Ploidacot
The ploidacot system is a scale naming scheme based on the classification of rank-2 temperaments by pergen, i.e. how a temperament can be thought of as a union of copies of Pythagorean tuning. It is a canonical naming scheme for pergen squares in that every pergen square that covers both 2/1 and 3/2 has a unique name in the ploidacot system.
The ploidacot system was developed by Praveen Venkataramana.
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
- shrutar is diploid alpha-dicot
- slendric is tricot
- tricot is alpha-tricot
- porcupine is beta-tricot
- hedgehog is diploid alpha-tricot
- tetracot is tetracot
- squares is beta-tetracot
- bleu is pentacot
- magic is alpha-pentacot
- amity is gamma-pentacot
- miracle is hexacot
- hanson is alpha-hexacot
- orwell is alpha-heptacot
- ennealimmal is enneaploid dicot
Notation
Todo: come up with canonical ups and downs notation systems for pergen squares