Orwell extensions: Difference between revisions
→Tuning spectra: -equal beating tuning, moved to the main page |
Undo revision 225002 by VectorGraphics (talk). Here only 22 and 31 are used with different warts for ease of comparison between these extensions. Plus 9 isn't a reasonable tuning for orwell. Tag: Undo |
||
| (13 intermediate revisions by 4 users not shown) | |||
| Line 1: | Line 1: | ||
{{Breadcrumb|Orwell}} | |||
[[Orwell]] has multiple competing [[extension]]s to the [[13-limit]]. This is evidenced by the fact that its [[support]]ing [[equal temperament]]s, [[22edo|22]] and [[31edo|31]], do less well in the 13-limit. The extensions are: | [[Orwell]] has multiple competing [[extension]]s to the [[13-limit]]. This is evidenced by the fact that its [[support]]ing [[equal temperament]]s, [[22edo|22]] and [[31edo|31]], do less well in the 13-limit. The extensions are: | ||
* ''' | * '''Tridecimal orwell''' ({{nowrap| 22 & 31 }}) – tempering out 99/98, 121/120, 176/175, and 275/273 | ||
* '''Blair''' (22 & 31f) – tempering out 65/64, 78/77, 91/90, and 99/98 | * '''Blair''' ({{nowrap| 22 & 31f }}) – tempering out 65/64, 78/77, 91/90, and 99/98 | ||
* '''Winston''' (22f & 31) – tempering out 66/65, 99/98, 105/104, and 121/120 | * '''Winston''' ({{nowrap| 22f & 31 }}) – tempering out 66/65, 99/98, 105/104, and 121/120 | ||
The most important of these is tridecimal orwell, which tempers out [[352/351]] and may also be characterized by tempering out [[275/273]] instead. | The most important of these is tridecimal orwell, which tempers out [[352/351]] and may also be characterized by tempering out [[275/273]] instead. Supported by [[53edo|53]], it has the highest accuracy in its approximation of 13/8, but also the highest complexity. The other two extensions have lower complexity, but also lower accuracy. In winston, ~13/8 is conflated with ~18/11 and is generally tuned worse than in 31edo as a result of an improved ~18/11. In blair, ~13/8 is conflated with ~8/5 and is generally tuned worse than in 22edo as a result of an improved ~8/5. | ||
Another possible path which relates a sense of compromise is to temper out [[169/168]], leading to [[doublethink]]. This has the effect of slicing the generator in two, and is supported by [[44edo|44]], 53, and [[62edo|62]]. | Another possible path which relates a sense of compromise is to temper out [[169/168]], leading to [[doublethink]]. This has the effect of slicing the generator in two, and is supported by [[44edo|44]], 53, and [[62edo|62]]. | ||
See [[Semicomma family #Orwell]], [[Semicomma family #Blair|#Blair]], and [[Semicomma family #Winston|#Winston]] for technical data. | |||
== Interval chain == | == Interval chain == | ||
Odd harmonics 1–21 and their inverses are in '''bold'''. | Odd harmonics 1–21 and their inverses are in '''bold'''. | ||
{| class="wikitable center-1 right-2" | {| class="wikitable center-1 right-2" | ||
|- | |- | ||
| Line 193: | Line 198: | ||
|- | |- | ||
! Edo<br>generators | ! Edo<br>generators | ||
! [[Eigenmonzo| | ! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]] | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||
| Line 225: | Line 230: | ||
| | | | ||
| 270.968 | | 270.968 | ||
| | | Lower bound of 9- to 15-odd-limit diamond monotone | ||
|- | |- | ||
| | | | ||
| Line 325: | Line 330: | ||
| | | | ||
| 271.698 | | 271.698 | ||
| | | Upper bound of 9- to 15-odd-limit diamond monotone | ||
|- | |- | ||
| | | | ||
| Line 367: | Line 372: | ||
|- | |- | ||
! Edo<br>generators | ! Edo<br>generators | ||
! [[Eigenmonzo| | ! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]] | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||
| Line 439: | Line 444: | ||
| | | | ||
| 270.968 | | 270.968 | ||
| | | Lower bound of 9- to 15-odd-limit diamond monotone | ||
|- | |- | ||
| | | | ||
| Line 519: | Line 524: | ||
| | | | ||
| 272.727 | | 272.727 | ||
| 22f val | | 22f val, upper bound of 9- to 15-odd-limit diamond monotone | ||
|- | |- | ||
| | | | ||
| Line 542: | Line 547: | ||
|- | |- | ||
! Edo<br>generators | ! Edo<br>generators | ||
! [[Eigenmonzo| | ! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]] | ||
! Generator (¢) | ! Generator (¢) | ||
! Comments | ! Comments | ||
| Line 714: | Line 719: | ||
[[Category:Orwell]] | [[Category:Orwell]] | ||
[[Category:Temperament extensions]] | [[Category:Temperament extensions]] | ||
[[Category:Rank-2 temperaments]] | |||