39edo: Difference between revisions

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A particular anecdote with this 39 divisions per 2/1 was made in the Teliochordon, in 1788 by Charles Clagget (Ireland, 1740?–1820), a little extract [http://ml.oxfordjournals.org/content/76/2/291.extract.jpg here].

As a [[superpyth]] system, 39edo is intermediate between [[17edo]] and [[22edo]] (39 being 17+22). While 17edo is superb for melody (as documented by [[George Secor]]), it doesn't approximate the 5th harmonic at all and only poorly approximates the 7th. 22edo is much better for 5-limit and 7-limit harmony but is less effective for melody because the "diatonic semitone" is quarter-tone-sized, which results in a very strange-sounding diatonic scale. 39edo offers a compromise, since it still supports good 5- and 7-limit harmonies (though less close than 22edo), while at the same time having a diatonic semitone of 61.5 cents (the ideal diatonic semitone for melody being somewhere in between 60 and 80 cents, by Secor's estimates).

As a [[superpyth]] system, 39edo is intermediate between [[17edo]] and [[22edo]] (39 being 17+22). While 17edo is superb for melody (as documented by [[George Secor]]), it doesn't approximate the 5th harmonic at all and only poorly approximates the 7th. 22edo is much better for 5-limit and 7-limit harmony but is less effective for melody because the "diatonic semitone" is quarter-tone-sized, which results in a very strange-sounding diatonic scale. 39edo offers a compromise, since it still supports good 5- and 7-limit harmonies (though less close than 22edo), while at the same time having a diatonic semitone of 61.5 cents (the ideal diatonic semitone for melody being somewhere in between 60 and 80 cents, i. e. a third tone, by Secor's estimates).

39edo offers not one, but many, possible ways of extending tonality beyond the diatonic scale, even if it doesn't do as good of a job at approximating [[JI]] as some other systems do. Because it can also approximate mavila as well as "anti-mavila" ([[oneirotonic]]), the latter of which it inherits from [[13edo]], this makes 39edo an extremely versatile temperament usable in a wide range of situations (both harmonic and inharmonic).

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 A particular anecdote with this 39 divisions per 2/1 was made in the Teliochordon, in 1788 by Charles Clagget (Ireland, 1740?–1820), a little extract [http://ml.oxfordjournals.org/content/76/2/291.extract.jpg here].
-As a [[superpyth]] system, 39edo is intermediate between [[17edo]] and [[22edo]] (39 being 17+22). While 17edo is superb for melody (as documented by [[George Secor]]), it doesn't approximate the 5th harmonic at all and only poorly approximates the 7th. 22edo is much better for 5-limit and 7-limit harmony but is less effective for melody because the "diatonic semitone" is quarter-tone-sized, which results in a very strange-sounding diatonic scale. 39edo offers a compromise, since it still supports good 5- and 7-limit harmonies (though less close than 22edo), while at the same time having a diatonic semitone of 61.5 cents (the ideal diatonic semitone for melody being somewhere in between 60 and 80 cents, by Secor's estimates).
+As a [[superpyth]] system, 39edo is intermediate between [[17edo]] and [[22edo]] (39 being 17+22). While 17edo is superb for melody (as documented by [[George Secor]]), it doesn't approximate the 5th harmonic at all and only poorly approximates the 7th. 22edo is much better for 5-limit and 7-limit harmony but is less effective for melody because the "diatonic semitone" is quarter-tone-sized, which results in a very strange-sounding diatonic scale. 39edo offers a compromise, since it still supports good 5- and 7-limit harmonies (though less close than 22edo), while at the same time having a diatonic semitone of 61.5 cents (the ideal diatonic semitone for melody being somewhere in between 60 and 80 cents, i. e. a third tone, by Secor's estimates).
 edo offers not one, but many, possible ways of extending tonality beyond the diatonic scale, even if it doesn't do as good of a job at approximating [[JI]] as some other systems do. Because it can also approximate mavila as well as "anti-mavila" ([[oneirotonic]]), the latter of which it inherits from [[13edo]], this makes 39edo an extremely versatile temperament usable in a wide range of situations (both harmonic and inharmonic).