13edo scales: Difference between revisions
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The root-major third-major ninth (approximating 4:5:9; J-L-K in Kentaku notation) and its minor equivalent root-minor third-major ninth (J-Lb-K in Kentaku notation) may be considered equivalents of root-third-fifth chords in diatonic music. Archeotonic scales have 6 such triads, 5 "major" and 1 "minor". The 11th and 13th harmonics are also plentiful, as already noted by Cryptic Ruse; 4 roots have the 11th harmonic over them and 4 roots have the 13th harmonic over them. | The root-major third-major ninth (approximating 4:5:9; J-L-K in Kentaku notation) and its minor equivalent root-minor third-major ninth (J-Lb-K in Kentaku notation) may be considered equivalents of root-third-fifth chords in diatonic music. Archeotonic scales have 6 such triads, 5 "major" and 1 "minor". The 11th and 13th harmonics are also plentiful, as already noted by Cryptic Ruse; 4 roots have the 11th harmonic over them and 4 roots have the 13th harmonic over them. | ||
The chord spelled root-major third-major fourth-minor sixth in archeotonic nomenclature occurs twice in archeotonic and I call it The Beloved Extra Special | The chord spelled root-major third-major fourth-minor sixth in archeotonic nomenclature occurs twice in archeotonic and I call it The Beloved Extra Special Tetrad (BEST). The reason it's beloved and extra special is that it can be interpreted both as an 8:10:11:13 and as a 13:16:18:21 (which can be revoiced as 8:9:13:21), thanks to the way 13edo conflates higher-limit JI intervals together. | ||
Archeotonic offers fairly familiar-sounding chord progressions by major seconds, thirds, and (both major and minor) fourths. One example is root-major third-two major thirds-root (spelled J major - L major - N# major - J major in J Ryonian), where the (two major thirds) is a 21/16 minor fourth away from the root. | Archeotonic offers fairly familiar-sounding chord progressions by major seconds, thirds, and (both major and minor) fourths. One example is root-major third-two major thirds-root (spelled J major - L major - N# major - J major in J Ryonian), where the (two major thirds) is a 21/16 minor fourth away from the root. | ||
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Minor tritones (approximating 11/8) work like tritones and they like to resolve inward to a third. Major tritones (16/11) are the opposite: they like to resolve outward to a sixth. Unlike in 12edo, fourths and tritones, and their octave inversions are very different in quality. Minor fourths and minor tritones are more consonant than their inversions major tritones and major fifths; they can also both be spread out to make them more consonant, whereas their inversions cannot. | Minor tritones (approximating 11/8) work like tritones and they like to resolve inward to a third. Major tritones (16/11) are the opposite: they like to resolve outward to a sixth. Unlike in 12edo, fourths and tritones, and their octave inversions are very different in quality. Minor fourths and minor tritones are more consonant than their inversions major tritones and major fifths; they can also both be spread out to make them more consonant, whereas their inversions cannot. | ||
The diminished fourth can work either like the diatonic diminished fourth, or (uniquely in 13edo among all oneirotonic tunings) serve as an extra 5/4 in the scale and can be part of extra consonant chords (such as the aforementioned | The diminished fourth can work either like the diatonic diminished fourth, or (uniquely in 13edo among all oneirotonic tunings) serve as an extra 5/4 in the scale and can be part of extra consonant chords (such as the aforementioned BEST that represents both 8:10:11:13 and 13:16:18:21, which occurs as O-J-K-M in J Ilarnekian, but it only represents 13:16:18:21 in other oneirotonic-supporting tunings such as [[31edo]]). | ||
Basic chord progressions can move by minor fourths or major seconds: J major-M minor-P minor-O major-J major (in Ilarnekian) or J major-K major-O# major-M major-J major (in Dylathian) | Basic chord progressions can move by minor fourths or major seconds: J major-M minor-P minor-O major-J major (in Ilarnekian) or J major-K major-O# major-M major-J major (in Dylathian) | ||
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#Sarnathian: 1 2 1 2 2 1 2 2 (diminished + natural minor) | #Sarnathian: 1 2 1 2 2 1 2 2 (diminished + natural minor) | ||
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 | 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). | Hlanithian also has the tetrad 8:13:17:21 on the tonic (in the 13edo tuning). | ||