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. | ||
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; 300 and beyond | ; 300 and beyond | ||
* [[314edt|314]], [[316edt|316]], [[336edt|336]], [[372edt|372]], [[415edt|415]], [[499edt|499]], [[527edt|527]], [[613edt|613]], [[729edt|729]], [[800edt|800]], [[953edt|953]], [[1213edt|1213]], [[1342edt|1342]], [[3401edt|3401]], [[6181edt|6181]], [[27208edt|27208]] | * [[314edt|314]], [[316edt|316]], [[336edt|336]], [[372edt|372]], [[415edt|415]], [[428edt|428]], [[499edt|499]], [[527edt|527]], [[613edt|613]], [[729edt|729]], [[800edt|800]], [[953edt|953]], [[1213edt|1213]], [[1342edt|1342]], [[3401edt|3401]], [[6181edt|6181]], [[27208edt|27208]] | ||
* A [[list of tritave reduced harmonics]] for easy comparison of JI and temperaments in tritave-based systems. | * A [[list of tritave reduced harmonics]] for easy comparison of JI and temperaments in tritave-based systems. | ||
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* [[Consistency levels of small EDTs]] | * [[Consistency levels of small EDTs]] | ||
* [[Relative errors of small EDTs]] | * [[Relative errors of small EDTs]] | ||
* [[ | * [[List of tritave reduced harmonics]] | ||
* [[List of no-twos chords in JI]] | * [[List of no-twos chords in JI]] | ||
* Heinz Bohlen's work: [http://www.huygens-fokker.org/bpsite/otherscales.html ''The Bohlen-Pierce Site: Other Unusual Scales''] | * Heinz Bohlen's work: [http://www.huygens-fokker.org/bpsite/otherscales.html ''The Bohlen-Pierce Site: Other Unusual Scales''] | ||
[[Category:Edt| ]] <!-- main article --> | [[Category:Edt| ]] <!-- main article --> | ||
[[Category:Tritave]] | [[Category:Tritave]] | ||
[[Category:Acronyms]] | [[Category:Acronyms]] | ||