[tuning-math] Re: A 5-limit, "geometric" temperament list
- From: "wallyesterpaulrus" <perlich@xxxxxxxxxxxx>
- To: tuning-math@xxxxxxxxxxxxxxx
- Date: Mon, 29 Jul 2002 21:56:35 -0000
--- 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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