To Mike Battaglia

Mike,

When looking at the one second response of any chord wave (only waves) we can only see a dark area due to the compacted printed waves. If the electronic signal that produced the darken area is connected to an audio amplifier – speaker we reproduce the constant sound of the triad (during one second). I gave this explanation because in my preceding message I wrote that “the three wave response gives a completely dark area and no information.”

 Now you say that: 

 < “Well, that doesn't make sense - if there was no wave response, there 

< would be no <sound.”

 The dark area contains data rather than visual information.

 Actually, the dark area contains compacted printed waves which are unavailable for 

the eyes. Since there are a lot of wave peaks in that area, like hundreds of needles, 

most of these peaks are converted to marks. On each graph I sent you I sent mark 

combinations to show either chaotic tempered responses or aesthetic Piagui marks.

< I don't understand your math. Can you frame it in terms of just intervals, i.e.      

< rational number, fractional relationships here? I'm not sure what you mean.                                                                        

Here you are: (9/8) (1/2) (2)(1/4) = 1,26134462288, (1/2) and (1/4) are exponents.

This tone frequency is supported by cell # 205 of the progression: 

It is the third tone of Piagui II and Piagui III scales and made up by (K)(3) (P), 

where (3) is an exponent. Besides, the position of 1,26134462288 in the progression 

follows the expected position for Piagui II and III major scales.

< Your entire basis for calling it perfect is that the wave is slightly

< closer to periodic. The wave of C major is NOT fully periodic, as it

< would have to be in rational multiple relationships to be periodic.

The wave of C Major is perfectly periodic. I sent you its response and 

measured the periodicity and stability of all triads during thirty minutes. 

< My biggest problem with the scale is that the fifths that are better

< are only better by 2 cents, which is indistinguishable. The fifths

< that are worse, though, are flatter by 6 cents, which is very

< distinguishable.

Until you give the total amount of indistinguishable and distinguishable 

cents in both scales Piagui and equal tempered, your incomplete report 

has no sense. It is time to know the truth in both sides. I know that truth, 

however I prefer that another person that is not involved in the subject do it.

¿Did you ever added the total cents of fifths, fourths and third deviations 

of the equal tempered scale?.

> <That C-E is not periodic by any measure of the scale - in order for

> <that dyad to be periodic, the two frequencies would have to be in some

> <kind of rational relationship to one another. That E-G is pretty close 

(No, it is equal to the minor third – (2)(1/4) = 1,189207115 = Eq. T. Eb.

> <to a 19/16 ratio and the C-G is exactly 3/2. That means that the C-E

> <is going to be pretty close to a 24/19 ratio. BUT, even though it's

> <going to be close to 24/19, having a scale that is close to periodic

> <still won't mean that it's "perfect" for what western music

> <traditionally wants, which is a major third that is close to 5/4.

About E—G = (1,5 / 1,26134462288 ) = Eb = (2)(1/4)) = 1,189207115 

This quotient is the needed relation between E and G and at the same 

time another support of E = 1,26134462288.     

The tones (2)(1/4), (2)(1/2), (2)(3/4) and 2 are fundamental frequencies of 

(Eb, F#, A and Do) of Piagui and equal tempered scale. Thanks to this feature 

the only correct chord of equal tempered is DIMIN. DO, DIM. Eb, DIM F#, DIM A.

Note Eb = (2)(1/4)) = 1,189207115      

Regards

MARIO PIZARRO

 June 26--07:30 pm

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