159edo: Difference between revisions
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== Intervals == | == Intervals == | ||
{{ | {{See also| 159edo interval names and harmonies}} | ||
The following table assumes 17-limit patent val {{val|159 252 369 446 550 588 650}}. | The following table assumes 17-limit patent val {{val| 159 252 369 446 550 588 650 }}. | ||
Intervals highlighted in '''bold''' are prime harmonics or subharmonics. In addition, intervals that differ from assigned steps by more than 50%, multiples of such intervals, and intervals of odd limit higher than 1024, are not shown. Furthermore, when multiple well-known intervals for a given prime-limit share a step size, they may share a cell in the chart; conversely, a "?" in the chart means that no known interval meets the criteria for inclusion. Note that no 5-limit intervals can be represented by degrees other than multiples of 3, so those entries are left blank. | Intervals highlighted in '''bold''' are prime harmonics or subharmonics. In addition, intervals that differ from assigned steps by more than 50%, multiples of such intervals, and intervals of odd limit higher than 1024, are not shown. Furthermore, when multiple well-known intervals for a given prime-limit share a step size, they may share a cell in the chart; conversely, a "?" in the chart means that no known interval meets the criteria for inclusion. Note that no 5-limit intervals can be represented by degrees other than multiples of 3, so those entries are left blank. | ||
| Line 1,378: | Line 1,378: | ||
| 0.412 | | 0.412 | ||
| 5.46 | | 5.46 | ||
|- | |||
| 2.3.5.7.11.13.17.19 | |||
| 273/272, 325/324, 343/342, 361/360, 364/363, 375/374, 385/384 | |||
| {{mapping| 159 252 369 446 550 588 650 675 }} | |||
| +0.385 | |||
| 0.409 | |||
| 5.42 | |||
|- | |||
| 2.3.5.7.11.13.17.19.23 | |||
| 273/272, 325/324, 343/342, 361/360, 364/363, 375/374, 385/384, 392/391 | |||
| {{mapping| 159 252 369 446 550 588 650 675 719 }} | |||
| +0.388 | |||
| 0.386 | |||
| 5.11 | |||
|} | |} | ||
* 159et has lower absolute errors in the 19- and 23-limit than any previous equal temperaments, past [[152edo|152fg]]. The next equal temperament that does better in the 19-limit is [[161edo|161]], and in the 23-limit, [[183edo|183]]. | * 159et has lower absolute errors in the 19- and 23-limit than any previous equal temperaments, past [[152edo|152fg]]. The next equal temperament that does better in the 19-limit is [[161edo|161]], and in the 23-limit, [[183edo|183]]. | ||
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* [[:File:Welcome to Dystopia.mp3|''Welcome to Dystopia'']] (2021) | * [[:File:Welcome to Dystopia.mp3|''Welcome to Dystopia'']] (2021) | ||
* [[:File:The Forest of Loss.mp3|''The Forest of Loss'']] (2021) | * [[:File:The Forest of Loss.mp3|''The Forest of Loss'']] (2021) | ||
* [https://soundcloud.com/aura-945595763/life-in-a-brave-new-world ''Life in a Brave New World''] ( | * [https://soundcloud.com/aura-945595763/life-in-a-brave-new-world ''Life in a Brave New World''] (2024) | ||
; [[Ozan Yarman]] | ; [[Ozan Yarman]] | ||