Gutierrez Samanez's harmonic binodic periodicity in Acrobat.

[Julio gutierrez samanez]

Dear colleagues, I have been bringing this graph and article to your attention for a long time. It may be useful to explain some concerns such as periodicity and period doubling, as well as the ambivalence of the number n, both as the principal quantum number and therefore the energy level number: K, L, M, N... and as the binode number or the number of each symmetric pair of periods. Perhaps these are two different quantum numbers: one to define the order number of the periods, and the other to explain the phenomenon of periodicity, based on pairs of periods with the same number of elements (binode) or pairs of periods that appear through the addition of a new azimuthal quantum number, which is (in my opinion) the reason for the increasing periodicity. Thank you for your attention to this proposal.

Julio A. Gutierrez Samanez, 

from Cusco, Peru.

https://acrobat.adobe.com/id/urn:aaid:sc:VA6C2:fe58cf03-2442-4785-aa8a-c3c19f5b94ee

Paper in : 

https://academia.edu/resource/work/124043401

Estimados colegas, de mucho tiempo vuelvo a molestar vuestra atencion con este gráfico y artículo, que quizá pueda ser útil para explicar algunas inquietudes como la periodicidad y la duplicación de los periodos, así como la ambivalencia del número n, como número cuántico principal y por lo tanto numero del nivel de energía: K, L, M, N… y como numero de bínodo o de cada par simétrico de periodos. quizá se trate de dos números cuánticos distintos: uno para definir el numero de orden de los periodos y el otro para explicar el fenómeno de la periodicidad, basándose en pares de periodos con el mismo número de elementos (bínodo) o pares de periodos aparecidos por la adición de un nuevo número cuántico azimutal, que es (a mi parecer), la razón de la periodicidad creciente. Gracias por darle atención a esta propuesta. 

 Julio A. Gutierrez Samanez, 

desde Cusco, Perú.

Enviado con Gmail Mobile

[Rene]

Dear Julio

The title of your article, HARMONIC PERIODICITY OF THE CHEMICAL PROPERTIES OF GUTIERREZ SAMANEZ, unfortunately reads as though it is referring to the personal chemical properties of Gutiérrez-Samanez—which I’m sure was not your intention.

A clearer alternative may be: Harmonic periodicity of the chemical properties of the elements.

Your article also uses the expression, "there are exceptions that confirm the rule."

The phrase “exceptions that confirm the rule” is often misapplied, and in a scientific context it is particularly problematic.

What the expression originally meant
The old legal maxim exceptio probat regulam in casibus non exceptis means “the existence of an exception proves that there is a rule in cases not excepted.” For example, a sign reading “Parking is permitted on Sundays” implies that parking is not permitted on other days. It does not mean that the exception itself validates the rule; rather, it points to the rule’s existence elsewhere.

I suggest the exceptions you refer to are better understood as:

• demonstrating the approximate nature of the rule,
• pointing to underlying factors not captured in the simplified scheme, and
• indicating where the model’s predictive power is limited.

In this context, more accurate wording would be something like:

• “There are exceptions, which show the approximate nature of the rule.”
• “The exceptions highlight the limitations of the model but do not negate its general usefulness.”
• “As with the Madelung rule, the pattern holds broadly, with exceptions reminding us that not all factors influencing periodicity among the chemical elements are fully accounted for.”

This way, the article still acknowledges the overall regularity involved while presenting the exceptions in their proper role: not as confirmations, but as boundaries of applicability.

René

[Julio gutierrez samanez]

Thank you, Rene, for your insightful suggestions. I will make the changes you suggest. I also ask you to share with me the exact quote or text where Henry Bent published the colored boxes or grids for the chemical properties of the elements.
Thank you very much.
Your Peruvian colleague
Julio

[Rene]

On 11 Oct 2025, at 16:57, Julio gutierrez samanez <kut...@gmail.com> wrote:

Thank you, Rene, for your insightful suggestions. I will make the changes you suggest. I also ask you to share with me the exact quote or text where Henry Bent published the colored boxes or grids for the chemical properties of the elements.

You are welcome Julio, and I apologise for the delay in responding to your question.

The coloured boxes appear on the cover of Bent's self-published 2006 book, New Ideas in Chemistry from Fresh Energy for the Periodic Law:

https://www.meta-synthesis.com/webbook/35_pt/pt_database.php?PT_id=42

The colours are explained on page i of the book, as follows:

Yellow Alkali metal

Red Alkaline earth

Black  Element with a MON of +3 following an element with a MON of +2

Gray Element with a MON of +4 following an element with a MON of +3

Blue Halogen

Green Noble gas

Hatched downward to the right Coinage metals

Hatched downward to the left Volatile metal

MON = maximum oxidation number.

Note the irregularity in Group 3, which has two black elements (Sc, Y) and two white (Lu, Lr).

René

[Julio gutierrez samanez]

Interesting, Rene. In the graphs I'm sharing below, the black line follows the sequence: 5B, 13Al, 21Sc, 39Y, 57La, 89Ac, 121 (unknown).
But there's another black line that apparently follows the sequence: 5B, 13Al, 21Sc, ... However, it appears or begins with: 31Ga, 49In, 81Tl, 113, ....
Just as you say, the 71Lu, 103Lr are white, because they don't correspond to either of the two black lines.

Julio Antonio Gutiérrez Samanez

Libre de virus.www.avg.com

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