39edo: Difference between revisions
Here's help |
Improve infobox, intro, and section titles |
||
| Line 4: | Line 4: | ||
| Fifth = 23\39 (708¢) | | Fifth = 23\39 (708¢) | ||
| Major 2nd = 7\39 (215¢) | | Major 2nd = 7\39 (215¢) | ||
| Minor 2nd = 2 | | Minor 2nd = 5:2 (154¢:62¢) | ||
| | | Consistency = 5 | ||
}} | }} | ||
'''39 | The '''39 equal divisions of the octave''' ('''39edo'''), or '''39(-tone) equal temperament''' ('''39tet''', '''39et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] in 39 equal parts of about 30.8 [[cent]]s each one. | ||
== Theory == | == Theory == | ||
'''39-EDO''', '''39-ED2''' or '''39-tET''' divides the [[octave]] in 39 equal parts. If we take 22\39 as a fifth, 39edo can be used in [[Mavila|mavila temperament]], and from that point of view it 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]. | '''39-EDO''', '''39-ED2''' or '''39-tET''' divides the [[octave]] in 39 equal parts. If we take 22\39 as a fifth, 39edo can be used in [[Mavila|mavila temperament]], and from that point of view it 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]. | ||
| Line 72: | Line 19: | ||
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). | 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). | ||
=== Odd harmonics === | |||
{{Harmonics in equal|39}} | |||
== Intervals == | == Intervals == | ||
| Line 565: | Line 515: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 64/63, 126/125, 2430/2401 | | 64/63, 126/125, 2430/2401 | ||
| [{{val| 39 62 91 110 }}] | | [{{val| 39 62 91 110 }}] (39d) | ||
| -3.78 | | -3.78 | ||
| 2.35 | | 2.35 | ||
| Line 572: | Line 522: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 64/63, 99/98, 121/120, 126/125 | | 64/63, 99/98, 121/120, 126/125 | ||
| [{{val| 39 62 91 110 135 }}] | | [{{val| 39 62 91 110 135 }}] (39d) | ||
| -3.17 | | -3.17 | ||
| 2.43 | | 2.43 | ||
| Line 578: | Line 528: | ||
|} | |} | ||
== | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-3 left-4" | {| class="wikitable center-all left-3 left-4" | ||
|- | |- | ||