Tetracot: Difference between revisions

Line 7:

{{About|the regular temperament|the ploidacot signature|Ploidacot/Tetracot}}

'''Tetracot''', in this article, is the rank-2 [[regular temperament]] in the 2.3.5.11.13 [[subgroup]] [[generator|generated]] by a ~~"sub-major"~~ second of about 174–178{{cent}} which represents both [[10/9]] and [[11/10]]. It is so named because the generator is a quarter of fifth: four such generators make a perfect fifth which approximates [[3/2]], which cannot occur in [[12edo]], resulting in [[100/99]], [[144/143]], and [[243/242]] being [[tempering out|tempered out]]. This is in contrast to [[meantone]], where 10/9 is tuned sharper than or equal to just in order to be equated with [[9/8]].

'''Tetracot''', in this article, is the [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] in the 2.3.5.11.13 [[subgroup]] [[generator|generated]] by a submajor second of about 174–178{{cent}} which represents both [[10/9]] and [[11/10]]. It is so named because the generator is a quarter of fifth: four such generators make a perfect fifth which approximates [[3/2]], which cannot occur in [[12edo]], resulting in [[100/99]], [[144/143]], and [[243/242]] being [[tempering out|tempered out]]. This is in contrast to [[meantone]], where 10/9 is tuned sharper than or equal to just in order to be equated with [[9/8]].

Tetracot has many [[extension]]s for the 7-, 11-, and 13-limit. See [[Tetracot extensions]]. Equal temperaments that support tetracot include {{EDOs| 27, 34, and 41 }}.

See [[Tetracot family~~]] or [[No-sevens subgroup temperaments #Tetracot~~]] for more technical data.

See [[Tetracot family]] for more technical data.

== Interval chain ==

Line 18:

{| class="wikitable right-1 right-2"

|-

! &#~~35;~~

! #

! Cents*

! Approximate ~~Ratios~~

! Approximate ratios

|-

| 0

| 0.00

| 0.0

| '''1/1'''

|-

Line 97:

{| class="wikitable center-all left-4"

|-

! Edo<br />~~Generator~~

! Edo<br>generator

! [[Eigenmonzo|Eigenmonzo<br />(~~Unchanged~~-interval)]]*

! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]*

! Generator (¢)

! Comments

Line 212:

|

|}

<nowiki />* Besides the octave

<nowiki/>* Besides the octave

== Music ==

; [[Flora Canou]]

* [https://soundcloud.com/floracanou/october-dieting-plan?in=floracanou/sets/totmc-suite-vol-1 "October Dieting Plan"] from [https://soundcloud.com/floracanou/sets/totmc-suite-vol-1 ''TOTMC Suite Vol. 1''] (2023) – [[modus]] in 34edo tuning

* [https://soundcloud.com/floracanou/october-dieting-plan?in=floracanou/sets/totmc-suite-vol-1 "October Dieting Plan"] from [https://soundcloud.com/floracanou/sets/totmc-suite-vol-1 ''TOTMC Suite Vol. 1''] (2023) – in [[modus]], 34edo tuning

; [[Zhea Erose]]

Line 222:

; [[Xotla]]

* "Electrostat" from ''Lesser Groove'' (2020) – [https://open.spotify.com/track/5LIPr8n6uQySeLUfM11U2W Spotify] | [https://xotla.bandcamp.com/track/electrostat-tetracot-13 Bandcamp] | [https://www.youtube.com/watch?v=5SAuoyDwpgc YouTube] – ambient electro, ~~tetracot~~[13] in 34edo tuning

* "Electrostat" from ''Lesser Groove'' (2020) – [https://open.spotify.com/track/5LIPr8n6uQySeLUfM11U2W Spotify] | [https://xotla.bandcamp.com/track/electrostat-tetracot-13 Bandcamp] | [https://www.youtube.com/watch?v=5SAuoyDwpgc YouTube] – ambient electro, in Tetracot[13], 34edo tuning

[[Category:Tetracot| ]]

[[Category:Rank-2 temperaments]]

[[Category:Tetracot family]]

[[Category:Rastmic clan]]

@@ Line 7: / Line 7: @@
 {{About|the regular temperament|the ploidacot signature|Ploidacot/Tetracot}}
-'''Tetracot''', in this article, is the rank-2 [[regular temperament]] in the 2.3.5.11.13 [[subgroup]] [[generator|generated]] by a "sub-major" second of about 174–178{{cent}} which represents both [[10/9]] and [[11/10]]. It is so named because the generator is a quarter of fifth: four such generators make a perfect fifth which approximates [[3/2]], which cannot occur in [[12edo]], resulting in [[100/99]], [[144/143]], and [[243/242]] being [[tempering out|tempered out]]. This is in contrast to [[meantone]], where 10/9 is tuned sharper than or equal to just in order to be equated with [[9/8]].
+'''Tetracot''', in this article, is the [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] in the 2.3.5.11.13 [[subgroup]] [[generator|generated]] by a submajor second of about 174–178{{cent}} which represents both [[10/9]] and [[11/10]]. It is so named because the generator is a quarter of fifth: four such generators make a perfect fifth which approximates [[3/2]], which cannot occur in [[12edo]], resulting in [[100/99]], [[144/143]], and [[243/242]] being [[tempering out|tempered out]]. This is in contrast to [[meantone]], where 10/9 is tuned sharper than or equal to just in order to be equated with [[9/8]].
 Tetracot has many [[extension]]s for the 7-, 11-, and 13-limit. See [[Tetracot extensions]]. Equal temperaments that support tetracot include {{EDOs| 27, 34, and 41 }}.
-See [[Tetracot family]] or [[No-sevens subgroup temperaments #Tetracot]] for more technical data.
+See [[Tetracot family]] for more technical data.
 == Interval chain ==
@@ Line 18: / Line 18: @@
 {| class="wikitable right-1 right-2"
 |-
-! &#35;
+! #
 ! Cents*
-! Approximate Ratios
+! Approximate ratios
 |-
 | 0
-| 0.00
+| 0.0
 | '''1/1'''
 |-
@@ Line 97: / Line 97: @@
 {| class="wikitable center-all left-4"
 |-
-! Edo<br />Generator
+! Edo<br>generator
-! [[Eigenmonzo|Eigenmonzo<br />(Unchanged-interval)]]*
+! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]*
 ! Generator (¢)
 ! Comments
@@ Line 212: / Line 212: @@
 |
 |}
-<nowiki />* Besides the octave
+<nowiki/>* Besides the octave
 == Music ==
 ; [[Flora Canou]]
-* [https://soundcloud.com/floracanou/october-dieting-plan?in=floracanou/sets/totmc-suite-vol-1 "October Dieting Plan"] from [https://soundcloud.com/floracanou/sets/totmc-suite-vol-1 ''TOTMC Suite Vol. 1''] (2023) – [[modus]] in 34edo tuning
+* [https://soundcloud.com/floracanou/october-dieting-plan?in=floracanou/sets/totmc-suite-vol-1 "October Dieting Plan"] from [https://soundcloud.com/floracanou/sets/totmc-suite-vol-1 ''TOTMC Suite Vol. 1''] (2023) – in [[modus]], 34edo tuning
 ; [[Zhea Erose]]
@@ Line 222: / Line 222: @@
 ; [[Xotla]]
-* "Electrostat" from ''Lesser Groove'' (2020) – [https://open.spotify.com/track/5LIPr8n6uQySeLUfM11U2W Spotify] | [https://xotla.bandcamp.com/track/electrostat-tetracot-13 Bandcamp] | [https://www.youtube.com/watch?v=5SAuoyDwpgc YouTube] – ambient electro, tetracot[13] in 34edo tuning
+* "Electrostat" from ''Lesser Groove'' (2020) – [https://open.spotify.com/track/5LIPr8n6uQySeLUfM11U2W Spotify] | [https://xotla.bandcamp.com/track/electrostat-tetracot-13 Bandcamp] | [https://www.youtube.com/watch?v=5SAuoyDwpgc YouTube] – ambient electro, in Tetracot[13], 34edo tuning
 [[Category:Tetracot| ]] <!-- Main article -->
 [[Category:Rank-2 temperaments]]
 [[Category:Tetracot family]]
+[[Category:Rastmic clan]]