Comment by Devlin_Donnelly | Hacker News Reader

Comment by Devlin_Donnelly | Hacker News Reader

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Devlin_Donnelly

As to why some sets of notes sound good or harmonious and others sound "bad" or dissonant, we find that frequencies with the simplest mathematical ratios tend to sound the most harmonious, while frequencies with more complex ratios sound more dissonant.

So for example the simplest ratio 2:1 corresponds to an octave interval. Notes which are an octave apart sound so similar that we describe them with same letter. So concert A is 440Hz and the "A" note one octave higher is 880Hz.

The next simplest ratio, 3:2 corresponds to the interval known as a perfect fifth. So given the example of concert A at 440Hz again, one perfect fifth above concert A is the note E which has a frequency of 660Hz as (440 * 3) / 2 = 660.

We find the simplest ratios of frequency intervals present in music from cultures the world over. The traditional classical Western twelve-note scale consists of the 12 simplest frequency ratios. In some Eastern music we hear a pentatonic or five note scale, which consists of the five simplest frequency ratios.

So this aspect of music we can attribute to innate psycho-acoustics or even physics rather than cultural bias.

> So this aspect of music we can attribute to innate psycho-acoustics or even physics rather than cultural bias.

It's inextricable from cultural bias, though the physics obviously plays some role. The cultural bias comes into play more strongly around the question of how much dissonance is "good" vs. "bad", and how the more dissonant bits should interplay with the more consonant bits of music.

Certainly, "more consonant = better" isn't true in any culture I can think of.... Imagine an orchestra that tunes up, then they all play the note A in various octaves for 3 hours.

Possibly also worth mentioning that this isn't quite correct:

> The traditional classical Western twelve-note scale consists of the 12 simplest frequency ratios

You're thinking of the major scale, maybe? The ratios for a tritone, major 7th, etc. are more complex (and not the first 12 simplest...) and if you try to actually come up with ratios for an even-tempered scale you're really in trouble.

> It's inextricable from cultural bias, though the physics obviously plays some role.

Of course, as you say, our cultural biases/values play a role in how we create music and what music we appreciate with how much consonance/dissonance.

But the fact that certain musical intervals sound more harmonious or more dissonant seems to be a result of the human ear's response to the physical nature of the frequency of the sound waves, and thus a response that is shared across cultures.

> The ratios for a tritone, major 7th, etc. are more complex

Yeah, I guess that's true that the ratios between those 12 frequencies aren't the 12 simplest, but they can be derived by following the simplest non-octave ratio - 3:2 or a perfect fifth - starting from a root note and moving up one perfect fifth 12 times.

Thus if you start from C: C - G - D - A - E - B - F# - C# - G# - D# - A#/Bb - F and that's all 12 notes. I guess I thought that because of that pattern those were the twelve simplest ratios. Thanks for the heads up.

And yes this principle applies to the Just tempered Scale not the even-tempered scale.

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