Cotoneum: Difference between revisions

Line 16:

'''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 0.4-0.5 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.

It can seen as a detemperament of [[41edo|41 equal temperament]], with the [[countercomp comma|41-comma]] shrunk down to about 5 cents, representing important intervals such as the [[schisma]], [[5120/5103]], [[325/324]], [[352/351]], [[385/384]], [[~~540~~/~~539]], [[729/728~~]], etc.

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

[[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.

@@ Line 16: / Line 16: @@
 '''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 0.4-0.5 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.
-It can seen as a detemperament of [[41edo|41 equal temperament]], with the [[countercomp comma|41-comma]] shrunk down to about 5 cents, representing important intervals such as the [[schisma]], [[5120/5103]], [[325/324]], [[352/351]], [[385/384]], [[540/539]], [[729/728]], etc.
+It can seen as a detemperament of [[41edo|41 equal temperament]], with the [[countercomp comma|41-comma]] shrunk down to about 5 cents, representing important intervals such as the [[schisma]], [[5120/5103]], [[325/324]], [[352/351]], [[385/384]], [[513/512]], etc.
 [[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.