2.3.7/(1029/1024)：修订间差异

来自律学维基
跳到导航跳到搜索
←上一编辑
可视化wikitext
无编辑摘要
Null​（留言 | 贡献）
211次编辑
 
（未显示2个用户的10个中间版本）
第1行： 第1行：
{| style="float:right; border:1px solid black; width:270px; background-color: #f0f0f0; border-collapse: collapse;"
{| style="float:right; border:1px solid black; background-color: #f0f0f0; border-collapse: collapse;"
!colspan="2" | 8/7-3ed3/2律
!colspan="2" | 8/7-3ed3/2律
|-
|-
! 子群
!    子群   
| style="background-color: #FFFFFF; font-weight: bold;" | 2.3.7
| style="background-color: #FFFFFF; font-weight: bold;" | 2.3.7 
|-
|-
! 音差
!    音差   
| style="background-color: #FFFFFF; font-weight: bold;" | 1029/1024
| style="background-color: #FFFFFF; font-weight: bold;" | 1029/1024 
|-
|-
! 映射
!    映射   
| 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
!    平均律   
| style="background-color: #FFFFFF; font-weight: bold;" | 36 & 41
| style="background-color: #FFFFFF; font-weight: bold;" | 36 & 41 
|-
|-
! 生程
!    生程   
| style="background-color: #FFFFFF; font-weight: bold;" | 2, 8/7
| style="background-color: #FFFFFF; font-weight: bold;" | 2/1, 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).
8/7-3ed3/2律是2.3.7子群上的规则调律，其生程为8/7, 三个8/7表示一个3/2, 四个8/7表示一个12/7.


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.
== 调音 ==
假设生程2/1是纯的，则2.3.7/(1029/1024)的调音完全由8/7的调音决定。


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.
下图为8/7, 7/6和3/2的误差与8/7的调音的关系，其中横坐标为8/7的调音（[[音分]]值），纵坐标为误差（音分值），橙色点为最小化这三者最大误差的调音，也就是1/4音差调音(8/7的调音为(8/7) * (1029/1024)^(1/4), n3/2的调音为(3/2) / (1029/1024)^(1/4), 7/6是准确的)，生程大小约为233.282¢.


This article concerns the basic [[2.3.7 subgroup]] temperament, slendric itself.
[[文件:123.png ]]


For technical data, see [[Gamelismic clan #Slendric]].
== 和弦 ==
将8/7叠加三遍，可以得到1-8/7-21/16-3/2[[本质调和和弦]]，其相邻两音的音程为8/7，而根音与冠音之间的音程为3/2.
 
== 作品 ==
; Adriaan Fokker
* [https://www.huygens-fokker.org/music/rmten.html ''Tenacita'']
 
; Jan van Dijk
* [https://www.huygens-fokker.org/music/rmcap.html ''Capriccio'']
* [https://www.huygens-fokker.org/music/rmctta.html ''Canzonetta'']

2026年3月17日 (二) 10:59的最新版本

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    2/1, 8/7 

8/7-3ed3/2律是2.3.7子群上的规则调律，其生程为8/7, 三个8/7表示一个3/2, 四个8/7表示一个12/7.

调音

[编辑 | 编辑源代码]

假设生程2/1是纯的，则2.3.7/(1029/1024)的调音完全由8/7的调音决定。

下图为8/7, 7/6和3/2的误差与8/7的调音的关系，其中横坐标为8/7的调音（音分值），纵坐标为误差（音分值），橙色点为最小化这三者最大误差的调音，也就是1/4音差调音(8/7的调音为(8/7) * (1029/1024)^(1/4), n3/2的调音为(3/2) / (1029/1024)^(1/4), 7/6是准确的)，生程大小约为233.282¢.

和弦

[编辑 | 编辑源代码]

将8/7叠加三遍，可以得到1-8/7-21/16-3/2本质调和和弦，其相邻两音的音程为8/7，而根音与冠音之间的音程为3/2.

作品

[编辑 | 编辑源代码]
Adriaan Fokker
Jan van Dijk
检索自“https://tun.wiki/index.php?title=2.3.7/(1029/1024)&oldid=530”