Sorry, no online dictionaries contain the exact phrase harmonic cross-ratio.
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Reverse dictionary results:
1. inverse ratio
 2. reciprocal ratio
3. uncrossed ratio
4. anharmonic
5. anticipation
6. cadence
7. chord
8. chordal
9. euphonic
10. first harmonic
 11. fundamental
12. fundamental frequency
13. glide
14. harmonical
15. harmonically
16. harmonics
17. harmony
18. key
19. mixture
20. music
 21. nonharmonic
22. octave
23. overtone
24. partial
25. pitch
26. polyphonic
27. proportion
28. proportioned
29. proportions
30. second
 31. seconds
32. slide
33. tonal
34. unison
35. auxiliary note
36. bop
37. bugle
38. cadenced
39. cadences
40. center

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You can look up the words in the phrase individually using these links:   harmonic ?   cross-ratio ?
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