39edo: Difference between revisions

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==Theory==

'''39-EDO, 39-ED2''' or '''39-tET''' divides the Octave (Ditave 2/1) in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group that use the scheme of [[7L 2s|Superdiatonic]] LLLsLLLLs like a basical scale for notation and theory, suited in [[16edo|16-ED2]], and allied systems: [[25edo|25-ED2]] [1/3-tone 3;2]; [[41edo|41-ED2]] [1/5-tone 5;3]; and [[57edo|57]] ED2 [1/7-tone 7;4]. '''Hornbostel Temperaments''' is included too with: [[23edo|23-ED2]] [1/3-tone 3;1]; 39-ED2 [1/5-tone 5;2] & [[62edo|62-ED2]] [1/8-tone 8;3]. [[223edo|223-ED2]], the best accuracy for Hornbostel temperament fits very good with Armodue like 1/29-tone 29;10 version. Note that [[101edo|101]], [[131edo|131]], [[177edo|177]] & [[200edo|200]] ED2s are tempered systems that [http://www.h-pi.com/eop-ogolevets.html Alexei Ogolevets] (Ukraine, 1891 - 1967) was proposing in his List of Temperaments, in which the Armodue system fits very well in all these.

'''39-EDO, 39-ED2''' or '''39-tET''' divides the Octave (Ditave 2/1) in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group that use the scheme of [[7L 2s|Superdiatonic]] LLLsLLLLs like a basical scale for notation and theory, suited in [[16edo|16-ED2]], and allied systems: [[25edo|25-ED2]] [1/3-tone 3;2]; [[41edo|41-ED2]] [1/5-tone 5;3]; and [[57edo|57]] ED2 [1/7-tone 7;4]. '''Hornbostel Temperaments''' is included too with: [[23edo|23-ED2]] [1/3-tone 3;1]; 39-ED2 [1/5-tone 5;2] & [[62edo|62-ED2]] [1/8-tone 8;3].

However, its 23\39 fifth, 5.737 Cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 Cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO, in some few ways, allied to 12-ET in supporting augene temperament, and is in fact, an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is <39 62 91 110 135|.

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 ==Theory==
-'''39-EDO, 39-ED2''' or '''39-tET''' divides the Octave (Ditave 2/1) in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group that use the scheme of [[7L 2s|Superdiatonic]] LLLsLLLLs like a basical scale for notation and theory, suited in [[16edo|16-ED2]], and allied systems: [[25edo|25-ED2]] [1/3-tone 3;2]; [[41edo|41-ED2]] [1/5-tone 5;3]; and [[57edo|57]] ED2 [1/7-tone 7;4]. '''Hornbostel Temperaments''' is included too with: [[23edo|23-ED2]] [1/3-tone 3;1]; 39-ED2 [1/5-tone 5;2] &amp; [[62edo|62-ED2]] [1/8-tone 8;3]. [[223edo|223-ED2]], the best accuracy for Hornbostel temperament fits very good with Armodue like 1/29-tone 29;10 version. Note that [[101edo|101]], [[131edo|131]], [[177edo|177]] &amp; [[200edo|200]] ED2s are tempered systems that [http://www.h-pi.com/eop-ogolevets.html Alexei Ogolevets] (Ukraine, 1891 - 1967) was proposing in his List of Temperaments, in which the Armodue system fits very well in all these.
+'''39-EDO, 39-ED2''' or '''39-tET''' divides the Octave (Ditave 2/1) in 39 equal parts of 30.76923 Cents each one. If we take 22\39 as a fifth, can be used in Mavila Temperament, and from that point of view seems to have attracted the attention of the Armodue school, an Italian group that use the scheme of [[7L 2s|Superdiatonic]] LLLsLLLLs like a basical scale for notation and theory, suited in [[16edo|16-ED2]], and allied systems: [[25edo|25-ED2]] [1/3-tone 3;2]; [[41edo|41-ED2]] [1/5-tone 5;3]; and [[57edo|57]] ED2 [1/7-tone 7;4]. '''Hornbostel Temperaments''' is included too with: [[23edo|23-ED2]] [1/3-tone 3;1]; 39-ED2 [1/5-tone 5;2] &amp; [[62edo|62-ED2]] [1/8-tone 8;3].
 However, its 23\39 fifth, 5.737 Cents sharp, is in much better tune than the Mavila fifth which like all Mavila fifths is very, very flat, in this case, 25 Cents flat. Together with its best third which is the familiar 400 cents of 12 equal, we get a system which tempers out the diesis, 128/125, and the amity comma, 1600000/1594323. We have two choices for a map for 7, but the sharp one works better with the 3 and 5, which adds 64/63 and 126/125 to the list. Tempering out both 128/125 and 64/63 makes 39EDO, in some few ways, allied to 12-ET in supporting augene temperament, and is in fact, an excellent choice for an augene tuning, but one difference is that 39 has a fine 11, and adding it to consideration we find that 39-EDO tempers out 99/98 and 121/120 also. This better choice for 39et is &lt;39 62 91 110 135|.