Path-based goodness: Difference between revisions
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Path-based goodness can also be calculated for scales without JI interpretations; we assign to each note and just interval a tempered interval rooted on that note, and compute the goodness of the best assignment. | Path-based goodness can also be calculated for scales without JI interpretations; we assign to each note and just interval a tempered interval rooted on that note, and compute the goodness of the best assignment. | ||
=== Path-based goodnesses and octave stretches for the equal temperaments 7-41: === | |||
1. 41et: goodness 30.8. 2: 0.10. score <3, <6: 3.9%, 11.5% | |||
2. 31et: goodness 28.2. 2: 0.33. score <3, <6: 4.2%, 13.0% | |||
3. 34et: goodness 26.0. 2: -1.06. score <3, <6: 4.6%, 13.9% | |||
4. 36et: goodness 26.0. 2: 0.44. score <3, <6: 4.5%, 13.2% | |||
5. 37et: goodness 24.3. 2: -0.68. score <3, <6: 4.6%, 13.0% | |||
6. 38et: goodness 23.3. 2: 2.26. score <3, <6: 4.8%, 13.6% which is likely easy to navigate due to sharing features with 19edo | |||
7. 24et: goodness 22.8. 2: 0.03. score <3, <6: 4.9%, 15.3% | |||
8. 29et: goodness 22.8. 2: 2.45. score <3, <6: 4.6%, 14.0% Note that in the 13-limit, 29et is identical to 58et on the 2.3.7/5.11/5.13/5 subgroup | |||
9. 40et: goodness 22.7. 2: 1.51. score <3, <6: 4.4%, 12.4% which is likely easy to navigate due to supporting orwell and diminished | |||
10. 22et: goodness 22.5. 2: -0.51. score <3, <6: 4.8%, 15.1% | |||
11. 26et: goodness 22.4. 2: 2.57. score <3, <6: 4.5%, 15.0% | |||
12. 27et: goodness 22.4. 2: -2.56. score <3, <6: 5.0%, 14.4% | |||
13. 19et: goodness 21.5. 2: 3.75. score <3, <6: 5.5%, 17.7% | |||
14. 32et: goodness 20.2. 2: -0.45. score <3, <6: 4.9%, 14.3% which is likely easy to navigate due to supporting pajara | |||
15. 39et: goodness 20.1. 2: -1.63. score <3, <6: 5.6%, 14.4% | |||
16. 33et: goodness 19.2. 2: -0.02. score <3, <6: 4.9%, 13.3% somewhat surprisingly | |||
17. 35et: goodness 18.7. 2: 1.97. score <3, <6: 5.2%, 14.7% | |||
18. 17et: goodness 17.4. 2: -2.42. score <3, <6: 7.1%, 21.4% | |||
19. 30et: goodness 16.9. 2: -2.47. score <3, <6: 5.4%, 14.8% which shares many features with 15et and lands close to it in badness | |||
20. 28et: goodness 16.7. 2: -0.05. score <3, <6: 6.5%, 16.8% | |||
21. 21et: goodness 16.5. 2: -0.21. score <3, <6: 5.8%, 17.6% | |||
22. 12et: goodness 16.3. 2: 0.35. score <3, <6: 8.7%, 28.2% octave-stretched for an even worse 5/1 because it was never that good anyway | |||
23. 25et: goodness 15.9. 2: 0.90. score <3, <6: 7.2%, 19.0% | |||
24. 15et: goodness 15.8. 2: -3.91. score <3, <6: 5.9%, 19.6% | |||
25. 20et: goodness 14.7. 2: 1.79. score <3, <6: 6.3%, 16.2% | |||
26. 16et: goodness 14.6. 2: 4.64. score <3, <6: 6.3%, 18.1% | |||
27. 14et: goodness 12.6. 2: 9.46. score <3, <6: 8.2%, 21.3% near 22edt even though we're using the wrong mapping for prime 5, thus ignoring it | |||
28. 10et: goodness 12.6. 2: 3.35. score <3, <6: 6.7%, 15.6% | |||
29. 23et: goodness 12.0. 2: 0.03. score <3, <6: 9.2%, 21.7% | |||
30. 18et: goodness 11.4. 2: 1.48. score <3, <6: 8.4%, 18.0% | |||
31. 13et: goodness 9.8. 2: 4.95. score <3, <6: 9.2%, 26.7% | |||
32. 9et: goodness 9.7. 2: -0.26. score <3, <6: 13.1%, 38.8% | |||
33. 7et: goodness 8.6. 2: 10.80. score <3, <6: 12.1%, 38.2% near 11edt | |||
34. 8et: goodness 6.9. 2: -0.07. score <3, <6: 21.9%, 71.7% | |||
35. 11et: goodness 6.9. 2: -0.28. score <3, <6: 21.9%, 83.5% | |||