49edo: Difference between revisions

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| Prime factorization = 7<sup>2</sup>

| Step size = 24.490¢

| Fifth = 29\49 = 710.2¢

| Fifth = 29\49 (710.2¢)

| Major 2nd = 9\49 = 220.4¢

| Major 2nd = 9\49 (220.4¢)

| ~~Minor 2nd~~ = 2~~\49 =~~ 49.0¢

| Semitones = 7:2 (171.4¢ : 49.0¢)

| ~~Augmented 1sn~~ = 7~~\49~~ = ~~171.4¢ (→[[7edo|1\7]])~~

| Consistency = 7

| Monotonicity = 15

}}

'''49~~-EDO~~''', or '''49 equal temperament''' divides the octave into 49 equal parts of 24.~~490~~ [[cent]]s each.

The '''49 equal divisions of the octave''' ('''49edo'''), or the '''49(-tone) equal temperament''' ('''49tet''', '''49et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 49 [[equal]] parts of about 24.5 [[cent]]s each.

== Theory ==

49edo is very much on the sharp side of things, with sharp tunings of harmonics 3 (it is the first square equal division with a "real" 3 of step coprime to its cardinality), 5, 7, and 11. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7 and 11 ~~limits~~, [[Archytas family #Archytas|archytas]] ([[7-limit]]) and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments and almost identical to the e-based analog of [[Lucy tuning]]. It [[tempering out|tempers out]] [[64/63]], [[245/243]] and [[3125/3087]] in the 7-limit, and [[100/99]] and [[1375/1372]] in the 11-limit.

49edo is very much on the sharp side of things, with sharp tunings of harmonics 3 (it is the first square equal division with a "real" 3 of step coprime to its cardinality), 5, 7, and 11. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7- and 11-limit, [[Archytas family #Archytas|archytas]] ([[7-limit]]) and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments and almost identical to the e-based analog of [[Lucy tuning]]. It [[tempering out|tempers out]] [[64/63]], [[245/243]] and [[3125/3087]] in the 7-limit, and [[100/99]] and [[1375/1372]] in the 11-limit.

=== Prime harmonics ===

== Intervals ==

@@ Line 2: / Line 2: @@
 | Prime factorization = 7<sup>2</sup>
 | Step size = 24.490¢
-| Fifth = 29\49 = 710.2¢
+| Fifth = 29\49 (710.2¢)
-| Major 2nd = 9\49 = 220.4¢
+| Major 2nd = 9\49 (220.4¢)
-| Minor 2nd = 2\49 = 49.0¢
+| Semitones = 7:2 (171.4¢ : 49.0¢)
-| Augmented 1sn = 7\49 = 171.4¢ (&rarr;[[7edo|1\7]])
+| Consistency = 7
+| Monotonicity = 15
 }}
-'''49-EDO''', or '''49 equal temperament''' divides the octave into 49 equal parts of 24.490 [[cent]]s each.
+The '''49 equal divisions of the octave''' ('''49edo'''), or the '''49(-tone) equal temperament''' ('''49tet''', '''49et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 49 [[equal]] parts of about 24.5 [[cent]]s each.
 == Theory ==
-edo is very much on the sharp side of things, with sharp tunings of harmonics 3 (it is the first square equal division with a "real" 3 of step coprime to its cardinality), 5, 7, and 11. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7 and 11 limits, [[Archytas family #Archytas|archytas]] ([[7-limit]]) and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments and almost identical to the e-based analog of [[Lucy tuning]]. It [[tempering out|tempers out]] [[64/63]], [[245/243]] and [[3125/3087]] in the 7-limit, and [[100/99]] and [[1375/1372]] in the 11-limit.
+edo is very much on the sharp side of things, with sharp tunings of harmonics 3 (it is the first square equal division with a "real" 3 of step coprime to its cardinality), 5, 7, and 11. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7- and 11-limit, [[Archytas family #Archytas|archytas]] ([[7-limit]]) and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments and almost identical to the e-based analog of [[Lucy tuning]]. It [[tempering out|tempers out]] [[64/63]], [[245/243]] and [[3125/3087]] in the 7-limit, and [[100/99]] and [[1375/1372]] in the 11-limit.
-{{primes in edo|49}}
+=== Prime harmonics ===
+{{Primes in edo|49}}
 == Intervals ==