13edo: Difference between revisions

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Important [[mos]]ses (values in parentheses are (''period'', ''generator'')):

* [[oneirotonic]] [[5L 3s]] 22122121 (5\13, 1\1)

* ~~archeotonic~~ [[6L 1s]] 2222221 (2\13, 1\1)

* archaeotonic [[6L 1s]] 2222221 (2\13, 1\1)

* [[Chromatic_pairs#Lovecraft|lovecraft]] [[4L 5s]] 212121211 (3\13, 1\1)

* [[Chromatic_pairs#Sephiroth|Sephiroth]] [[3L 4s]] 3131311 (4\13, 1\1)

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To facilitate discussion of these scales, [[Cryptic Ruse]] has ascribed them names based on H.P. Lovecraft's "Dream Cycle" mythos.

==== Modes and harmony in the ~~archeotonic~~ scale ====

==== Modes and harmony in the archaeotonic scale ====

The 2\13-based heptatonic has been named '''~~archeotonic~~''' after the "Old Ones" that rule the Dreamlands. Modes of the ~~archeotonic~~ are named after the individual Old Ones.

The 2\13-based heptatonic has been named '''archaeotonic''' after the "Old Ones" that rule the Dreamlands. Modes of the archaeotonic are named after the individual Old Ones.

A 7-nominal notation is proposed, using the letters A-G. The "C natural" scale is proposed to be degrees 0-2-4-6-8-10-12-(13), with the note "C" tuned to a reference pitch of concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13-edo.

[[File:~~Archeotonic~~.png|alt=~~Archeotonic~~.png|~~Archeotonic~~.png]]

[[File:Archaeotonic.png|alt=Archaeotonic.png|Archaeotonic.png]]

Treating 13edo as a temperament as proposed above leads to a chord of degrees 0-2-4-6-9 representing the JI harmony 8:9:10:11:13; two such pentads exist in this scale, on E and F. Smaller harmonic units exist as follows: 8:9:10:11 on C, D, E, and F; 8:9:10:13 on E, F and G; 8:9:10 on C, D, E, F, and G; 8:9:11 on C, D, E, and F; 8:9:13 on E, F, G, and A. Finally, on B we have the relatively-discordant 16:17:21:26 (0-1-5-9, or the notes B-C-E-G), which can be octave-inverted into a more concordant 8:13:17:21.

@@ Line 1,131: / Line 1,131: @@
 Important [[mos]]ses (values in parentheses are (''period'', ''generator'')):
 * [[oneirotonic]] [[5L 3s]] 22122121 (5\13, 1\1)
-* archeotonic [[6L 1s]] 2222221 (2\13, 1\1)
+* archaeotonic [[6L 1s]] 2222221 (2\13, 1\1)
 * [[Chromatic_pairs#Lovecraft|lovecraft]] [[4L 5s]] 212121211 (3\13, 1\1)
 * [[Chromatic_pairs#Sephiroth|Sephiroth]] [[3L 4s]] 3131311 (4\13, 1\1)
@@ Line 1,184: / Line 1,184: @@
 To facilitate discussion of these scales, [[Cryptic Ruse]] has ascribed them names based on H.P. Lovecraft's "Dream Cycle" mythos.
-==== Modes and harmony in the archeotonic scale ====
+==== Modes and harmony in the archaeotonic scale ====
-The 2\13-based heptatonic has been named '''archeotonic''' after the "Old Ones" that rule the Dreamlands. Modes of the archeotonic are named after the individual Old Ones.
+The 2\13-based heptatonic has been named '''archaeotonic''' after the "Old Ones" that rule the Dreamlands. Modes of the archaeotonic are named after the individual Old Ones.
 A 7-nominal notation is proposed, using the letters A-G. The "C natural" scale is proposed to be degrees 0-2-4-6-8-10-12-(13), with the note "C" tuned to a reference pitch of concert middle C. The modes are laid out in the following table, excerpted from an unfinished paper on 13-edo.
-[[File:Archeotonic.png|alt=Archeotonic.png|Archeotonic.png]]
+[[File:Archaeotonic.png|alt=Archaeotonic.png|Archaeotonic.png]]
 Treating 13edo as a temperament as proposed above leads to a chord of degrees 0-2-4-6-9 representing the JI harmony 8:9:10:11:13; two such pentads exist in this scale, on E and F. Smaller harmonic units exist as follows: 8:9:10:11 on C, D, E, and F; 8:9:10:13 on E, F and G; 8:9:10 on C, D, E, F, and G; 8:9:11 on C, D, E, and F; 8:9:13 on E, F, G, and A. Finally, on B we have the relatively-discordant 16:17:21:26 (0-1-5-9, or the notes B-C-E-G), which can be octave-inverted into a more concordant 8:13:17:21.