Quite a different scale

Dear friends,

Five hours ago I successfully finished the design of a twelve tone scale. I will mention some of its features.

-- The uncommon feature that helped to get a nice appearance when looking at its semitone factors distribution is that the scale works with two G's whose frequency ratio is 1.001953125, about 3.378 cents. With such a ratio, almost the schisma, we might be sure that there is only one G.

-- The semitone factors distribution complies with the following factors:

alpha, beta. alpha, beta, alpha, beta, gamma, alpha, beta, alpha, beta, alpha.

-- The tone frequency values differ from the common values I used to work with, excepting 19/16, 4/3, 3/2, 57/32.

-- Seven perfect fifths (G = 1.5) and five fifths with (G' = 1.497076023333.....). I believe that the twelve fifths would sound as twelve perfect fifths.

-- The product alpha x beta gives the D note frequency.

Thanks

Mario Pizarro

piagui@...

Lima, July 30, 2009

Hi Mario - would you happen to have a scala file for this new tuning?

Thanks,

Chris

On Thu, Jul 30, 2009 at 11:38 PM, Mario Pizarro <piagui@...> wrote:

>
>
> Dear friends,
>
> Five hours ago I successfully finished the design of a twelve tone scale. I
> will mention some of its features.
>
> -- The uncommon feature that helped to get a nice appearance when looking
> at its semitone factors distribution is that the scale works with two G's
> whose frequency ratio is 1.001953125, about 3.378 cents. With such a ratio,
> almost the schisma, we might be sure that there is only one G.
>
> -- The semitone factors distribution complies with the following factors:
>
> alpha, beta. alpha, beta, alpha, beta, gamma, alpha, beta, alpha, beta,
> alpha.
>
> -- The tone frequency values differ from the common values I used to work
> with, excepting 19/16, 4/3, 3/2, 57/32.
>
> -- Seven perfect fifths (G = 1.5) and five fifths with (G' =
> 1.497076023333.....). I believe that the twelve fifths would sound as twelve
> perfect fifths.
>
> -- The product alpha x beta gives the D note frequency.
>
> Thanks
>
> Mario Pizarro
>
> piagui@...
>
> Lima, July 30, 2009
>
>
>
>
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Hi Mario - would you happen to have a scala file for this new tuning?
>
> Thanks,
>
> Chris
-------------------------------------------------------------

Hi Chris,

In the recent days I did more research on the double G's scale and thanks to thess new concepts I knew the real values of all tones comprised within C = 1 up to 4C = 4, more exactly up to 4F. It was a complex matter.

Now I will give you basic information regarding how the perfect link 3/2 works to get its higher perfect relations,(1.5 x tone frequency), like Cx 1.5, C#x 1.5, ....F#x 1.5, and why G x 1.5, Ab x 1.5, A x 1.5, Bb x 1.5 and B x 1.5 give wrong values in the second octave.

Nature has "virtually" inserted a second G' in all the octaves to make a right coupling between any two consecutive octaves. The G/G' ratio is a little bit higher than the schisma. I wonder the posibility of a tentative average of both G's. Need to study this point.

I am making a detailed list of the natural tones (C to 8C) where the second G' works periodically in all octaves and explains how these links work.

Since I am wording about 30 pages on this subject to register it in the Peruvian Registration Office, what I can do is to give it to you and to the tuning list the global concept of the double G octaves which do not mean that the new scale is having two frequency values for G, it keeps the normal G = 1.5.

I am unable to give the information through my file, as moderator Carl Luma knows, my recent two files I tried to place in my file were rejected by unknown reasons. Another possibility is to place it in a folder, if so, I hope won't have any problem.

Once it is registered the pamphlet in about 30 days, I will send you and to the list full information regarding this subject if you agree.

I suggest you to give me your private e-mail address and use this way in further messages.

Below I give you preliminar information:

--C = 1

x alpha = C#

x beta = D

x alpha = Eb

x alpha = E

x beta = F =(4/3)

x beta = F#

x alpha = G' (Virtual G)

x A factor that is Slightly higher than the schisma = G = 1.5.

x beta ..... = Ab

x alpha .... = A

x ........ = Bb

x ........ = B

x ........ = 2C

The above tone frequencies let the obtainment of 2F = 2.666...= (8/3), 2G = 3, 4C = 4 plus the remaining tones which work in the second octave. The perfect link of 3/2 equally works in all the octaves.

Thanks

Mario Pizarro

piagui@ec-red.com

Lima, August 02, 2009

---------------------------------------
>
> On Thu, Jul 30, 2009 at 11:38 PM, Mario Pizarro <piagui@...> wrote:
>
> >
> >
> > Dear friends,
> >
> > Five hours ago I successfully finished the design of a twelve tone scale. I
> > will mention some of its features.
> >
> > -- The uncommon feature that helped to get a nice appearance when looking
> > at its semitone factors distribution is that the scale works with two G's
> > whose frequency ratio is 1.001953125, about 3.378 cents. With such a ratio,
> > almost the schisma, we might be sure that there is only one G.
> >
> > -- The semitone factors distribution complies with the following factors:
> >
> > alpha, beta. alpha, beta, alpha, beta, gamma, alpha, beta, alpha, beta,
> > alpha.
> >
> > -- The tone frequency values differ from the common values I used to work
> > with, excepting 19/16, 4/3, 3/2, 57/32.
> >
> > -- Seven perfect fifths (G = 1.5) and five fifths with (G' =
> > 1.497076023333.....). I believe that the twelve fifths would sound as twelve
> > perfect fifths.
> >
> > -- The product alpha x beta gives the D note frequency.
> >
> > Thanks
> >
> > Mario Pizarro
> >
> > piagui@...
> >
> > Lima, July 30, 2009
> >
> >
> >
> >
> >
>