[tuning-math] Re: A 5-limit, "geometric" temperament list

--- In tuning-math@xxxx, "hs" <straub@xxxx> wrote:
> >81/80 (3)^4/(2)^4/(5) meantone
> >[[1, 0, -4], [0, 1, 4]]
> 
> Newbie question: what is the meaning of this vector notation? From 
what I read so 
> far, all I can imagine are unison vectors determining a periodicity 
block. Something 
> like this?
> 
> 
> Hans Straub

Luckily there are no wedgies here, so i think i can explain this one.

Meantone temperament takes the just lattice and modifies it 
by "tempering out" the interval 81/80. that is, all the consonant 
intervals, the "rungs" of the just lattice, are detuned slightly so 
that 81/80 comes out to a unison.

(3)^4/(2)^4/(5) is simply the prime factorization of 81/80. 81 = (3)
^4; 1/80 = 1/(2)^4/(5), get it?

Then the next line tells you the mapping of the primes in terms of 
the generators. You left out this line, which was included with the 
ones you report below:

generators   [1200., 1896.164845]
(these are in cents)

So . . . [1, 0, -4], [0, 1, 4] would be better arranged like this:

[1]   [0]
[0]   [1]
[-4]  [4]

the first row tells you that the 2/1 is represented by [1]*1200 + [0]
*1896; the second row tells you that the 3/1 is represented by [0]
*1200 + [1]*1896; the third row tells you that the 5/1 is represented 
by [-4]*1200 + [4]*1896.

Making sense?






p.s. i tried to reply directly to the freelists list, but i got the 
following error message:



The original message was received at Mon, 29 Jul 2002 21:21:32 GMT 
from user10.acadian-asset.com [208.253.47.10] (may be forged)

   ----- The following addresses had permanent fatal errors ----- 
<tuning-math@xxxxxxxxxxxxx>

   ----- Transcript of session follows -----
... while talking to turing.freelists.org. [206.53.239.180]:
>>> RCPT To:<tuning-math@xxxxxxxxxxxxx>
<<< 554 Service unavailable; [199.171.54.106] blocked using 
relays.osirusoft.com, reason: 
http://www.appliedinfogroup.com/html/emarketing.html (services 
(appending, also look for 'opt-out')) 554 <tuning-
math@xxxxxxxxxxxxx>... Service unavailable




anyone know what's up?


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