In this vid, “mathemusician” Vi Hart and Sal Khan (of the amazing Khanacademy) discuss the difference between linear and logarithmic scales and human perception. I like their joking idea of a liner scaled piano where the keys would get fatter and fatter as you moved up the scale.
For those who are sticklers enough to be annoyed by the fact that Vi just makes up frequency numbers for “C” (’cause she can’t remember the freq off the top of her head), on the blog Drew’s Day, Andrew Morrison provides some details Vi and Sal did not concern themselves with (the point of their video being more about conveying the idea of linear vs. logarithmic conceptually) and expands on several ideas.
12 thoughts on “How Humans Perceive Nonlinearity”
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You CAN see the logarithmic scale when looking inside a piano. The lengths of the strings correspond to the to the vibrating frequencies. The lowest notes have the longest strings and the upper notes have the shorter strings. So, the lowest C string IS (roughly) 4 times as long as its counterpart, 4 octaves higher.
Your idea of widening piano keys is interesting and funny, but the strings do show that piano makers think logarithmicaly – the keys are just a means to the sound, not the sound itself.
Wow, Vi Hart and Sal Khan, what a mind blowing combination.
This discussion reminds me of the “Numbers” episode of Radiolab. http://www.radiolab.org/2009/nov/30/ and http://www.radiolab.org/2009/nov/30/innate-numbers/ discusses how we naturally have a logarithmic concept of numbers.
Wow, Vi Hart and Sal Khan, what a mind blowing combination.
This discussion reminds me of the “Numbers” episode of Radiolab. http://www.radiolab.org/2009/nov/30/ and http://www.radiolab.org/2009/nov/30/innate-numbers/ discusses how we naturally have a logarithmic concept of numbers.
Wow, Vi Hart and Sal Khan, what a mind blowing combination.
This discussion reminds me of the “Numbers” episode of Radiolab. http://www.radiolab.org/2009/nov/30/ and http://www.radiolab.org/2009/nov/30/innate-numbers/ discusses how we naturally have a logarithmic concept of numbers.
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