# Tune your piano to the top quality musical scale



## C. Mario Pizarro (Aug 9, 2005)

*Tune your piano to the top quality musical scale.*
The equal-tempered scale permits the performance of all kinds of music at the expense of small imperfections in all sorts of chords. It is based on elementary reasoning unlinked to matters dealing with consonance derived from science subjects. The opinions of noted researchers regarding the tempered scale are given here. (W.T.Bartholomew "Acoustics of Music"): 
"Equal temperament enables us to play equally well, or perhaps we should say equally badly, in all keys"; "Thus the "tuning" of a tempered instrument is in reality a process of controlled mistuning".
I have set in my book: *The Piagui Musical Scale: Perfecting Harmony * new concepts of the scientific basis of a new musical scale. 
The smallest comma M= (32805/32768)=1.00112915 and the new J and U ones, define a progression of 612 relative frequencies from note Do = 1 up to 2Do=2. 
The treatment is based on limited information from the ancient scales for detecting K and P semitone factors that rule the harmony of the "Piagui" scale and replace the Tempered T. 
The combined work of K and P can set the needed twelve-tone frequencies for any octave. Their precise and suitable values determine that perfect fifths and perfect fourths link all tone frequencies of the piano keyboard in cycles. These remarkable results made possible the attainment of the best expressions of harmony. 
The book shows and evaluates the quality of harmony of all major and minor triads of both, Tempered and Piagui scales. It also deals with the application of the new scale to the piano, electronic organ, electronic tuner and other instruments.
Sufficient data are given for tuning the piano to the top quality musical scale.
The Piagui scale is not an invention; it is a discovery that resolves the slight discordance problem of the equal-tempered scale.
C. Mario Pizarro


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## C. Mario Pizarro (Aug 9, 2005)

*The Commas and the Piagui musical scale*

The Commas and the Piagui Musical Scale
The smallest comma M= (32805/32768)=1.00112915 together with J=1.00113137 and U=1.00121369 determine the tone frequencies of the pythagorean and Just Intonation ancient scales as well as the twelve tone frequencies of the Piagui musical scale. The Piagui tone frequencies were deduced thanks to the data given by the successive comma products of the following progression: 
1 x (QRQQRo Q) (QRQQRo Q) (QRQQRo Q) (QRQQRo Q) ...., where 1 = Do.
Q= (M M J J M M M M J J M M M M J J M M)
R= (J J M M U U M M J J M M M M J J)
Ro = (J J M M M M J J M M U U M M J J) (Inverse sequence of R).
The product of the first 612 commas gives 2 Do = 2.
Note D= 9/8= 1.125 of both ancient scales is given by the product of 104 commas comprised in (Q R Q Q Ro Q). 
The pythagorean note E = 1.265625= (Q R Q Q Ro Q) (Q R Q Q Ro Q) 
My book: "The Piagui Musical Scale: Perfecting Harmony" also deals with the application of the new intonation to the piano, electronic organ, electronic tuner and other instruments.
If note Do = 1, any tempered octave is ruled by 1xTxTxTxTxTxTxTxTxTxTxTxT = 2 while 1 x K K P K K P K K P K K P = 2 corresponds to the Piagui octave. The values of K and P are deduced in the book.
Sufficient data is given for tuning the piano to the top quality musical scale. Perfect fifths and perfect fourths link all the keyboard.
The Piagui scale is not an invention; it is a discovery that resolves the slight discordance problem of the equal-tempered scale.
C. Mario Pizarro
[email protected]


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