On the Sensations of Tone

What Hacker News says

1. jngJul 2025
   The white keys form a sequence of notes (frequencies) that is known as the diatonic scale. It's the foundation underlying all popular western music. It is not random or arbitrary, it has some nice dual mathematical and musical properties: intervals between the notes in the scale have special frequency ratios that sound pleasing to the ear (read Helmholtz's "On the sensations of tone" for a fascinating physically-based take on why it is like that -- he is known as "the father of acoustics", and that book contains the distillation of 8 years of deep, smart research way before we had the means or understanding we hav today). A ton, if not most, of popular music can be played using only the white keys.

   There used to be keyboards with other different arrangements, which were actually extremely cumbersome and actually didn't allow very rich and interesting musical excursions like modulations (look up "microtonal keyboards"). Today's standard keyboard and tuning is a compromise between those fundamentally mathematical and perceptual acoustic relations (the tonic, the fourth, the fifth, the sixth, the major and minor third, the "sensible" or subtonic...) and the ability to perform those trans-tonality excursions. A fully regular keyboard like you propose would lend itself more easily to those excursions, at the cost of being less apt at the foundational diatonic model and most popular music.

   Interestingly also, the notes used by modern keyboards and all modern instruments, and to which we are all so accustomed that we thing it "just is", is an imperfect compromise that needed a lot of selling back in the day, much of which was done by Bach (the compromise scale is called the "tempered scale", and Bach authored the arch-famous "Well-tempered clavier" pieces to show it off -- impossible to perform on keyboards with other tunings).

   And of course, there is a tradition factor. English isn't written like this because it's optimizing for any easily describable or measurable optimization metric, more like it minimized a socio-perceptual function covering many centuries of UX.

   Finally, if you want an instrument where all keys are equal, you can always move to a fretboard based one like the guitar. Funnily, it has a one-semitone-short jump between strings 3 and 2 that will throw off the desire of full regularity... again due to diatonic leanings. A bass guitar is fully regular, even when they add a 5th and 6th string, so that may fulfill your wish of a fully regular instrument... and it sounds awesome! Just can't do the same things as a piano or a guitar.

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2. jngApr 2021
   Next to this interesting article and comments, I think mention should be made of von Helmholtz's XIX century book "On the sensations of tone". He is considered to be the father of acoustics, and derived the consonance/dissonance of the notes in the diatonic scale from first physical principles. He extracted and computed what is described as "roughness" here as the amount of "beats" between the upper partials of the notes - where beats are the slow phase oscillations caused by two vibrations of very close frequencies. But of course, he first had to study strings and pipes for 8 years, and come up with the (then) innovative concept of upper partials (harmonics). I'm a software person by trade, amateur but very dedicated musician, read this book many years ago, thoroughly enjoyed it, and I heartily recommend it today.
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3. lucas_membraneSep 2019
   On the Sensations of Tone by Hermann von Helmholtz

   The Road by Jack London

   all of the Oz books by L. Frank Baum

   The Scottish Students' Song Book

   Heart Songs

   The Age of Reason

   The Art of Money Getting by Barnum

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4. jngJul 2016
   I urge anyone interested in this topic to read Helmholtz's "On the sensations of tone", a fascinating 19th-century tour-de-force trying to understand music sensation as coming from physical principles, deriving the standard western intervals and consonance/dissonance from first principles (beats between upper partials), and for which he is considered the father of acoustics. He spent 8 years researching in order to produce it, and is to me a great example of a 19th century hacker.
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