3L 5s: Difference between revisions

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'''3L 5s''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 1\3 (one degree of [[3edo]] = 400¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 3edo, s becomes so small it disappears (and all that remains are the three equal L's). The pattern is also named ''antioneirotonic'' because it is the [[oneirotonic]] (5L 3s) MOS pattern with large and small steps switched. In contrast to oneirotonic scales, which often require the usage of completely new chords to have consonant-sounding music, some checkertonic scales contain approximations to a perfect fifth (usually as a dim. chk6th or ~~min~~. chk5th), and thus can be used for traditional root-3rd-P5 harmony.

'''3L 5s''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 1\3 (one degree of [[3edo]] = 400¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 3edo, s becomes so small it disappears (and all that remains are the three equal L's). The pattern is also named ''antioneirotonic'' because it is the [[oneirotonic]] (5L 3s) MOS pattern with large and small steps switched. In contrast to oneirotonic scales, which often require the usage of completely new chords to have consonant-sounding music, some checkertonic scales contain approximations to a perfect fifth (usually as a dim. chk6th or maj. chk5th), and thus can be used for traditional root-3rd-P5 harmony.

There are two significant harmonic entropy minima with this MOS pattern. [[Sensipent family|Sensi]], in which the generator is a 9/7, two of them make a 5/3, and seven of them make a 3/2, is the proper one. [[Meantone family #Squares|Squares]], in which the generator is also a 9/7, but two of them make an 18/11 and four of them make a 4/3, is improper.

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-'''3L 5s''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 1\3 (one degree of [[3edo]] = 400¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 3edo, s becomes so small it disappears (and all that remains are the three equal L's). The pattern is also named ''antioneirotonic'' because it is the [[oneirotonic]] (5L 3s) MOS pattern with large and small steps switched. In contrast to oneirotonic scales, which often require the usage of completely new chords to have consonant-sounding music, some checkertonic scales contain approximations to a perfect fifth (usually as a dim. chk6th or min. chk5th), and thus can be used for traditional root-3rd-P5 harmony.
+'''3L 5s''' refers to the structure of octave-equivalent [[MOS]] scales with generators ranging from 1\3 (one degree of [[3edo]] = 400¢) to 3\8 (three degrees of [[8edo]] = 450¢). In the case of 8edo, L and s are the same size; in the case of 3edo, s becomes so small it disappears (and all that remains are the three equal L's). The pattern is also named ''antioneirotonic'' because it is the [[oneirotonic]] (5L 3s) MOS pattern with large and small steps switched. In contrast to oneirotonic scales, which often require the usage of completely new chords to have consonant-sounding music, some checkertonic scales contain approximations to a perfect fifth (usually as a dim. chk6th or maj. chk5th), and thus can be used for traditional root-3rd-P5 harmony.
 There are two significant harmonic entropy minima with this MOS pattern. [[Sensipent family|Sensi]], in which the generator is a 9/7, two of them make a 5/3, and seven of them make a 3/2, is the proper one. [[Meantone family #Squares|Squares]], in which the generator is also a 9/7, but two of them make an 18/11 and four of them make a 4/3, is improper.