41, 1, 2011 9 23 50 The estimate of 12-tone temperament in Japan by the application of basic statistics methods Akedo Shin-ya 1884 3 95% 291.333 Hz In China and Japan, the musical pitches have each meaning. Ancient people made the 12-tone temperament correspond to the signs of the zodiac in Chinese and the names of the months. Therefore the distinction of the names of musical pitches is important, but the theoretical values of the frequencies are not clarified. On the other hand, Alexander Ellis measured the frequencies of three tuning fork groups that contain the group to show 12-tone temperament of Japanese music in 1884. In this article, I scanned the theoretical values of two pentatonic scales and the measured values by Ellis, and concluded that the frequency of former standard sound was 291.333Hz in Japan. In addition, I clarified the 12-tone temperament of Japanese court music by scanning the tuning methods of the musical instruments. Based on these, I judged that 12-tone temperament of Japanese music was the 12-tone temperament that integrated true Japanese court music with Japanese traditional popular music. :. 1. (2009), p.49 56 (E-mail: akedo shinya@yahoo.co.jp).
24 41 1 2011 (2009), p.57 1) 2) 3) 4) (2004), p.46 47 5) (1989), p.128 6) 12 2 (1989), p.122 7) 2 3 4 1) 2) (1989), p.124 125 3) 4) 5) 8 12 (1989), p.121 6) (1989), p.173
25 5 2. 2.1 5 4 12 2.1.1 4 239 735 8) 3/2 3/4 3/2 3/4 3/2 3/4 3/4 3/2 3/4 3/2 3/4 (1982), p.167 173 5 3/2 4 3/4 1 3/2 2 2.027 23.5 1 2 1 5 4 1 5 3/2 4 4/3 1 2 7) 1394 1428 1504 1521 (1989), p.131 (1956), p.8 14 8)
26 41 1 2011 5 3/2 4 3/4 6 3 12 /2 18 23.5 23.5 1 2 2/3 5 4/3 4 23.5 2/3 5 23.5 11 23.5 9) 447 24 1584 2.1.2 6 (1989), p.122 (2000), p.179 180 (1989), p.122 4 5 3/2 3/4 3/2 3/4 3/2 3/4 3/4 3/2 3/4 3/2 3/4 4/3 4/3 2/3 4/3 2/3 4/3 4/3 2/3 4/3 2/3 9) 2 12
27 1 4/3 23.5 (1982), p.167 173 4 5 1664
28 41 1 2011 10) 1 (1989), p.202 203 (1982), p.141 142 2 1 1 1 1 2 8 3 4 4 2 3 5 11) 12) 1 8 4 5 5 4 4 5 13) 10) 11) 12) (1989), p.109 13) 1996 12 2 4 5 8 (1982), p.168
29 (1989), p.112 6 2 5 5 23.5 23.5 1692 5 (1990), p.7 9 1584 735 12 m n m-n 11 11-0 4.1 (2001), p.642 649 3-8 12 4.2
30 41 1 2011 2.2 2.2.1 1884 14) (1951), p.181 205 15) 16) 1885 3 17) 4 8 13 (1987), p.193 (1989), p.86 4.3 2.2.2 1 (1951), p.200 201 (1981), p.24 1 2 1 1 14) 15) 16) 17)
31 1 [cents] [cents] [Hz] 1 [Hz] 1 D 585.4 109.6 1200.0 573.33 113.7 1200.0 C D 549.5 104.5 1090.4 536.89 90.2 1086.3 C 517.3 88.6 985.9 509.63 90.2 996.1 B 491.5 113.5 897.3 483.75 113.7 905.9 A B 460.3 89.9 783.8 453.00 90.2 792.2 A 437.0 110.0 693.9 430.00 113.7 702.0 G A 410.1 80.4 583.9 402.67 90.2 588.3 G 391.5 118.0 503.5 382.22 90.2 498.0 F G 365.7 110.4 385.5 362.81 113.7 407.8 F 343.1 87.4 275.0 339.75 90.2 294.1 E 326.2 112.9 187.6 322.50 113.7 203.9 D E 305.6 74.7 74.7 302.00 90.2 90.2 D 292.7 0 286.67 0 f 0 f 1 1200 log 2 (f 1 /f 0 ) 2 1 1200 f 2 2f 2 2f 2 4f 2 f 2 2f 2 f 2 2f 2 4f 2 2f 2 1 7 18) 13 (1982), p.129 7 13 7 4 10 13 10 16 18)
32 41 1 2011 19) 2 20) 21) (1987), p.193 7 4 10 13 10 16 2.2.3 4-7 22) (1981), p.24 (1956), p.67 70 4-7 4-7 292.7 Hz (1951), p.200 201 4 7 (1956), p.67 70 (1951), p.197 201 19) 20) 1870 (1989), p.657 21) 1880 (1989), p.759 22) (1981), p.24
33 292.7 Hz 2 3-8 2 365.7 Hz (1951), p.200 201 370.5 Hz 4.8 Hz 365.5 Hz 0.2 Hz A 10 Hz 430 Hz 286.67 Hz (1981), p.24 4 5 3. 95% 3.1 2 292.7 Hz (1956), p.67 70 23) 12 7 735 4 26 (1966), p.137 437 Hz (1981), p.23 437.0 Hz (1951), p.200 201 (1989), p.122 11 23) 12 (1989), p.327
34 41 1 2011 437 Hz 5 2/3 3 291.333 Hz 11 3 2 2 95% 1 1 1 291.333 Hz 8.1 292.7 Hz 3.2 (1984), p.263 264 3.2.1 (1951), p.204 205 1/2 4 3/4 4 4/3 (1989), p.121 122 5 3/2 3.2.2 162.9 Hz 246.3 Hz 326.4 Hz 436.7 Hz (1951), p.204 205 291.333 Hz 4 3.8 3.1 95% 3.8 ± 9.8 95% 291.333 Hz [289.1, 292.4] 24) 291.333 Hz 292.7 Hz 95% 24) 292.7 Hz 8.1 8.1 95% 291.333 Hz 292.7 Hz 95%
35 95% 291.333 Hz 95% 292.7 Hz 291.333 Hz 10.3 13 10 16 292.7 Hz 18.4 13 10 16 291.333 Hz 292.7 Hz 3.3 25) (1989), p.280 3.3.1 5 4 2 2 5 (1986), p.76 2 2 1 4 25)
36 41 1 2011 5 1895 5 70 100 26) (1982), p.236 242 2 (1951), p.202 204 90.2 3.3.2 2 2 A B (1987), p.194 A B (1987), p.194 291.333 Hz 291.333 Hz A B A B 8 (1987), p.193 A A 12 2 A A B B 3 291.333 Hz A A B B I A B A B II I 6 0 II 1.8 0.6 0.8 2 I II 3 I 0 4 I 0 1/4 6 I II Levene p 0.001 8 A A B B B 26)
37 2 [Hz] 291.333 Hz [cents] A B A B A B A B 582.4 581.8 582.4 581.8 1200.0 1199.2 1197.4 1199.2 1197.4 465.1 464.9 459.8 460.6 792.2 809.8 809.1 790.0 793.0 437.9 438.1 437.9 438.1 702.0 705.5 706.3 705.5 706.3 389.0 389.4 389.9 389.4 498.0 500.5 502.3 504.5 502.3 309.0 309.0 306.0 306.0 90.2 101.9 101.9 85.0 85.0 291.5 291.4 291.5 291.4 0 1.0 0.4 1.0 0.4 B A A 389.0 389.9 0 9 A A B B III IV Welch t p 0.001 III A A 0 A A 4.0 IV 17.4 21.4 13 10 16 A A 12 0.4 1.1 95% 0.4 ± 2.4 4.8 95% 291.333 Hz [291.0, 291.8] 291.333 Hz 292.7 Hz 95% 95% 291.333 Hz 95% 292.7 Hz A 389.9 Hz A 389.0 Hz A 389.0 Hz 12 0.1 1.0 95% 0.1 ± 2.1 4.2 95% 95% 4.8 4.2 7 4 10 4
38 41 1 2011 291.333 Hz 2 291.333 Hz A 389.9 Hz A 6.5 A 389.0 Hz A B 5.2 7 4 10 291.333 Hz 291.333 Hz 27) 28) 11 15 13mm 80mm (1980), p.73 4 11 11 3 5 (1927), p.17 18 11 582 ± 0.5 Hz (1910), p.233 235 ±1.5 1 291 Hz 291.333 Hz 2 3.5 7 4 10 291.333 Hz 27) (1989), p.744 28) 1 1989 : p. 328
39 3.4 3.2 3.3 A 389.9 Hz 4.2 7 4 10 Welch t p 0.267 A 389.0 Hz 3.9 Welch t p 0.298 2 291.333 Hz 4. 2 5 4 m-n 4.1 1 8 5 4 2 (1986), p.70 2 x 2 y xy 1 xy 5 x 2 = 2 x 90.2 (2001), p.644 649 3/2 3/4 3/2 3 4/3 4/3 2/3 4/3 2/3 4/3 4/3
40 41 1 2011 2/3 8 29) 3-8 4.2 2.1.2 11 30) 1690 3 (1989), p.125 2.1.2 (1984), p.350 351 5 7 (1989), p.105 106 3 1192 3 31) 13 2 (1973), p.208 216 29) F (2001), p.645 30) 50 (1989), p.591 31) (1989), p.735
41 (1973), p.208 216 (1989), p.121 122 4 3 32) 4 (1984), p.263 284 (1989), p.127 128 5 20 6 4 (1984), p.529 531 32) (1989), p.732
42 41 1 2011 8 3 4 3 (1989), p.128 (1989), p.321 322 (1989), p.102 (1989), p.321 322 (1989), p.321 322 (1989), p.338 339 1 33) 3 3 3 34) 33) 34) 3 ( )
43 3 ( ) 3 3/2 3/4 3/2 3/4 3/2 3/4 6 4/3 4/3 2/3 4/3 2/3 5 6-5 4-7 3 4.3 4.3.1 35) (2005), A1 A2 35) 1872 (2010), p.124 125
44 41 1 2011 5 4 112 204 386 36) (1982), p.218 4.3.2 2.2.1 3 5 3 18 (2009), p.238 242 4.1 (2001), p.646 648 3 9 2 (1985), p.140 142 (1956), p.60 6 8 (2009), p.238 242 5-6 5-6 2.1 12 12 291.333 Hz 36) 112 3.3 90.2 102.4 386 407.8 (1982), p.218
45 4 0-11 16.1 2.9 1351.0 B 1-10 5.6 2.7 1104.1 B 2-9 3.8 2.7 1157.6 B 3-8 2.0 2.2 761.6 A 4-7 0.2 2.4 928.0 A 5-6 1.6 2.4 869.8 A 6-5 3.5 2.7 1127.7 B 7-4 5.3 3.4 1823.4 B 8-3 7.1 3.7 2098.4 B 9-2 8.9 4.2 2790.3 B 10-1 10.7 4.4 2980.3 B 11-0 12.5 3.6 2351.0 B 13 4 4 0-11 1-10 0-11 1-10 12 7 4 10 13 10 16 13 10 16 13 10 16 A 13 10 16 B 4 3-8 4-7 5-6 3 3 A 9 B 291.333 Hz
46 41 1 2011 13 10 16 12 3-8 5-6 4-7 3 3 0 2.0 1.6 3 Levene p 0.989 5% Tukey-Kramer HSD 3 3 4-7 5 18 3-8 5-6 2 2 (1987), p.193 2
47 410.1 Hz 3.7 7 4 10 19.8 13 10 16 5-6 12 1 4.3.1 1 1200 1 1 1 1 1 2 8 3 4 4 2 3 5 37) 37)
48 41 1 2011 5. 3 4 3 291.333 Hz 5-6 95% 29 1.1 1.2 95% 1.1 ± 2.5 A 389.9 Hz 389.0 Hz 29 1.2 1.2 95% 1.2 ± 2.5 2 95% 291.333 Hz [290.7, 291.6] 291.333 Hz 95% 5 7 4 10 1 95% 291.333 Hz 291.333 Hz 437 Hz 1981: 23 1885 38) 291.333 Hz 4 5 2 1 2 1 2 3 / 291.333 Hz 38) 95%
49 5 6-5 3-8 5-6 [cents] [cents] [cents] [Hz] 1 [Hz] 1 [Hz] 1 582.67 90.2 1200.0 582.67 113.7 1200.0 582.67 90.2 1200.0 553.08 113.7 1109.8 545.63 90.2 1086.3 553.08 113.7 1109.8 517.93 90.2 996.1 517.93 90.2 996.1 517.93 90.2 996.1 491.62 113.7 905.9 491.62 113.7 905.9 491.62 113.7 905.9 460.38 90.2 792.2 460.38 90.2 792.2 460.38 90.2 792.2 437.00 90.2 702.0 437.00 113.7 702.0 437.00 113.7 702.0 414.81 113.7 611.7 409.22 90.2 588.3 409.22 90.2 588.3 388.44 90.2 498.0 388.44 113.7 498.0 388.44 90.2 498.0 368.72 113.7 407.8 363.76 90.2 388.4 368.72 113. 407.8 345.28 90.2 294.1 345.28 90.2 294.1 345.28 90.2 294.1 327.75 113.7 203.9 327.75 113.7 203.9 327.75 113.7 203.9 306.92 90.2 90.2 306.92 90.2 90.2 306.92 90.2 90.2 291.33 0 291.33 0 291.33 0 23 39) 291.333 Hz 291.333 Hz 292.7 Hz 6. 39) 220 (1989), p.290 291 1
50 41 1 2011 40) A J (1951). (2009). 11(1), 49 58. (2000). (1986). (2001). 42(3), 642 649. (1985). 2 (1956). 43 44, 1 14,. (1973). (1989). (1989). 39 (1966). 2 (1982). 54 (1999). (2004). (1989). 183 204 (1990). 1 (1981). (1910). 344, 230 236. (1956). (1982). (2005). 1884 24, A1 A29. (1987). (1989). (1982). (1984). (1980). 23, 71 73,. (1927). 7(9), 16 18,. (2010). 40) 437 Hz A 440 Hz 11.8 13 10 16 A