5L 2s/Temperaments: Difference between revisions

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Scales (Scala files): [[Meantone5]], [[Meantone7]], [[Meantone12]]

<div style="line-height:1.6;">Interval table (7-note MOS, 2.3.5.7 POTE tuning)</div>

<div style="line-height: 1.6;">Interval table (7-note MOS, 2.3.5.7 POTE tuning)</div>

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

|-

! #

! Cents*

! class="unsortable"| Approximate ratios**

! class="unsortable" | Approximate ratios**

|-

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Mapping generators: ~2, ~3

~~[[Wedgie]]: {{wedgie| 1 4 4 }}~~

[[Tuning ranges]]:

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Scales (Scala files): [[Flattone12]]

<div style="line-height:1.6;">Interval table (12-note MOS, 2.3.5.7.13 POTE tuning)</div>

<div style="line-height: 1.6;">Interval table (12-note MOS, 2.3.5.7.13 POTE tuning)</div>

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

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! #Gens up

! Cents*

! class="unsortable"| Approximate ratios**

! class="unsortable" | Approximate ratios**

|-

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* 9-odd-limit diamond monotone and tradeoff: ~3/2 = [692.308, 694.737]

Algebraic generator: Squarto, the positive root of 8''x''<sup>2</sup> - 4''x'' - 9, at 506.3239 ~~cents~~, equal to (1 + sqrt (19))/4.

Algebraic generator: Squarto, the positive root of {{nowrap|8''x''<sup>2</sup> − 4''x'' − 9}}, at 506.3239{{c}}, equal to <math>\frac{1+\sqrt{19}}{4}</math>.

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Scales (Scala files): [[Meantone5]], [[Meantone7]], [[Meantone12]]

<div style="line-height:1.6;">Interval table (12-note MOS, 2.3.5.7 POTE tuning)</div>

<div style="line-height: 1.6;">Interval table (12-note MOS, 2.3.5.7 POTE tuning)</div>

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

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! #Gens up

! Cents*

! class="unsortable"| Approximate ratios**

! class="unsortable" | Approximate ratios**

|-

| 0

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* 9-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 700.000]

Algebraic generator: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, which comes to 503.4257 ~~cents~~. The recurrence converges quickly.

Algebraic generator: Cybozem, the real root of {{nowrap|15''x''<sup>3</sup> − 10''x''<sup>2</sup> − 18}}, which comes to 503.4257{{c}}. The recurrence converges quickly.

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* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 696.774]

Algebraic generator: Cybozem; or else Radieubiz, the real root of 3''x''<sup>3</sup> + 6''x'' - 19. Unlike Cybozem, the recurrence for Radieubiz does not converge.

Algebraic generator: Cybozem; or else Radieubiz, the real root of {{nowrap|3''x''<sup>3</sup> + 6''x'' − 19}}. Unlike Cybozem, the recurrence for Radieubiz does not converge.

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* 11-odd-limit diamond monotone and tradeoff: ~3/2 = [696.774, 700.000]

[[Algebraic generator]]: Traverse, the positive real root of ''x''<sup>4</sup> + 2''x'' - 13, or 696.9529 ~~cents~~.

[[Algebraic generator]]: Traverse, the positive real root of {{nowrap|''x''<sup>4</sup> + 2''x'' − 13}}, or 696.9529{{c}}.

{{Optimal ET sequence|legend=1| 12, 19e, 31, 105, 136b, 167be, 198be }}

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Scales: [[Garibaldi12]], [[Garibaldi17]]

<div style="line-height:1.6;">Interval table (29-note MOS, 2.3.5.7.11.13.19 POTE tuning)</div>

<div style="line-height: 1.6;">Interval table (29-note MOS, 2.3.5.7.11.13.19 POTE tuning)</div>

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

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! #Gens up

! Cents*

! class="unsortable"| Approximate ratios**

! class="unsortable" | Approximate ratios**

|-

| 0

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EDO generators: [[17edo|10\17]], [[29edo|17\29]], [[46edo|27\46]]

<div style="line-height:1.6;">Interval table (17-note MOS, 2.3.7.11.13 POTE tuning)</div>

<div style="line-height: 1.6;">Interval table (17-note MOS, 2.3.7.11.13 POTE tuning)</div>

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

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! #Gens up

! Cents*

! class="unsortable"| Approximate ratios**

! class="unsortable" | Approximate ratios**

|-

| 0

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Scales: [[Archy5]], [[Archy7]], [[Archy12]]

<div style="line-height:1.6;">Interval table (7-note MOS, 2.3.7 POTE tuning)</div>

<div style="line-height: 1.6;">Interval table (7-note MOS, 2.3.7 POTE tuning)</div>

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

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! #Gens up

! Cents*

! class="unsortable"| Approximate ratios**

! class="unsortable" | Approximate ratios**

|-

| 0

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Scales: [[Supra7]], [[Supra12]]

<div style="line-height:1.6;">Interval table (12-note MOS, 2.3.7.11 POTE tuning)</div>

<div style="line-height: 1.6;">Interval table (12-note MOS, 2.3.7.11 POTE tuning)</div>

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

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! #Gens up

! Cents*

! class="unsortable"| Approximate ratios**

! class="unsortable" | Approximate ratios**

|-

| 0

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EDO generators: [[22edo|13\22]], [[27edo|16\27]], [[49edo|29\49]]

<div style="line-height:1.6;">Interval table (12-note MOS, 2.3.5.7 POTE tuning)</div>

<div style="line-height: 1.6;">Interval table (12-note MOS, 2.3.5.7 POTE tuning)</div>

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

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! #Gens up

! Cents*

! class="unsortable"| Approximate ratios**

! class="unsortable" | Approximate ratios**

|-

| 0

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[[Mapping]]: [{{val|1 1 -3 4}}, {{val|0 1 9 -2}}]

~~[[Wedgie]]: {{wedgie|1 9 -2 12 -6 -30}}~~

[[Val]]s: {{Optimal ET sequence| 5, 17, 22, 27, 49 }}

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EDO generators: [[32edo|19\32]], [[37edo|22\37]]

<div style="line-height:1.6;">Interval table (22-note MOS, 2.3.5.7.13 POTE tuning)</div>

<div style="line-height: 1.6;">Interval table (22-note MOS, 2.3.5.7.13 POTE tuning)</div>

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

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! #Gens up

! Cents*

! class="unsortable"| Approximate ratios**

! class="unsortable" | Approximate ratios**

|-

| 0

@@ Line 14: / Line 14: @@
 Scales (Scala files): [[Meantone5]], [[Meantone7]], [[Meantone12]]
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div class="toccolours mw-collapsible mw-collapsed" style="width: 600px; overflow: auto;">
-<div style="line-height:1.6;">Interval table (7-note MOS, 2.3.5.7 POTE tuning)</div>
+<div style="line-height: 1.6;">Interval table (7-note MOS, 2.3.5.7 POTE tuning)</div>
 <div class="mw-collapsible-content">
 {| class="wikitable right-1 right-2 sortable"
 |-
 ! &#35;
 ! Cents*
-! class="unsortable"| Approximate ratios**
+! class="unsortable" | Approximate ratios**
 |-
 | 0
@@ Line 61: / Line 60: @@
 Mapping generators: ~2, ~3
-[[Wedgie]]: {{wedgie| 1 4 4 }}
 [[Tuning ranges]]:
@@ Line 84: / Line 81: @@
 Scales (Scala files): [[Flattone12]]
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div class="toccolours mw-collapsible mw-collapsed" style="width: 600px; overflow: auto;">
-<div style="line-height:1.6;">Interval table (12-note MOS, 2.3.5.7.13 POTE tuning)</div>
+<div style="line-height: 1.6;">Interval table (12-note MOS, 2.3.5.7.13 POTE tuning)</div>
 <div class="mw-collapsible-content">
 {| class="wikitable right-1 right-2 sortable"
@@ Line 91: / Line 88: @@
 ! #Gens up
 ! Cents*
-! class="unsortable"| Approximate ratios**
+! class="unsortable" | Approximate ratios**
 |-
 | 0
@@ Line 164: / Line 161: @@
 * 9-odd-limit diamond monotone and tradeoff: ~3/2 = [692.308, 694.737]
-Algebraic generator: Squarto, the positive root of 8''x''<sup>2</sup> - 4''x'' - 9, at 506.3239 cents, equal to (1 + sqrt (19))/4.
+Algebraic generator: Squarto, the positive root of {{nowrap|8''x''<sup>2</sup> − 4''x'' − 9}}, at 506.3239{{c}}, equal to <math>\frac{1+\sqrt{19}}{4}</math>.
 {{Optimal ET sequence|legend=1| 7, 19, 26, 45f }}
@@ Line 181: / Line 178: @@
 Scales (Scala files): [[Meantone5]], [[Meantone7]], [[Meantone12]]
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div class="toccolours mw-collapsible mw-collapsed" style="width: 600px; overflow: auto;">
-<div style="line-height:1.6;">Interval table (12-note MOS, 2.3.5.7 POTE tuning)</div>
+<div style="line-height: 1.6;">Interval table (12-note MOS, 2.3.5.7 POTE tuning)</div>
 <div class="mw-collapsible-content">
 {| class="wikitable right-1 right-2 sortable"
@@ Line 188: / Line 185: @@
 ! #Gens up
 ! Cents*
-! class="unsortable"| Approximate ratios**
+! class="unsortable" | Approximate ratios**
 |-
 | 0
@@ Line 258: / Line 255: @@
 * 9-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 700.000]
-Algebraic generator: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, which comes to 503.4257 cents. The recurrence converges quickly.
+Algebraic generator: Cybozem, the real root of {{nowrap|15''x''<sup>3</sup> − 10''x''<sup>2</sup> − 18}}, which comes to 503.4257{{c}}. The recurrence converges quickly.
 {{Optimal ET sequence|legend=1| 12, 19, 31, 81, 112b, 143b }}
@@ Line 290: / Line 287: @@
 * 11-odd-limit diamond monotone and tradeoff: ~3/2 = [694.737, 696.774]
-Algebraic generator: Cybozem; or else Radieubiz, the real root of 3''x''<sup>3</sup> + 6''x'' - 19. Unlike Cybozem, the recurrence for Radieubiz does not converge.
+Algebraic generator: Cybozem; or else Radieubiz, the real root of {{nowrap|3''x''<sup>3</sup> + 6''x'' − 19}}. Unlike Cybozem, the recurrence for Radieubiz does not converge.
 {{Optimal ET sequence|legend=1| 12e, 19, 31, 81 }}
@@ Line 322: / Line 319: @@
 * 11-odd-limit diamond monotone and tradeoff: ~3/2 = [696.774, 700.000]
-[[Algebraic generator]]: Traverse, the positive real root of ''x''<sup>4</sup> + 2''x'' - 13, or 696.9529 cents.
+[[Algebraic generator]]: Traverse, the positive real root of {{nowrap|''x''<sup>4</sup> + 2''x'' − 13}}, or 696.9529{{c}}.
 {{Optimal ET sequence|legend=1| 12, 19e, 31, 105, 136b, 167be, 198be }}
@@ Line 339: / Line 336: @@
 Scales: [[Garibaldi12]], [[Garibaldi17]]
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div class="toccolours mw-collapsible mw-collapsed" style="width: 600px; overflow: auto;">
-<div style="line-height:1.6;">Interval table (29-note MOS, 2.3.5.7.11.13.19 POTE tuning)</div>
+<div style="line-height: 1.6;">Interval table (29-note MOS, 2.3.5.7.11.13.19 POTE tuning)</div>
 <div class="mw-collapsible-content">
 {| class="wikitable right-1 right-2 sortable"
@@ Line 346: / Line 343: @@
 ! #Gens up
 ! Cents*
-! class="unsortable"| Approximate ratios**
+! class="unsortable" | Approximate ratios**
 |-
 | 0
@@ Line 486: / Line 483: @@
 EDO generators: [[17edo|10\17]], [[29edo|17\29]], [[46edo|27\46]]
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div class="toccolours mw-collapsible mw-collapsed" style="width: 600px; overflow: auto;">
-<div style="line-height:1.6;">Interval table (17-note MOS, 2.3.7.11.13 POTE tuning)</div>
+<div style="line-height: 1.6;">Interval table (17-note MOS, 2.3.7.11.13 POTE tuning)</div>
 <div class="mw-collapsible-content">
 {| class="wikitable right-1 right-2 sortable"
@@ Line 493: / Line 490: @@
 ! #Gens up
 ! Cents*
-! class="unsortable"| Approximate ratios**
+! class="unsortable" | Approximate ratios**
 |-
 | 0
@@ Line 587: / Line 584: @@
 Scales: [[Archy5]], [[Archy7]], [[Archy12]]
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div class="toccolours mw-collapsible mw-collapsed" style="width: 600px; overflow: auto;">
-<div style="line-height:1.6;">Interval table (7-note MOS, 2.3.7 POTE tuning)</div>
+<div style="line-height: 1.6;">Interval table (7-note MOS, 2.3.7 POTE tuning)</div>
 <div class="mw-collapsible-content">
 {| class="wikitable right-1 right-2 sortable"
@@ Line 594: / Line 591: @@
 ! #Gens up
 ! Cents*
-! class="unsortable"| Approximate ratios**
+! class="unsortable" | Approximate ratios**
 |-
 | 0
@@ Line 647: / Line 644: @@
 Scales: [[Supra7]], [[Supra12]]
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div class="toccolours mw-collapsible mw-collapsed" style="width: 600px; overflow: auto;">
-<div style="line-height:1.6;">Interval table (12-note MOS, 2.3.7.11 POTE tuning)</div>
+<div style="line-height: 1.6;">Interval table (12-note MOS, 2.3.7.11 POTE tuning)</div>
 <div class="mw-collapsible-content">
 {| class="wikitable right-1 right-2 sortable"
@@ Line 654: / Line 651: @@
 ! #Gens up
 ! Cents*
-! class="unsortable"| Approximate ratios**
+! class="unsortable" | Approximate ratios**
 |-
 | 0
@@ Line 726: / Line 723: @@
 EDO generators: [[22edo|13\22]], [[27edo|16\27]], [[49edo|29\49]]
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div class="toccolours mw-collapsible mw-collapsed" style="width: 600px; overflow :auto;">
-<div style="line-height:1.6;">Interval table (12-note MOS, 2.3.5.7 POTE tuning)</div>
+<div style="line-height: 1.6;">Interval table (12-note MOS, 2.3.5.7 POTE tuning)</div>
 <div class="mw-collapsible-content">
 {| class="wikitable right-1 right-2 sortable"
@@ Line 733: / Line 730: @@
 ! #Gens up
 ! Cents*
-! class="unsortable"| Approximate ratios**
+! class="unsortable" | Approximate ratios**
 |-
 | 0
@@ Line 789: / Line 786: @@
 [[Mapping]]: [{{val|1 1 -3 4}}, {{val|0 1 9 -2}}]
-[[Wedgie]]: {{wedgie|1 9 -2 12 -6 -30}}
 [[Val]]s: {{Optimal ET sequence| 5, 17, 22, 27, 49 }}
@@ Line 805: / Line 800: @@
 EDO generators: [[32edo|19\32]], [[37edo|22\37]]
-<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
+<div class="toccolours mw-collapsible mw-collapsed" style="width: 600px; overflow: auto;">
-<div style="line-height:1.6;">Interval table (22-note MOS, 2.3.5.7.13 POTE tuning)</div>
+<div style="line-height: 1.6;">Interval table (22-note MOS, 2.3.5.7.13 POTE tuning)</div>
 <div class="mw-collapsible-content">
 {| class="wikitable right-1 right-2 sortable"
@@ Line 812: / Line 807: @@
 ! #Gens up
 ! Cents*
-! class="unsortable"| Approximate ratios**
+! class="unsortable" | Approximate ratios**
 |-
 | 0