My understanding is 'simple' ratios for intervals are considered acoustically consonant and this is often used to explain is considered musically consonant.
So, a unison 1:1 (1.000) is simple - it's just 1 to 1 - and therefore consonant.
The octave and perfect fifth seem easy enough to understand 2:1 (2.000) and 3:2 (1.500) respectively. The octave deemed more consonant than the fifth, because the fifth is not a whole number.
But when moving on the the perfect fourth and major third we get 4:3 (1.333) and 5:4 (1.250) respectively and the notion of "simple" becomes unclear to me.
Is the fourth not simple, because the decimal part repeats?
Is the third less consonant than a fifth, because the remainder of the fifth - the .5 part - is closer to 1 than the third's .25?
It seems like numbers involving basic division by half are considered simple and consonant - the ones with decimal vales of .0 .5 .25 rather that .333.
But then consider this list...
m3 6/5 (1.200) m6 8:5 (1.600) M6 5:3 (1.667) M7 15:8 (1.875)
I get that the m3 and m6 are 'simpler' as they only go out to the first decimal place as apposed to the M6 and M7 which go out past the tenths. But should they be considered more, less, or the same simplicity as the major third (1.250)?
Especially unclear to me is how the M6 is simpler than the M7 - (1.667) compared to (1.875). In what numeric way can one be simpler than the other?
Can someone explain the acoustic or numeric meaning of simple with these ratios?
Please let me know if I'm conflating acoustic and numeric ideas.