Harmonic materials of modern music; resources of the tempered scale.

New York, Appleton-Century-Crofts [1960] .

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Subjects Harmonie.
Intervallen (muziek)
Musical intervals and scales.
Musique -- Intervalles et gammes.
Stemmingen (muziek)
Description 381 pages illustrations 24 cm
Copyright Date [1960]
Contents 1. Equal temperament -- 2. The analysis of intervals -- 3. The theory of involution
I. The six basic tonal series : 4. Projection of the perfect fifth -- 5. Harmonic-melodic material of the perfect-fifth hexad -- 6. Modal modulation -- 7. Key modulation -- 8. Projection of the minor second -- 9. Projection of the major second -- 10. Projection of the major second beyond the six-tone series -- 11. Projection of the minor third -- 12. Involution of the six-tone minor-third projection -- 13. Projection of the minor third beyond the six-tone series -- 14. Projection of the major third -- 15. Projection of the major third beyond the six-tone series -- 16. Recapitulation of the triad forms -- 17. Projection of the tritone -- 18. Projection of the perfect-fifth -- tritone series beyond six tones -- 19. The pmn-tritone projection -- 20. Involution of the pmn-tritone projection -- 21. Recapitulation of the tetrad forms
II. Construction of hexads by the superposition of forms : 22. Projection of the triad pmn -- 23. Projection of the triad pns -- 24. Projection of the triad pmd -- 25. Projection of the triad mnd -- 26. Projection of the triad nsd
III. Six-tone scales formed by the simultaneous projection of two intervals : 27. Simultaneous projection of the minor third and perfect fifth -- 28. Simultaneous projection of the minor third and major third -- 29. Simultaneous projection of the minor third and major second -- 30. Simultaneous projection of the minor third and minor second -- 31. Simultaneous projection of the perfect fifth and major third -- 32. Simultaneous projection of the major third and minor second -- 33. Simultaneous projection of the perfect fifth and minor second
IV. Projection by involution and at foreign intervals : 34. Projection by involution -- 35. Major-second hexads with foreign tone -- 36. Projection of triads at foreign intervals -- 37. Recapitulation of pentad forms
V. The theory of complementary sonorities : 38. The complementary hexad -- 39. The hexad "quartets"
VI. Complementary scales : 40. Expansion of the complementary-scale theory -- 41. Projection of the six basic series with their complementary sonorities -- 42. Projection of the triad forms with their complementary sonorities -- 43. The pmn-tritone projection with its complementary sonorities -- 44. Projection of two similar intervals at a foreign interval with complementary sonorities -- 45. Simultaneous projection of intervals with their complementary sonorities -- 46. Projection by involution with complementary sonorities -- 47. The "maverick" sonority -- 48. Vertical projection by involution and complementary relationship -- 49. Relationship of tones in equal temperament -- 50. Translation of symbolism into sound
Network Numbers (OCoLC)397635
WorldCat Search OCLC WorldCat
WorldCat Identities Hanson, Howard, 1896-1981.
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