User:FloraC/Fokker analysis of rank-3 scales: Difference between revisions

Paradigm Shift: clarification based on feedback
mNo edit summary
Line 126: Line 126:
<math>\displaystyle C_\text{r} = 135/128, C_\text{d} = 81/80</math>
<math>\displaystyle C_\text{r} = 135/128, C_\text{d} = 81/80</math>


It is the same as Aura's diatonic scale. Therefore, we find
It is the same as bilawal. Therefore, we find


<math>\displaystyle L = 9/8, l = 10/9, S = 16/15, s = 256/243</math>
<math>\displaystyle L = 9/8, l = 10/9, S = 16/15, s = 256/243</math>
Line 242: Line 242:
|}
|}


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 chromas ''C''<sub>r</sub> = 800/729 and ''C''<sub>d</sub> = 256/243. In the 5-steps, they are 27/20, 45/32, 64/45, 40/27. This corresponds to a different set of chromas: ''C''<sub>r</sub> = 256/243 and ''C''<sub>d</sub> = 25/24. No Fokker block has different set of chromas.  
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 chromas ''C''<sub>r</sub> = 800/729 and ''C''<sub>d</sub> = 256/243. In the 5-steps, they are 27/20, 45/32, 64/45, 40/27. This corresponds to a different set of chromas: ''C''<sub>r</sub> = 256/243 and ''C''<sub>d</sub> = 25/24. No Fokker block has different sets of chromas.  


Indeed, blackdye cannot be decomposed into the product word of two mosses.  
Indeed, blackdye cannot be decomposed into the product word of two mosses.