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Comment by tpeo | Hacker News Reader

Well, I'm not a sound engineer, but I think it's conceivable that 432Hz tuning might sound better due to entirely non-mystical reasons. From the perspective of harmonic entropy, or at least I think so, the tighter differences between each notes' frequencies and that makes the problem of fitting intervals into ratios harder.

I recognize that this bit is entirely personal, but I think that can make otherwise "simple" music more enjoyable. But my enjoyment of music is almost entirely dependent on the careful management of the "Wall of Sound" effect and by how much noise (in the form of timbre, attacks, number of different voices) is introduced or removed from the track. And I think that's the key difference between, say: a library piece, or a movie score; and pieces meant to be listened on their own.

Also, the expression "cargo cult numerology" pretty much made my day.

http://sethares.engr.wisc.edu/paperspdf/HarmonicEntropy.pdf

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What???

Tighter differences between each notes' frequencies??

Please explain this thought.

Well, I'm assuming that the ease or difficulty of recognizing the difference between two notes bears some proportion to difference between their frequencies (the frequency of one minus that of the other), and not just their relative frequencies. The intervals in the 432Hz are "tighter" in the sense that, because the interval they correspond to in 440Hz is smaller for every possible interval, there are more notes in 432Hz tuning in any given arbitrary frequency range (say, from 100Hz to 1,000,000Hz) than in 440Hz tuning. And this makes the problem of recognizing them harder. I should've made this out clearer.

For instance, a half-tone from 432Hz is 457.69Hz, which gives out a difference of 25.69Hz; but a half-tone from 440Hz is 446.16Hz, which gives out a difference of 26.16Hz. Between 432Hz and 864Hz we can fit a whole scale, while in the same frequency range we'd be missing a note with 440Hz tuning.

Of course, this is a slight difference and it might not be noticeable at all. I personally don't hear much difference between the two tuning. Instead, I'm playing devil's advocate.

I don't follow you. Are you saying that if I detune my guitar enough, then it will grow an extra fret?

If I understand correctly, he's guessing that pitch discrimination is finer at lower frequencies, so tuning at 432Hz would allow our ears to be more 'exact'. Of course, this advantage would be negligible, and pitch discrimination decreases past a certain point. The songwriter intended their piece to be heard by human ears at A=440Hz, knowing the various propensities of human hearing at various levels.

Ok, I see what you mean.

Then most songs would sound 'better' a half-step down, etc.

Look at it like Celsius vs Fahrenheit (this isn't a perfect analogy because both scales measuring the same value, where we're discussing different values, but it'll do).

The boiling point of water in Celsius is 100 degrees, and the freezing point is 0 degrees; in Fahrenheit, 212 and 32, respectively. What's significant is the scale of each unit. 99C is colder than 211 Fahrenheit.

In the case of music, which is all about relative frequencies, establishing A determines the size of the steps. The above poster is proposing that A=432 yields more interesting frequency relationships than A=440. I have no idea.

Well... It doesn't. The same ratios exist for A=440:A=440 * 3/2 and A=432:A=432 : 3/2, for example

I wouldn't say that's the case for most songs, but rather only for simple melodies. But yeah, a graver voice would sound better in most cases.

Consider the beggining of Bach's "Little" Fugue in G Minor (BWV 578), where the subject of the fugue is first introduced by a soprano voice and then repeated by an alto voice, while the soprano voice does the coutersubject. I'd say that, played in isolation, the melody sounds better when sung by the alto voice. But lowering the whole Fugue by a half-step wouldn't make it much better.

With respect to recorded music it tends to be the opposite: if you pitch up a track then the rhythm feels tighter and the vocals more steady, because the differences between the intent and the performance are relatively smaller. Hence an old studio trick dating at least back to the Chipmunks was to record in a lower key. Listener discrimination seems relatively less important in practice, on the other hand.

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