EDO vs ET: Difference between revisions

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Consider also 9-EDO; this has nearly pure intervals of 7/6 and 12/7, so close (one fifth of a cent) that they really cannot be heard as other than JI. However that is not enough to give 9-EDO the overall character of approximate JI. Nor does the fact that it possesses the same 400 cent major thirds as 12-EDO really do it, and the attempt to hear 667 cents as a fifth is at best marginally successful. What we find is a peculiar hybrid, a chimera neither fish nor fowl.

==~~The~~ EDO ~~paradigm~~==

==Temperament-agnostic EDO paradigms==

There are potentially many ways in which an EDO can be viewed without any reference to JI, or at least without the specific RTT framework of "linear map from JI subgroup", though so far this has been a less established area of xen theory.

~~While the equal temperament paradigm is firmly established, with its benefits clearly understood, little has been done to establish a competitive EDO paradigm.~~ Ivor Darreg is probably the first composer and writer to discuss EDOs without any explicit reference to their proximity to JI. Easley Blackwood (in his microtonal work) seems to have ignored or been otherwise ignorant of Just Intonation and its relationship to EDOs, instead focusing on the "recognizably diatonic" properties held by each EDO he worked with. Various other microtonal composers have, in recent years, produced compositions in various EDOs without making any conscious musical references to JI, but the question may still be asked: what is gained in this approach, that is not present in the ET paradigm?

Ivor Darreg is probably the first composer and writer to discuss EDOs without any explicit reference to their proximity to JI. Easley Blackwood (in his microtonal work) seems to have ignored or been otherwise ignorant of Just Intonation and its relationship to EDOs, instead focusing on the "recognizably diatonic" properties held by each EDO he worked with. Various other microtonal composers have, in recent years, produced compositions in various EDOs without making any conscious musical references to JI, but the question may still be asked: what is gained in this approach, that is not present in the ET paradigm?

A common JI-agnostic way of looking at edos is by looking at which [[MOS scale|mosses]] they contain. Small edos especially have limited palettes of these scales, which can help define an edo's sound. Any particular mos pattern (e.g. [[5L 3s]]) is present in multiple edos, but a mos's [[step ratio]] can be different in different edos. The step ratio of a mos has a clear effect on its sound, an effect not defined by any JI interpretation. Using the [[TAMNAMS]] system for naming mosses and their step ratios, you can list some of the characteristic mos sounds of an edo. For example, [[26edo]] contains supersoft [[5L 2s|diatonic]], basic [[5L 3s|oneirotonic]], and semihard [[4L 3s|smitonic]].

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 Consider also 9-EDO; this has nearly pure intervals of 7/6 and 12/7, so close (one fifth of a cent) that they really cannot be heard as other than JI. However that is not enough to give 9-EDO the overall character of approximate JI. Nor does the fact that it possesses the same 400 cent major thirds as 12-EDO really do it, and the attempt to hear 667 cents as a fifth is at best marginally successful. What we find is a peculiar hybrid, a chimera neither fish nor fowl.
-==The EDO paradigm==
+==Temperament-agnostic EDO paradigms==
+There are potentially many ways in which an EDO can be viewed without any reference to JI, or at least without the specific RTT framework of "linear map from JI subgroup", though so far this has been a less established area of xen theory.
-While the equal temperament paradigm is firmly established, with its benefits clearly understood, little has been done to establish a competitive EDO paradigm. Ivor Darreg is probably the first composer and writer to discuss EDOs without any explicit reference to their proximity to JI. Easley Blackwood (in his microtonal work) seems to have ignored or been otherwise ignorant of Just Intonation and its relationship to EDOs, instead focusing on the "recognizably diatonic" properties held by each EDO he worked with. Various other microtonal composers have, in recent years, produced compositions in various EDOs without making any conscious musical references to JI, but the question may still be asked: what is gained in this approach, that is not present in the ET paradigm?
+Ivor Darreg is probably the first composer and writer to discuss EDOs without any explicit reference to their proximity to JI. Easley Blackwood (in his microtonal work) seems to have ignored or been otherwise ignorant of Just Intonation and its relationship to EDOs, instead focusing on the "recognizably diatonic" properties held by each EDO he worked with. Various other microtonal composers have, in recent years, produced compositions in various EDOs without making any conscious musical references to JI, but the question may still be asked: what is gained in this approach, that is not present in the ET paradigm?
 A common JI-agnostic way of looking at edos is by looking at which [[MOS scale|mosses]] they contain. Small edos especially have limited palettes of these scales, which can help define an edo's sound. Any particular mos pattern (e.g. [[5L 3s]]) is present in multiple edos, but a mos's [[step ratio]] can be different in different edos. The step ratio of a mos has a clear effect on its sound, an effect not defined by any JI interpretation. Using the [[TAMNAMS]] system for naming mosses and their step ratios, you can list some of the characteristic mos sounds of an edo. For example, [[26edo]] contains supersoft [[5L 2s|diatonic]], basic [[5L 3s|oneirotonic]], and semihard [[4L 3s|smitonic]].