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.

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

Greek letter prefixes

The Greek letter prefixes follow the ancient gematria/isopsephic system, detailed below:

Greek letter prefixes in ploidacot

Number n		1	2	3	4	5	6	7	8	9
Prefix	n	alpha	beta	gamma	delta	epsilon	digamma	zeta	eta	theta
	10n	iota	kappa	lambda	mu	nu	xi	omicron	pi	qoppa
	n + 10	iota-alpha	iota-beta	iota-gamma	iota-delta	iota-epsilon	iota-digamma	iota-zeta	iota-eta	iota-theta

Prefixes for numbers between 21 and 99 are constructed the same way as number words in English, for instance 21 is kappa-alpha and 99 is qoppa-theta.

Alternatively, Arabic numerals may be used in place of the Greek alphabetical and numeric prefixes, with the word "sheared" or its equivalent in other languages used in place of the alphabetic prefixes, so a diploid epsilon-heptacot system may be referred to as a 2-ploid 5-sheared 7-cot system.

Examples

• Meantone and schismic are haploid monocot
• Mohajira and dicot are dicot
• Bug and semaphore are alpha-dicot
• Shrutar is diploid alpha-dicot
• Ennealimmal is enneaploid dicot
• Hemiennealimmal is octodecaploid (18-ploid) 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
• Sycamore is hendecacot
• Chromo is tridecacot
• Pajara and injera are diploid
• Antitonic is diploid acot
• Augene is triploid
• Diminished is tetraploid
• Blackwood is pentaploid acot
• Whitewood is heptaploid acot
• Ennealimmal is enneaploid
• Compton is dodecaploid acot

Notation

TODO: Come up with canonical ups and downs notation systems for pergen squares