Harmony in Gradation formula and its modifications are promoted for use in all branches of science.

 

The Fundamental of Harmony in Gradation

The Harmony in Gradation is the formula that has been made by Sigit Haryadi on April 28, 2016, which was originally named as “Haryadi Index” since only focus to use in the Competition Law field, to replace the Herfindahl-Hirschman Index (HHI). But, after studying for two years, the inventor was very confident that the formula can be used as an alternative to replace many existing methods in all branches of science, because in the formula both contain two contradictory things that no one has ever thought to merge them, namely “the Harmony” and “the Gradation”, on the other hand, the existing formulas contain only that one element.

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More specifically, pay close attention to the Images of Equalizer which is the closest form of the Harmony in Gradation, where each calculator that is on this website is a representation of one or more of the equalizer images.
A painting or natural landscape that has a combination of shapes and colors will look very beautiful if there is a harmony of the gradation of the shapes and colors that lie in suitable positions. Also, a musical composition that has a combination of tone and rhythm will sound very melodious if there is a harmony of the tonal gradation and the rhythm that lies in the appropriate time sequence. Then, inspired by paintings, natural scenery, and music, we suppose that most of the mathematical formula in all sciences should have two elements simultaneously that “the Harmony” and “the Gradation”.
It has been proven, the existence of “the harmony” and “the gradation” at the same time on a formula when used to analyze a Union or a random variable is to produce an index or level that accurately and precisely represents the “harmony level” of the Union or random variable regardless of the population. This means that an index equal to one is showing the perfect conditions of the harmony level, a value equal to 0.95 means that the harmony level is 0.95 of the perfect, a value equal to 0.75 indicates the harmony level is equal to 0.75 of the perfect, and so on. The consequence, the Harmony in Gradation will produce an index that represents the nature of the union or the random variable very accurately and precisely.
More specifically, the branch of science that is worth considering the use of Harmony in Gradation is that it uses “the level of harmony” which represents “the beauty” as the keyword of the research, which in each branch of science are called in different terms such as “level of balance”, “equilibrium level”, “stability level”, “level of parity”, “equipoise level”, “level of competition”, “level of justice”, “fairness level”, “level of correlation”, “entropy”, “level of performance”, “Level of quality”, “level of certainty”, “level of health”, “level of similarity”, “confidence level”, “level of consistency”, “level of equity”,  “level of equality”, and others. And, don’t forget, since some branches of science prefer to use the negative of these terms, then the spirit of Harmony in Gradation also corresponds to the terms of “the level of imbalance”, “the level of concentration”, “the level of injustice”, “unfairness level”, “complement level”, “counterbalance level”, “level of uncertainty”, “level of relativity”, “level of inequality”, “level of inequity”, and others.
Furthermore, there are three ways to use the Harmony in Gradation formula. First is to replace the existing formula. Second, only the spirit is utilized, in the sense that the existing formula is modified in such a way so that in the same time it has the two elements which “the Harmony” and “the Gradation”. And third, the Harmony in Gradation formula is only used to calculate the harmony level of the union or random variables that are being observed, which are formed or defined through an existing formula or a formula that was just made.
In essence, the name of the formula is the Harmony in Gradation, not the Gradation in Harmony because the goal is to form the harmony. Moreover, when we are analyzing a Union or a random variable that has the harmony level that we consider too low and want to increase it, then there are several alternatives that can be done. First, combining several elements that have relatively small strength so that the union population will be less but there will be a balance of power between the existing elements that have great power with new elements which are a combination of small elements.  Second, let the elemental population not change, but shift or give a portion of the strength of the elements that are relatively large to the small elements. Third, combines the first and second ways. The fourth way, if you have a Union or random variable that is less harmonious, then we put it side by side and compare to the other Union or random variable which also not harmonious, but these two unions have the same relative strength distribution so that the combination of these Unions will appear harmonious. Fifth, is done if we cannot change the harmony level of pairs of objects and/or waves, and can only observe, then we should use the Harmony in Gradation to examine what will happen in the future in pairs of objects and/or waves that will change or move continuously caused by disharmony that is slightly less perfect between them. In the future, it may take the sixth method, the seventh strategy and so on.
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The Formula of Harmony in Gradation

The formula “Harmony in Gradation” is written as follows:

Harmony in Gradation Formula

Where: HiG is “the Harmony in Gradation” of a random variable (or set) which has a sample population (or subset) = N, and Si is “the Share” of each sample (or subset) = comparison between strengths or the value of each sample (or subset) with the total strength of the random (or set) variable.

 

Harmony in Gradation formula; N = 2, 3, 4, 5, 6, 7, and 8
Calculation Example of Harmony in Gradation on Competition between Firms in Industry

Calculation Example of Harmony in Gradation on the Degree of Linear Correlation
Note: The weakness of Existing Formulas (the formula containing one of the Harmony or the Gradation)
    • The weakness of the formulas containing only “the Harmony” is cannot give the exact same index to the random variable (or set) that have the same nature but have different sample populations.
    • The weakness of the formulas containing only “The Gradation” is to give the possibility that some random variables (or sets) of a different nature that have same sample populations will get the same index.
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References:

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