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

Author: Howard Hanson
Publisher: New York, Appleton-Century-Crofts [1960]
Edition/Format:   Book : EnglishView all editions and formats
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Additional Physical Format: Online version:
Hanson, Howard, 1896-1981.
Harmonic materials of modern music.
New York, Appleton-Century-Crofts [1960]
(OCoLC)654477103
Document Type: Book
All Authors / Contributors: Howard Hanson
OCLC Number: 397635
Description: 381 pages illustrations 24 cm
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

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schema:description"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"@en
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