Cotoneum: Difference between revisions

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| Odd limit 2 = 21 | Mistuning 2 = 2.48 | Complexity 2 = 176

}}

'''Cotoneum''' is a [[rank]]-2 [[regular temperament|temperament]] for the 7- through 19-limit~~. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]~~. The generator of cotoneum is a perfect fifth sharp by about 0.3–0.4 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found ~~at the~~ diminished fourth. Instead, 5/4 is found ~~at the~~ sextuple-diminished octave (~~–49~~ fifths). It is a weak extension of the [[2.5.7 subgroup|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison.

'''Cotoneum''' is a [[rank]]-2 [[regular temperament|temperament]] for the 7- through 19-limit. The generator of cotoneum is a [[3/2|perfect fifth]] sharp by about 0.3–0.4 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found as a diminished fourth. Instead, 5/4 is found as a sextuple-diminished octave (−49 fifths). It is a weak extension of the [[2.5.7 subgroup|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]].

It can seen as a detemperament of [[41edo|41 equal temperament]], with the [[countercomp comma|41-comma]] shrunk down to about ~~5-6~~ cents, ~~representing many important intervals such as~~ the [[schisma]], [[~~5120/5103~~]], [[176/175]], [[243/242]], [[~~273~~/~~272~~]], [[~~325~~/~~324~~]], [[~~352~~/~~351~~]], [[~~385~~/~~384~~]], [[~~513~~/~~512~~]], [[~~896~~/~~891~~]]~~, etc~~.

It can seen as a detemperament of [[41edo|41 equal temperament]], with the [[countercomp comma|41-comma]] shrunk down to about 5–6 cents for a generic aberschisma, which represents the [[schisma]] and [[aberschisma]].

This generic aberschisma takes on more important roles from the 11-limit onwards, where it represents [[176/175]], [[243/242]], [[385/384]], [[540/539]] and [[896/891]]. In the 13-limit it represents [[352/351]], in the 17-limit [[273/272]], and in the 19-limit the undevicesimal schisma of [[513/512]].

[[217edo]] is an excellent tuning for cotoneum, with a fifth generator of 127\217, and [[mos scale]]s of 12, 17, 29, 41, 53, 94, 135, or 176 notes are available.

The temperament was named by [[~~User:Xenllium|~~Xenllium]] in 2021. ''Cotoneum'' is Latin for "quince".

The temperament was named by [[Xenllium]] in 2021. ''Cotoneum'' is Latin for "quince".

For technical data, see [[Garischismic clan #Cotoneum]].

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

! ~~Fifths~~

! #

! Cents ~~<br>value~~*

! Cents*

! Approximate ~~Ratios~~

! Approximate ratios

|-

| 0

@@ Line 13: / Line 13: @@
 | Odd limit 2 = 21 | Mistuning 2 = 2.48 | Complexity 2 = 176
 }}
-'''Cotoneum''' is a [[rank]]-2 [[regular temperament|temperament]] for the 7- through 19-limit. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]]. The generator of cotoneum is a perfect fifth sharp by about 0.3–0.4 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found at the diminished fourth. Instead, 5/4 is found at the sextuple-diminished octave (–49 fifths). It is a weak extension of the [[2.5.7 subgroup|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison.
+'''Cotoneum''' is a [[rank]]-2 [[regular temperament|temperament]] for the 7- through 19-limit. The generator of cotoneum is a [[3/2|perfect fifth]] sharp by about 0.3–0.4 cents, and it maps [[8/7]] to the double-augmented unison (+14 fifths), [[tempering out]] the [[garischisma]]. However, unlike in [[garibaldi]], the schisma is not tempered out, meaning 5/4 is not found as a diminished fourth. Instead, 5/4 is found as a sextuple-diminished octave (−49 fifths). It is a weak extension of the [[2.5.7 subgroup|2.5.7-subgroup]] temperament [[mercy]], with its secor-sized generator mapped to the augmented unison. It is a member of the [[hemimage temperaments]], [[quince clan]], and [[garischismic clan]].
-It can seen as a detemperament of [[41edo|41 equal temperament]], with the [[countercomp comma|41-comma]] shrunk down to about 5-6 cents, representing many important intervals such as the [[schisma]], [[5120/5103]], [[176/175]], [[243/242]], [[273/272]], [[325/324]], [[352/351]], [[385/384]], [[513/512]], [[896/891]], etc.
+It can seen as a detemperament of [[41edo|41 equal temperament]], with the [[countercomp comma|41-comma]] shrunk down to about 5–6 cents for a generic aberschisma, which represents the [[schisma]] and [[aberschisma]].
+This generic aberschisma takes on more important roles from the 11-limit onwards, where it represents [[176/175]], [[243/242]], [[385/384]], [[540/539]] and [[896/891]]. In the 13-limit it represents [[352/351]], in the 17-limit [[273/272]], and in the 19-limit the undevicesimal schisma of [[513/512]].
 [[217edo]] is an excellent tuning for cotoneum, with a fifth generator of 127\217, and [[mos scale]]s of 12, 17, 29, 41, 53, 94, 135, or 176 notes are available.
-The temperament was named by [[User:Xenllium|Xenllium]] in 2021. ''Cotoneum'' is Latin for "quince".
+The temperament was named by [[Xenllium]] in 2021. ''Cotoneum'' is Latin for "quince".
 For technical data, see [[Garischismic clan #Cotoneum]].
@@ Line 27: / Line 29: @@
 {| class="wikitable center-1 right-2"
-! Fifths
+! #
-! Cents <br>value*
+! Cents*
-! Approximate Ratios
+! Approximate ratios
 |-
 | 0