Ed4: Difference between revisions
Tags: Mobile edit Mobile web edit |
No edit summary |
||
| Line 1: | Line 1: | ||
Equal Divisions of the Double Octave -- frequency ratio 4/1, aka "Quadruple" -- are closely related to Equal Divisions of the Octave -- frequency ratio 2/1, aka "Duple" -- in other words, ED2 or [[EDO]] scales. Given any odd-numbered ED2, an ED4 can be generated by taking every other tone of the ED2. For example, given 5ED2 (aka [[5edo]]), two octaves of which, in cents are: | Equal Divisions of the Double Octave -- frequency ratio 4/1, aka "Quadruple" -- are closely related to Equal Divisions of the Octave -- frequency ratio 2/1, aka "Duple" -- in other words, ED2 or [[EDO]] scales. Given any odd-numbered ED2, an ED4 can be generated by taking every other tone of the ED2. Such a tuning will show the pathological trait of inconsistency in any non-trivial integer limit. For example, given 5ED2 (aka [[5edo]]), two octaves of which, in cents are: | ||
0 240 480 720 960 1200 1440 1680 1920 2160 2400... | [[Tel:0 240 480 720 960|0 240 480 720 960]] [[Tel:1200 1440 1680 1920|1200 1440 1680 1920]] [[Tel:2160 2400|2160 2400]]... | ||
...taking every other tone yields: | ...taking every other tone yields: | ||
| Line 7: | Line 7: | ||
'''0''' 240 '''480''' 720 '''960''' 1200 '''1440''' 1680 '''1920''' 2160 '''2400'''... | '''0''' 240 '''480''' 720 '''960''' 1200 '''1440''' 1680 '''1920''' 2160 '''2400'''... | ||
'''0 480 960 1440 1920 2400...''' | '''[[Tel:0 480 960 1440 1920|0 480 960 1440 1920]] 2400...''' | ||
The resultant scale we can call 5ED4. | The resultant scale we can call 5ED4. | ||