12edt: Difference between revisions

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=== Macrodiatonic and macromeantone ===

12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic|macrodiatonic]] {{sl|5L 2s}} scale. This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable, since, for example, the [[generator]] is now the size of a major seventh instead of a perfect fifth. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 [[subgroup]], equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/4]] octave-reduced (although this is not a completely exact stretching of meantone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).

12edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic|macrodiatonic]] {{mos scalesig|5L 2s<3/1>}} scale. This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable, since, for example, the [[generator]] is now the size of a major seventh instead of a perfect fifth. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 [[subgroup]], equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/4]] octave-reduced (although this is not a completely exact stretching of meantone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).

Another example of a macrodiatonic scale is [[17ed5|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.

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 === Macrodiatonic and macromeantone ===
-edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic|macrodiatonic]] {{sl|5L 2s}} scale. This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable, since, for example, the [[generator]] is now the size of a major seventh instead of a perfect fifth. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 [[subgroup]], equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/4]] octave-reduced (although this is not a completely exact stretching of meantone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).
+edt can be viewed as a version of [[12edo]] with octaves stretched out to [[3/1|tritaves]], so it contains an extremely stretched diatonic scale or [[macrodiatonic and microdiatonic|macrodiatonic]] {{mos scalesig|5L 2s<3/1>}} scale. This scale has an identical structure to diatonic, but with everything stretched out to be unrecognizable, since, for example, the [[generator]] is now the size of a major seventh instead of a perfect fifth. The stretched perfect fifth can be approximated by [[17/9]] and the stretched major third by [[13/9]]. This gives rise to a "macromeantone" temperament which operates in the 3.13.17 [[subgroup]], equating 4 [[17/9]] to [[13/9]] tritave-reduced, rather than 4 [[3/2]] to [[5/4]] octave-reduced (although this is not a completely exact stretching of meantone, unlike some macromeantones like [[meansquared]] which repeats at [[4/1]]).
 Another example of a macrodiatonic scale is [[17ed5|hyperpyth]] which repeats at the fifth harmonic and is based on the 5:9:13:(17):(21) chord.