User:FloraC/Fokker analysis of rank-3 scales: Difference between revisions
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=== Example 1: Bilawal === | === Example 1: Bilawal === | ||
The bilawal scale is Aura's preferred diatonic scale. It is a very typical rank-3 Fokker block. The steps are: | The bilawal scale is Aura's preferred variant of diatonic scale. It is a very typical rank-3 Fokker block. The steps are: | ||
<pre>9/8, 5/4, 4/3, 3/2, 27/16, 15/8, 2/1</pre> | <pre>9/8, 5/4, 4/3, 3/2, 27/16, 15/8, 2/1</pre> | ||
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=== Example 4: Blackdye === | === Example 4: Blackdye === | ||
Finally, as a counterexmaple, blackdye is ''not'' a Fokker block. Here we try analysing the 5-limit JI tuning of blackdye. The steps are: | Finally, as a counterexmaple, blackdye is ''not'' a rank-3 Fokker block. Here we try analysing the 5-limit JI tuning of blackdye. The steps are: | ||
<pre>81/80, 9/8, 6/5, 4/3, 27/20, 3/2, 8/5, 16/9, 9/5, 2/1</pre> | <pre>81/80, 9/8, 6/5, 4/3, 27/20, 3/2, 8/5, 16/9, 9/5, 2/1</pre> | ||
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However, the step size relations do not satisfy the property of rank-3 Fokker blocks. Specifically, the 3-steps are 729/640, 6/5, 5/4 and 320/243, and we have (6/5)/(729/640) = (320/243)/(5/4). Therefore, we find the | However, the step size relations do not satisfy the property of rank-3 Fokker blocks. Specifically, the 3-steps are 729/640, 6/5, 5/4 and 320/243, and we have (6/5)/(729/640) = (320/243)/(5/4). Therefore, we find the chroma basis composed of ''C''<sub>r</sub> = 800/729 and ''C''<sub>d</sub> = 256/243. Meanwhile, the 5-steps are 27/20, 45/32, 64/45, 40/27. This corresponds to a different chroma basis: ''C''<sub>r</sub> = 256/243 and ''C''<sub>d</sub> = 25/24. No Fokker block has different chroma bases. | ||
Indeed, blackdye cannot be decomposed into the product word of two mosses. | Indeed, blackdye cannot be decomposed into the product word of two mosses. | ||
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© 2022 Flora Canou | © 2022 Flora Canou | ||
Version Stable | Version Stable 2 | ||
This work is licensed under the [https://creativecommons.org/licenses/by-sa/4.0/ Creative Commons Attribution-ShareAlike 4.0 International License]. | This work is licensed under the [https://creativecommons.org/licenses/by-sa/4.0/ Creative Commons Attribution-ShareAlike 4.0 International License]. | ||