Ever wondered why all humans like certain frequencies?? And not just certain regions and races, but throughout the world, all humans tend to like the same notes – from Western to Indian, all music is based on notes of the same frequencies.
And it just isnt music, any form of art – there are certain shades, certain colours, that appease all humans in general. And yes – that includes members of the opposite sex as well (with reference to their shapes and sizes i.e.) – And the reason for this – is Mathematics.
All humans react to logarithmic increments. And tend to like logarithmic increments. And let me explain this using music (becuase art and human bodies are a little bit more complex ;-))
Now – lets first understand scales (with reference to music – and not fish) – a musical scale is defined as a series of notes differing in pitch according to a specific scheme. The most simple of these is the regular heptatonic (consisting of 8 notes) scale which most of us are aware of – C D E F G A B C(next octave) or in Indian terms, (Sa Re Ga Ma Pa Dha Ni Sa). Another scale of note, is the Pentatonic scale – C D E G A C or Sa Re Ga Pa Ni Sa.
Now – it is very interesting that the Pentatonic scale is kind of imbibed in us – all of us like it – whether in music, or art (if it is kinduv converted to shades), or with reference to human bodies (i.e., the proportions of the body). But the very interesting bit, is that how this is completely mathematical –
Let us first see what a Logarithmic scale is –
We all know what a linear scale is – i.e., where the numbers form a sequence – 1,2,3,4,5,6…. and so on…
A logarithmic scale is one in which the next number is obtained by multiplying the previous one with a common factor. That is, a logarithmic scale in base 2 would be – 1,2,4,8,16,32… every number being multiplied by two to give the next number – similarly, a log scale in base 10 would be – 1,10,100,1000 and so on…
Now, the standard frequency of a C note is 256Hz. The C note of the next higher octave, is exactly twice of that – 512Hz… and so on – so the various C’s on different octaves are at 256,512,1024,2048 Hz. and so on – that is, they follow a base 2 logarithmic scale.
From C to the C on the next higher octave, are 12 intervals – C > C# > D > D# > E > F > F# > G > G# > A > A# > B > C
So, given a factor of 2 between the two C’s (as it is following a base 2 log. scale) the factor between two individual notes is the 12th root of 2 (or in simpler terms, 6%)
That is, Frequency of C multiplied by the 12th root of 2 will give you Frequency of C#
C * (12th root of 2) = C#
C + (6% * C) = C#
and this continues…
so, C# * (12th root of 2) = D
and so on..continue for 12 times, and you shall get the frequency of the C in the next octave.
So – the music scale is logarithmic in frequency.
And – humans have a certain liking for logarithms- that is why people all over the world – in olden times – even when there was no form of communication between two cultures, developed the same notes at the same frequencies and created music.
If we even deviate slightly from these logarithmic increments, it tends towards noise – and not music.
No wonder – that some of the best musicians have been people with high IQ’s – and mathemetically proficient!
Interesting – aint it??