EDF: Difference between revisions

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Incidentally, one way to treat 3/2 as an equivalence is the use of the 8:9:10:(12) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone, and conversely one way to treat secundal chords (relative to scales where the large step is no larger than 253¢) as the one true type of triad is the use of 3/2 as the (formal) equivalence. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes six 5/4 to get to 9/8 (tempering out the comma 15625/15552. So, doing this yields 9, 11, and 20 note MOS which the Carlos scales temper equally. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it if it hasn't been named yet, but in any case here is an [http://www.youtube.com/watch?v=x_HSMND6RnA example] of it.

Alternatively, [[User:CompactStar|CompactStar]] has also suggeted the usage of half-prime (such as 3/2.5/2.7/2.11/2.…) subgroups for a JI/RTT-based interpretation of EDFs. But such a system, even for the simplest case of 3/2.5/2.7/2, would require very high odd-limit intervals if we want everything to fit within 3/2. The simplest chord in the 7/2-limit which fits inside 3/2 is already quite complex as 1-[[28/27]]-[[10/9]] (27:28:30) and that is a very dense tone cluster–to have a non-tone cluster it is required to go up to 1-[[10/9]]-[[7/5]] (45:50:63). However this approach has the advantage, or disadvantage depending on your compositional approach, of completely avoiding octaves similar to no-twos subgroups that are used for [[EDT]]s.

Alternatively, [[User:CompactStar|CompactStar]] has also suggeted the usage of [[Half-prime subgroup|half-prime]] (such as 3/2.5/2.7/2.11/2.…) subgroups for a JI/RTT-based interpretation of EDFs. But such a system, even for the simplest case of 3/2.5/2.7/2, would require very high odd-limit intervals if we want everything to fit within 3/2. The simplest chord in the 7/2-limit which fits inside 3/2 is already quite complex as 1-[[28/27]]-[[10/9]] (27:28:30) and that is a very dense tone cluster–to have a non-tone cluster it is required to go up to 1-[[10/9]]-[[7/5]] (45:50:63). However this approach has the advantage, or disadvantage depending on your compositional approach, of completely avoiding octaves similar to no-twos subgroups that are used for [[EDT]]s.

== Individual pages for EDFs ==

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 Incidentally, one way to treat 3/2 as an equivalence is the use of the 8:9:10:(12) chord as the fundamental complete sonority in a very similar way to the 4:5:6:(8) chord in meantone, and conversely one way to treat secundal chords (relative to scales where the large step is no larger than 253¢) as the one true type of triad is the use of 3/2 as the (formal) equivalence. Whereas in meantone it takes four 3/2 to get to 5/1, here it takes six 5/4 to get to 9/8 (tempering out the comma 15625/15552. So, doing this yields 9, 11, and 20 note MOS which the Carlos scales temper equally. While the notes are rather closer together, the scheme is uncannily similar to meantone. "Microdiatonic" might be a good term for it if it hasn't been named yet, but in any case here is an [http://www.youtube.com/watch?v=x_HSMND6RnA example] of it.
-Alternatively, [[User:CompactStar|CompactStar]] has also suggeted the usage of half-prime (such as 3/2.5/2.7/2.11/2.…) subgroups for a JI/RTT-based interpretation of EDFs. But such a system, even for the simplest case of 3/2.5/2.7/2, would require very high odd-limit intervals if we want everything to fit within 3/2. The simplest chord in the 7/2-limit which fits inside 3/2 is already quite complex as 1-[[28/27]]-[[10/9]] (27:28:30) and that is a very dense tone cluster–to have a non-tone cluster it is required to go up to 1-[[10/9]]-[[7/5]] (45:50:63). However this approach has the advantage, or disadvantage depending on your compositional approach, of completely avoiding octaves similar to no-twos subgroups that are used for [[EDT]]s.
+Alternatively, [[User:CompactStar|CompactStar]] has also suggeted the usage of [[Half-prime subgroup|half-prime]] (such as 3/2.5/2.7/2.11/2.…) subgroups for a JI/RTT-based interpretation of EDFs. But such a system, even for the simplest case of 3/2.5/2.7/2, would require very high odd-limit intervals if we want everything to fit within 3/2. The simplest chord in the 7/2-limit which fits inside 3/2 is already quite complex as 1-[[28/27]]-[[10/9]] (27:28:30) and that is a very dense tone cluster–to have a non-tone cluster it is required to go up to 1-[[10/9]]-[[7/5]] (45:50:63). However this approach has the advantage, or disadvantage depending on your compositional approach, of completely avoiding octaves similar to no-twos subgroups that are used for [[EDT]]s.
 == Individual pages for EDFs ==