Trisedodge family: Difference between revisions

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== Trisedodge ==

The generator of trisedodge is ~864/625 at around 554 cents, which in all 11-limit extensions is used to represent [[11/8]], and three of them and a period is equal to ~~the harmonic~~ 3. This generator, when reduced to the minimal size, represents 25/24. However, another possible generator is ~6/5, reached by a period plus 25/24, that is, (144/125)(25/24) = 6/5.

The generator of trisedodge is ~864/625 at around 554 cents, which in all 11-limit extensions is used to represent [[11/8]], and three of them and a period is equal to [[3/1]]. This generator, when reduced to the minimal size, represents [[25/24]]. However, another possible generator is ~6/5, reached by a period plus 25/24, that is, (144/125)(25/24) = 6/5.

In the 11-limit the generator can be taken to be ~11/10, reached as a period minus 25/24, that is, (55/48)/(25/24) = 11/10. Therefore, since a period plus a gen is 6/5 and a period minus a gen is 11/10, we reach 12/11 at 2 gens.

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Badness: 0.043508

=== ~~13-limit~~ ===

==== Trisey ====

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 325/324, 640/637~~, 833/825~~

Comma list: 176/175, 325/324, 364/363, 640/637

Mapping: {{mapping| 5 1 7 21 15 0 | 0 3 2 -3 1 8 }}

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Optimal tunings:

* CTE: ~55/48 = 1\5, ~11/8 = 554.7405 (~25/24 = 74.7405)

* ~~POTE~~: ~55/48 = 1\5, ~11/8 = 555.~~261~~ (~25/24 = 75.261)

* CWE: ~55/48 = 1\5, ~11/8 = 555.1626 (~25/24 = 75.261)

Optimal ET sequence: {{Optimal ET sequence| 15, 80, 175bcde, 255bcdde }}

Badness: 0.0380

==== Dodgy ====

Subgroup: 2.3.5.7.11.13

Comma list: 176/175, 351/350, 1040/1029, 1331/1323

Mapping: {{mapping| 5 1 7 21 15 37 | 0 3 2 -3 1 -8 }}

Optimal tunings:

* CTE: ~55/48 = 1\5, ~11/8 = 554.6802 (~25/24 = 74.6802)

* CWE: ~55/48 = 1\5, ~11/8 = 554.6627 (~25/24 = 74.6627)

Optimal ET sequence: {{Optimal ET sequence| 15f, 50df, 65d, 80, 145d }}

Badness: 0.0446

== Coblack ==

@@ Line 6: / Line 6: @@
 == Trisedodge ==
-The generator of trisedodge is ~864/625 at around 554 cents, which in all 11-limit extensions is used to represent [[11/8]], and three of them and a period is equal to the harmonic 3. This generator, when reduced to the minimal size, represents 25/24. However, another possible generator is ~6/5, reached by a period plus 25/24, that is, (144/125)(25/24) = 6/5.
+The generator of trisedodge is ~864/625 at around 554 cents, which in all 11-limit extensions is used to represent [[11/8]], and three of them and a period is equal to [[3/1]]. This generator, when reduced to the minimal size, represents [[25/24]]. However, another possible generator is ~6/5, reached by a period plus 25/24, that is, (144/125)(25/24) = 6/5.
 In the 11-limit the generator can be taken to be ~11/10, reached as a period minus 25/24, that is, (55/48)/(25/24) = 11/10. Therefore, since a period plus a gen is 6/5 and a period minus a gen is 11/10, we reach 12/11 at 2 gens.
@@ Line 71: / Line 71: @@
 Badness: 0.043508
-=== 13-limit ===
+==== Trisey ====
 Subgroup: 2.3.5.7.11.13
-Comma list: 176/175, 325/324, 640/637, 833/825
+Comma list: 176/175, 325/324, 364/363, 640/637
 Mapping: {{mapping| 5 1 7 21 15 0 | 0 3 2 -3 1 8 }}
@@ Line 80: / Line 80: @@
 Optimal tunings:
 * CTE: ~55/48 = 1\5, ~11/8 = 554.7405 (~25/24 = 74.7405)
-* POTE: ~55/48 = 1\5, ~11/8 = 555.261 (~25/24 = 75.261)
+* CWE: ~55/48 = 1\5, ~11/8 = 555.1626 (~25/24 = 75.261)
-{{Optimal ET sequence|legend=1| 15, 80, 175bcde, 255bcdde }}
+Optimal ET sequence: {{Optimal ET sequence| 15, 80, 175bcde, 255bcdde }}
 Badness: 0.0380
+==== Dodgy ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 176/175, 351/350, 1040/1029, 1331/1323
+Mapping: {{mapping| 5 1 7 21 15 37 | 0 3 2 -3 1 -8 }}
+Optimal tunings:
+* CTE: ~55/48 = 1\5, ~11/8 = 554.6802 (~25/24 = 74.6802)
+* CWE: ~55/48 = 1\5, ~11/8 = 554.6627 (~25/24 = 74.6627)
+Optimal ET sequence: {{Optimal ET sequence| 15f, 50df, 65d, 80, 145d }}
+Badness: 0.0446
 == Coblack ==