Modus: Difference between revisions

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| Title = Modus

| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13

| Comma basis = [[64/63]], [[4375/4374]] (7-limit); [[64/63]], [[100/99]], [[243/242]] (11-limit) [[64/63]], [[78/77]], [[100/99]], [[144/143]] (13-limit)

| Comma basis = [[64/63]], [[4375/4374]] (7-limit); [[64/63]], [[100/99]], [[243/242]] (11-limit); [[64/63]], [[78/77]], [[100/99]], [[144/143]] (13-limit)

| Edo join 1 = 27e | Edo join 2 = 34d

| Mapping = 1; 4 9 -8 10 -2

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| Generators tuning = 176.8

| Optimization method = CWE

| MOS scales = [[6L 1s]], [[7L 6s]], [[7L 13s]], [[7L 20s]]

| MOS scales = [[6L 1s]], [[7L 6s]], [[7L 13s]], [[7L 20s]]

| Odd limit 1 = 9 | Mistuning 1 = 13.6 | Complexity 1 = 20

| Odd limit 2 = 13 | Mistuning 2 = 16.7 | Complexity 2 = 20

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The '''modus''' [[regular temperament|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (20000/19683), and is naturally a full [[13-limit]] temperament.

In addition to the tetracot comma, modus tempers out [[64/63]], making it a member of the [[archytas clan]]. As such, septimal intervals are tempered together with Pythagorean intervals; in particular, a stack of two perfect fifths [[octave reduction|octave reduced]] represents [[8/7]][[~]][[9/8]] at 8 generator steps. Modus also tempers out [[4375/4374]], making it a [[ragismic microtemperaments|ragismic temperament]]. In the 11- and 13-limit it can be viewed as a [[weak extension]] of [[suhajira]] as well.

In addition to the tetracot comma, modus tempers out [[64/63]], making it a member of the [[archytas clan]]. As such, septimal intervals are tempered together with Pythagorean intervals; in particular, a stack of two perfect fifths [[octave reduction|octave reduced]] represents {{nowrap|[[8/7]][[~]][[9/8]]}} at 8 generator steps. Modus also tempers out [[4375/4374]], making it a [[ragismic microtemperaments|ragismic temperament]]. In the 11- and 13-limit it can be viewed as a [[weak extension]] of [[suhajira]] as well.

Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at -5 generator steps.

Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at −5 generator steps.

Modus was named by [[Mike Battaglia]] in 2012 for its fantastic [[modmos]] structures<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_102416.html#102467 Yahoo! Tuning Group | ''Guaranteed meantone successor'']</ref>.

Modus was named by [[Mike Battaglia]] in 2012 for its fantastic [[modmos]] structures. Mike spoke highly of this temperament in its 7-form, considering it as a rival of [[meantone]].<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_102416.html#102467 Yahoo! Tuning Group | ''Guaranteed meantone successor'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_102423.html Yahoo! Tuning Group | ''Weasels and Tetracots'']</ref> Indeed, the vanishing of 64/63 and [[100/99]] very much contrasts meantone, and the vanishing of [[243/242]] gives it a neutral-ish flavor similar to that of [[migration]] or [[mohajira]].

See [[Tetracot family #Modus]] for technical data.

@@ Line 2: / Line 2: @@
 | Title = Modus
 | Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13
-| Comma basis = [[64/63]], [[4375/4374]] (7-limit);<br>[[64/63]], [[100/99]], [[243/242]] (11-limit)<br>[[64/63]], [[78/77]], [[100/99]], [[144/143]]<br>(13-limit)
+| Comma basis = [[64/63]], [[4375/4374]] (7-limit);<br>[[64/63]], [[100/99]], [[243/242]] (11-limit);<br>[[64/63]], [[78/77]], [[100/99]], [[144/143]]<br>(13-limit)
 | Edo join 1 = 27e | Edo join 2 = 34d
 | Mapping = 1; 4 9 -8 10 -2
@@ Line 8: / Line 8: @@
 | Generators tuning = 176.8
 | Optimization method = CWE
-| MOS scales = [[6L 1s]], [[7L 6s]], [[7L 13s]], [[7L 20s]]
+| MOS scales = [[6L&nbsp;1s]], [[7L&nbsp;6s]], [[7L&nbsp;13s]], [[7L&nbsp;20s]]
 | Odd limit 1 = 9 | Mistuning 1 = 13.6 | Complexity 1 = 20
 | Odd limit 2 = 13 | Mistuning 2 = 16.7 | Complexity 2 = 20
@@ Line 14: / Line 14: @@
 The '''modus''' [[regular temperament|temperament]] is one of the [[7-limit]] [[extension]]s of [[tetracot]], the [[5-limit]] temperament [[tempering out]] the [[tetracot comma]] (20000/19683), and is naturally a full [[13-limit]] temperament.
-In addition to the tetracot comma, modus tempers out [[64/63]], making it a member of the [[archytas clan]]. As such, septimal intervals are tempered together with Pythagorean intervals; in particular, a stack of two perfect fifths [[octave reduction|octave reduced]] represents [[8/7]][[~]][[9/8]] at 8 generator steps. Modus also tempers out [[4375/4374]], making it a [[ragismic microtemperaments|ragismic temperament]]. In the 11- and 13-limit it can be viewed as a [[weak extension]] of [[suhajira]] as well.
+In addition to the tetracot comma, modus tempers out [[64/63]], making it a member of the [[archytas clan]]. As such, septimal intervals are tempered together with Pythagorean intervals; in particular, a stack of two perfect fifths [[octave reduction|octave reduced]] represents {{nowrap|[[8/7]][[~]][[9/8]]}} at 8 generator steps. Modus also tempers out [[4375/4374]], making it a [[ragismic microtemperaments|ragismic temperament]]. In the 11- and 13-limit it can be viewed as a [[weak extension]] of [[suhajira]] as well.
-Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at -5 generator steps.
+Additionally, the generator can be taken to represent [[21/19]], which gives us an extension for prime 19 at −5 generator steps.
-Modus was named by [[Mike Battaglia]] in 2012 for its fantastic [[modmos]] structures<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_102416.html#102467 Yahoo! Tuning Group | ''Guaranteed meantone successor'']</ref>.
+Modus was named by [[Mike Battaglia]] in 2012 for its fantastic [[modmos]] structures. Mike spoke highly of this temperament in its 7-form, considering it as a rival of [[meantone]].<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_102416.html#102467 Yahoo! Tuning Group | ''Guaranteed meantone successor'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_102423.html Yahoo! Tuning Group | ''Weasels and Tetracots'']</ref> Indeed, the vanishing of 64/63 and [[100/99]] very much contrasts meantone, and the vanishing of [[243/242]] gives it a neutral-ish flavor similar to that of [[migration]] or [[mohajira]].
 See [[Tetracot family #Modus]] for technical data.

Modus: Difference between revisions

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