Slendric: Difference between revisions

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'''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 ~~several~~ intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).

'''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 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 [[10/1]] at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing the 5th harmonic 24 generators (8 fifths) down.

Revision as of 15:46, 27 January 2025 view source Lériendil (talk \| contribs) autopatrolled, Interface administrators, Sysops 7,651 edits added link to quark ← Older edit		Revision as of 22:53, 1 February 2025 view source Godtone (talk \| contribs) autopatrolled, emailconfirmed 2,289 edits m im not sure it's distributed over more than 3 intervals as we have 8/7 * 8/7 = 21/16 so the pure-21/16's tuning has half the error on 8/7 so that the pure-3/2's tuning is distributing over three intervals; either three 8/7's or two 8/7's and a 21/16 Newer edit →
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	'''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 ~~several~~ intervals, slendric is quite an accurate temperament (approximating many intervals within 1 or 2 cents in optimal tunings).		'''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 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 [[10/1]] at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing the 5th harmonic 24 generators (8 fifths) down.		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 [[10/1]] at 17 generators up; and guiron tempers out the schisma, [[32805/32768]], placing the 5th harmonic 24 generators (8 fifths) down.