27ed4: Difference between revisions
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27ed4 is an equal tuning that divides the 4/1 ratio (double-octave, tetratave, fifteenth) into steps of 88+(8/9) cents. | 27ed4 is an equal tuning that divides the 4/1 ratio (double-octave, tetratave, fifteenth) into steps of 88+(8/9) cents. | ||
It serves as a good first approximation to [[Nelinda#Xenharmonic Systems for Nelinda|nelindic temperament]], and is in many respects a "3n+1 cousin" of [[12edo|12et]] for 5-limit music (even though it takes every other step of the dissimilar [[27edo|27et]]), with relatively high error but low complexity, similar step size, and even sharing a common comma ([[128/125]]). Note the latter means that 27ed4 divides 4/1 into three approximate 8/5's, just as 12ed2 divides 2/1 into three 5/4's, and thus it has a 5/2 equally sharp of rational as the 5/4 in 12ed2. Its 7 and 13 approximations are a bit sharp themselves, and overall it lends itself to IoE compression: the TE tuning gives one of 2395.819236 cents. | It serves as a good first approximation to [[Nelinda#Xenharmonic Systems for Nelinda|nelindic temperament]], and is in many respects a "3n+1 cousin" of [[12edo|12et]] for 5-limit music (even though it takes every other step of the dissimilar [[27edo|27et]]), with relatively high error but low complexity, similar step size, and even sharing a common comma ([[128/125]]). Note the latter means that 27ed4 divides 4/1 into three approximate 8/5's, just as 12ed2 divides 2/1 into three 5/4's, and thus it has a 5/2 equally sharp of rational as the 5/4 in 12ed2. Its 7 and 13 approximations are a bit sharp themselves, and overall it lends itself well to IoE compression: the TE tuning gives one of 2395.819236 cents. | ||
Revision as of 03:50, 7 January 2019
27ed4 is an equal tuning that divides the 4/1 ratio (double-octave, tetratave, fifteenth) into steps of 88+(8/9) cents.
It serves as a good first approximation to nelindic temperament, and is in many respects a "3n+1 cousin" of 12et for 5-limit music (even though it takes every other step of the dissimilar 27et), with relatively high error but low complexity, similar step size, and even sharing a common comma (128/125). Note the latter means that 27ed4 divides 4/1 into three approximate 8/5's, just as 12ed2 divides 2/1 into three 5/4's, and thus it has a 5/2 equally sharp of rational as the 5/4 in 12ed2. Its 7 and 13 approximations are a bit sharp themselves, and overall it lends itself well to IoE compression: the TE tuning gives one of 2395.819236 cents.