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What is the basis of triad formation of elements?

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Hint: Dobereiner's triads were defined as gatherings of components with equivalent properties that were predictable by the German physicist Johann Wolfgang Dobereiner. He saw and noticed that gatherings of three components (which is termed as triads) could be shaped in which all the three components had comparable physical as well as synthetic properties.

Complete step by step solution:
Dobereiner's law of triads states that or defined as the atomic mass of the middle element of a triad consisting of three components is the arithmetic mean of the atomic masses of the other two elements present in the triad.
Triads were basically based on both physical as well as chemical properties.
Dobereiner mainly found that the atomic masses of these three elements, as well as other triads, formed a specific type of pattern.
For example:
 In the triad of lithium, sodium and potassium. The atomic mass of each of them is lithium is $7$ and the atomic mass of potassium is $39$. The average masses of lithium and potassium gives atomic mass of sodium $23$means the first and third are the average mass of its second element.

Additional information:
Through the whole presence of the intermittent table, Dobereiner's groups of three were an early effort to sort the components into some intelligent and different requests by their physical properties. In 1817, a letter having detailed Johann Wolfgang Dobereiner's perceptions of the soluble earth; to be more specific, that strontium had properties that were intermediate to those of calcium and barium. By 1829, Dobereiner had discovered various other gatherings of three components ("triads") whose physical properties were similarly related. He similarly noticed that some quantifiable properties of components (for instance nuclear weight and thickness) in a triads followed a specific pattern whereby the estimation of the center component in the group of three components would be actually or almost predicted by taking the math mean of qualities for that one property of the other two components.

Note: In the periodic table there's only four main triads that are Major, Minor, Augmented, and Diminished. These four triad types are the basis for nearly every chord that we will need. If you can immediately identify these four triads and once you add seventh, ninth, eleventh, and thirteenth to the triad, it will be expressively easier to direct these sounds.