Ploidacot: Difference between revisions
→Examples: explain how the ploidacots can be derived from an understanding of the temperament |
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The Greek letter omega, proposed by [[User:Godtone|Godtone]], is used for −1. This simplifies the classification of certain temperaments, e.g. porcupine, which instead of beta-tricot can be omega-tricot, as splitting the interval 4/3 into three is arguably more intuitive than splitting the interval 6. This effectively shifts the possible values of shear to -1, 0, 1, …, {{nowrap|(''n'' − 2)}} if ''n'' ≥ 3. | The Greek letter omega, proposed by [[User:Godtone|Godtone]], is used for −1. This simplifies the classification of certain temperaments, e.g. porcupine, which instead of beta-tricot can be omega-tricot, as splitting the interval 4/3 into three is arguably more intuitive than splitting the interval 6. This effectively shifts the possible values of shear to -1, 0, 1, …, {{nowrap|(''n'' − 2)}} if ''n'' ≥ 3. | ||
Note that omega should only be used with ''n'' ≥ 3. When ''n'' = 1, there is only monocot. When ''n'' = 2, alpha-dicot is preferred over omega-dicot. | Note that omega should only be used with {{nowrap| ''n'' ≥ 3 }}. When {{nowrap| ''n'' {{=}} 1 }}, there is only monocot. When {{nowrap| ''n'' {{=}} 2 }}, alpha-dicot is preferred over omega-dicot. | ||
=== Non-octave temperaments === | === Non-octave temperaments === | ||
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== Examples == | == Examples == | ||
The ploidacots of most common temperaments can be intuitively derived from a basic understanding of its mapping. [[Meantone]] and [[helmholtz]] are monocot since they have a period of a whole octave and are generated by the perfect fifth. Dicot is dicot since it has a period of a whole octave and splits the perfect fifth in two. Semaphore has a period of a whole octave and splits the perfect twelfth in two. It requires one period to add to the fifth to make it a twelfth, and one is alpha. So it is alpha-dicot. | The ploidacots of most common temperaments can be intuitively derived from a basic understanding of its mapping. [[Meantone]] and [[Helmholtz (temperament)|helmholtz]] are monocot since they have a period of a whole octave and are generated by the perfect fifth. Dicot is dicot since it has a period of a whole octave and splits the perfect fifth in two. Semaphore has a period of a whole octave and splits the perfect twelfth in two. It requires one period to add to the fifth to make it a twelfth, and one is alpha. So it is alpha-dicot. | ||
For a more complex example, let us consider sensi and its weak extension bison. Sensi splits 6/1 in seven. It requires two periods to the fifth to reach 6/1, and two is beta. So it is beta-heptacot. Bison splits the period of sensi in two. As a result, it now requires four periods to the fifth to reach 6/1, and four is delta. So it is diploid delta-heptacot. | For a more complex example, let us consider sensi and its weak extension bison. Sensi splits 6/1 in seven. It requires two periods to the fifth to reach 6/1, and two is beta. So it is beta-heptacot. Bison splits the period of sensi in two. As a result, it now requires four periods to the fifth to reach 6/1, and four is delta. So it is diploid delta-heptacot. | ||
Below is a list of ploidacots for common temperaments | Below is a list of ploidacots for common temperaments | ||
* [[Meantone]] and [[helmholtz]] are haploid monocot | * [[Meantone]] and [[Helmholtz (temperament)|helmholtz]] are haploid monocot | ||
* [[Mohajira]] and [[dicot]] are dicot | * [[Mohajira]] and [[dicot]] are dicot | ||
* [[Bug]] and [[semaphore]] are alpha-dicot | * [[Bug]] and [[semaphore]] are alpha-dicot | ||
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* [[Hemiennealimmal]] is octodecaploid (18-ploid) dicot | * [[Hemiennealimmal]] is octodecaploid (18-ploid) dicot | ||
* [[Slendric]], [[mothra]], and [[rodan]] are tricot | * [[Slendric]], [[mothra]], and [[rodan]] are tricot | ||
* [[ | * [[Alphatricot]] is alpha-tricot | ||
* [[Porcupine]] is beta-tricot | * [[Porcupine]] is beta-tricot | ||
* [[Hedgehog]] is diploid alpha-tricot | * [[Hedgehog]] is diploid alpha-tricot | ||
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== Notation == | == 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'' | ||
== List of ploidacots == | |||
=== Acot === | |||
* Pentaploid acot ([[blackwood]], [[5edo]]) | |||
* Heptaploid acot ([[whitewood]], [[7edo]]) | |||
* Dodecaploid acot ([[compton]], [[12edo]]) | |||
=== Monocot === | |||
* [[Ploidacot/Monocot|Monocot]] | |||
* [[Ploidacot/Diploid monocot|Diploid monocot]] | |||
* [[Ploidacot/Triploid monocot|Triploid monocot]] | |||
* [[Ploidacot/Tetraploid monocot|Tetraploid monocot]] | |||
=== Dicot === | |||
* [[Ploidacot/Dicot|Dicot]] | |||
* [[Ploidacot/Alpha-dicot|Alpha-dicot]] | |||
* [[Ploidacot/Diploid dicot|Diploid dicot]] | |||
=== Tricot === | |||
* [[Ploidacot/Tricot|Tricot]] | |||
* [[Ploidacot/Alpha-tricot|Alpha-tricot]] | |||
* [[Ploidacot/Diploid alpha-tricot|Diploid alpha-tricot]] | |||
* [[Ploidacot/Omega-tricot|Omega-tricot]] | |||
=== Tetracot === | |||
* [[Ploidacot/Tetracot|Tetracot]] | |||
* [[Ploidacot/Alpha-tetracot|Alpha-tetracot]] | |||
* [[Ploidacot/Beta-tetracot|Beta-tetracot]] | |||
* [[Ploidacot/Omega-tetracot|Omega-tetracot]] | |||
=== Pentacot === | |||
* [[Ploidacot/Pentacot|Pentacot]] | |||
* [[Ploidacot/Alpha-pentacot|Alpha-pentacot]] | |||
* [[Ploidacot/Gamma-pentacot|Gamma-pentacot]] | |||
=== Hexacot === | |||
* [[Ploidacot/Hexacot|Hexacot]] | |||
* [[Ploidacot/Alpha-hexacot|Alpha-hexacot]] | |||
=== Heptacot === | |||
* [[Ploidacot/Heptacot|Heptacot]] | |||
* [[Ploidacot/Alpha-heptacot|Alpha-heptacot]] | |||
* [[Ploidacot/Beta-heptacot|Beta-heptacot]] | |||
=== Octacot === | |||
* [[Ploidacot/Octacot|Octacot]] | |||
* [[Ploidacot/Beta-octacot|Beta-octacot]] | |||
=== Enneacot === | |||
* [[Ploidacot/Enneacot|Enneacot]] | |||
=== >10 cots === | |||
* [[Ploidacot/Icosacot|Icosacot]] | |||
== See also == | |||
* [[Wedgie]] - a mathematical generalization of the concept of ploidacots that uniquely characterizes a temperament | |||
[[Category:Temperament naming]] | [[Category:Temperament naming]] | ||