EDF: Difference between revisions

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Division of the 3:2 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] is still in its infancy. The utility of 3:2 as a base though, is apparent by being one of the strongest consonances after the octave. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.

Perhaps the first to divide the perfect fifth was [[Wendy Carlos]] ( http://www.wendycarlos.com/resources/pitch.html). [[Carlo Serafini]] has also made much use of the alpha, beta and gamma scales.

Perhaps the first to divide the perfect fifth was [[Wendy Carlos]] (http://www.wendycarlos.com/resources/pitch.html). [[Carlo Serafini]] has also made much use of the alpha, beta and gamma scales.

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.

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 Division of the 3:2 into equal parts can be conceived of as to directly use this interval as an equivalence, or not. The question of [[equivalence]] is still in its infancy. The utility of 3:2 as a base though, is apparent by being one of the strongest consonances after the octave. Many, if not all, of these scales have a perceptually important pseudo (false) octave, with various degrees of accuracy.
-Perhaps the first to divide the perfect fifth was [[Wendy Carlos]] ( http://www.wendycarlos.com/resources/pitch.html). [[Carlo Serafini]] has also made much use of the alpha, beta and gamma scales.
+Perhaps the first to divide the perfect fifth was [[Wendy Carlos]] (http://www.wendycarlos.com/resources/pitch.html). [[Carlo Serafini]] has also made much use of the alpha, beta and gamma scales.
 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.