Chord wave peaks- E. tempered in comparison with Piagui scale. C major

A single line starting from t = 0 depicts the e-tempered and Piagui chord waves like the wave of G Major.
There are a great number of positive and negative peaks in a chord wave in just one second. In some cases, such as graphs Nos. 1 and 2, the peak density increases as the scanned area approaches the time axis, where we cannot get information regarding harmony. However, consecutive peaks somewhat distant from the mentioned axis are seen as linked by small lines in the form of an envelope.
Graphs Nos. 3 and 4 show periodic and empty spaces around the time axis that do not give information concerning aesthetic or non-aesthetic envelopes due to high mark densities. For this reason,
e-tempered and Piagui I - C Major chord wave peaks and some of the remaining graphs do not show the marks in the mentioned areas. However, the positive and negative envelope marks somewhat distant from the time axis may determine the quality of harmony and
slight frequency discords. The analysis and discussion of e-tempered and Piagui mark distribution given by chord wave peaks eases the harmony comparison between both types of chords.
By comparing their chord wave peaks also called mark waves, an aesthetic mark distribution in graph No. 4 is seen. Contrasted with this feature, the mark distribution of the tempered response is a non-periodic and disorderly display. Therefore, the aesthetic display of Piagui I - C Major is a sign of a high quality harmony. The chord wave peaks of C Major and G Major are similar. By examining their graphs, only one difference was seen in the periodic displays, and that is the number of equal empty areas around the time axis as a result of the higher tone frequencies of G Major. Chord wave peaks of Gm and Am with h, h, H and o, o, h discrepancies respectively –which produce the same increase of frequencies– are similar graphs.

Lima, May 30, 2009
Mario Pizarro

--- In tuning@yahoogroups.com, "piaguiscale" wrote:
>
> A single line starting from t = 0 depicts the e-tempered and Piagui chord waves like the wave of G Major.
> There are a great number of positive and negative peaks in a chord wave in just one second. In some cases, such as graphs Nos. 1 and 2, the peak density increases as the scanned area approaches the time axis, where we cannot get information regarding harmony. However, consecutive peaks somewhat distant from the mentioned axis are seen as linked by small lines in the form of an envelope.
> Graphs Nos. 3 and 4 show periodic and empty spaces around the time axis that do not give information concerning aesthetic or non-aesthetic envelopes due to high mark densities. For this reason,
> e-tempered and Piagui I - C Major chord wave peaks and some of the remaining graphs do not show the marks in the mentioned areas. However, the positive and negative envelope marks somewhat distant from the time axis may determine the quality of harmony and
> slight frequency discords. The analysis and discussion of e-tempered and Piagui mark distribution given by chord wave peaks eases the harmony comparison between both types of chords.
> By comparing their chord wave peaks also called mark waves, an aesthetic mark distribution in graph No. 4 is seen. Contrasted with this feature, the mark distribution of the tempered response is a non-periodic and disorderly display. Therefore, the aesthetic display of Piagui I - C Major is a sign of a high quality harmony. The chord wave peaks of C Major and G Major are similar. By examining their graphs, only one difference was seen in the periodic displays, and that is the number of equal empty areas around the time axis as a result of the higher tone frequencies of G Major. Chord wave peaks of Gm and Am with h, h, H and o, o, h discrepancies respectively –which produce the same increase of frequencies– are similar graphs.
>
> Lima, May 30, 2009
> Mario Pizarro

Hi, Mario!

It might be easier to understand your message if you showed the graphs you mention. As it is, I am almost entirely mystified as to what, exactly, you mean. As a musician, physicist and mathematician, I am not used to being baffled so easily by what appears to be a technical discussion about ranking relative harmoniousness of different chords. Yet even with those graphs in front of me, some questions would remain. Here are a few of them:

1. What is a chord wave?
2. What is an e-tempered chord wave?
3. What is a Piagui chord wave?
4. What is an h, H, and o discrepancy?

Thanks.

Regards,
Yahya
---------------------------
Yahya Abdal-Aziz
Convener, Music SIG, Melbourne PC User Group
http://groups.melbpc.org.au/~music/

> Hi, Mario!
>
> It might be easier to understand your message if you showed the graphs you mention. As it is, I am almost entirely mystified as to what, exactly, you mean. As a musician, physicist and mathematician, I am not used to being baffled so easily by what appears to be a technical discussion about ranking relative harmoniousness of different chords. Yet even with those graphs in front of me, some questions would remain. Here are a few of them:
>
> 1. What is a chord wave?
> 2. What is an e-tempered chord wave?
> 3. What is a Piagui chord wave?
> 4. What is an h, H, and o discrepancy?
>
> Thanks.
>
> Regards,
> Yahya
> ---------------------------
> Yahya Abdal-Aziz
> Convener, Music SIG, Melbourne PC User Group
> http://groups.melbpc.org.au/~music/
>
--------------------------------------------------
Hello Yahya,

** As you know it is not possible to post diagrams via tuning. I **tried to insert at least one diagram but it didn´t work. Let me **suggest you to confirm your e-mail address <yahya@yahoogroups.com> **or <yahya@...>. Diagrams and additional information can be **sent you via your alternate e-mail address. My e-mail address **follows:

**<piagui@...>.

My name: Mario Pizarro; Electronic Engineer,

**physicist, mathematician. Age: 75.

**Agree, just a message can´t give sufficient information. Now you **will have more and I will be pleased to give more details if we **keep in contact. This matter that took me more than 20 years **deserves to be examined by learned persons like you.

About your questions:

**Once you get basic/detailed information on the Piagui musical scale
**and its fundamental principles as well as the new developed **sources used to get this system you might conclude that this **matter deserves to be part of the physics science.

-- What is a chord wave?
If we take a pure sinusoid (no overtones)whose frequency is f1 we can depict this wave on an XY coordinates starting with the wave zero amplitude or origin at the positive going of line.
A second sinusoid with f2 frequency is placed on the diagram and again its positive going origin (Y = 0) coincides with the former wave origin which also coincides with the XY origin.

Similarly, a third sinusoid with a f3 frequency is placed in the diagram. Each wave represents a triad tone and these three sinusoidal vaves are added. It is evident that the total wave is not a sinusoidal variation; the combined wave shape formed by three audio-frequencies show a darkened area near the abscisa axis, however at higher positive and negative amplitudes appear positive and negative peaks which are not producing darkened areas and these data gave important information regarding the triad harmony. It was necessary to transform the useful peaks of the combined wave (CHORD WAVE) to point marks (CHORD WAVE PEAKS)by using a suitable software.

-- What is an e-tempered chord wave?
The preceding paragraph explains how a CHORD WAVE is displayed. The type of the three sinusoidal components (f1, f2, f3) was not specified. When the three wave triad components correspond to the e-tempered scale then we have an e-tempered chord wave.

-- What is a Piagui chord wave?
The preceding lines answer your question for in this case the three combined sinusoids are tone frequencies of the Piagui scale system. I said system because it offers three optimal scales.

-- What is an h, H and 0 discrepancy?
In my book I explain these parameters. Below I give one example.

NOTE.... PIAGUI I .......E.TEMPERED....DISCREPANCY %
D....... 294.3287 Hz.....293.6648 Hz... + 0.226 %

According to the relative discrepancy magnitude it is classified with the h, H, 0 figures to compare the triad tone discrepancies.

I would be pleased to give you more information and hope to get your full e-mail address to send you the graphs.

Regards

Mario Pizarro

piagui@...

Lima, June 02, 2009

--- In tuning@yahoogroups.com, "piaguiscale" <piagui@...> wrote:
> ** As you know it is not possible to post diagrams via tuning. I **tried to insert at least one diagram but it didn´t work ...

Hello Mario,
there is a "Files" area for the group, as well as the "Messages" area; you could upload the diagram(s) there perhaps.

Steve M.

--- In tuning@yahoogroups.com, "martinsj013" <martinsj@...> wrote:
>
> --- In tuning@yahoogroups.com, "piaguiscale" <piagui@> wrote:
> > ** As you know it is not possible to post diagrams via tuning. I **tried to insert at least one diagram but it didn´t work ...
>
> Hello Mario,
> there is a "Files" area for the group, as well as the "Messages" area; you could upload the diagram(s) there perhaps.
>
> Steve M.
>
--------------------

Steve,

I just sent you two pages,via "Files". Each contains 2 chord wave peak graphs.

Regards

Mario Pizarro
Lima, June 02, 2009
piagui@...