Mike, your statements are correct

Mike's statements regarding cent deviations are correct. If we want a new scale better than 12 TET, its deviation cents should be greater than 4 cents. Before, I had considered that 2 cents sets the threshold for entering to a sector of distinguishable scales respect to 12 tet. A threshold of 4 cents establishes the needed gap.

It means that Piagui scales don't comply with this requirement and that the research I did produced three scales which lie in the group of 12 tet variants or something like that.

Piagui and Justharm scale parameters (K, P, M, J, U, The progression of musical cells) might perhaps do something to delete this unexpected final.

Thanks

Mario Pizarro
piagui@...

Lima, January 14, 2010 ---- 09:50 a.m.
----- Original Message -----
From: Mike Battaglia
To: tuning@yahoogroups.com
Sent: Monday, January 11, 2010 2:15 PM
Subject: Re: [tuning] Four cents + two cents

There are certain contexts in which a 4 cent deviation would be noticeable. If you play a C major chord and the E is 4 cents flat and the G is 4 cents sharp, that would actually be an 8 cent difference, for example. But my point was that compared to the other tunings floating around here, yours is closer to 12-tet than those. It differs only minimally from 12-tet, and as you yourself said, it is right on the threshold of a barely perceptible difference for -some- people.

As for the validity of the progression of musical cells, I still don't understand exactly what you're doing, because you have never explained it with terminology that I am familiar with. Referring to a interval as 1.05237428346953274 doesn't mean much to me. It isn't like I have a lookup table in my head of fractions and their corresponding decimals.

-Mike

On Mon, Jan 11, 2010 at 1:50 PM, Mario Pizarro <piagui@...> wrote:

Hi,

Some weeks ago I needed information regarding man sensitivity respect to cents deviations from 12tet and received a fully explanation from a wise member of the list (Mike Battaglia is another wise member). There I knew, among other important data, that man sensitivity varies; that some people can even distinguish 2 cents deviation though this is not a common figure. His opinions on this matter let me understand that a figure of 4 cents is a safe sensitive degree for an unknown percentage of people that use to hear music so a scale having 4, 2.5, 0.2, 4, 2.5, 0.2, 4, 2.5, 02, 4, 2.5, 0.2 deviation cents should be at least weakly distinguishable from 12tet.
I am giving the above information/opinions due to what Mike stated on this matter that is copied below. Let me add that nobody analyzed the clar features of the Progression of Musical Cells.
-------
>I am using the standard in this case of what the human ear will be able to distinguish, and it will be able to distinguish only minimal differences between 12-tet and your scale. I am also seeing how it compares to other temperaments, and in this respect it is a -LOT- closer to 12-tet than many commonly used ones. So in both of regards, a temperament that is within 4 cents at all times of 12-tet will be a LOT "closer" to 12-tet than a temperament that has a major third that is 10 cents closer to 5/4 than 12-tet's is, or that represents 7/4 to within 3 cents. 41-equal, 53-equal, miracle temperament, etc can do all of these things, your temperament cannot. Your temperament can in general handle all of the intervals that 12-tet can.

>Those are my standards for judging how "valid" a temperament is or how "close" to 12-tet it is. What are yours?

-Mike
---------------

Thanks

Mario Pizarro

Lima, Jan.11, 2010 ---- 01:50 p:m.

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