Vydubychi

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Revision as of 21:01, 8 September 2023 by Eliora (talk | contribs) (17-limit)
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Vydubychi is a rank-two temperament which is produced by temperament-merging 311edo and 313edo. The temperament can also be described as 311 & 624, which is the canonical way to extend it as high as the 23-limit.

311edo and 313edo are known for two reasons: one is due to it's high consistency, and the second one due to its usage by Sevish. It is not common for two EDOs quite close to each other in the hundreds to be notable this way.

The temperament derives its way from a bus station and a historical area in Kyiv, Ukraine, where buses number 311 and 313 both terminate.

Vydubychi

5-limit

Subgroup: 2.3.5

Comma list: [299 -111 -53

Mapping: [1 28 -53], 0 -53 111]]

Optimal tuning (CTE): ~[119 -44 -21 = 598.075

Optimal ET sequence311, 313, 624, 935, 1246, 1248, 1559, 1870, 2183, 2494

7-limit

Subgroup: 2.3.5.7

Comma list: 52734375/52706752, 2199023255552/2197176384375

Mapping: [1 28 -53 -57], 0 -53 111 120]]

Optimal tuning (CTE): ~10125/7168 = 598.075

11-limit

Subgroup: 2.3.5.7.11

Comma list: 131072/130977, 759375/758912, 151263/151250

Mapping: [1 28 -53 -57 -9], 0 -53 111 120 25]]

Optimal tuning (CTE): ~847/600 = 598.075

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 4096/4095, 91125/91091, 151263/151250

Mapping: [1 28 -53 -57 -9 66], 0 -53 111 120 25 -125]]

Optimal tuning (CTE): ~572/405 = 598.075

17-limit

Subgroup: 2.3.5.7.11.13

Comma list: 2080/2079, 2058/2057, 2500/2499, 4096/4095, 11016/11011

Mapping: [1 28 -53 -57 -9 66 -124], 0 -53 111 120 25 -125 257]]

Optimal tuning (CTE): ~572/405 = 598.074

Supporting ETs: 311, 313g, 624, 935

19-limit

Subgroup: 2.3.5.7.11.13.17.19

Comma list: 2080/2079, 2500/2499, 3136/3135, 5985/5984, 11016/11011

Mapping: [1 28 -53 -57 -9 66 -124 -74], 0 -53 111 120 25 -125 257 157]]

Optimal tuning (CTE): ~572/405 = 598.074

23-limit

Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 2025/2024, 2080/2079, 2500/2499, 3136/3135, 5985/5984, 8625/8624

Mapping: [1 28 -53 -57 -9 66 -124 -74 12], 0 -53 111 120 25 -125 257 157 -15]]

Optimal tuning (CTE): ~572/405 = 598.074