EDO vs ET: Difference between revisions

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~~=EDOs vs. Equal Temperaments=~~

'''Equal divisions of the octave''' ('''[[EDO]]''') and '''equal [[temperament]]s''' ('''ET''') are not the same thing, at least not in concept. An equal division of the octave is just that--a division of the pure 2/1 octave of 1200 cents into some number of equal parts. An equal temperament, on the other hand, is what you get when you take an EDO and declare its intervals to be approximations to Just Intonation, thus adding a new conceptual layer on top of the bare equal division.

~~[[de:EDO]]~~

~~[[EDO|~~Equal divisions of the octave]] and equal [[temperament]]s are not the same thing, at least not in concept. An equal division of the octave is just that--a division of the pure 2/1 octave of 1200 cents into some number of equal parts. An equal temperament, on the other hand, is what you get when you take an EDO and declare its intervals to be approximations to Just Intonation, thus adding a new conceptual layer on top of the bare equal division.

==Why bother making this distinction?==

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Another benefit to the temperament-free approach to EDOs is that it can avoid confusion that sometimes comes when applying the ET paradigm to tunings that provide questionable approximations to JI. It is a common topic of debate within the microtonal community whether a given EDO supports a given temperament, or even what it means for an EDO to support a temperament. For example, the question of whether or not 11-EDO supports Hanson temperament has been debated without a consensus having been reached. Another source of confusion in many EDOs is that the chords which are closest to a Just sonority are not always the most pleasant. A triad of 0-5-9 degrees of 14-EDO can be said to approximate 7:9:11, and is the lowest-error triad in 14-EDO, yet its comparative pleasantness to, say, 0-5-8 or 0-6-9 is definitely debatable. When temperament is left out of the picture, there is nothing to debate--EDOs simply "are what they are", and can be taken or left according solely to the whims of the composer.

[[Category:~~edo~~]]

[[Category:Terminology]]

[[Category:Equal]]

[[Category:Edo]]

[[de:EDO]]

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-=EDOs vs. Equal Temperaments=
+'''Equal divisions of the octave''' ('''[[EDO]]''') and '''equal [[temperament]]s''' ('''ET''') are not the same thing, at least not in concept. An equal division of the octave is just that--a division of the pure 2/1 octave of 1200 cents into some number of equal parts. An equal temperament, on the other hand, is what you get when you take an EDO and declare its intervals to be approximations to Just Intonation, thus adding a new conceptual layer on top of the bare equal division.
-[[de:EDO]]
-[[EDO|Equal divisions of the octave]] and equal [[temperament]]s are not the same thing, at least not in concept. An equal division of the octave is just that--a division of the pure 2/1 octave of 1200 cents into some number of equal parts. An equal temperament, on the other hand, is what you get when you take an EDO and declare its intervals to be approximations to Just Intonation, thus adding a new conceptual layer on top of the bare equal division.
 ==Why bother making this distinction?==
@@ Line 20: / Line 18: @@
 Another benefit to the temperament-free approach to EDOs is that it can avoid confusion that sometimes comes when applying the ET paradigm to tunings that provide questionable approximations to JI. It is a common topic of debate within the microtonal community whether a given EDO supports a given temperament, or even what it means for an EDO to support a temperament. For example, the question of whether or not 11-EDO supports Hanson temperament has been debated without a consensus having been reached. Another source of confusion in many EDOs is that the chords which are closest to a Just sonority are not always the most pleasant. A triad of 0-5-9 degrees of 14-EDO can be said to approximate 7:9:11, and is the lowest-error triad in 14-EDO, yet its comparative pleasantness to, say, 0-5-8 or 0-6-9 is definitely debatable. When temperament is left out of the picture, there is nothing to debate--EDOs simply "are what they are", and can be taken or left according solely to the whims of the composer.
-[[Category:edo]]
+[[Category:Terminology]]
+[[Category:Equal]]
+[[Category:Edo]]
+<!-- interwiki, but not in 1-to-1 relation -->
+[[de:EDO]]