EDT: Difference between revisions
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== Rank two temperaments == | == Rank two temperaments == | ||
{{Todo|cleanup|inline=1|text=Rewrite for clarity}} | {{Todo|cleanup|improve readability|inline=1|text=Rewrite for clarity}} | ||
If factors of two are eliminated, the search for consonant intervals begins with the odd harmonic series, 1:3:5:7:9:.... We can take the second tritave of the series, 3:5:7:9, and find within it the two [[isoharmonic]] triads 3:5:7 and 5:7:9; the analogy here is with the third octave of the full harmonic series, 4:5:6:7:8, and the isoharmonic triad 4:5:6, the foundation of triadic harmony in [[5-limit]] theory. Hence, 3:5:7 or 5:7:9 can be viewed as the fundamental consonant triad of no-twos music, and if we then apply the 5-limit analogy one more time, these triads are bounded by the intervals [[7/3]] or [[9/5]] respectively, either of them filling the role of the "fifth" in diatonicism. | If factors of two are eliminated, the search for consonant intervals begins with the odd harmonic series, 1:3:5:7:9:.... We can take the second tritave of the series, 3:5:7:9, and find within it the two [[isoharmonic]] triads 3:5:7 and 5:7:9; the analogy here is with the third octave of the full harmonic series, 4:5:6:7:8, and the isoharmonic triad 4:5:6, the foundation of triadic harmony in [[5-limit]] theory. Hence, 3:5:7 or 5:7:9 can be viewed as the fundamental consonant triad of no-twos music, and if we then apply the 5-limit analogy one more time, these triads are bounded by the intervals [[7/3]] or [[9/5]] respectively, either of them filling the role of the "fifth" in diatonicism. | ||