 5/22 = 7/6, and 4/22 = 8/7...

I tried n=8 and it doesn't work.

[Paul H. Erlich:]
> This morning I had a dream that I lost a tooth. Very strange . . . I
tried n=8 and it doesn't work.

I honestly need to take a closer at all this (as it was a sort of
inspired aside), but I think it dose work (though you may mean
something different by "work")...

8-16

(16) 15 14 13 12 11 10 9 8
0 15 29 42 54 65 75 84 92
0 196 378 548 704 848 978 1096 1200

Dan

In your original post you wrote,

>So
>where n = 4 for instance, 4:5:6:7 becomes the 7, 13, 18, and 22 in 22e
>where 7/22 = 5/4, 6/22 = 6/5, 5/22 = 7/6, and 4/22 = 8/7...

Now you write,

>(16) 15 14 13 12 11 10 9 8
> 0 15 29 42 54 65 75 84 92
> 0 196 378 548 704 848 978 1096 1200

You must mean:

8 9 10 11 12 13 14 15 16
0 15 29 42 54 65 75 84 92
0 196 378 548 704 848 978 1096 1200

right? But in 92-tET, 9:8 is closer to 16 steps than 15 steps. So it doesn't
seem to work.

I tried n=32 and it's really bad. The "e" is 1584; 33:32 is 70.3203 steps,
and 34:33 is 68.2209 steps.

[Paul H. Erlich:]
> You must mean:

No, I meant it the way I wrote it

>But in 92-tET, 9:8 is closer to 16 steps than 15 steps.

Right, as you get up higher you could never have the superparticular
ratios as *consecutive* integer sequence where their sum is e.

>So it doesn't seem to work.

Well again, it works just as I said it does (or at least I think it
does to the tiny degree that I've really looked at it), but that still
may not mean that it actually means much of anything other than an
interesting numerical aside...

Dan

[Paul H. Erlich:]
> I tried n=32 and it's really bad. The "e" is 1584; 33:32 is 70.3203
steps, and 34:33 is 68.2209 steps.

Actually if n = 32 then e = 1552 and you get a max deviation of ~12�
at the 39/32... I suppose if you want to hang something 'musically
sensible' on it you could say that it tempers the superparticular
ratios by rendering them as a *consecutive* integer sequence where
their sum is e... but that isn't necessarily what I wanted to hang on
it... I just noticed it and thought, "gee, that's interesting..."

Dan

>> I tried n=32 and it's really bad. The "e" is 1584; 33:32 is 70.3203
>>steps, and 34:33 is 68.2209 steps.

>Actually if n = 32 then e = 1552 and you get a max deviation of ~12�
>at the 39/32...

A max deviation of what from what?

>I suppose if you want to hang something 'musically
>sensible' on it you could say that it tempers the superparticular
>ratios by rendering them as a *consecutive* integer sequence where
>their sum is e...

In 1552-tET, 33:32 is 68.8997 steps, and 34:33 is 66.8427 steps. Doesn't
look like it's going to be a consecutive integer sequence to me. But perhaps
I'm misunderstanding.

[Paul Erlich:]
>But perhaps I'm misunderstanding.

Yes.

Dan

p.s. I'll see if I can't make it any clearer after dinner (I really
gotta run now), but I think a bit from one of those rapid-fire posts
from the last half-hour should've been pretty decipherable though,
here it is...

I think I should have wrote something more like:

I was also scribbling away on the back of an envelope when I noticed
that when you take an overtone sequence as say h...2h-1, the undertone
sequence, i.e., 2h-1...h (or 2h...h+1 and h+1...2h) will also be the
superparticular ratios in the guise of a consecutive integer sequence
where their sum is e, i.e., n-tone equal temperament...

harmonics 2-4

(4) 3 2
0 3 5
0 720 1200

4 3 (2)
0 4 7
0 686 1200

har. 3-6

(6) 5 4 3
0 5 9 12
0 500 900 1200

6 5 4 (3)
0 6 11 15
0 480 880 1200

har. 4-8

(8) 7 6 5 4
0 7 13 18 22
0 382 709 982 1200

8 7 6 5 (4)
0 8 15 21 26
0 369 692 969 1200

etc.