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'''10WTN''' is the [[EDF|equal division of the just perfect fifth]] into five parts of 140.391 [[cent|cents]] each alternated with a sequence of five equal steps of another interval between 120 and 160 cents. | '''10WTN''' is optimally the [[EDF|equal division of the just perfect fifth]] into five parts of 140.391 [[cent|cents]] each alternated with a sequence of five equal steps of another interval between 120 and 160 cents in its patent tunings. It is also the smallest wtn with two patent tunings which alternate an [[EDO|edo]] and an *ed(9/8). | ||
== Intervals == | == Patent Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||
| | |||
!Optimal | |||
! | !Alternating edo and *ed(9/8) a | ||
! | !Alternating edo and *ed(9/8) b | ||
! | |||
|- | |- | ||
|1 | |1 | ||
|140.391 | |140.391 | ||
|150.000 | |||
|133.333 | |||
|- | |- | ||
|2 | |2 | ||
|280.782 | |280.782 | ||
|300.000 | |||
|266.667 | |||
|- | |- | ||
|3 | |3 | ||
|421.173 | |421.173 | ||
|450.000 | |||
|400.000 | |||
|- | |- | ||
|4 | |4 | ||
|561.564 | |561.564 | ||
|600.000 | |||
|533.333 | |||
|- | |- | ||
|5 | |5 | ||
|701.955 | |701.955 | ||
|750.000 | |||
|666.667 | |||
|- | |- | ||
|6 | |6 | ||
| | |826.466 | ||
|900.000 | |||
|800.000 | |||
|- | |- | ||
|7 | |7 | ||
| | |950.978 | ||
|1050.000 | |||
|933.333 | |||
|- | |- | ||
|8 | |8 | ||
| | |1075.489 | ||
|1200.000 | |||
|1066.667 | |||
|- | |- | ||
|9 | |9 | ||
| | |1200.000 | ||
|1301.955 | |||
|1200.000 | |||
|- | |- | ||
|10 | |10 | ||
| | |1324.511 | ||
! colspan="2" |1403.910 | |||
|} | |} | ||
[[Category:Well tempered nonet]] | |||
{{todo|clarify|inline=1}} | |||
Latest revision as of 17:16, 31 March 2025
10WTN is optimally the equal division of the just perfect fifth into five parts of 140.391 cents each alternated with a sequence of five equal steps of another interval between 120 and 160 cents in its patent tunings. It is also the smallest wtn with two patent tunings which alternate an edo and an *ed(9/8).
Patent Intervals
| Optimal | Alternating edo and *ed(9/8) a | Alternating edo and *ed(9/8) b | |
|---|---|---|---|
| 1 | 140.391 | 150.000 | 133.333 |
| 2 | 280.782 | 300.000 | 266.667 |
| 3 | 421.173 | 450.000 | 400.000 |
| 4 | 561.564 | 600.000 | 533.333 |
| 5 | 701.955 | 750.000 | 666.667 |
| 6 | 826.466 | 900.000 | 800.000 |
| 7 | 950.978 | 1050.000 | 933.333 |
| 8 | 1075.489 | 1200.000 | 1066.667 |
| 9 | 1200.000 | 1301.955 | 1200.000 |
| 10 | 1324.511 | 1403.910 | |
|
Todo: clarify |