Diameter for JI? (was Nano-temperament)

On Wed, 12 Aug 1998, Paul Hahn wrote:
> Or, if you don't like that example, how 'bout a JI-ist who wanted to
> tune up Ellis' duodene, which is a 5-limit scale with a diameter of 5.
^^^^^^^^

"Hold it, pH" I hear some of you saying, "I thought you'd only defined
'diameter' in terms of ETs. What's the diameter of a JI scale mean?"

Well, it's not all that different. It still means the number of primary
intervals (within the particular limit) it takes to get between the two
pitches within the scale that are farthest from each other. In this
case, to get from 16/15 to 45/32 takes five steps:

5/3 --3-- 5/4 --4-- 15/8 --5-- 45/32

/ \ / \ / \ /
2 \ 3 \ 4 \ 5
/ \ / \ / \ /

4/3 --2-- 1/1 --3-- 3/2 --4-- 9/8

/ \ / \ / \ /
1 \ 2 \ 3 \ 4
/ \ / \ / \ /

16/15 --1-- 8/5 --2-- 6/5 --3-- 9/5

You can substitute a 36/25 tritone for the 45/32 without reducing the
number of consonant triads, and reduce the diameter from 5 to 4, but
it's not as symmetrical.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

>From: Joseph Milne
>
>I am new to trying to understand sysex and would be very help with some
>basic guidance.
>
>I am trying to send the commands in Cakewalk to my Roland card to tune in
>just tuning, but I seem to get no result. I suspect I am not writing the
>sysex quite properly. I have some demo midi's which show the difference
>between tempered and just tuning and they definitely work and the
>differences are quite audible, so I know my card responds to the tuning
>commands.
>
>The message I am writing is the following:
>
>F0 41 10 6A 12 00 00 20 00 50 5B 54 5F 42 4E 3E 52 5D 40 30 44 2F F7
>
>Cakewalk sends it but the tuning remains tempered. So what am I missing
out?
>
It appears you have an extra byte from somewhere. All of Ben Tubb's GS
tuning examples at my web site are 22 bytes long. Yours is 23 bytes.

John Loffink
jloffink@pdq.net
http://freeweb.pdq.net/jloffink/