EDF: Difference between revisions

Line 11:

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.

Interestingly, there are not many harmonically useful JI [[subgroup]]s including [[3/2]], aside from complicated fractional subgroups, and subgroups including 2 or 3 (which all contain octaves). This is because the 3/2-reduced 5th and 11th harmonics are very near 3/2 (680 and 641 cents respectively), in contrast to [[EDO]]s and [[EDT]]s where most harmonics are closer to the middle. The smallest subgroup that could be compared to say,

Interestingly, there are not many harmonically useful JI [[subgroup]]s including [[3/2]], aside from complicated fractional subgroups, and subgroups including 2 or 3 (which all contain octaves). This is because the 3/2-reduced 5th and 11th harmonics are very near 3/2 (680 and 641 cents respectively), in contrast to [[EDO]]s and [[EDT]]s where most harmonics are closer to the middle. The smallest subgroup without octaves that could be compared to say, the [[5-limit]], would be 3/2.7.13.

== Individual pages for EDFs ==

@@ Line 11: / Line 11: @@
 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.
-Interestingly, there are not many harmonically useful JI [[subgroup]]s including [[3/2]], aside from complicated fractional subgroups, and subgroups including 2 or 3 (which all contain octaves). This is because the 3/2-reduced 5th and 11th harmonics are very near 3/2 (680 and 641 cents respectively), in contrast to [[EDO]]s and [[EDT]]s where most harmonics are closer to the middle. The smallest subgroup that could be compared to say,
+Interestingly, there are not many harmonically useful JI [[subgroup]]s including [[3/2]], aside from complicated fractional subgroups, and subgroups including 2 or 3 (which all contain octaves). This is because the 3/2-reduced 5th and 11th harmonics are very near 3/2 (680 and 641 cents respectively), in contrast to [[EDO]]s and [[EDT]]s where most harmonics are closer to the middle. The smallest subgroup without octaves that could be compared to say, the [[5-limit]], would be 3/2.7.13.
 == Individual pages for EDFs ==