Editing Equal temperament (section)

=== Five-, seven-, and nine-tone temperaments in ethnomusicology ===<!--[[7 equal temperament]] and [[5 equal temperament]] redirect directly here-->
[[File:7-tet scale on C.png|thumb|300px|Approximation of {{nobr|7 {{sc|tet}}}}]]

Five- and seven-tone equal temperament (''{{nobr|5 {{sc|TET}}}}'' {{audio|5-tet scale on C.mid|Play}} and ''7 {{sc|TET}}''{{audio|7-tet scale on C.mid|Play}} ), with 240&nbsp;cent {{Audio|1 step in 5-et on C.mid|Play}} and 171&nbsp;cent {{Audio|1 step in 7-et on C.mid|Play}} steps, respectively, are fairly common.

{{nobr|5 {{sc|TET}}}} and {{nobr|7 {{sc|TET}}}} mark the endpoints of the [[syntonic temperament]]'s valid tuning range, as shown in [[#Figure 1|Figure&nbsp;1]].
* In {{nobr|5 {{sc|TET}},}} the tempered perfect fifth is 720&nbsp;cents wide (at the top of the tuning continuum), and marks the endpoint on the tuning continuum at which the width of the minor second shrinks to a width of 0&nbsp;cents.
* In {{nobr|7 {{sc|TET}},}} the tempered perfect fifth is 686&nbsp;cents wide (at the bottom of the tuning continuum), and marks the endpoint on the tuning continuum, at which the minor second expands to be as wide as the major second (at 171&nbsp;cents each).

====5&nbsp;tone and 9&nbsp;tone equal temperament====
According to [[Jaap Kunst|Kunst]] (1949), Indonesian [[gamelan]]s are tuned to {{nobr|5 {{sc|TET}},}} but according to [[Mantle Hood|Hood]] (1966) and [[Colin McPhee|McPhee]] (1966) their tuning varies widely, and according to [[Michael Tenzer|Tenzer]] (2000) they contain [[pseudo-octave|stretched octaves]]. It is now accepted that of the two primary tuning systems in gamelan music, [[slendro]] and [[pelog]], only slendro somewhat resembles five-tone equal temperament, while pelog is highly unequal; however, in 1972 Surjodiningrat, Sudarjana and Susanto analyze pelog as equivalent to {{nobr|9 {{sc|TET}}}} (133-cent steps {{Audio|Semitone Maximus on C.mid|Play}}).<ref>{{harvp|Surjodiningrat|Sudarjana|Susanto|1972}}</ref>

====7-tone equal temperament====
A [[Thai music|Thai]] xylophone measured by Morton in 1974 "varied only plus or minus 5&nbsp;cents" from {{nobr|7 {{sc|TET}}}}.<ref>{{harvp|Morton|1980}}</ref> According to Morton,
: "Thai instruments of fixed pitch are tuned to an equidistant system of seven pitches per octave ... As in Western traditional music, however, all pitches of the tuning system are not used in one mode (often referred to as 'scale'); in the Thai system five of the seven are used in principal pitches in any mode, thus establishing a pattern of nonequidistant intervals for the mode."<ref>{{cite book |last=Morton |first=David |year=1980 |title=The Music of Thailand |series=Musics of Many Cultures |page=70 |editor-last=May |editor-first=Elizabeth |isbn=0-520-04778-8 }}</ref> {{audio|Thai pentatonic scale mode 1.mid|Play}}

A South American Indian scale from a pre-instrumental culture measured by Boiles in 1969 featured 175&nbsp;cent seven-tone equal temperament, which stretches the octave slightly, as with instrumental gamelan music.<ref>{{harvp|Boiles|1969}}</ref>

[[Music of China|Chinese music]] has traditionally used {{nobr|7 {{sc|TET}}}}.{{efn|
'Hepta-equal temperament' in our folk music has always been a controversial issue.<!-- mostly from Google translate, please verify --><ref>{{cite web |url=http://www.wanfangdata.com.cn/qikan/periodical.Articles/ZHONGUOYY/ZHON2004/0404/040425.htm |script-title=zh:有关"七平均律"新文献著作的发现 |language=zh |trans-title=Findings of new literatures concerning the hepta – equal temperament |archive-url=https://web.archive.org/web/20071027064731/http://www.wanfangdata.com.cn/qikan/periodical.Articles/ZHONGUOYY/ZHON2004/0404/040425.htm |archive-date=2007-10-27}}</ref>
}}{{efn|From the flute for two thousand years of the production process, and the Japanese shakuhachi remaining in the production of Sui and Tang Dynasties and the actual temperament, identification of people using the so-called 'Seven Laws' at least two thousand years of history; and decided that this law system associated with the flute law.<!-- from Google translate, please verify --><ref>{{cite web |url=http://scholar.ilib.cn/Abstract.aspx?A=xhyyxyxb200102005 |script-title=zh:七平均律"琐谈--兼及旧式均孔曲笛制作与转调 |language=zh |trans-title=abstract of ''About "Seven- equal- tuning System"''  |access-date=2007-06-25 |archive-url=https://web.archive.org/web/20070930155436/http://scholar.ilib.cn/Abstract.aspx?A=xhyyxyxb200102005 |archive-date=2007-09-30 |url-status=dead }}</ref>
}}