2.3.7/(1029/1024)：修订间差异
Administrator（留言 | 贡献） 无编辑摘要 |
Administrator（留言 | 贡献） 无编辑摘要 |
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| 第11行： | 第11行： | ||
| style="background-color: #FFFFFF; font-weight: bold;" | [1 1 3; 0 3 -1] | | style="background-color: #FFFFFF; font-weight: bold;" | [1 1 3; 0 3 -1] | ||
|- | |- | ||
! | ! 平均律 | ||
| style="background-color: #FFFFFF; font-weight: bold;" | 36 & 41 | | style="background-color: #FFFFFF; font-weight: bold;" | 36 & 41 | ||
|- | |- | ||
| 第17行： | 第17行： | ||
| style="background-color: #FFFFFF; font-weight: bold;" | 2, 8/7 | | style="background-color: #FFFFFF; font-weight: bold;" | 2, 8/7 | ||
|} | |} | ||
'''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. | |||
For technical data, see [[Gamelismic clan #Slendric]]. | |||
2026年1月21日 (三) 14:13的版本
| 8/7-3ed3/2律 | |
|---|---|
| 子群 | 2.3.7 |
| 音差 | 1029/1024 |
| 映射 | [1 1 3; 0 3 -1] |
| 平均律 | 36 & 41 |
| 生程 | 2, 8/7 |
Slendric, alternatively and originally named wonder by Margo Schulter[1], 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 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 extensions 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 extensions 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 supported by the slendric extensions listed above.
This article concerns the basic 2.3.7 subgroup temperament, slendric itself.
For technical data, see Gamelismic clan #Slendric.