15edo: Difference between revisions

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== Theory ==

15edo can be thought of as three sets of [[5edo]] which do not connect by [[3/2|fifths]]. The fifth at 720 cents is quite wide yet still usable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. 15edo contains 3 circles of five [[3/2]]~~<nowiki/>~~s (supporting [[blackwood]], which tempers out the [[Pythagorean limma]]), and 5 circles of three [[5/4]]~~<nowiki/>~~s (supporting [[augmented temperament]]). This is radically different than a meantone system, and has a variety of ramifications for chord progressions based on diatonic {{w|Function (music)|functional harmony}}, because if you use the equipentatonic as your "diatonic scale", the same interval can have multiple functions.

15edo can be thought of as three sets of [[5edo]] which do not connect by [[3/2|fifths]]. The fifth at 720 cents is quite wide yet still usable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. 15edo contains 3 circles of five [[3/2]]'s (supporting [[blackwood]], which tempers out the [[Pythagorean limma]]), and 5 circles of three [[5/4]]'s (supporting [[augmented (temperament)|augmented]] temperament). This is radically different than a meantone system, and has a variety of ramifications for chord progressions based on diatonic {{w|Function (music)|functional harmony}}, because if you use the equipentatonic as your "diatonic scale", the same interval can have multiple functions.

A useful way to visualize the pitches and intervals of 15edo is to arrange the notes in a grid, with 3/2s or 7/4s on one axis and 5/4s on the other, to create a 3x5 rectangle of notes which tiles the plane.

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| 1\15

| 16/15

| [[Augmented]] / [[augene]]

| [[Augmented (temperament)|Augmented]] / [[augene]]

|[[3L 3s]], [[3L 6s]], [[3L 9s]]

|-

@@ Line 10: / Line 10: @@
 == Theory ==
-edo can be thought of as three sets of [[5edo]] which do not connect by [[3/2|fifths]]. The fifth at 720 cents is quite wide yet still usable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. 15edo contains 3 circles of five [[3/2]]<nowiki/>s (supporting [[blackwood]], which tempers out the [[Pythagorean limma]]), and 5 circles of three [[5/4]]<nowiki/>s (supporting [[augmented temperament]]). This is radically different than a meantone system, and has a variety of ramifications for chord progressions based on diatonic {{w|Function (music)|functional harmony}}, because if you use the equipentatonic as your "diatonic scale", the same interval can have multiple functions.
+edo can be thought of as three sets of [[5edo]] which do not connect by [[3/2|fifths]]. The fifth at 720 cents is quite wide yet still usable as a perfect fifth. Some would describe the fifth as more shimmery and pungent than anything closer to a just 3/2. 15edo contains 3 circles of five [[3/2]]'s (supporting [[blackwood]], which tempers out the [[Pythagorean limma]]), and 5 circles of three [[5/4]]'s (supporting [[augmented (temperament)|augmented]] temperament). This is radically different than a meantone system, and has a variety of ramifications for chord progressions based on diatonic {{w|Function (music)|functional harmony}}, because if you use the equipentatonic as your "diatonic scale", the same interval can have multiple functions.
 A useful way to visualize the pitches and intervals of 15edo is to arrange the notes in a grid, with 3/2s or 7/4s on one axis and 5/4s on the other, to create a 3x5 rectangle of notes which tiles the plane.
@@ Line 870: / Line 870: @@
 | 1\15
 | 16/15
-| [[Augmented]] / [[augene]]
+| [[Augmented (temperament)|Augmented]] / [[augene]]
 |[[3L 3s]], [[3L 6s]], [[3L 9s]]
 |-