36edo: Difference between revisions

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=Tuning by Ear=

<ul><li>After 9edo and 19edo, 36edo is one of the easiest tuning systems to recreate tuning solely by ear, due to the way it's purest intervals are arranged. If you view it as a lattice of 4 9edo's (which can be formed by stacking 9 7/6s with a comma of less than 2 cents) connected by 3/2's, you get a tonal diamond with a wolf note between the extreme corners of approximately 7.7 cents, about the same relative error as stacking 12 perfect 3/2's, and obviously a much smaller absolute error. In addition, this kind of tempering makes major thirds 6.3 cents closer to just in the majority of keys, making them sound sweeter than equal temperament. It's a good system to use on large organs that have three manuals. </li></ul>

<ul><li>After [[9edo|9edo]] and [[19edo|19edo]], 36edo is one of the easiest tuning systems to recreate tuning solely by ear, due to the way it's purest intervals are arranged. If you view it as a lattice of 4 9edo's (which can be formed by stacking 9 [[7/6|7/6's]] with a comma of less than 2 cents) connected by [[3/2|3/2's]], you get a tonal diamond with a wolf note between the extreme corners of approximately 7.7 cents, about the same relative error as stacking 12 perfect 3/2's compared to [[12edo|12edo]] and obviously a much smaller absolute error. In addition, this kind of tempering makes major thirds 6.3 cents closer to just in the majority of keys, making them sound sweeter than equal temperament. It's a good system to use on large organs that have three manuals. </li></ul>

=Music=

<ul><li>[https://soundcloud.com/overtoneshock/exponentially-more-lost-and-forgetful-36-edo?in=overtoneshock/sets/xenharmonic-microtonal Exponentially More Lost and Forgetful] by [https://soundcloud.com/overtoneshock Stephen Weigel] played by flautists Orlando Cela and Wei Zhao</li><li>[http://micro.soonlabel.com/gene_ward_smith/36edo/something.mp3 Something] by [[Herman_Klein|Herman Klein]]</li><li>[http://micro.soonlabel.com/gene_ward_smith/36edo/hay.mp3 Hay] by [[Joe_Hayseed|Joe Hayseed]]</li><li>[http://micro.soonlabel.com/gene_ward_smith/36edo/boomers.mp3 Boomers] by [[Ivan_Bratt|Ivan Bratt]]</li><li>[http://micro.soonlabel.com/36edo/20120418-36edo.mp3 Thoughts in Legolas Tuning] by [[Chris_Vaisvil|Chris Vaisvil]]</li></ul>

@@ Line 409: / Line 409: @@
 =Tuning by Ear=
-<ul><li>After 9edo and 19edo, 36edo is one of the easiest tuning systems to recreate tuning solely by ear, due to the way it's purest intervals are arranged. If you view it as a lattice of 4 9edo's (which can be formed by stacking 9 7/6s with a comma of less than 2 cents) connected by 3/2's, you get a tonal diamond with a wolf note between the extreme corners of approximately 7.7 cents, about the same relative error as stacking 12 perfect 3/2's, and obviously a much smaller absolute error. In addition, this kind of tempering makes major thirds 6.3 cents closer to just in the majority of keys, making them sound sweeter than equal temperament. It's a good system to use on large organs that have three manuals. </li></ul>
+<ul><li>After [[9edo|9edo]] and [[19edo|19edo]], 36edo is one of the easiest tuning systems to recreate tuning solely by ear, due to the way it's purest intervals are arranged. If you view it as a lattice of 4 9edo's (which can be formed by stacking 9 [[7/6|7/6's]] with a comma of less than 2 cents) connected by [[3/2|3/2's]], you get a tonal diamond with a wolf note between the extreme corners of approximately 7.7 cents, about the same relative error as stacking 12 perfect 3/2's compared to [[12edo|12edo]] and obviously a much smaller absolute error. In addition, this kind of tempering makes major thirds 6.3 cents closer to just in the majority of keys, making them sound sweeter than equal temperament. It's a good system to use on large organs that have three manuals. </li></ul>
 =Music=
 <ul><li><span style="">[https://soundcloud.com/overtoneshock/exponentially-more-lost-and-forgetful-36-edo?in=overtoneshock/sets/xenharmonic-microtonal Exponentially More Lost and Forgetful] by [https://soundcloud.com/overtoneshock Stephen Weigel] played by flautists Orlando Cela and Wei Zhao</span></li><li><span style="">[http://micro.soonlabel.com/gene_ward_smith/36edo/something.mp3 Something]</span> by [[Herman_Klein|Herman Klein]]</li><li><span style="">[http://micro.soonlabel.com/gene_ward_smith/36edo/hay.mp3 Hay]</span> by [[Joe_Hayseed|Joe Hayseed]]</li><li><span style="">[http://micro.soonlabel.com/gene_ward_smith/36edo/boomers.mp3 Boomers]</span> by [[Ivan_Bratt|Ivan Bratt]]</li><li>[http://micro.soonlabel.com/36edo/20120418-36edo.mp3 Thoughts in Legolas Tuning] by [[Chris_Vaisvil|Chris Vaisvil]]</li></ul>