Yahoo Tuning Groups Ultimate Backup tuning Four cents + two cents

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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🔗Mike Battaglia <battaglia01@...>

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@ec-red.com> 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.
>
>
> __________ Información de ESET NOD32 Antivirus, versión de la base de
> firmas de virus 4762 (20100111) __________
>
> ESET NOD32 Antivirus ha comprobado este mensaje.
>
> http://www.eset.com
>
>
>

🔗Mario Pizarro <piagui@...>

1) Miike Battaglia. As I said before, the Progression of musical cells was derived in 1983-1985. At that time computers and obviously the excel program were not available so the only ways to develope the progression were to work with a 12 digit electronic calculator or by using common fractions; I already had decided (32805/32768) = schisma = M as the first cell.

2) By analysis and reasoning the second cell had to be (32805/32768)^2 and got a second cell that was a big common fraction. Then the three initial cells were 1, M, M^2.

3) The progression requirements opposed to a third M comma factor and I had to devote about two months to derive the second type of comma factor that was named
J = (2^25)*2^(1/4) / (3^13)*5^2. The third cell was the product J* (32805/32768)^2 that gave a monstrous combination of common fractions and powers even after reducing terms.

4) I continued with common fractions up to the 7th cell and after knowing that the octave would comprise about 600 cells, stopped working with common fractions and powers.

5) Converted all the obtained monstruos cells to 8 digit decimal numbers but soon I realized that 11 decimal digits could reduce errors that meant 12 digits like 1.05349794239.

6) Mike: Now you know why had to use decimal frequencies in the progression.

I will continue this message as soon as possible.

Thanks

Mario Pizarro
piagui@...
Lima, January 11, 2010
----- 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,

>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.

__________ Información de ESET NOD32 Antivirus, versión de la base de firmas de virus 4762 (20100111) __________

ESET NOD32 Antivirus ha comprobado este mensaje.

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🔗Mario Pizarro <piagui@...>

Regarding Mike Battaglia statement on deviation cents, the three underlined rows (first paragraph) of his message copied below does not coincide with what I wrote.

In fact, I wrote:
>
>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.

When I wrote :ªso a scale having XYXYXY deviation cents should be at least weakly distinguishable from 12 tet", I mentioned the worst imaginable case and even in this case the scale should be distinguishable. Therefore, since the average of those deviatons is greater than 2 which is considered the sensitivity threshold according to a skilled adviser, we can conclude that this scale is distinguishabe from 12 tet. And this was proven when a similar scale (Piagui I) was compared to 12 tet by listening dozens of chords given by two grand pianos in 2004. Now, since Piagui I D major showed imperfection, I am talking about JUSTHARM II scale.

Yesterday, I explained you the origins of 11 digit decimal cell values of the progression; if I wouldn't had used decimal numbers for cell frequencies, I wouldn't had settled the progression. When I was a boy, a long time ago, I didn't claim for using 12 decimal figures given by the logarithm table and had no any problem with the meaning of each of its thousands values. Technology cancelled the use of that table, however, I could cite many natural variables which now are measured with decimal numbers, you know that. More, all people know within a tenth of a second that frequency 1.5802469 is higher than 1.5625 but all of them need to make calculations to know if 25/16 is or it is not higher than 405/256.
Conclusion: The progression of cells given in decimal number facilitate the obtainment of frequency ratios, rate of cells expansion toward the octave 2C = 2 and other features.

Thanks

Mario Pizarro
piagui@...

Lima, January 12, 2010 -- 12:20 p.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,

>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.

__________ Información de ESET NOD32 Antivirus, versión de la base de firmas de virus 4762 (20100111) __________

ESET NOD32 Antivirus ha comprobado este mensaje.

http://www.eset.com

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