Rodan: Difference between revisions

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{{Infobox ~~Regtemp~~

{{Infobox regtemp

| Title = Rodan

| Subgroups = 2.3.5.7, 2.3.5.7.11

| Comma basis = [[245/243]], [[1029/1024]] (7-limit); <br> [[245/243]], [[385/384]], [[441/440]] (11-limit)

| Edo join 1 = 41 | Edo join 2 = 46

| ~~Generator~~ = 8/7 | ~~Generator~~ tuning = 234.4 | Optimization method = CWE

| Mapping = 1; 3 17 -1 -13

| Generators = 8/7 | Generators tuning = 234.4 | Optimization method = CWE

| MOS scales = [[1L 4s]], [[5L 1s]], [[5L 6s]], …, [[5L 36s]], [[41L 5s]]

~~| Mapping = 1; 3 17 -1 -13~~

| Pergen = (P8, P5/3)

| Odd limit 1 = 9 | Mistuning 1 = 5.05 | Complexity 1 = 41

| Odd limit 1 = 9 | Mistuning 1 = 5.05 | Complexity 1 = 21

| Odd limit 2 = ~~(2.3.5.7.~~11) 21 | Mistuning 2 = 5.34 | Complexity 2 = 87

| Odd limit 2 = 11-limit 21 | Mistuning 2 = 5.34 | Complexity 2 = 36

}}

'''Rodan''' is one of the notable [[extension]]s of the [[slendric]] [[regular temperament|temperament]], which divides the perfect fifth, [[3/2]], into three equal intervals representing [[8/7]] ([[tempering out]] the gamelisma, [[1029/1024]]), reaching the full [[7-limit]] such that 17 of these [[generators]] [[stacking|stack]] to reach the interval class of the [[5/1|5th harmonic]]. It tempers out [[245/243]], making it a [[sensamagic clan|sensamagic temperament]], so that [[5/3]] is divided into two intervals of [[9/7]]; and it tempers out [[5120/5103]], making it also a [[hemifamity temperaments|hemifamity temperament]], so that [[9/8]] stacks thrice into [[10/7]].

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== Tunings ==

=== Norm-based 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: ~8/7 = 234.4502{{c}}

| CWE: ~8/7 = 234.4259{{c}}

| POTE: ~8/7 = 234.4168{{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: ~8/7 = 234.4628{{c}}

| CWE: ~8/7 = 234.4594{{c}}

| POTE: ~8/7 = 234.4587{{c}}

|}

=== Tuning spectrum ===

{| class="wikitable center-all left-4 left-5"

|-

! ~~EDO~~<br>generator

! Edo<br>generator

! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]

! Generator (¢)

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[[Category:Gamelismic clan]]

[[Category:Sensamagic clan]]

[[Category:~~Hemifamity~~ temperaments]]

[[Category:Aberschismic temperaments]]

@@ Line 1: / Line 1: @@
-{{Infobox Regtemp
+{{Infobox regtemp
 | Title = Rodan
 | Subgroups = 2.3.5.7, 2.3.5.7.11
 | Comma basis = [[245/243]], [[1029/1024]] (7-limit); <br> [[245/243]], [[385/384]], [[441/440]] (11-limit)
 | Edo join 1 = 41 | Edo join 2 = 46
-| Generator = 8/7 | Generator tuning = 234.4 | Optimization method = CWE
+| Mapping = 1; 3 17 -1 -13
+| Generators = 8/7 | Generators tuning = 234.4 | Optimization method = CWE
 | MOS scales = [[1L 4s]], [[5L 1s]], [[5L 6s]], …, [[5L 36s]], [[41L 5s]]
-| Mapping = 1; 3 17 -1 -13
 | Pergen = (P8, P5/3)
-| Odd limit 1 = 9 | Mistuning 1 = 5.05 | Complexity 1 = 41
+| Odd limit 1 = 9 | Mistuning 1 = 5.05 | Complexity 1 = 21
-| Odd limit 2 = (2.3.5.7.11) 21 | Mistuning 2 = 5.34 | Complexity 2 = 87
+| Odd limit 2 = 11-limit 21 | Mistuning 2 = 5.34 | Complexity 2 = 36
 }}
 '''Rodan''' is one of the notable [[extension]]s of the [[slendric]] [[regular temperament|temperament]], which divides the perfect fifth, [[3/2]], into three equal intervals representing [[8/7]] ([[tempering out]] the gamelisma, [[1029/1024]]), reaching the full [[7-limit]] such that 17 of these [[generators]] [[stacking|stack]] to reach the interval class of the [[5/1|5th harmonic]]. It tempers out [[245/243]], making it a [[sensamagic clan|sensamagic temperament]], so that [[5/3]] is divided into two intervals of [[9/7]]; and it tempers out [[5120/5103]], making it also a [[hemifamity temperaments|hemifamity temperament]], so that [[9/8]] stacks thrice into [[10/7]].
@@ Line 312: / Line 312: @@
 == Tunings ==
+=== Norm-based 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: ~8/7 = 234.4502{{c}}
+| CWE: ~8/7 = 234.4259{{c}}
+| POTE: ~8/7 = 234.4168{{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: ~8/7 = 234.4628{{c}}
+| CWE: ~8/7 = 234.4594{{c}}
+| POTE: ~8/7 = 234.4587{{c}}
+|}
 === Tuning spectrum ===
-{{see also|Slendric #Tuning spectrum}}
+{{See also| Slendric #Tuning spectrum }}
 {| class="wikitable center-all left-4 left-5"
 |-
-! EDO<br>generator
+! Edo<br>generator
 ! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
 ! Generator (¢)
@@ Line 562: / Line 595: @@
 [[Category:Gamelismic clan]]
 [[Category:Sensamagic clan]]
-[[Category:Hemifamity temperaments]]
+[[Category:Aberschismic temperaments]]