2, 3, 4, 5 ....direct links to tone frequencies

I don´t know why I don´t receive copy of the messages containing discussions on some advanced topcs where Mike, genewardsmith are working. On vacations?.

In the meantime I am finding that the square roots and double square roots of the first 16 integer numbers in many cases give tone frequencies of microtonal scales. I know this procedure is not a research really; I am trying to find the explanations so I could discard the possibility that these results are only numbers that do not pertain to the music.

Thanks
Mario

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On Tue, Feb 8, 2011 at 10:30 AM, Mario Pizarro <piagui@...> wrote:
>
> I don´t know why I don´t receive copy of the messages containing discussions on some advanced topcs where Mike, genewardsmith are working. On vacations?.

A lot of the stuff we're talking about is taking place on the sister
"tuning-math" list - feel free to join and check it out. It's pretty
heavygoing and a lot of the stuff on there is over my head as well.

> In the meantime I am finding that the square roots and double square roots of the first 16 integer numbers in many cases give tone frequencies of microtonal scales. I know this procedure is not a research really; I am trying to find the explanations so I could discard the possibility that these results are only numbers that do not pertain to the music.

They do pertain to the music. If you take the fourth root of 5, which
I think you called the "double square root," you end up with 5^(1/4),
which on a log scale is 696.578 cents. This is the fifth of
quarter-comma meantone, set up precisely so that four of them gets you
a perfect 5. Other such relationships exist and the whole thing is
very strongly related to the theory of regular temperament that we
keep talking about around here.

-Mike

Mike, thanks for suggesting me to join "tuning - math". I appreciate your kind invitation. Now I will get the wanted information where your viewpoints and data are always welcomed.
As respect to 2, 3, 4, 5 direct links, I started a more serious analysis in excel.
Thanks
Mario
February 09

----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Tuesday, February 08, 2011 10:37 AM
Subject: Re: [tuning] 2, 3, 4, 5 ....direct links to tone frequencies

On Tue, Feb 8, 2011 at 10:30 AM, Mario Pizarro <piagui@...> wrote:
>
> I don�t know why I don�t receive copy of the messages containing > discussions on some advanced topcs where Mike, genewardsmith are working. > On vacations?.

A lot of the stuff we're talking about is taking place on the sister
"tuning-math" list - feel free to join and check it out. It's pretty
heavygoing and a lot of the stuff on there is over my head as well.

> In the meantime I am finding that the square roots and double square roots > of the first 16 integer numbers in many cases give tone frequencies of > microtonal scales. I know this procedure is not a research really; I am > trying to find the explanations so I could discard the possibility that > these results are only numbers that do not pertain to the music.

They do pertain to the music. If you take the fourth root of 5, which
I think you called the "double square root," you end up with 5^(1/4),
which on a log scale is 696.578 cents. This is the fifth of
quarter-comma meantone, set up precisely so that four of them gets you
a perfect 5. Other such relationships exist and the whole thing is
very strongly related to the theory of regular temperament that we
keep talking about around here.

-Mike

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