Re: [cm] X.J. Scott and Jacky Ligon get Froggy...

> From: <jacky_ligon@yahoo.com>
> To: <crazy_music@yahoogroups.com>
> Sent: Tuesday, August 07, 2001 8:20 PM
> Subject: [cm] X.J. Scott and Jacky Ligon get Froggy...
>
>
</tuning-math/files/Jacky%20Ligon/Frog_Choir.mp
3>

Hi Jacky,

This is awesome! (and the post describing it was hilarious!)

> Cents Note Names
> 0 Throaty
> 369.398 Croaker
> 564.028 Jeep Jeep
> 1509.372 Screech
> 1688.114 Jeepers
> 2307.751 High Screech
> 2895.611 Extra High Jeepers
>
> I would like to request for Master Monz to chart this out on a
> Frog Lattice (if possible and convenient to do).

Ask and ye shall receive... (partially, anyway...)

I did a search thru a 13-limit ratio database delimited by
3^(-10...10) * 5^(-2...2) * (7,11,13)^(-1...1),
(that's 2,835 different 8ve-invariant pitches), adjusted the
exponents of 2 to match Jacky's 8ve-specific list,
and came up with the following:

ratio Jacky's delta note
2 3 5 7 11 13 decimal fraction cents cents cents names

| 0 0 0 0 0 0| 1.0 1/1 0.000 0.000 0
Throaty
| 8 0 -2 -1 1 -1| 1.237802198 2816/2275 369.337 369.398 -0.061
Croaker
| 6 -1 1 -1 -1 0| 1.385281385 320/231 564.215 564.028 +0.187 Jeep
Jeep
| 8 -7 0 -1 1 1| 2.391273107 36608/15309 1509.335 1509.372 -0.037
Screech
|-1 -1 2 1 -1 0| 2.651515152 175/66 1688.180 1688.114 +0.066
Jeepers
| 9 -3 -1 0 0 0| 3.792592593 512/135 2307.821 2307.751 +0.070 High
Screech
| 7 -7 0 1 0 1| 5.326017375 11648/2187 2895.669 2895.611 +0.058 Extra
High Jeepers

The greatest error between my ratios and Jacky's cents values
is less than 1/5-cent (in the case of "jeep jeep"). The errors
for the other notes are all less than 1/10-cent, mostly in the
range of about 1/15 to 1/30 of a cent.

I've been working on the Frog Lattice for several hours,
but it's quite complicated and will take much longer to finish.
When it's done I'll make a webpage of it, with this data.

It would be nice to have an algorithm that can
convert from cents values into prime-factorized format,
to varying degrees of accuracy, for general use.

Any takers?

(Dan Stearns once showed me an algorithm for converting
from cents values to ratios, but prime-factoring irrational
numbers seems a bit more difficult as the possibilities
are endless.)

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

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