Macrodiatonic and microdiatonic scales: Difference between revisions

Line 1:

'''Macrodiatonic scales''' are [[nonoctave]] [[MOS scale]]s that have 5 large and 2 small steps like the diatonic scale, but have a period greater than 2/1 so are stretched. The equivalent term for compressed diatonic scales (period < 2/1) is '''microdiatonic'''. Macrodiatonic/microdiatonic scales typically sound completely unrecognizable due to the stretching/squishing, yet are structurally identical to diatonic (with it being possible to translate from diatonic to macrodiatonic/microdiatonic scales "on the fly"). Nonoctave [[regular temperament]]s assosciated with macrodiatonic/microdiatonic scales are sometimes termed as macro[[meantone]]/micromeantones. However, it is controversial to use the ~~names~~ of ~~temperaments~~ for things that only share a scale ~~structure~~ rather than ~~harmony~~.

'''Macrodiatonic scales''' are [[nonoctave]] [[MOS scale]]s that have 5 large and 2 small steps like the diatonic scale, but have a period greater than 2/1 so are stretched. The equivalent term for compressed diatonic scales (period < 2/1) is '''microdiatonic'''. Macrodiatonic/microdiatonic scales typically sound completely unrecognizable due to the stretching/squishing, yet are structurally identical to diatonic (with it being possible to translate from diatonic to macrodiatonic/microdiatonic scales "on the fly"). Nonoctave [[regular temperament]]s assosciated with macrodiatonic/microdiatonic scales are sometimes termed as macro[[meantone]]/micromeantones. However, it is controversial to use the name of the temperament for things that only share a scale pattern rather than harmonic structure.

In broader sense, a scale created by repeating one simple intonation ("fifth" analogue) and it has low otonal limit triad (with "third" analogue, but not always at 4 ~~genstep~~.)

In broader sense, a scale created by repeating one simple intonation ("fifth" analogue) and it has low otonal limit triad (with "third" analogue which is but not always genspan +4.) But, if 3/2 is used as generator, such as [[angel]] and [[obikhod]], another name should be considered.

== Examples of macrodiatonic and microdiatonic scales ==

* [[5L 2s (3/2-equivalent)|5L 2s<3/2>]]: ~~(bright)~~ Generator is a neogothic major third near [[81/64]] and [[14/11]].

* [[5L 2s (3/2-equivalent)|5L 2s<3/2>]]: Generator is a neogothic major third near [[81/64]] and [[14/11]].

* [[Ed7/4|5L 2s<7/4>]]: ~~(dark) Generator~~ is approximately 5/4.

* [[Ed7/4|5L 2s<7/4>]]: Dark generator is approximately 5/4.

* [[Ed9/5|5L 2s<9/5>]]: ~~(bright)~~ Generator is approximately 7/5.

* [[Ed9/5|5L 2s<9/5>]]: Generator is approximately 7/5.

* [[5L 2s (12/5-equivalent)|5L 2s<12/5>]]: ~~(bright)~~ Generator is approximately [[5/3]], and interestingly, major triads (4:5:6) are stretched to approximately ~~first~~ inversion major triads (3:4:5).

* [[5L 2s (12/5-equivalent)|5L 2s<12/5>]]: Generator is approximately [[5/3]], and interestingly, major triads (4:5:6) are stretched to approximately second inversion major triads (3:4:5).

* [[5L 2s (3/1-equivalent)|5L 2s<3/1>]]: Generator is approximately [[17/9]], and 4 generators is vaguely equivalent to [[13/9]]. This relates this scale to the no-twos macromeantone temperament [[tempering out]] 85293/83521 in the 3.13.17 subgroup (equating 4 17/9 to 13/9, instead of 4 3/2 to 5/4), as documented on the page for [[12edt]].

== In ~~a broad~~ sense ==

== In broader sense ==

* [[EDF|9L 2s<3/2>]]: ~~(bright)~~ Generator is approximately 5/4 and 6 ~~genstep~~ is 9/8.

=== Macrodiatonic/microdiatonic ===

* [[~~Ed8~~/5|~~6L 1s~~<8/5>]]: ~~(dark)~~ Generator is approximately 3/2 and 4 ~~genstep~~ is 6/5.

* [[EDF|9L 2s<3/2>]]: Generator is approximately 5/4 and 6 generators is 9/8.

* [[~~Ed5~~/3|~~7L 2s~~<5/3>]]: ~~(bright) Generator~~ is approximately 4/3 and 4 ~~genstep~~ is 8/7.

* [[Ed5/3|7L 2s<5/3>]]: Generator is approximately 4/3 and 4 generators is 8/7.

* [[3L 4s (9/5-equivalent)|3L 4s<9/5>]]: ~~(dark) Generator~~ is just 3/2 and 2 ~~genstep~~ is just 5/4.

=== Longdiatonic/shortdiatonic ===

* [[Ed8/5|6L 1s<8/5>]]: Dark generator is approximately 3/2 and 4 generators is 6/5.

* [[3L 4s (9/5-equivalent)|3L 4s<9/5>]]: Dark generator is just 3/2 and 2 generators is just 5/4. Merely this is a lattice by 5/4 and 6/5.

[[Category:7-tone scales]]

@@ Line 1: / Line 1: @@
-'''Macrodiatonic scales''' are [[nonoctave]]  [[MOS scale]]s that have 5 large and 2 small steps like the diatonic scale, but have a period greater than 2/1 so are stretched. The equivalent term for compressed diatonic scales (period < 2/1) is '''microdiatonic'''. Macrodiatonic/microdiatonic scales typically sound completely unrecognizable due to the stretching/squishing, yet are structurally identical to diatonic (with it being possible to translate from diatonic to macrodiatonic/microdiatonic scales "on the fly"). Nonoctave [[regular temperament]]s assosciated with macrodiatonic/microdiatonic scales are sometimes termed as macro[[meantone]]/micromeantones. However, it is controversial to use the names of temperaments for things that only share a scale structure rather than harmony.
+'''Macrodiatonic scales''' are [[nonoctave]]  [[MOS scale]]s that have 5 large and 2 small steps like the diatonic scale, but have a period greater than 2/1 so are stretched. The equivalent term for compressed diatonic scales (period < 2/1) is '''microdiatonic'''. Macrodiatonic/microdiatonic scales typically sound completely unrecognizable due to the stretching/squishing, yet are structurally identical to diatonic (with it being possible to translate from diatonic to macrodiatonic/microdiatonic scales "on the fly"). Nonoctave [[regular temperament]]s assosciated with macrodiatonic/microdiatonic scales are sometimes termed as macro[[meantone]]/micromeantones. However, it is controversial to use the name of the temperament for things that only share a scale pattern rather than harmonic structure.
-In broader sense, a scale created by repeating one simple intonation ("fifth" analogue) and it has low otonal limit triad (with "third" analogue, but not always at 4 genstep.)
+In broader sense, a scale created by repeating one simple intonation ("fifth" analogue) and it has low otonal limit triad (with "third" analogue which is but not always genspan +4.) But, if 3/2 is used as generator, such as [[angel]] and [[obikhod]], another name should be considered.
 == Examples of macrodiatonic and microdiatonic scales ==
-* [[5L 2s (3/2-equivalent)|5L 2s<3/2>]]: (bright) Generator is a neogothic major third near [[81/64]] and [[14/11]].
+* [[5L 2s (3/2-equivalent)|5L 2s<3/2>]]: Generator is a neogothic major third near [[81/64]] and [[14/11]].
-* [[Ed7/4|5L 2s<7/4>]]: (dark) Generator is approximately 5/4.
+* [[Ed7/4|5L 2s<7/4>]]: Dark generator is approximately 5/4.
-* [[Ed9/5|5L 2s<9/5>]]: (bright) Generator is approximately 7/5.
+* [[Ed9/5|5L 2s<9/5>]]: Generator is approximately 7/5.
-* [[5L 2s (12/5-equivalent)|5L 2s<12/5>]]: (bright) Generator is approximately [[5/3]], and interestingly, major triads (4:5:6) are stretched to approximately first inversion major triads (3:4:5).
+* [[5L 2s (12/5-equivalent)|5L 2s<12/5>]]: Generator is approximately [[5/3]], and interestingly, major triads (4:5:6) are stretched to approximately second inversion major triads (3:4:5).
 * [[5L 2s (3/1-equivalent)|5L 2s<3/1>]]: Generator is approximately [[17/9]], and 4 generators is vaguely equivalent to [[13/9]]. This relates this scale to the no-twos macromeantone temperament [[tempering out]] 85293/83521 in the 3.13.17 subgroup (equating 4 17/9 to 13/9, instead of 4 3/2 to 5/4), as documented on the page for [[12edt]].
-== In a broad sense ==
+== In broader sense ==
-* [[EDF|9L 2s<3/2>]]: (bright) Generator is approximately 5/4 and 6 genstep is 9/8.
+=== Macrodiatonic/microdiatonic ===
-* [[Ed8/5|6L 1s<8/5>]]: (dark) Generator is approximately 3/2 and 4 genstep is 6/5.
+* [[EDF|9L 2s<3/2>]]: Generator is approximately 5/4 and 6 generators is 9/8.
-* [[Ed5/3|7L 2s<5/3>]]: (bright) Generator is approximately 4/3 and 4 genstep is 8/7.
+* [[Ed5/3|7L 2s<5/3>]]: Generator is approximately 4/3 and 4 generators is 8/7.
-* [[3L 4s (9/5-equivalent)|3L 4s<9/5>]]: (dark) Generator is just 3/2 and 2 genstep is just 5/4.
+=== Longdiatonic/shortdiatonic ===
+* [[Ed8/5|6L 1s<8/5>]]: Dark generator is approximately 3/2 and 4 generators is 6/5.
+* [[3L 4s (9/5-equivalent)|3L 4s<9/5>]]: Dark generator is just 3/2 and 2 generators is just 5/4. Merely this is a lattice by 5/4 and 6/5.
 [[Category:7-tone scales]]