Ploidacot/Omega-tricot: Difference between revisions

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{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=2|Cots=3|Pergen=[P8, P4/3]|Forms=7, 8, 15|Title=Omega-tricot}}

{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=2|Cots=3|Pergen=[P8, P4/3]|Forms=7, 8, 15, 22|Title=Omega-tricot (beta-tricot)|Wedgie=3}}

'''Omega-tricot''' is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-tricot temperaments usually generate the [[1L 6s]] and [[7L 1s]] MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts.

== ~~Notation~~ ==

== Intervals and notation ==

While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second. ^^C and vC# are enharmonic.

While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second, allowing for an ^ or v to stand for 1/3 of a chromatic semitone, so ^^C and vC# are enharmonic.

{| class="wikitable"

|+ style="font-size: 105%;" | Omega-tricot intervals (assuming pure fifth and octave)

|-

! #

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| 0

| C

| perfect unison ~~/ perfect octave~~

| perfect unison

|-

| 1

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=== Superpine ===

In [[superpine]], the ~~subminor seventh (C–vBb, 13 generators up)~~ is mapped to 7/4, and the ~~mappings~~ for ~~3 and~~ 5 ~~are~~ as in meantone, so −3 generators is [[3/2]] ~~and −12~~ generators is [[5/4]]. It is best tuned with a slightly sharp generator of about 168{{c}}.

In [[superpine]], the generator is again mapped to 11/10, and the mapping for 5 is as in [[meantone]], so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}.

~~{{Todo~~| ~~unify precision }}~~

[[Category:Ploidacots|Omega-tricot]]

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-{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=2|Cots=3|Pergen=[P8, P4/3]|Forms=7, 8, 15|Title=Omega-tricot}}
+{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=2|Cots=3|Pergen=[P8, P4/3]|Forms=7, 8, 15, 22|Title=Omega-tricot (beta-tricot)|Wedgie=3}}
 '''Omega-tricot''' is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-tricot temperaments usually generate the [[1L&nbsp;6s]] and [[7L&nbsp;1s]] MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts.
-== Notation ==
+== Intervals and notation ==
-While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second. ^^C and vC# are enharmonic.
+While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second, allowing for an ^ or v to stand for 1/3 of a chromatic semitone, so ^^C and vC# are enharmonic.
 {| class="wikitable"
+|+ style="font-size: 105%;" | Omega-tricot intervals (assuming pure fifth and octave)
 |-
 ! #
@@ Line 60: / Line 61: @@
 | 0
 | C
-| perfect unison / perfect octave
+| perfect unison
 |-
 | 1
@@ Line 113: / Line 114: @@
 === Superpine ===
-In [[superpine]], the subminor seventh (C–vBb, 13 generators up) is mapped to 7/4, and the mappings for 3 and 5 are as in meantone, so −3 generators is [[3/2]] and −12 generators is [[5/4]]. It is best tuned with a slightly sharp generator of about 168{{c}}.
+In [[superpine]], the generator is again mapped to 11/10, and the mapping for 5 is as in [[meantone]], so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}.
-{{Todo| unify precision }}
+[[Category:Ploidacots|Omega-tricot]]