Ploidacot

The Ploidacot system is a classification of rank 2 temperaments based on pergen, i.e. how a temperament can be thought of as a union of copies of Pythagorean tuning.

Ploids

Any rank 2 temperament must split the octave into a number of ploids, for instance pajara divides the octave into two so it's diploid. Temperaments that don't divide the octave are called haploid.

Cots

If 3/2 is represented by a linearly independent element to the ploid, there is a number of ploids which when added to 3/2 gives the interval which splits into the largest number of parts by the temperament. Each of these parts is called a cot and the Ploidacot system uses a Greek letter to describe the smallest number of ploids should be added to 3/2 to form a whole number of cots, and this number of cots is indicated by a Greek numerical prefix.

Examples

pajara and injera are diploid

augene is triploid

diminished is tetraploid

mohajira is dicot

semaphore is alpha-dicot

slendric is tricot

tricot is alpha-tricot

porcupine is beta-tricot

tetracot is tetracot

squares is beta-tetracot

bleu is pentacot

magic is alpha-pentacot

miracle is hexacot

hanson is alpha-hexacot

ennealimmal is enneaploid dicot

Notation

(placeholder for Ploidacot accidentals)