Yahoo Tuning Groups Ultimate Backup tuning have utensils ready

Here it is folks - for your piano's dining enjoyment -

Cooked up by Harry Partch - served in 43 different flavors -

Served on a bed of 11-limit lattice:

(did somebody say Monophony?)

33:32
/| 81:80
/ | /
/ | 27:16 /
11:7-------------11:8 | / '-._ /
| /|'-._ | / 27:20
| / | 11:10 | / /
| / 9:7|---|---|-----9:8 /
| 11:6 / | | | / |'-._ /
| /| / | 15:8 | / | 9:5
| / |/ |/ '|._ |/ | /
| /12:7|------/|---|-3:2-------------21:16
11:9 / | / | |/ |'-._ / | / '-._
10:7--||-------|-5:4 | /| | 6:5-------/-----21:20
/'-._ ||/ |/ |'-._|/ | | / | / /
/ 8:7|------/|-----1:1---|----------7:4 /
/ / | / | | / |'-._|/ | /||'-._ /
40:21----------|-5:3 | / | 8:5-------/-----7:5
'-._ / |/ '-._ |/ | | / | / 18:11
32:21-----/|-----4:3--------------7:6 / |
/ | / |'-._ / | /| / |
10:9 | / | 16:15| / |/ |
/ '-._ |/ | | | / 12:11 |
/ 16:9------------14:9 / |
/ / | 20:11 | / |
40:27 / | '-._|/ |
/ '-._ / | 16:11-------------14:11
/ 32:27 | /
/ | /
160:81 |/
64:33

(a suggestion: print it and draw darker lines over these)

- Monzo

|\=/|.-"""-. Joseph L. Monzo....................monz@juno.com
/6 6\ \ http://www.ixpres.com/interval/monzo/homepage.html
=\_Y_/= (_ ;\ c/o Sonic Arts, PO Box 620027, San Diego, CA, USA
_U//_/-/__/// | "The ability of the human ear |
/monz\ ((jgs; | is vastly underestimated" - Harry Partch |

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🔗Joseph L Monzo <monz@xxxx.xxxx>

[Me:]
> (did somebody say Monophony?)

In the ASCII version of the Lattice of Harry Partch's
System of Monophony it was difficult to see some of
the relationships. For those who are interested,
I thought I'd clarify by simplifying the lattice first.
Take out all the ratios with factors of 11, and you
get this 7-prime-limit lattice:

81:80
/
27:16 /
/ '-._ /
/ 27:20
/ /
9:7|-------------9:8 /
/ / '-._ /
/ 15:8 / 9:5
/ / '-._ / /
12:7-------/------3:2-------------21:16
/ / / '-._ / / '-._
10:7-------------5:4 / 6:5-------/-----21:20
/'-._ / / '-._ / / / /
/ 8:7 ------/------1:1--------------7:4 /
/ / / / '-._ / / '-._ /
40:21------------5:3 / 8:5-------/-----7:5
'-._ / / '-._ / / /
32:21-----/ -----4:3--------------7:6
/ / '-._ / /
10:9 / 16:15 /
/ '-._ / /
/ 16:9------------14:9
/ /
40:27 /
/ '-._ /
/ 32:27
/
160:81

Now overlay onto that the ratios with factors of 11.
Here they are with the lower-prime central ratios
they bond with (which are already on the 7-limit lattice):

33:32
/|
/ |
/ |
11:7-------------11:8 |
| /|'-._ |
| / | 11:10 |
| / | | | (9:8)
| 11:6 | | | / |
| /| | | | / |
| / | | | |/ |
| / | | |(3:2) |
11:9 | | |/ | |
|| |(5:4) | /| | |
|| | |'-._|/ | | |
8:7|------ |--|-(1:1)-------------7:4
| | | / |'-._| | ||
| / | (8:5) | ||
| |/ | | | 18:11
| (4:3) | | | / |
| / | | | | / |
| / | | | |/ |
|/ | | | 12:11 |
(16:9) | | | / |
| 20:11 | / |
| '-._|/ |
| 16:11-------------14:11
| /
| /
|/
64:33

Put them all together and they spell hay:

(Hang it on the wall as a conversation piece.)
(Make jewellery of it.) . . .

- Monzo

🔗fasano@xxxxx.xxxxxxxxxxxxxxx)

At 11:52 PM 3/16/99 -0500, you wrote:
>From: Joseph L Monzo <monz@juno.com>
>
>
>
>Here it is folks - for your piano's dining enjoyment -
>
>Cooked up by Harry Partch - served in 43 different flavors -
>
>Served on a bed of 11-limit lattice:
>
>(did somebody say Monophony?)
>
>
>
>
> 33:32
> /| 81:80
> / | /
> / | 27:16 /
>11:7-------------11:8 | / '-._ /
> | /|'-._ | / 27:20
> | / | 11:10 | / /
> | / 9:7|---|---|-----9:8 /
> | 11:6 / | | | / |'-._ /
> | /| / | 15:8 | / | 9:5
> | / |/ |/ '|._ |/ | /
> | /12:7|------/|---|-3:2-------------21:16
> 11:9 / | / | |/ |'-._ / | / '-._
> 10:7--||-------|-5:4 | /| | 6:5-------/-----21:20
> /'-._ ||/ |/ |'-._|/ | | / | / /
> / 8:7|------/|-----1:1---|----------7:4 /
> / / | / | | / |'-._|/ | /||'-._ /
>40:21----------|-5:3 | / | 8:5-------/-----7:5
> '-._ / |/ '-._ |/ | | / | / 18:11
> 32:21-----/|-----4:3--------------7:6 / |
> / | / |'-._ / | /| / |
> 10:9 | / | 16:15| / |/ |
> / '-._ |/ | | | / 12:11 |
> / 16:9------------14:9 / |
> / / | 20:11 | / |
> 40:27 / | '-._|/ |
> / '-._ / | 16:11-------------14:11
> / 32:27 | /
> / | /
> 160:81 |/
> 64:33

Very nice (even if it is b&w ascii)!!! If someone could do this
in color (using Partch's ROYGBV scheme), and possibly in 3D, as a BMP or
other standard
graphics format, and attach it to an e-mail... What I'd like
to do is use it as a background to a (Windows) app, where
the user can click on ratios and select them as chords or as
melody notes and hear them, also show some of the relationships
(e.g. numerary nexus, the 28 tonalities, etc.), and show/hide
n-limit (e.g. show only 5-limit, then go back to 11). This would
be (I think) useful ear training for beginners **like myself**. If someone
could supply the graphic, I can supply the ear-training app (it will
use MIDI) and the C++ code for public consumption.

Perhaps there could be multiple lattice graphics for the various n-limits...

I don't think my piano would find it appetizing -- but I do (chomp, chomp) :)

Ken Fasano

🔗Joseph L Monzo <monz@juno.com>

[Fasano, commenting on my lattice:]
> Very nice (even if it is b&w ascii)!!!
> If someone could do this in color (using
> Partch's ROYGBV scheme), and possibly in
> 3D, as a BMP or other standard graphics
> format, and attach it to an e-mail...
> What I'd like to do is use it as a background
> to a (Windows) app, where the user can click
> on ratios and select them as chords or as
> melody notes and hear them, also show some
> of the relationships (e.g. numerary nexus,
> the 28 tonalities, etc.), and show/hide
> n-limit (e.g. show only 5-limit, then go
> back to 11). This would be (I think) useful
> ear training for beginners **like myself**.
> If someone could supply the graphic, I can
> supply the ear-training app (it will use MIDI)
> and the C++ code for public consumption.
>
> Perhaps there could be multiple lattice
> graphics for the various n-limits...
>
> I don't think my piano would find it
> appetizing -- but I do (chomp, chomp) :)
>
> Ken Fasano

You just described in pretty good detail
my own software application.

Email me privately.

- Monzo
http://www.ixpres.com/interval/monzo/homepage.html