Levitin, Professor Daniel - On ratios and pitch
Type of Spiritual Experience
A description of the experience
This is Your Brain on Music – Professor Daniel Levitin
A unison interval – the same note played with itself – is deemed consonant, as is an octave. These create simple integer ratios of 1:1 and 2:1 respectively….
Interestingly, if we divide the octave precisely in half, the interval we end up with is called a tritone and most people find it the most disagreeable interval possible. Part of the reason for this may be related to the fact that the tritone cannot be reduced to a simple integer ratio, its ratio being close to 41:29 (it is actually the square root of 2 to 1; an irrational number). We can look at consonance from an integer ratio perspective.
A ratio of 4:1 is a simple integer ratio and that defines two octaves. A ratio of 3:2 is also a simple integer ratio and that defines the interval of a perfect fifth….the perfect fifth is the distance between, for example, C and the G above it. The distance from from that G to the C above it forms an interval of a perfect fourth and its frequency ratio is nearly 4:3.