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 one or more Greek letters 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.

The Greek letter prefixes follow the ancient gematria/isopsephic system, so 6 is digamma, 7 is zeta, 8 is eta, etc.

Temperaments where the image of 3/2 is a whole number of ploids are called acot.

Examples

• meantone and schismic are haploid monocot
• pajara and injera are diploid
• augene is triploid
• diminished is tetraploid
• mohajira is dicot
• semaphore is alpha-dicot
• shrutar is diploid alpha-dicot
• ennealimmal is enneaploid dicot
• hemiennealimmal is octokaidecaploid dicot
• slendric, mothra, and rodan are 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
• harry is diploid delta-hexacot
• orwell is alpha-heptacot
• sensi is beta-heptacot
• vishnu is diploid epsilon-heptacot
• octacot is octacot
• würschmidt is beta-octacot
• valentine is enneacot
• blackwood is pentaploid acot
• compton is dodecaploid acot

Notation

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