A couple of weeks ago, while a road trip to Pittsburgh with my good friend Antonio, one topic jumped to the conversation, and it was why do we feel like a melody played in different octaves is the same.

The answer was not so difficult to find: Because we are hearing the same fundamental frequencies and their harmonics, but that is the mathematical point of view and unless the ear is good with Fourier series, this answer is not so obvious.

In fact, it happens to be that the ear is a good mathematician, or at least designed by a great one.

First of all, what is an octave. When you rise or decrease a note by an octave, it means you are multiplying or dividing the frequency by 2, therefore, an octave higher of a central A note (440Hz) has a frequency of 880Hz, and an octave lower, 220Hz. So there is an easy way to know if two melodies are alike, if their ratio is a power of 2, they must be the same!

Now our good ear has a pretty concrete task, still a little uncertain how can it be achieved though. Well the answer lies within would a Dream Theater song say, if we look at the process of how hearing is made, we can go deeper into the inner ear or labyrinth and find our answers. Here, after a mechanical process of sound transmission, there are located two chambers, each filled by liquids of different electronegativity.

These two chambers are separated by a thin layer that has several valves that can allow the two fluid to be mixed. Each of these valves are opened by a thin filament that, when excited, opens the valve. When the liquids mix, this produce an impulse that triggers a neuron and sends the sound information to the brain.

Now, here magic happens, one of these chambers is connected to the mechanical system that transmits the incoming sound wave, and it produces a standing wave in this chamber. The little filaments are arranged in such a way that the smaller ones are in front and the bigger ones in the back of the chamber. All the detection work is done by these little filaments, that have lengths growing exponentially, and moreover, each one is twice or half as long as its neighbors.

Hence, for a fixed frequency, any octave of it would excite the same filaments inside our inner ear, and therefore the same neurons are triggered and that makes us feel like is the same sound or melody we played a different octave, just with a little different flavor.

The answer was not so difficult to find: Because we are hearing the same fundamental frequencies and their harmonics, but that is the mathematical point of view and unless the ear is good with Fourier series, this answer is not so obvious.

In fact, it happens to be that the ear is a good mathematician, or at least designed by a great one.

First of all, what is an octave. When you rise or decrease a note by an octave, it means you are multiplying or dividing the frequency by 2, therefore, an octave higher of a central A note (440Hz) has a frequency of 880Hz, and an octave lower, 220Hz. So there is an easy way to know if two melodies are alike, if their ratio is a power of 2, they must be the same!

Now our good ear has a pretty concrete task, still a little uncertain how can it be achieved though. Well the answer lies within would a Dream Theater song say, if we look at the process of how hearing is made, we can go deeper into the inner ear or labyrinth and find our answers. Here, after a mechanical process of sound transmission, there are located two chambers, each filled by liquids of different electronegativity.

These two chambers are separated by a thin layer that has several valves that can allow the two fluid to be mixed. Each of these valves are opened by a thin filament that, when excited, opens the valve. When the liquids mix, this produce an impulse that triggers a neuron and sends the sound information to the brain.

Now, here magic happens, one of these chambers is connected to the mechanical system that transmits the incoming sound wave, and it produces a standing wave in this chamber. The little filaments are arranged in such a way that the smaller ones are in front and the bigger ones in the back of the chamber. All the detection work is done by these little filaments, that have lengths growing exponentially, and moreover, each one is twice or half as long as its neighbors.

Hence, for a fixed frequency, any octave of it would excite the same filaments inside our inner ear, and therefore the same neurons are triggered and that makes us feel like is the same sound or melody we played a different octave, just with a little different flavor.

What a description of something that seems to be common or we might dont notice or worth :) what a complex :)

ReplyDeleteWow, great post Peter. thanks for sharing your knowlegde with us

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ReplyDeleteIn fact, it happens to be that the ear is a good mathematician, or at least designed by a great oneDoes this mean you support intelligent design?

What do you mean by intelligent design?

ReplyDeleteI mean the usual stuff:

ReplyDeleteIntelligent desing is the assertion that "certain features of the universe and of living things are best explained by an intelligent cause, not an undirected process such as natural selection" (Wikipedia)

Well, i do support intelligent design in that sense, but i don't see why it has to disagree with evolution

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