Distinguishable

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 RegardsMARIO PIZARRO June 26--07:30 pmpiagui@...

> < 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.

Once again:

The C and the G together will be periodic. The C and the G together
will NOT be periodic, as the two frequencies are in IRRATIONAL NUMBER
relationships to one another. If you have measured the C major triad's
waveform and determined it to be periodic, then you have made an error
somewhere, because it is PHYSICALLY IMPOSSIBLE.

The wave might be close enough to periodic to be indistinguishable,
but that major third will certainly be a far cry from 5/4.

> < 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.

That is a lot of math. If you would like to provide us with a chart of
the errors from each interval, the RMS tuning error and TOP error and
all of that, as well as a corresponding chart from 12-tet, then I'd be
happy to compare and take a look and help you interpret what the
charts mean.

I will say that you cannot claim that the flat perfect fifth, which is
4 cents flat from 12-equal, will be indistinguishable, but that the
major third, which is 2 cents sharp from 12-equal, will be
distinguishable.

It's a lose-lose: whenever the fifth is better than 12-equal, the
major third will be slightly worse, and whenever the major third is
better than 12-equal, the perfect fifth will significantly worse.

> ¿Did you ever added the total cents of fifths, fourths and third deviations
> of the equal tempered scale?.

The equal tempered scale has an approximation of 3/2 that is roughly 2
cents sharp, an approximation of 4/3 that is roughly 2 cents flat, an
approximation of the 5/4 major third that is roughly 14 cents sharp,
and an approximation of the 6/5 minor third that is roughly 16 cents
flat. If you treat the equal tempered minor third as an approximation
to 19/16, then it is only 2.5 cents sharp.

>> <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.

The minor third that most people want to use is 6/5. The quarter of an
octave that is used in 12-tet and your scale is not 6/5 by any means,
and is closer to 19/16. It is a workable approximation to 6/5 that
most people won't notice: certainly does not make the scale offer
"perfect" harmony.

>> <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.

I don't know offhand what decimal numbers relate to what just
relationships. Please write using fractions and exponents, not
decimal.

> 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.

If you arbitrarily define the "correct" diminished chord as 4 equal
divisions of the octave.

> Note Eb = (2)(1/4)) = 1,189207115
> Regards
> MARIO PIZARRO

Mario, I will say this: You cannot "define" perfect harmony to be
something that is not in accordance with what the music community at
large needs, and then claim that your scale offers perfect harmony.
For the vast majority of western music out there, especially baroque
and classical pieces that were composed in some kind of meantone
tuning, then your scale will be just as imperfect, if not slightly
more in certain situations, than 12 tone equal temperament.

The fact that the wave appears to be periodic doesn't matter, as the
Hammond B3 organ's waves are all perfectly periodic, but the notes
have relationships to one another like 2808 / 2975. After a certain
point, the ear can no longer hear the periodicity of the wave except
for a slight difference in beating.

I don't know how you define "perfect," but the fact of the matter is
that periodicity does not mean "perfection" of a chord or a triad. The
other thing is that not only is the major third in the "perfect" chord
even FARTHER from 5/4 just, the perfect fifths in the "imperfect
chords", of which there are four in piagui, are even further from just
than the "perfect" piagui thirds are.

I think it is an interesting scale with interesting properties that in
certain situations might lead to it being more advantageous than
12-equal. I do not think it is a perfect scale that will handle the
musical requirements of most music any better than 12-equal, but in
certain situations, it may.

-Mike

> The C and the G together will be periodic. The C and the G together
> will NOT be periodic, as the two frequencies are in IRRATIONAL NUMBER
> relationships to one another. If you have measured the C major triad's
> waveform and determined it to be periodic, then you have made an error
> somewhere, because it is PHYSICALLY IMPOSSIBLE.

I meant the C and the E here. The C and the G will be periodic, the C
and the E will not. The C and the G are in a rational 3/2 relationship
to one another, meaning that for every 3 cycles of the G there will
have been 2 cycles of the C. This property does not apply to the C and
the E, the waves of which will NEVER sync up enough to be actually
periodic.

-Mike