Ploidacot: Difference between revisions

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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.

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.

~~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.

The ploidacot system was developed by Âthi Trydhen.

==Ploids==

== 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.

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.

==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==~~

== Examples ==

* [[pajara]] and injera are diploid

* [[augene]] is triploid

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==Notation==

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

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

[[Category:Temperament naming]]

~~[[Category:Naming]]~~

[[Category:~~Regular temperament theory~~]]

@@ Line 1: / Line 1: @@
-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.
+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.
-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.
+The ploidacot system was developed by Âthi Trydhen.
-==Ploids==
+== 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.
-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.
-==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==
+== Examples ==
 * [[pajara]] and injera are diploid
 * [[augene]] is triploid
@@ Line 34: / Line 31: @@
 ==Notation==
+Todo: come up with canonical ups and downs notation systems for pergen squares
-Todo: come up with canonical ups and downs notation systems for pergen squares
+[[Category:Temperament naming]]
-[[Category:Naming]]
-[[Category:Regular temperament theory]]