my print-out of 19-limit resolutions (was: Harmonic Entropy)

> [Glen Peterson, TD 394.10]
>
> From: Joe Monzo <monz@juno.com>
>
>> I haven't experimented with this to gain any empirical
>> knowledge myself, but years ago I wrote a computer program
>> to calculate Partch's 'Field of Attraction' for every
>> possible chord progression in the 19-Limit Tonality Diamond.
>> The printout gives the ratios and cents values in roughly
>> graphical page-layout for both the starting and ending
>> chords, with the interval size in cents for each 'permissible'
>> resolution. I followed Partch's guidelines exactly.
>
>
> Sounds interesting. How much output is there? Is it small
> enough to post somewhere?

Nah... way too big.

The 19-odd-limit tonality diamond is a 10x10 matrix,
that is, 10 otonalities and 10 utonalities, each one
a decad (i.e., containing 10 distinct tones).

Staying strictly within the matrix, each of the 20 tonalities
can be connected to 19 others: each otonality with the other
9 otonalities and all 10 utonalities, and each utonality
with all 10 otonalities and the other 9 utonalities.

20 x 19 = 380, and I put each resolution on a page of its
own, so the whole book is 380 pages.

The least expensive copy machines I see around Philly charge
5 cents per page, so that would make the whole book $19,
and then add a few bucks more for a binding, and another
$3.20 for US priority-mail postage, making the total cost
around $25 (international postage is $7-$15 more).

If enough people are interested, I could probably get a
bulk-copying rate that would make it cost less.

I printed this out 9 years ago on an old dot-matrix printer,
and the computer code includes commands that were specific
to my printer, so I don't think it would be worth putting the
program itself up on the web, because the output definitely
won't make sense if you print it out on any modern printer.
All I can do is make copies of the old hard-copy.

The way I had to make the output appear via my old printer
is very similar to the way we have to adapt graphics to
ASCII when we post here, so it's easy to give a sample:

Here's the 1/1-O - 4/3-O resolution
(that's Otonality built over 1/1 to Otonality built over 4/3,
the typical 'V7 - I' progression).

If any chord-member appears without a connection to a
chord-member in the previous chord, that's because according
to Partch's Observation there is no ratio in the first
chord which is close enough to fall within its 'field of
attraction'. The examples here are the 19/12 and 17/12
in the 4/3-O chord.

I separated the connections to the 1-identity of the
second chord in all cases, and presented them together
at the bottom of each otonal page and the top of each
utonal page.

The letter-names for 11- and 13-identities are chosen
for the closest letter-name in the 1/1 tonalities and
kept consistent for all others (altho there may be
some misprints - there was one in this example: 13/12
appears in the print-out as B instead of Bb).

The diagram gives letter-name, cents, identity, and ratio
for each chord, as well as the 'travelling distance' in
cents for each resolution.

My 1/1 is labelled 'A'. View in a fixed-width font.

1/1-O --- 4/3-O

C# 386 5 5/4 --- 0 --- 5/4 15 386 C#

B# 298 19 19/16 \
--- - 31 ---
\
7/6 7 267 C
/
--- + 63 ---
B 204 9 9/8 /
13/12 13 139 Bb

/
--- + 63 ---
/
Bb 105 17 17/16
\
--- - 105 ---
\
A 0 1 1/1 --- 0 --- 1/1 3 0 A
/
--- + 112 ---
/
G# 1088 15 15/8
\
--- - 39 ---
\
11/6 11 1049 G#
G 969 7 7/4
\
--- - 84 ---
\
5/3 5 884 F#
/
--- + 44 ---
/
F 841 13 13/8

19/12 19 796 E#

E 702 3 3/2 --- 0 --- 3/2 9 386 C#

17/12 17 603 Eb

G# 1088 15 15/8
\
--- - 590 ---
\
G 969 7 7/4
\
--- - 471 ---
\
F 841 13 13/8
\
--- - 342 ---
\
E 702 3 3/2
\
--- - 204 ---
\
D# 551 11 11/8
\
--- - 53 ---
\
4/3 1 498 D
/
--- + 112 ---
C# 386 5 5/4 /
/
--- + 201 ---
B# 298 19 19/16 /
/
--- + 294 ---
B 204 9 9/8 /
/
--- + 393 ---
Bb 105 17 17/16 /
/
--- + 498 ---
A 0 1 1/1 /

Print this out, and you have an idea of what the other
379 pages look like.

This type of print-out will be available on-screen as
one of the windows in my JustMusic software.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

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