German language

Para: tuning@yahoogroups.com
De: Brad Lehman <bpl@...>
Remitente: tuning@yahoogroups.com
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Fecha: 17 Sep 2008, 09:17:55 AM
Asunto: [tuning] Re: I just deduced.....

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Hi Brad,In my last message (Subject: "I got it") I had proposed Piagui VII. Since I removed the preceding Piagui IV, V, VI whose responses in your harpsichord are not satisfactory due to the number of narrow fifths they have, this numbering has been changed to Piagui IV The new Piagui IV you have, presents three consecutive pure fifths:E----- 1,5 Pure ------ 702 cents B----- 1,5 Pure ------ 702 cents F#----- 1,5 Pure ------ 702 cents C#I strongly believe that this particular feature disables the scale coincidence with any of the Marpurg proposals.Piagui IV works with the sequence KPK PKK KPK PKK = 2. Note that the colored groups differ fromthe black ones. Below, I present again this scale that very probably Marpurg did not include inhis table. SINCE MARPURG IGNORED THE VALUES OF K AND P, HE NEVER CONSTRUCTED THE PIAGUI IV SCALE AND ALSO NEVER PRECISED PIAGUI I, II, III. TWO SCALES CAN BE CONSIDERED THE SAME SHOULD THEIR CORRESPONDING TONE FREQUENCIES ARE THE SAME. THIS IS SOMETHING LOGIC AND CLEAR FOR ME. I WOULD LIKE TO KNOW YOUR OPINION ON THIS POINT BRAD. K = 1,06066017178P = 1,05707299111PIAGUI IV (New numbering)C = 1xK = 1,06066017178 = C#xP = 1,12119522033 = DxK = 1,189207115 = Eb = 2(1/4) xP = 1,25707872211 = E xK = 1,33333333333 = F = (4/3)xK = 1,41421356236 = F#= 2(1/2) xK = 1,5 = G = (3/2) xP = 1,58560948666 = AbxK = 1,6817928305 = A = 2(3/4) xP = 1,77777777777 = Bb = 16/9xK = 1,88561808314 = BxK = 2 (The numbers within parenthesis are exponents).FIFTHS: C----- 1,5 Pure ------ 702 cents G----- 1,49492696045 Narrow--- 696 centsD----- 1,5 Pure ------ 702 cents A----- 1,49492696045 Narrow--- 696 centsE----- 1,5 Pure ------ 702 cents *B----- 1,5 Pure ------ 702 cents *F#----- 1,5 Pure ------ 702 cents *C#----- 1,49492696045 Narrow--- 696 centsAb----- 1,5 Pure ------ 702 cents Eb----- 1,49492696045 Narrow--- 696 centsE----- 1,5 Pure ------ 702 cents F-----------------------------------------------------------------------------> Ahhh! Now what could be more refreshing than 11 pure fifths in a
> dodecatonic scale? Surely if Pythagoras were alive today he would be
> the first to congratulate you on this remarkable accomplishment!

I'm wondering where the wolf 5th goes, with its full Pythagorean comma. ---- ?

Neidhardt in his 1732 example
http://harpsichords.pbwiki.com/f/Neidhardt_1732_ascii.html
put it at C-G.

Marpurg in his "L" temperament of 1776 (see Barbour's 1948 article) put
it at C-F.

It's awful either way in practice, at least on harpsichords.

Brad Lehman

------------------------------------Brad,I read the above web. I understood nothing and by sure I also wouldn´t understand it even if it would be written in the English or Spanish languages. It is too late forgoing to your university.Do you approve the above Piagui IV ?It seems that you did not notice that in only two days I deduced a new musical systemthat works with ELEVEN PURE FIFTHS PER OCTAVE THAT WILL BE APPLIED TO THE 88 PIANO KEYS IN THE FOLLOWING DAYS.RegardsMarioLima, September 17, 2008piagui@...