(2009), p.57 1) 2) 3) 4) (2004), p ) (1989), p.128 6) 12 2 (1989), p.122 7) ) 2) (1989), p ) 4) 5) 8 12 (1989), p.

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1 41, 1, The estimate of 12-tone temperament in Japan by the application of basic statistics methods Akedo Shin-ya % 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 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 Hz 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 ( akedo

2 (2009), p.57 1) 2) 3) 4) (2004), p ) (1989), p.128 6) 12 2 (1989), p.122 7) ) 2) (1989), p ) 4) 5) 8 12 (1989), p.121 6) (1989), p.173

3 ) 3/2 3/4 3/2 3/4 3/2 3/4 3/4 3/2 3/4 3/2 3/4 (1982), p /2 4 3/4 1 3/ /2 4 4/ ) (1989), p.131 (1956), p )

4 /2 4 3/ / /3 5 4/ / ) (1989), p.122 (2000), p (1989), p /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

5 27 1 4/ (1982), p

6 ) 1 (1989), p (1982), p ) 12) ) 10) 11) 12) (1989), p ) (1982), p.168

7 29 (1989), p (1990), p m n m-n (2001), p

8 ) (1951), p ) 16) ) (1987), p.193 (1989), p (1951), p (1981), p ) 15) 16) 17)

9 31 1 [cents] [cents] [Hz] 1 [Hz] 1 D C D C B A B A G A G F G F E D E D f 0 f log 2 (f 1 /f 0 ) f 2 2f 2 2f 2 4f 2 f 2 2f 2 f 2 2f 2 4f 2 2f ) 13 (1982), p )

10 ) 2 20) 21) (1987), p ) (1981), p.24 (1956), p Hz (1951), p (1956), p (1951), p ) 20) 1870 (1989), p ) 1880 (1989), p ) (1981), p.24

11 Hz Hz (1951), p Hz 4.8 Hz Hz 0.2 Hz A 10 Hz 430 Hz Hz (1981), p % Hz (1956), p ) (1966), p Hz (1981), p Hz (1951), p (1989), p ) 12 (1989), p.327

12 Hz 5 2/ Hz % Hz Hz 3.2 (1984), p (1951), p /2 4 3/4 4 4/3 (1989), p / Hz Hz Hz Hz (1951), p Hz % 3.8 ± % Hz [289.1, 292.4] 24) Hz Hz 95% 24) Hz % Hz Hz 95%

13 35 95% Hz 95% Hz Hz Hz Hz Hz ) (1989), p (1986), p )

14 ) (1982), p (1951), p A B (1987), p.194 A B (1987), p Hz Hz A B A B 8 (1987), p.193 A A 12 2 A A B B Hz A A B B I A B A B II I 6 0 II I II 3 I 0 4 I 0 1/4 6 I II Levene p A A B B B 26)

15 37 2 [Hz] Hz [cents] A B A B A B A B B A A A A B B III IV Welch t p III A A 0 A A 4.0 IV A A % 0.4 ± % Hz [291.0, 291.8] Hz Hz 95% 95% Hz 95% Hz A Hz A Hz A Hz % 0.1 ± % 95%

16 Hz Hz A Hz A 6.5 A Hz A B Hz Hz 27) 28) mm 80mm (1980), p (1927), p ± 0.5 Hz (1910), p ± Hz Hz Hz 27) (1989), p ) : p. 328

17 A Hz Welch t p A Hz 3.9 Welch t p Hz m-n (1986), p.70 2 x 2 y xy 1 xy 5 x 2 = 2 x 90.2 (2001), p /2 3/4 3/2 3 4/3 4/3 2/3 4/3 2/3 4/3 4/3

18 /3 8 29) ) (1989), p (1984), p (1989), p ) 13 2 (1973), p ) F (2001), p ) 50 (1989), p ) (1989), p.735

19 41 (1973), p (1989), p ) 4 (1984), p (1989), p (1984), p ) (1989), p.732

20 (1989), p.128 (1989), p (1989), p.102 (1989), p (1989), p (1989), p ) ) 33) 34) 3 ( )

21 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/ ) (2005), A1 A2 35) 1872 (2010), p

22 ) (1982), p (2009), p (2001), p (1985), p (1956), p (2009), p Hz 36) (1982), p.218

23 B B B A A A B B B B B B A B A 9 B Hz

24 Levene p % Tukey-Kramer HSD (1987), p.193 2

25 Hz ) 37)

26 Hz % % 1.1 ± 2.5 A Hz Hz % 1.2 ± % Hz [290.7, 291.6] Hz 95% % Hz Hz 437 Hz 1981: ) Hz / Hz 38) 95%

27 [cents] [cents] [cents] [Hz] 1 [Hz] 1 [Hz] ) Hz Hz Hz 6. 39) 220 (1989), p

28 ) A J (1951). (2009). 11(1), (2000). (1986). (2001). 42(3), (1985). 2 (1956) , 1 14,. (1973). (1989). (1989). 39 (1966). 2 (1982). 54 (1999). (2004). (1989) (1990). 1 (1981). (1910). 344, (1956). (1982). (2005) , A1 A29. (1987). (1989). (1982). (1984). (1980). 23, 71 73,. (1927). 7(9), 16 18,. (2010). 40) 437 Hz A 440 Hz A

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