Dicot family: Difference between revisions

The [[5-limit]] parent [[comma]] for the dicot family is 25/24, the [[chromatic semitone]]. Its [[monzo]] is {{monzo| -3 -1 2 }}, and flipping that yields {{wedgie| 2 1 -3}} for the [[wedgie]]. This tells us the generator is a third (major and minor mean the same thing), and that two thirds gives a fifth. In fact, (5/4)^2 = 3/2 * 25/24. Possible tunings for dicot are [[7edo]], [[24edo]] using the val {{val|24 38 55}} (24c) and [[31edo]] using the val {{val|31 49 71}} (31c). In a sense, what dicot is all about is using neutral thirds and pretending that's 5-limit, and like any temperament which seems to involve pretending, dicot is at the edge of what can sensibly be called a temperament at all. In other words, it is an [[exotemperament]].

* [[diamond monotone]] range: [300.000, 400.000] (1\4 to 1\3)

[[Comma list]]: 15/14, 22/21, 25/24

[[POTE generator]]: ~5/4 = 342.125

[[Mapping]]: [{{val|1 1 2 2 2}}, {{val|0 2 1 3 5}}]

{{Val list|legend=1| 3de, 4e, 7 }}

== Eudicot ==

[[Comma list]]: 15/14, 25/24, 33/32

[[POTE generator]]: ~5/4 = 336.051

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

{{Val list|legend=1| 3d, 4, 7, 18bc, 25bccd }}

=== 13-limit ===

[[Comma list]]: 15/14, 25/24, 33/32, 40/39

[[POTE generator]]: ~5/4 = 338.846

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

{{Val list|legend=1| 3d, 4, 7, 25bccd, 32bccddef, 39bcccdddef }}

[[POTE tuning|POTE generator]]: ~5/4 = 331.916

[[Map]]: [{{val|1 1 2 3}}, {{val|0 2 1 -1}}]

Wedgie: {{wedgie|2 1 -1 -3 -7 -5}}

{{Vals|legend=1| 3, 4, 7d, 11cd, 18bcddd }}

 

Vals: {{Vals| 3, 4, 7d }}

 

Vals: {{Vals| 3, 4, 7d }}

[[POTE tuning|POTE generator]]: ~5/4 = 357.938

[[Map]]: [{{val|1 1 2 1}}, {{val|0 2 1 6}}]

Wedgie: {{wedgie|2 1 6 -3 4 11}}

{{Vals|legend=1| 3d, 7d, 10, 37cd, 47bccd, 57bccdd }}

 

Vals: {{Vals| 3de, 7d, 10, 17d, 27cde }}

[[POTE tuning|POTE generator]]: ~7/6 = 251.557

[[Map]]: [{{val|2 0 3 4}}, {{val|0 2 1 1}}]

Wedgie: {{wedgie|4 2 2 -6 -8 -1}}

{{Vals|legend=1| 4, 10, 14c, 24c, 38ccd, 62cccdd }}

 

Vals: {{Vals| 10, 14c, 24c, 38ccd, 52cccde }}

 

Vals: {{Vals| 4, 10e, 14c }}

 

Vals: {{Vals| 4, 6, 10 }}

[[POTE tuning|POTE generator]]: ~5/4 = 356.264

[[Map]]: [{{val|1 1 2 4}}, {{val|0 2 1 -4}}]

Wedgie: {{wedgie|2 1 -4 -3 -12 -12}}

{{Vals|legend=1| 3, 7, 10, 17, 27c, 37c, 64bccc }}

 

Vals: {{Vals| 7, 10, 17, 27ce, 44cce }}

 

Vals: {{Vals| 3, 7e, 10 }}

[[POTE tuning|POTE generator]]: ~8/7 = 258.139

[[Map]]: [{{val|7 11 16 0}}, {{val|0 0 0 1}}]

Wedgie: {{wedgie|0 0 7 0 11 16}}

{{Vals|legend=1| 7, 14c }}

 

Vals: {{Vals| 7, 14c }}

 

Vals: {{Vals| 7, 14c }}

 

Vals: {{Vals| 7, 14cf }}

[[POTE tuning|POTE generator]]: ~9/7 = 427.208

[[Map]]: [{{val|1 3 3 6}}, {{val|0 -4 -2 -9}}]

Wedgie: {{wedgie|4 2 9 -12 3 15}}

{{Vals|legend=1| 3d, 14c, 45cc, 59bcccd }}

 

Vals: {{Vals| 3de, 14c, 17, 45cce, 59bcccdee }}

[[POTE tuning|POTE generator]]: ~8/7 = 324.482

[[Map]]: [{{val|4 6 9 0}}, {{val|0 0 0 1}}]

Wedgie: {{wedgie|0 0 4 0 6 9}}

{{Vals|legend=1| 4 }}