Slendric: Difference between revisions
described relationship between slendric's 11-limit extensions and portent. i plan to make similar changes to other pages Tags: Mobile edit Mobile web edit Advanced mobile edit |
m Cleanup on infobox |
||
| (3 intermediate revisions by 3 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox | {{Interwiki | ||
| en = Slendric | |||
| de = Slendrisch | |||
}} | |||
{{Infobox regtemp | |||
| Title = Slendric | | Title = Slendric | ||
| Subgroups = 2.3.7 | | Subgroups = 2.3.7 | ||
| Comma basis = [[1029/1024]] | | Comma basis = [[1029/1024]] | ||
| Edo join 1 = 5 | Edo join 2 = 21 | | Edo join 1 = 5 | Edo join 2 = 21 | ||
| Mapping = 1; 3 -1 | | Mapping = 1; 3 -1 | ||
| Generators = 8/7 | Generators tuning = 233.7 | Optimization method = CWE | |||
| MOS scales = [[1L 4s]], [[5L 1s]], [[5L 6s]], [[5L 11s]], … | |||
| Pergen = (P8, P5/3) | | Pergen = (P8, P5/3) | ||
| Color name = Latrizoti | | Color name = Latrizoti | ||
| Odd limit 1 = 7 | Mistuning 1 = 2.11 | Complexity 1 = 11 | | Odd limit 1 = 7 | Mistuning 1 = 2.11 | Complexity 1 = 11 | ||
| Odd limit 2 = | | Odd limit 2 = 2.3.7 27 | Mistuning 2 = 2.81 | Complexity 2 = 21 | ||
}} | }} | ||
'''Slendric''', alternatively and originally named '''wonder''' by [[Margo Schulter]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_76975.html#77043 Yahoo! Tuning Group | ''Music Theory (was Re: How to keep discussions on-topic)''], and [https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_87455.html#88377 Yahoo! Tuning Group | ''The "best" scale.'']</ref>, or systematically '''gamelic''', is a [[regular temperament]] generated by [[8/7]], so that three of them stack to [[3/2]]. Thus the gamelisma, [[1029/1024]], is tempered out, which defines the [[gamelismic clan]]. Since 1029/1024 is a relatively small comma (8.4¢), and the error is distributed over a few intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings). | |||
The disadvantage, if you want to think of it that way, is that approximations to the [[5/1|5th]] [[harmonic]] do not occur until you go a large number of generators away from the unison. In other words, the 5th harmonic must have a large [[complexity]]. Possible [[extension]]s of slendric to the full [[7-limit]] include [[mothra]], [[rodan]], and [[guiron]], where mothra tempers out [[81/80]], placing 5/1 at 12 generators (4 fifths) up; rodan tempers out [[245/243]], placing 5/1 at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing 5/1 at 24 generators (8 fifths) down. [[Weak extension]]s such as [[miracle]] and [[valentine]] are somewhat more efficient, but they change the generator chain. | |||
From there, it is easy to extend these temperaments to the [[11-limit]] since 1029/1024 factorizes in this limit into ([[385/384]])⋅([[441/440]]), and so the logical extension of slendric is to temper out both commas; this places the interval of [[55/32]] at four generators up. Alternatively, giving 5/1 an independent generator and then tempering out 385/384 and 441/440 results in the rank-3 temperament [[portent]], the natural 11-limit [[expansion]] of slendric. Portent is [[support]]ed by the slendric extensions listed above. | |||
This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself. | This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself. | ||
| Line 324: | Line 329: | ||
== Tunings == | == Tunings == | ||
Notable edos that support slendric include {{EDOs| 31, 36, 41, 46, and 77}} | Notable edos that support slendric include {{EDOs| 31, 36, 41, 46, and 77}}. | ||
=== Norm-based tunings === | === Norm-based tunings === | ||