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