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Theory:

Law of Octaves:
John Alexander Reina Newlands (\(1837 - 1898\)) was a British chemist who studied element periodicity. He was the son of a Scottish Presbyterian minister and his Italian wife. He was born in London, England, in West Square in Lambeth. Newlands was the first to create a periodic table that listed chemical elements in their relative atomic masses.
JohnAlexanderReinaNewlands.jpg
 
Döbereiner's efforts inspired other chemists to try to correlate element properties with atomic masses. In \(1866\), John Newlands, arranged the then-known elements to increase atomic masses.
 
He began with the element having the lowest atomic mass (hydrogen) and ended at thorium, the \(56\)th element. He discovered that the properties of every eighth element were similar to those of the first. He likened it to the octaves found in music (sa, re, ga, ma, pa, da, ni, sa). As a result, he termed it the "Law of Octaves." It is defined as 'Newlands' Law of Octaves.'
 
muic sytem.JPG
Indian musical notes
  
We see the properties of lithium and sodium to be identical in Newlands' Octaves. Sodium is the eighth element, following lithium. Similarly, beryllium and magnesium are chemically similar. The table below depicts a portion of the original form of Newlands' Octaves.
 
Newlands’ octaves table.
sa
(do)
re
(ri)
ga
(mi)
ma
(fa)
pa
(so)
da
(la)
ni
(ti)
H
Li
Be
B
C
N
O
F
Na
Mg
Al
Si
P
S
Cl
K
Ca
Cr
Ti
Mn
Fe
Co and Ni
Cu
Zn
Y
In
As
Se
Br
Rb
Sr
Ce and La
Zr
-
-
In Indian music, there are seven musical notes on a scale: sa, re, ga, ma, pa, da, and ni. In the west, the notations do, re, mi, fa, so, la, ti are used. Tones and semitones are separated in a scale by whole and half-step frequency intervals. Musicians use these notes to compose music for songs. Naturally, there will be some note repetition. Every eighth note is similar to the first one, and it is the first note of the following scale.
Disadvantages of Newlands law of octaves:
  • The law of octaves did not apply to elements with atomic masses greater than calcium, as after calcium, every eighth element lacked properties similar to those of the first.
  • Newlands' table was limited to \(56\) elements and didn't allow for the addition of new ones. But, later on, many new elements were discovered whose properties did not fit into the Law of Octaves.
The two elements, cobalt and nickel, have occasionally been placed in the same slot (refer the above table).
 
Newlands altered two elements in the same slot and placed some different elements under the same note to fit elements into his table. Are there any examples of these in the table above? Nickel and cobalt are in the same slot, and they're in the same column as fluorine, chlorine, and bromine, which have entirely different properties. Iron, which possesses properties similar to cobalt and nickel, has been put far away from these metals. The Law of Octaves became irrelevant with the discovery of noble gases. As a result, Newlands' Law of Octaves was only applied with lighter elements.
Reference:
https://en.wikipedia.org/wiki/John_Newlands_(chemist)