User:VectorGraphics/Brightness analysis

It has recently come to my attention that the way we perceive the quality of intervals is not to do with just ratios, but rather with the size of the interval.

this is a major third, with a ratio of 5/4 and a size of about 385 cents. you can listen to it and it will sound like a major third.

this is another interval with a size of about 385 cents. however, its ratio is not 5/4; it is in fact 8192/6561. while it sounds like a major third, many people - in fact, most people, would call this a diminished fourth and not a major third, because it is an apotome lower than a just perfect fourth. but it is a major third. you can put it in a chord and it will sound as harmonious as the 5/4. most people can't even tell the difference between the two intervals, and they both sound like they relate to the fourth in the exact same way - being not only about one step lower than it, but a pretty much identically sized step. ok, this may be a special case. wanna hear my main argument?

All of temperament theory.

Temperament theory is based on the idea that intervals close enough to a given interval will sound basically the same as it, so you can slightly adjust the sizes of intervals to be more convenient mathematically while still keeping their sound. if simple ratios are consonant, then why does 12edo's major third, which is a full 14 cents sharper than either of the major thirds listed here, and is an irrational number, sound just as harmonious as both of them? when I compare them, neither sounds more consonant - the 385c third just sounds flatter (which it is). and also, if simple ratios are supposed to be consonant, why does 8192/6561 sound rather pleasing, and why does 7/5 sound so wrong?

My answer is that society has conditioned us to perceive these intervals in this way. The fact that major thirds - intervals around 370-410c - sound consonant is not a property of the sound itself (if it were, only 386c - 5/4 - would sound consonant; the others would sound horrible), but of tuning systems that have treated the perfect fifth as a consonance. And the fact that tritones - intervals around 570-630c, including 7/5 - are considered dissonant also has to do with the way society conditions us to hear music, hence the inconsistent logic.

The truth about intervals is that the rough size of the interval determines how it sounds - we consider neutral thirds to be between major and minor thirds, something that is only consistent with this way of viewing things.

Sorry if this is a little rambly, I'll make it better organized later.