13edo scales: Difference between revisions

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#Hlanithian: 1 2 2 1 2 1 2 2 (Locrian + natural minor)

#Sarnathian: 1 2 1 2 2 1 2 2 (diminished + natural minor)

===Modes with sharp tritone===

The overview of the intervals and their harmonic function in the brighter modes (Dylathian, Ilarnekian, Celephaïsian and Ultharian, Mnarian):

*The ''basis'', or the intervals that provide the basic consonances are: the major second, the thirds and the minor fourth. These are the most important for functional harmony.

*Consonant extensions: The sixths (counting the Dylathian augmented fifth) and the sevenths; the minor ninth.

*Dissonant extensions: The minor and major fifths, the most dissonant and categorically ambiguous intervals. Melodically they can function as fifths, or as other intervals like fourths or sixths depending on the

The brighter modes, can be viewed as providing a distorted version of diatonic functional harmony. For example, in the Dylathian mode, the 4:5:9 triad on the sixth degree can sound like both "V" and "III of iv" depending on context. Basic chord progressions can move by minor fourths, thirds, or major seconds: for example, J major-M minor-P minor-Ob major-J major (in Ilarnekian) or J major-K major-O major-M major-J major (in Dylathian).

Oneirotonic provides two Orwell tetrads, made of three stacked minor thirds making one minor sixth; we get them by taking every second degree of the scale, JLNP or KMOQ. They sound like squashed diminished chords, but not quite. One could play an earbending trick where a movement up a major third and up 3 minor thirds will get you back to where you started unlike in 12edo. The two Orwell tetrads contain the two copies of 8:11:13 in oneirotonic, Q-M-Ob or L-P-J in J Ilarnekian.

===Modes with flat tritone===

The darker modes are radically different in character than the brighter modes.

Modes with a flat 5th degree sound weirder to diatonic ears, but ironically this can sound more stable since the flat 5th degree approximates an 11/8. Mnarian has a 4:9:11 on the tonic, Hlanithian has an 8:11:13:17 on the tonic, and Sarnathian has the Beloved Extra Special Tetrad 4:5:11:13 on the tonic. Ironically Sarnathian makes the 5/4 in the chord sound very dark since it's a diminished fourth, rather than a major third.

Hlanithian also has the tetrad 8:13:17:21 on the tonic (in the 13edo tuning).

===Tetrachordal 8-note scales===

You can also view oneirotonic as scales made of two tetrachords each spanning a minor fourth and one trichord spanning a minor third. This will let you build 13edo "tetrachordal" scales with a similar structure that is not one of the 8 modes, with tetrachord structures similar to 12edo ones. For example:

*[2 1 1] [2 1] [1 3 1] is a kind of harmonic minor (also obtained by lowering the 7th degree of the Celephaïsian mode)

@@ Line 239: / Line 239: @@
 #Hlanithian: 1 2 2 1 2 1 2 2 (Locrian + natural minor)
 #Sarnathian: 1 2 1 2 2 1 2 2 (diminished + natural minor)
+===Modes with sharp tritone===
+The overview of the intervals and their harmonic function in the brighter modes (Dylathian, Ilarnekian, Celephaïsian and Ultharian, Mnarian):
+*The ''basis'', or the intervals that provide the basic consonances are: the major second, the thirds and the minor fourth. These are the most important for functional harmony.
+*Consonant extensions: The sixths (counting the Dylathian augmented fifth) and the sevenths; the minor ninth.
+*Dissonant extensions: The minor and major fifths, the most dissonant and categorically ambiguous intervals. Melodically they can function as fifths, or as other intervals like fourths or sixths depending on the
+The brighter modes, can be viewed as providing a distorted version of diatonic functional harmony. For example, in the Dylathian mode, the 4:5:9 triad on the sixth degree can sound like both "V" and "III of iv" depending on context. Basic chord progressions can move by minor fourths, thirds, or major seconds: for example, J major-M minor-P minor-Ob major-J major (in Ilarnekian) or J major-K major-O major-M major-J major (in Dylathian).
+Oneirotonic provides two Orwell tetrads, made of three stacked minor thirds making one minor sixth; we get them by taking every second degree of the scale, JLNP or KMOQ. They sound like squashed diminished chords, but not quite. One could play an earbending trick where a movement up a major third and up 3 minor thirds will get you back to where you started unlike in 12edo. The two Orwell tetrads contain the two copies of 8:11:13 in oneirotonic, Q-M-Ob or L-P-J in J Ilarnekian.
+===Modes with flat tritone===
+The darker modes are radically different in character than the brighter modes.
 Modes with a flat 5th degree sound weirder to diatonic ears, but ironically this can sound more stable since the flat 5th degree approximates an 11/8. Mnarian has a 4:9:11 on the tonic, Hlanithian has an 8:11:13:17 on the tonic, and Sarnathian has the Beloved Extra Special Tetrad 4:5:11:13 on the tonic. Ironically Sarnathian makes the 5/4 in the chord sound very dark since it's a diminished fourth, rather than a major third.
 Hlanithian also has the tetrad 8:13:17:21 on the tonic (in the 13edo tuning).
+===Tetrachordal 8-note scales===
 You can also view oneirotonic as scales made of two tetrachords each spanning a minor fourth and one trichord spanning a minor third. This will let you build 13edo "tetrachordal" scales with a similar structure that is not one of the 8 modes, with tetrachord structures similar to 12edo ones. For example:
 *[2 1 1] [2 1] [1 3 1] is a kind of harmonic minor (also obtained by lowering the 7th degree of the Celephaïsian mode)