Modus: Difference between revisions

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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>.

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

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== Tunings ==

{| class="wikitable mw-collapsible mw-collapsed"

|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings

|-

! rowspan="2" |

! colspan="3" | Euclidean

|-

! Constrained

! Constrained & skewed

! Destretched

|-

! Tenney

| CTE: ~10/9 = 176.8176{{c}}

| CWE: ~10/9 = 177.1188{{c}}

| POTE: ~10/9 = 177.2035{{c}}

|}

{| class="wikitable mw-collapsible mw-collapsed"

|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings

|-

! rowspan="2" |

! colspan="3" | Euclidean

|-

! Constrained

! Constrained & skewed

! Destretched

|-

! Tenney

| CTE: ~10/9 = 176.4456{{c}}

| CWE: ~10/9 = 176.9286{{c}}

| POTE: ~10/9 = 177.0530{{c}}

|}

{| class="wikitable mw-collapsible mw-collapsed"

|+ style="font-size: 105%; white-space: nowrap;" | 13-limit norm-based tunings

|-

! rowspan="2" |

! colspan="3" | Euclidean

|-

! Constrained

! Constrained & skewed

! Destretched

|-

! Tenney

| CTE: ~10/9 = 176.4708{{c}}

| CWE: ~10/9 = 176.8735{{c}}

| POTE: ~10/9 = 176.9532{{c}}

|}

=== Tuning spectrum ===

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

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|

|}

<nowiki/>* Besides the octave

== Music ==

See [[Tetracot #Music]].

== References ==

[[Category:Modus| ]]

@@ 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>.
 See [[Tetracot family #Modus]] for technical data.
@@ Line 116: / Line 118: @@
 == Tunings ==
+{| class="wikitable mw-collapsible mw-collapsed"
+|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
+|-
+! rowspan="2" |
+! colspan="3" | Euclidean
+|-
+! Constrained
+! Constrained & skewed
+! Destretched
+|-
+! Tenney
+| CTE: ~10/9 = 176.8176{{c}}
+| CWE: ~10/9 = 177.1188{{c}}
+| POTE: ~10/9 = 177.2035{{c}}
+|}
+{| class="wikitable mw-collapsible mw-collapsed"
+|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings
+|-
+! rowspan="2" |
+! colspan="3" | Euclidean
+|-
+! Constrained
+! Constrained & skewed
+! Destretched
+|-
+! Tenney
+| CTE: ~10/9 = 176.4456{{c}}
+| CWE: ~10/9 = 176.9286{{c}}
+| POTE: ~10/9 = 177.0530{{c}}
+|}
+{| class="wikitable mw-collapsible mw-collapsed"
+|+ style="font-size: 105%; white-space: nowrap;" | 13-limit norm-based tunings
+|-
+! rowspan="2" |
+! colspan="3" | Euclidean
+|-
+! Constrained
+! Constrained & skewed
+! Destretched
+|-
+! Tenney
+| CTE: ~10/9 = 176.4708{{c}}
+| CWE: ~10/9 = 176.8735{{c}}
+| POTE: ~10/9 = 176.9532{{c}}
+|}
 === Tuning spectrum ===
 {| class="wikitable center-all left-4"
@@ Line 264: / Line 312: @@
 |
 |}
+<nowiki/>* Besides the octave
 == Music ==
 See [[Tetracot #Music]].
+== References ==
 [[Category:Modus| ]] <!-- main article -->