User talk:VectorGraphics/Brightness analysis
Some of my opinion
Consonance and dissonance ARE, at least partially, a property of the interval itself. The conventional statement - that simple ratio is consonant - is true when using harmonic timbres, i.e. timbres that can be splitted into sine waves whose frequencies are integer multiples of a fundamental frequency. All periodic sound waves are harmonic, and many physical instruments are approximately harmonic. Consonance actually means some partials coincide, either exactly or closely enough, and dissonance means some partials are close but not enough, making annoying beats. (This can be visualized by plotting the sum of two sine waves with close frequencies e.g. [math]\sin x + \sin(1.1x)[/math] ) If neither happens, the notes actually sound “unrelated”, although some people call it “dissonant” too. If you work with single sine waves, you will find nothing, and if you work with inharmonic timbres, you may find different consonance and dissonance. I will assume harmonic timbre for the following discussion.
You say that the 12edo major third is consonant, but if you listen carefully enough, or with timbres with stronger harmonics, you may find that it is not. Maybe that is not enough to be dissonant for you, but definitely less consonant than 5/4. The 5th harmonic of the lower note and the 4th harmonic of the higher note make a beat. The fact that 8192/6561 is consonant is because it is close enough to 5/4 (only differing by a schisma measuring only ~2 cents), making the beat slow and not annoying - sometimes even inaudible. And actually 7/5 is consonant, it is only strange or “out of tune”. (Being dissonant and being out of tune is two different things, the latter is more related to the culture.)
A good example to show the machanism may be the 12edo fifth. Usually it is consonant because the beat between the 3rd harmonic of the lower note and the 2nd of the higher is slow and not annoying, but with strong higher harmonics, like working with sawtooth waves, it can be dissonant, since higher harmonics beat faster, and stronger beats are more annoying.
In short, when woring with inharmonic timbres, an interval is consonant when is is close enough to a simple ratio. The definition of “close enough” and “simple” may vary between contexts.