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.

Ploidacot is a canonical naming system for pergen squares in that every pergen square that covers both 2/1 and 3/2 has a unique name in the Ploidacot system.

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 or cotyledon 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
• hedgehog is diploid delta-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

Todo: come up with canonical ups and downs notation systems for pergen squares