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01. A (standed tone)¼Ð·Ç­µ=440 Hz
02. D ¤UÄÝ­µ(¤U5«×) ¡@ ¡@=293.33 Hz= -2cent
03. E ¤WÄÝ­µ(¤W5«×) ¡@¡@ =330 Hz= 2cent
04. #F ¤p¤¤­µ(A¤p3«×) ¡@ =366.66 Hz=-16cent
05. #C ¤W¤¤­µ(A¤j3«×) ¡@ =275 Hz=-14cent
06. F ¤U¤¤­µ(A¤j3«×) ¡@¡@ =352 Hz= 14cent
07. C ¤W¤p¤¤­µ(A¤p3«×)¡@¡@=264 Hz= 16cent
(Hz=cent?
·í¬O¡G
bE bB F C G D A E B #F #C #G
Hz 312.89 469.33 352 264 396 293.33 440 330 495 366.66 352 412.50
cent 10 12 14 16 18 -2 0 2 4 -16 -14 -12
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08. G C¤WÄÝ­µ(¤W5«×) =396 Hz= 18cent
09. bB F¤UÄÝ­µ(¤U5«×) =469.33 Hz= 12cent
10. #G E¤W¤¤­µ(E¤j3«×) =412.50 Hz=-12cent
11. B E¤WÄÝ­µ(¤W5«×) =495 Hz= 4cent
12. bE bB¤UÄÝ­µ(¤U5«×) =312.89 Hz= 10cent
¹Ï¤@
D___________ A____________E
A¤§ ¥D­µ A¤§
¤UÄÝ­µ ¤WÄÝ­µ
sub dominant tonic up dominant
D=2/3xA ¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@E=3/2xA
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(up mediant)
#C=Ax5/4
¡@¡@¡@¡@¡@¡@¡@¡@¡@¡@¡þ
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D___________ A____________E
A¤§ ¥D­µ A¤§
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sub dominant tonic up dominant
A¤§¤U¤¤­µ¡]sub mediant¡^
F=Ax4/5
D___________ A____________E
A¤§ ¥D­µ A¤§
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A¤§
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small mediant
¹Ï¤T
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#F=371.25=6cent
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371.25Hz=6centªÌ
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=6centªÌ¡A·í¬ObD­µ¤è¬O§a!
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(©MG=396=18cent¤£¦Ü¬Û®t¤Ó¤j)
(396-371=25HZ
´X¥Gµ¥©ó¤@­Ó¥b­µ¤F
¡§¤£¦Ü¬Û®t¤Ó¤j¡¨ªÌ¡A¦ó·N§r?
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D¤j½Õ¯Â«ß
#F=366.66=-16cent (Mi)
(D¤j¤T©M²Í
#F=Dx5/4=293.33x5/4=366.66)

B=488.88 (La)
#D=305.55(#Do?)
B¤j½Õ¯Â«ß
#F=371.25= 6cent(So)«h
B=495
#D=309.38 (Si)
(B=495
«h#F=366.66=-16cent
«ç·|=371.25= 6cent©O?)

bB¤j½Õ¯Â«ß
F=352 «h
bB=469.33
=bB D F
(?)
bB¤j½Õ¯Â«ß
F=348.33«h
bB=464.44
=bB D F
(F=348.33ªx­µ¯Â«ß)
(?)
bB(¤j¤T)©M²Í¡JbB/D/F
=469.33/293.33/352
(§_!·í¬O=235/293.33/352!)
F(¤j¤T)©M²Í¡JF/A/C
=352/440/264
(§_!·í¬O=352/440/528!)
C(¤j¤T)©M²Í¡JC/E/G
=264/330/396
(¨SÀYµL§Àªº
³æ¦C¥X¥H¤W¼Æ¾Ú¦ó¬°§r?
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#C bE #F #G bB
278.44 312.89 371.25 417.66 464.44
8cent 10cent 6cent 10cent(?) 12cent
(§_!10cent«ç·|µ¥©óbE
¤Sµ¥©ó#G©O?
·í¬O¡J
bD bE bG bB
8cent 10cent 6cent 12cent
)

F C G D A E B
Hz -348.33(?) 264.00 391.88(?) 297.00(?) 440.00 330.00 495
cent 14 16 18 20 0 2 4
(§_!¦p¤W¤§©Ò­z,·í¬O¡J
F C G D A E B
Hz 352 264 396 293.33 440 330 495
cent 14 16 18 -2 0 2 4
)

F¤j½Õ¤£¥ÎG©M²Í.
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(2/4/6/1=G/B/D/F)
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(1/3/5=bB/D/F)
G7¬O§_©M¿Ó?
D/F¤w¬O©w¦n­µ
«hG=396Hz¬O¦ó­µ¤§ªx­µ?
F=352¤§²Ä9ªx­µ(?)
bB=469.33¤§²Ä27ªx­µ (???)
(¨SÀY¨S¸£!
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¤p´£µ^©w©¶ G3 D4 A4 E5
12¥­§¡«ß 196.00 293.66 440.00 659.26
5«×¬Û¥Í«ß 195.55 293.33 440.00 660.00
(¨â«ß­µ®t) -4cent -2cent 0cent 2cent
(­YµM!
§@ªÌ¦b¤W­±¦ó¥H¦Û¤v¤S»¡
G(bSi)¬O18 cent©O?
­ì¨Ó³o¸Ìªºcent
¬O12¥­§¡»P¤­«×«ß¨âªÌªº­µ®t
¦Ó«e­±©ÒÁ|ªºcent
«h¬°12¥­§¡»P¯Â«ß¨âªÌªº­µ®t
§@ªÌ«o¥uHz=Cent!
¦Ó§¹¥þ¥¼¥[¥Hµù¦W
¨º´NÅã±o¦Û»¡¦Û¸Ü¤F)

¹Ï¤».¤p´£µ^©w©¶¹Ï ¾A¦X G D A ¤j½Õ
(¡§¾A¦X(GDA¤j½Õ)¡¨ªÌ,¦ó·N§r?
¤p´£µ^¬O±Ä¤­«×«ßªº
¤p´£µ^©w©¶¬J¤]±Ä¤­«×«ß
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B3 #F4 #C5
244.44 366.66 550.00
-18cent -16cent -14cent
(«x!³o¤S¬O¥H¤°»ò«ß¨î¬°½×ªº©O?
ÎA¨Ì«eªí«h·í¬O
¤p´£µ^©w©¶ G3 D4 A4 E5 B5 #F6 #C7
12¥­§¡«ß 196.00 293.66 440.00 659.26
5«×¬Û¥Í«ß 195.55 293.33 440.00 660.00 495 366.66 704
(¨â«ß­µ®t) -4cent -2cent 0cent 2cent 4cent 6cent 8cent
¤~¹ï»ò!
«ç»ò¤S¥H¯Â«ß¬°½×¤F©O?)

G3 D4 A4 E5
195.55 293.33 440.00 660.00
-4cent -2cent -0cent 2cent
(¼H![:D]
¤S¦^¨ì¤­«×«ß¨Ó¤F
¤¤§¦b«e¥G²j¦b«á
¦p¦¹ªº¯«¥X°­¨S
¯u¯àÅý¤H¤£ª¾©Ò½×
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(¤@)¤p´£µ^D¤j½Õ¤­«×©w©¶¤§¯Â«ß­µ¶¥
(¤p´£µ^¬O±Ä¤­«×«ß
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§@ªÌ¯S¦b¦¹
¤Ï°Q½×°_¤p´£µ^ªº¡¨¯Â«ß­µ¶¥¡¨¨Ó
(¥B¬O¡¨D¤j½Õ¤­«×©w©¶¡¨)
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¥D ©M²ÍD=d /#f/ a
¤UÄÝ©M²ÍG=g /b/ d
¤WÄÝ©M²ÍA=a /#c/ e
§t¦³G D A ¥D©M²Í­µ
(§t¦³G D A ¥D©M²Í­µªÌ¡A
¦ó·N§r?)

D¤j½Õ¤p´£µ^
­µ ¦W -- C G D A E B #F #C
¤­«×«ß 260.74 391.11 293.33 440.00 330.00 488.89 366.66 275.00
»P¥­§¡«ß­µ®t -6 -4 -2 0 2 -18 -16 -14
(§_!¬J¬OD¤j½Õ
¦ó¶·°Q½×C(bSi)­µ©O?
¥B³oB¡B#F¡B#C¤T­µ
¤w¤£¬O¤­«×«ß
¦Ó¬O¯Â«ß
¦ýC(bSi)­µ
«o¤S¬O¤­«×«ß
¦Ó¤£¬O¯Â«ß)

1.do=D=293.33 -2cent
2.Re=E=330 2cent
3.Mi=#F=366.66 -16cent
4.Fa=G=391.11 -4cent
5.So=A=440
6.La=B=488.88 -18cent
7.Si=#C=275 -14cent
4 1 5 2 6 3 7 8
Fa Do So Re La Mi Si Fi?
bE bB F C G D A E B #F #C #G
10 12 -4 -2 0 2 -18 -16 -14 -12
(¤S¦^¨ì¯Â«ß¤F!
¦ý¤£ª¾¬°¦ó¦C¥X#G¡BbE¡BbB
«o¤S¯Ê¤FF¡BC?)

8.Fi=#G=412.5 -12cent
9.Di=#D=309.34 -10cent C D E F G A B
10.Li=#A=469.86 -8cent -6 -2 2 -8 -4 0 -18
11 F=347.65 -8cent
12 C=260.74 -6cent
(«z! F¡BC¡B©ó¥X²{¤F
¦ýbE¡BbB¤S¤£¨£¤F
«o¤S¶]¥XFi¡BDi¡BLi¨Ó!)

12¥­§¡«ß
C4=A4x2/3 x2/3 x2/3 x2=260.74 ¤ñ­È -6cent 261.63
#C5=A4x5/4=550
(#C4=275) ¤ñ­È -14cent 277.18 *
D4=A4x2/3=440x2/3=293.33 ¤ñ­È 9/8 -2cent 293.66
#D4=B3x5/4=244.44x5/4=305.55 ¤ñ­È -25cent 311.13
E5=A4x3/2=440x3/2=660
(E4=330) ¤ñ­È 2cent 329.63
F=C4x4/3=347.65 ¤ñ­È -8cent 369.99 *
G3=Ax2/3 x2/3=195.55
(G4=391.12) ¤ñ­È 3/2 -4cent 392.00
#G4=#C5x3/2=550x3/2=825
(#G4=412.50) -12cent 415.30
A4=440 ¤ñ­È 0 cent 440.00
#A4=#D4x3/2=305.55x3/2=458.33 ¤ñ­È -23cent 466.16
B3=G3x5/4=195.55x5/4=244.44
(B4=488.89) ¤ñ­È -18cent 493.89 *
F C G D A E B #F #C #G #D #A
-8 -6 -4 -2 0 2 -18 -16 -14 -12 -25 -23
___
(FC(b3¡BbSi)Äݤ­«×«ß
B¡B#F¡B#C¡B#G
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(¤Q)¤p´£µ^G¤j½Õ¤­«×©w©¶¤§¯Â«ß­µ¶¥
(«x!¤S¨Ó¤F!
¦ý(¤@)¤§«á¡A«ç»ò©¿µM´N¨ì(¤Q)¤F©O?
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´Nºâ¦p¦¹
³oºØ±¾¤@º|¸Uªº°Q½×¤è¦¡
¤S¯à°Q½×¥X¤°»òµ²½×¨Ó¤F§r?)

¥D©M²Í G=g b d
¤UÄÝ©M²Í C=c e g
¤WÄÝ©M²Í D=d #f a
­Y¦³(?)C¤UÄÝ©M²Í®É
«hE=325.9Hz
©M©w©¶¤§E=660Hz¤£©M¿Ó(?)
¬GºÞ²Í¼Ö¥HD¤j½Õ¯Â«ß­µ¶¥¸û¦n.
(¡§ºÞ²Í¼Ö¥H(D¤j½Õ)¯Â«ß­µ¶¥¸û¦n¡¨ªÌ
¦ó·N§r?
¢w¢wºÞ²Í¼Ö¤¤¬O¤T«ß¨Ã§eªº
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1.do=G=391.11 -4cent
2.Re=A=440 0cent
3.Mi=B=488.88 -18cent
4.Fa=C=260.74 -6cent
5.So=D=293.33 -2cent
#C #D #F #G #A
(?)
6. La= E=325.9 -20cent
-14 -25 -16 -12 -23(?)
7. Si=#F=366.66 -16cent
8. Fi=#C=275 -14cent
C D E F G A B(?)
9. Di=#G=412.5 -12cent
-6 -2 -20 -8 -4 0 ¡V18(?)
10.Soi=#D=309.375 -10cent
11. Ri= #A=464.06 -8cent
12. Li= #E=348.05 -6cent .
12¥­§¡«ß
C4=260.74 ¤ñ­È -6cent 261.63
#C5=550
(#C4=275) ¤ñ­È -14cent 277.18 *
D4=293.33 ¤ñ­È 9/8 -2cent 293.66
#D4=305.55 ¤ñ­È -25cent 311.13
E5=660
(E4=330) ¤ñ­È 2cent 329.63
F=348.33 ¤ñ­È -16cent 369.99 *
G3=195.55
(G4=391.12) ¤ñ­È 3/2 -4cent 392.00
#G4=825
(#G4=412.50 -12cent 415.30
A4=440 ¤ñ­È 0 cent 440.00
#A4=458.33 ¤ñ­È -23cent 466.16
B3= 244.44
(B4=488.89)¤ñ­È -18cent 493.89 *
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305.56 458.33
#D4 #A4 #C #D #F #G #A
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244.44 / \ / \550 825
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195.55 293.33 440.00 660.00
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2.Re=D=297 20cent
3.Mi=E=330 2cent
4.Fa=F=352 14cent
5.So=G=396 18cent
6.La=A=440 0cent
7.Si=B=495 4cent
8.Fi=#F=371.25 6cent
9.Di=#C=278.44 8cent
10.Soi=#G=417.66 10cent
11.Ri= bB=469.33 12cent (bBx3/2=F bBx3/2=352 bB=469.33)
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2.Re=#F=371.25 6cent
3.Mi=#G=412.5 -12cent
4.Fa=A=440 0cent
5.So=B=495 4cent
6.La=#C=275 -14cent
7.Si=#D=309.375 -10cent #C #D #F #G #A
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2.Re=A=445.5 22cent
3.Mi=B=495 4cent
4.Fa=C=264 16cent
5.So=D=297 20cent
6.La=E=330 2cent
7.Si=#F=371.25 6cent
8.Fi=#C=278.44 8cent
9.Di=#G=417.66 10cent
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2.Re=E=330 2cent
3.Mi=#F=366.66 -16cent
4.Fa=G=391.11 -4cent
5.So=A=440
6.La=B=488.88 -18cent
7.Si=#C=275 -14cent #C bE #F #G bB
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8.Fi=#G=412.5 -12cent
9.Di=#D=309.34 -10cent C D E F G A B
10.Li=#A=469.86 -8cent 16 -2 2 14 18 0 -18
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12 C=260.74 -6cent
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1.do=A=440 0cent
2.Re=B=495 4cent
3.Mi=#C=275 -14cent
4.Fa=D=293.33 -2cent
5.So=E=330 2cent
6.La=#F=366.66 -16cent
7.Si=#G=412.5 -12cent
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#F=371.25= 6cent
1.do=B=495 4cent
2.Re=#C=278.44 cent
3.Mi=#D=309.375 -14cent
4.Fa=E=330 2cent
5.So=#F=371.25 6cent
6.La=#G=412.5 -12cent
7.Si=#A=464.06 cent
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-2cent -4cent 0cent
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-0.5cent 4cent -2cent
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C4=261.25 ¤ñ­È -2cent C 261.63
#C2=68.75 ¤ñ­È -14cent #C277.18
D3=A3x2/3=73.33(D4=293.33) ¤ñ­È 9/8 -2cent D293.66
#D=Bx5/4=122.22x5/4=152.78(#D4=305.56) ¤ñ­È -25cent #D311.13
E4=330 ¤ñ­È 2cent E329.63
F=²Ä19¤À­µ440x2/3 x19=5573.3/16=348.33 ¤ñ­È 76/57 -4cent F349.23
#F3=183.33(#F4=366.66 ) ¤ñ­È -16cent #F369.99
G4=391.88 Cx3/2=G A²Ä57¤À­µ(G4=391.11) ¤ñ­È 3/2 -0.5cent G392.00
#G=97.775 =412.50 -12cent #G415.30
A4=440 ¤ñ­È 96/57 0 cent A440.00
#A2=#Fx5/4=366.66x5/4 x1/4=114.58 ¤ñ­È -23cent #A466.16
B4=495 ¤ñ­È 4cent B493.89
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bE=309.63=-8cent bB=464.44=-6cent D=293.33=-2cent
F=348.33=-4cent A=440 C=261.25=-2cent E=330=2cent G=0cent
#A4
528 - 458.33=69.67
200 /69.67=2.87CENT
458.33-466.16=-7.83
-7.83x2.87 = -22.47
#A458.33 = -23 CENT
¹Ï¤K ¾A¦X G D A B #F ¤j½Õ
-25cent -23cent
305.56 458.33
#D4 #A4 #C #D #F #G #A
-18cent /\-16 /\ -14cent -14 -25 -16 -12 -23
244.44 / \ / \550 825
A E B3/___ #F4___#C5___#G5 C D E F G A B
/\ /\ /\ /\ /\ /\ -6 -2 2 -8 -4 0 4
/ \ / \ / \ / \ / \ / /____\/____\ /____\/____\/____\/____ F4 C4 G3 D4 A4 E5
260.74 195.55 293.33 440.00 660.00
-6cent -4cent -2cent -0cent 2cent
¹Ï¤E ¾A¦X C G D A B #F ¤j½Õ
-25cent -23cent
305.56 458.33
#D4 #A4 #C #D #F #G #A
-20cent -18cent/\-16 /\-14cent-12cent-10cent -14 -25 -16 -12 -23
325.93 244.44/ \ / \550 825 309.34
E B3/___ #F4___#C5___#G5 #D C D E F G A B
/\ /\ /\ /\ /\ /\ /\ -6 -2 -20 -8 -4 0 -18
/ \ / \ / \ / \ / \ / \ / /____\/____\ /____\/____\/____\/____\/____ F4 C4 G4 D4 A4 E4 B4 #F4
260.74 391.11 293.33 440 330 495 371.25
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¹Ï¤Q
-25cent -23cent
305.56 458.33
#D4 #A4
-20cent -18cent/\-16 /\-14cent-12cent-10cent
325.93 244.44/ \ / \550 825 309.34
E B3/___ #F4___#C5___#G5 #D
/\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / /____\/____\ /____\/____\/____\/____\/____\/____\/____\ /____\/____\/____\/____\/____\/____\/____\/____ bG bD bA bE bB F C G D4 A4 E4 B4 #F4 #C #G #D #A #E
417.18 312.89 469.33 347.65 260.74 391.11 293.33 440 330 495 371.25 278.44 417.66 313.245 469.86 352.4
10cent -6cent-6cent -6cent -4cent -2cent 0cent2cent 4cent6cent 8cent 10cent 12cent 14cent 16cent
¤j´£µ^©w©¶ C2 G2 D3 A3
12¥­§¡«ß 65.406 98.000 146.83 220.00
A©¶A4=442 65.705 98.445 147.505 221.00
2cent 4cent 6cent 8cent
¤­«×¬Û¥Í«ß65.185 97.775 146.66 220.00
-5cent -4cent -2cent 0cent
¤j3«×¯Â«ß 66 99 148.5 222.75
16cent 18cent 20cent 22cent
¥D­µ¯Â«ß 65.3125 97.9688 146.665 220.00
-2cent 0 cent -2cent 0cent
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C2=Ax2/3 x2/3 x2/3=65.185(c4=260.74) ¤ñ­È -6cent C 261.63
#C2=68.75 ¤ñ­È -14cent #C277.18
D3=A3x2/3=73.33(D4=293.33) ¤ñ­È 9/8 -2cent D293.66
#D=Bx5/4=122.22x5/4=152.78(#D4=305.56) ¤ñ­È -25cent #D311.13
E2=65.185x5/4 =81.49 (E4=325.96) ¤ñ­È -20cent E329.63
F=²Ä19¤À­µ440x2/3 x19=5573.3/16=348.33 ¤ñ­È 76/57 -4cent F349.23
#F3=183.33(#F4=366.66 ) ¤ñ­È -16cent #F369.99
G2=Ax2/3x2/3=97.775 (G4=391.11) ¤ñ­È 3/2 -4cent G392.00
#G=97.775 =412.50 -12cent #G415.30
A2=110.00(A4=440) ¤ñ­È 96/57 0 cent A440.00
#A2=#Fx5/4=366.66x5/4 x1/4=114.58 ¤ñ­È -23cent #A466.16
B2=G2x5/4=97.775x5/4=122.22(B4=488.89=391.11x5/4)¤ñ­È -18cent #B493.89
¹Ï¤Q¤@. ¤j´£µ^¤­«×¬Û¥Í«ß©w©¶ ¹Ï
-20cent -18cent -16cent
81.49 122.22 183.33 #C #D #F #G #A
E2 B2 #F3 -14 -25 -16 -12 -23
/\ /\ /\ C D E F G A B
/ \ / \ / \ -6 -2 -20 -8 -4 0 -18
/____\/____\/____ C2 G2 D3 A3
65.185 97.775 146.66 220
-6cent -4cent -2cent 0cent
-20cent -18cent-16cent-14cent-12cent
81.49 122.22 183.33 137.5
E B3 #F4 #C5 #G5 #D
/\ /\ /\ /\ /\ /\ /\ /\ /\
/ \ / \ / \ / \ / \ / \ / \ / \ / \
/....\/....\/....\/____\/____\/____\/....\/....\/....bE bB F C G D A4 E4 B4 #F4
117.33 86.912 65.185 97.775 146.66 220 330 495 371.25 278.44
10cent -8cent -6cent -4cent -2cent 0cent2cent 4cent 6cent 8cent
¾A¦X C G D ¤j½Õ E4=325.96(-20cent) B4=488.89(-18cent)
¦bG¤j½Õ®É(G=391.11)¤j¤T«×B­µ¬° 488.89 (-18cent)
¦ý¦bA.E¤j½Õ®É(E=330.00)¯Â¤­«×B­µ¬° 495.00 ( 4 cent)
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-6cent -4cent -2cent 0cent 2cent -18cent
c260.74 g391.11 d293.33 a 440 e 330 b488.89
-14cent -16cent -12cent
#c275 #f366.66 #a458.33 #d311.13 #g412.5
1.A4=440 ¯Â«ß 12¥­§¡«ß
2.D4= A4_D4 440x 2/3 =293.33 -2cent 220.00
3.G4= D4_G4 293.33x2/3 =391.11 -4cent 261.63
4.C4= G4_C4 391.11x2/3 =260.74 -6cent 329.63
5.E4= A4_E4 440x 3/4 =330.00 2cent 392.00
6.B4= G4-B4 391.11x5/4 =488.89 -18cent 493.89
7
8
9
C #F
293.33 - 264 = 29.33 Hz 412.5 - 366.66 = 45.84
200 /29.33 = 6.8189 CENT 200 / 45.84 = 4.37 CENT
264 - 261.63 = 2.37 Hz 366.66 - 369.99 =-3.33
2.37 x 6.8189 = 16.16 CENT -3.33x 4.37 =-14.56CENT
C264 = 16 CENT #F366.6 =-15 CENT
#C G
305.55 - 275 = 30.55 440 - 396 = 44
200 / 30.55=6.5466CENT 200 / 44 = 4.54
275 - 277.18 = 2.18 396 - 392 = 4
6.5466x2.18 = 14.27 CENT 4 x 4.54 = 18.16 CENT
#C275 = 14 CENT G396 = 18 CENT
D #G
330 - 293.33=36.67 458.33 - 412.5 = 45.83
200/36.67= 5.45 CENT 200 / 45.83 = 4.36 CENT
293.33-293.66=-0.33 412.50 - 415.30 = -2.8
-0.33x5.45 =-1.79 CENT -2.8 x 4.36 = -12.2 CENT
D293.33=-2 CENT #G412.50 = -12 CENT
#D A
352 - 309.375 = 42.625 A = 440
200 / 42.625= 4.672 CENT
309.375 - 311.13 =-1.755
4.672x -1.755=-8.2ENT
#D305.55 =-8 CENT A440 = 0 CENT
E #A
366.66 - 330 = 36.66 528 - 458.33=69.67
200 / 36.66 = 5.45 CENT 200 /69.67=2.87 CENT
330 - 329.63 = 0.37 458.33 - 466.16 = -7.83
0.37 x5.45 = 2.21 CENT -7.83x 2.87 = -22.47
E330 = 2 CENT #A458.33 = -23 CENT
F B
396 - 352 = 44 550 - 495 = 55
200 / 44 = 4.54 CENT 200 / 55 = 3.63 CENT
352 - 349.23 = 2.77 495 - 493.89 = 1.11
2.77 x 4.54 = 12.57 CENT 1.11 x 3.63 = 4.02 CENT
F352 = 12.57 CENT B495 = 4 CENT
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01. A (standed tone)¼Ð·Ç­µ=440 Hz
02. D ¤UÄÝ­µ(¤U5«×) =293.33 Hz= -2cent
03. E ¤WÄÝ­µ(¤W5«×) =330 Hz= 2cent
04. #F ¤p¤¤­µ(A¤p3«×) =366.66 Hz=-16cent
05. #C ¤W¤¤­µ(A¤j3«×) =275 Hz=-14cent
06. F ¤U¤¤­µ(A¤j3«×) =352 Hz= 14cent
07. C ¤W¤p¤¤­µ(A¤p3«×)=264 Hz= 16cent
08. G C¤WÄÝ­µ(¤W5«×) =396 Hz= 18cent
09. bB F¤UÄÝ­µ(¤U5«×) =469.33 Hz= 12cent
10. #G E¤W¤¤­µ(E¤j3«×) =412.50 Hz=-12cent
11. B E¤WÄÝ­µ(¤W5«×) =495 Hz= 4cent
12. bE bB¤UÄÝ­µ(¤U5«×) =312.89 Hz= 10cent
¹Ï¤@
D___________ A____________E
A¤§¤UÄÝ­µ ¥D­µ A¤§¤WÄÝ­µ
sub dominant tonic up dominant
D=2/3xA E=3/2xA
¹Ï¤G
A¤§¤W¤¤­µ
up mediant
#C=Ax5/4
#C
l
I
I
I
l
l
D___________ A____________E
A¤§¤UÄÝ­µ ¥D­µ A¤§¤WÄÝ­µ
sub dominant tonic up dominant
D=2/3xA I E=3/2xA
l
l
I
l
F
A¤§¤U¤¤­µ
sub mediant
F=Ax4/5
A¤§¤p¤¤­µ A¤§¤W¤¤­µ
small mediant up mediant
#F=2/3xAx5/4 #C=Ax5/4
#F #C
/\ / / \ / / \ / / \ / D/________\A/________\E
A¤§¤UÄÝ­µ ¥D­µ A¤§¤WÄÝ­µ
sub dominant tonic up dominant
D=2/3A E=3/2A
¹Ï¤T
A¤U¤p¤¤­µ A¤§¤W¤¤­µ
sub-small mediant up mediant
#F=2/3xAx5/4 #C=Ax5/4
#F #C
/\ / / \ / / \ / / \ / D/________\A/________\E
A¤§¤UÄÝ­µ ¥D­µ A¤§¤WÄÝ­µ
sub dominant tonic up dominant
D=2/3A / \ E=3/2A
/ / / F/__________\C
A¤§¤U¤¤­µ A¤W¤p¤¤­µ
sub mediant up-small mediant
F=Ax4/5 C=Ax4/5x3/2
¹Ï¥|
#F #C
/\ / D/__\A/__\E
/\ /\ / /__\/__\/__ bB F C G

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-16 -14 -12 -10 (cent)
366.66 275 412.5 309.34 (Hz)
#F #C #G #D #A
/\ /\ 2 /\ 4 /\ 6cent
G__D/__\A/__\E/__\B/__\#F 371.25=Bx3/2x1/2=495x3/4
391.11 /\ /\ /\ /\ / __ /__\/__\ /__\ /__\ /__\
bE bB F C G D A
312.89 469.33 352 264 396 297 (Hz)
10 12 14 16 18 20 (cent)
C¤j½Õ¯Â«ß#F=371.25=6cent (©MG=396=18cent¤£¦Ü¬Û®t¤Ó¤j)
D¤j½Õ¯Â«ß#F=366.66=-16cent (D¤j3©M²Í#F=Dx5/4=293.33x5/4=366.66)
D¤j½Õ¯Â«ß#F=366.66«h B=488.88 #D=305.55 #F=366.66=-16cent
B¤j½Õ¯Â«ß#F=371.25«h B=495 #D=309.38 #F=371.25= 6cent
bB¤j½Õ¯Â«ßF=352 «hbB=469.33=bB D F
bB¤j½Õ¯Â«ßF=348.33«hbB=464.44=bB D F(F=348.33ªx­µ¯Â«ß)
bB©M²Í: bB=469.33 D=293.33 F=352
F ©M²Í: F=352 A=440 C=264
C ©M²Í: C=264 E=330 G=396
#C bE #F #G bB
278.44 312.89 371.25 417.66 464.44
8cent 10cent 6cent 10cent 12cent
C D E F G A B
264.00 297.00 330.00 -348.33 391.88 440.00 495
16cent 20cent 2cent 14cent 18cent 0cent 4cent
F¤j½Õ¤£¥ÎG©M²Í.¥ÎG7©M²Í.©MbB©M²ÍªºD¦³½Ä¬ð.
G7¬O§_©M¿Ó.DF¤w¬O©w¦n­µ«hG=396Hz¬O¦ó­µ¤§ªx­µ?
F=352¤§²Ä9ªx­µ bB=469.33¤§²Ä27ªx­µ.
³ü. ¤j¤T«×¯Â«ßªº­µ¶¥ ©¶¼Ö
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12¥­§¡«ß 196.00 293.66 440.00 659.26
5«×¬Û¥Í«ß 195.55 293.33 440.00 660.00
-4cent -2cent 0cent 2cent
¹Ï¤».¤p´£µ^©w©¶¹Ï ¾A¦X G D A ¤j½Õ
-18cent -16cent -14cent
244.44 366.66 550.00
B3 #F4 #C5
/\ /\ / / \ / \ / /____\/____\/____ G3 D4 A4 E5
195.55 293.33 440.00 660.00
-4cent -2cent -0cent 2cent
(¤@)¤p´£µ^D¤j½Õ¤­«×©w©¶¤§¯Â«ß­µ¶¥
¥D©M²ÍD=d #f a ¤UÄÝ©M²ÍG=g b d ¤WÄÝ©M²ÍA=a #c e §t¦³G D A ¥D©M²Í­µ

­µ ¦W C #C D E #F G A B
D¤j½Õ¤p´£µ^5«×«ß 260.74 275.00 293.33 330.00 366.66 391.11 440.00 488.89
¥[¤j3«×¯Â«ßD¤j½Õ -6 -14 -2 2 -16 -4 0 -18

1.do=D=293.33 -2cent
2.Re=E=330 2cent
3.Mi=#F=366.66 -16cent
4.Fa=G=391.11 -4cent
5.So=A=440
6.La=B=488.88 -18cent
7.Si=#C=275 -14cent #C bE #F #G bB
-14 10 -16 -12 12
8.Fi=#G=412.5 -12cent
9.Di=#D=309.34 -10cent C D E F G A B
10.Li=#A=469.86 -8cent -6 -2 2 -8 -4 0 -18
11 F=347.65 -8cent
12 C=260.74 -6cent
12¥­§¡«ß
C4=A4x2/3 x2/3 x2/3 x2=260.74 ¤ñ­È -6cent 261.63
#C5=A4x5/4=550(#C4=275) ¤ñ­È -14cent 277.18 *
D4=A4x2/3=440x2/3=293.33 ¤ñ­È 9/8 -2cent 293.66
#D4=B3x5/4=244.44x5/4=305.55 ¤ñ­È -25cent 311.13
E5=A4x3/2=440x3/2=660 (E4=330) ¤ñ­È 2cent 329.63
F=C4x4/3=347.65 ¤ñ­È -8cent 369.99 *
G3=Ax2/3 x2/3=195.55 (G4=391.12) ¤ñ­È 3/2 -4cent 392.00
#G4=#C5x3/2=550x3/2=825(#G4=412.50) -12cent 415.30
A4=440 ¤ñ­È 0 cent 440.00
#A4=#D4x3/2=305.55x3/2=458.33 ¤ñ­È -23cent 466.16
B3=G3x5/4=195.55x5/4=244.44(B4=488.89)¤ñ­È -18cent 493.89 *
#C #D #F #G #A
-14 -25 -16 -12 -23
C D E F G A B
-6 -2 2 -8 -4 0 -18
(¤Q)¤p´£µ^G¤j½Õ¤­«×©w©¶¤§¯Â«ß­µ¶¥ ¥D©M²Í G=g b d ¤UÄÝ©M²Í C=c e g ¤WÄÝ©M²Í D=d #f a
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1.do=G=391.11 -4cent
2.Re=A=440 0cent
3.Mi=B=488.88 -18cent
4.Fa=C=260.74 -6cent
5.So=D=293.33 -2cent
#C #D #F #G #A
6.La=E=325.9 -20cent -14 -25 -16 -12 -23
7.Si=#F=366.66 -16cent
8.Fi=#C=275 -14cent C D E F G A B
9.Di=#G=412.5 -12cent -6 -2 -20 -8 -4 0 -18
10.Soi=#D=309.375 -10cent
11.Ri= #A=464.06 -8cent
12.Li= #E=348.05 -6cent .
12¥­§¡«ß
C4=A4x2/3 x2/3 x2/3 x2=260.74 ¤ñ­È -6cent 261.63
#C5=A4x5/4=550(#C4=275) ¤ñ­È -14cent 277.18 *
D4=A4x2/3=440x2/3=293.33 ¤ñ­È 9/8 -2cent 293.66
#D4=B3x5/4=244.44x5/4=305.55 ¤ñ­È -25cent 311.13
E5=A4x3/2=440x3/2=660 (E4=330) ¤ñ­È 2cent 329.63
F=348.33 ¤ñ­È -16cent 369.99 *
G3=Ax2/3 x2/3=195.55 (G4=391.12) ¤ñ­È 3/2 -4cent 392.00
#G4=#C5x3/2=550x3/2=825(#G4=412.50) -12cent 415.30
A4=440 ¤ñ­È 0 cent 440.00
#A4=#D4x3/2=305.55x3/2=458.33 ¤ñ­È -23cent 466.16
B3=G3x5/4=195.55x5/4=244.44(B4=488.89)¤ñ­È -18cent 493.89 *

¹Ï¤C ¤p´£µ^C¥D©M²Í¹Ï ¾A¦X G D A B #F ¤j½Õ
-25cent -23cent
305.56 458.33
#D4 #A4 #C #D #F #G #A
-18cent /\-16 /\ -14cent -14 -25 -16 -12 -23
244.44 / \ / \550 825
B3/___ #F4___#C5___#G5 C D E F G A B
/\ /\ /\ /\ -6 -2 -20 -8 -4 0 -18
/ \ / \ / \ / /____\/____\/____\/____ G3 D4 A4 E5
195.55 293.33 440.00 660.00
-4cent -2cent -0cent 2cent
#D4=B3x5/4=244.44x5/4=305.55 -25cent
#A4=#D4x3/2=305.55x3/2=458.33 -23cent
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(¤@)F¤j½Õ¯Â«ß­µ¶¥ ¥D©M²Í F A C ¤UÄÝ©M²Í bB D F ¤WÄÝ©M²Í C E G
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1.do=F=352 14cent F=Ax 4/5=352 ¥D©M²Í F A C
2.Re=G=396 18cent Cx3/2=G=396 ¤WÄÝ©M²Í C E G
3.Mi=A=440 0cent ¼Ð·Ç­µ
4.Fa=bB=469.33 12cent Fx2/3 x2=bB=469.33 ¤UÄÝ©M²Í bB D F
5.So=C=264 16cent Fx3/2 /2=C=264 ¥D©M²Í F A C
6.La=D=293.33 20cent bBx5/4 /2=293.33 ¤UÄÝ©M²Í bB D F
7.Si=E=330 2cent Cx5/4=E=330 ¤WÄÝ©M²Í C E G
8.Fi=B=495 4cent
9.Di=#F=371.25 6cent
10.Soi=#C=278.44 8cent (#Fx3/2 x1/2=371.25x3/2 x1/2=278.4375)
11.Ri= #G=417.66 10cent (#Cx3/2=278.4375 x3/2=417.66)
12.Li= bE=312.89 10cent (bEx3/2=bB 469.33x2/3=bE=312.89)
(¤G)bB¤j½Õ¯Â«ß­µ¶¥ ¥D©M²Í bB D F ¤UÄÝ©M²Í bE G bB ¤WÄÝ©M²Í F A C
bB¤p³â¥z¤§°ò­µ
1.do=bB=469.33 12cent Fx2/3 x2=bB=469.33 ¥D©M²Í bB D F
2.Re=C=264 16cent Fx3/2 /2=C=264 ¤WÄÝ©M²Í F A C
3.Mi=D=293.33 -2cent bBx5/4 /2=293.33 ¥D©M²Í bB D F
4.Fa=bE=312.89 10cent bE=bBx2/3=312.89 ¤UÄÝ©M²Í bE G bB
5.So=F=352 14cent F=Ax 4/5=352 ¤WÄÝ©M²Í F A C
6.La=G=391.11 -4cent G=bEx5/4=391.11 ¤UÄÝ©M²Í bE G bB
7.Si=A=440 0cent ¼Ð·Ç­µ ¤WÄÝ©M²Í F A C
8.Fi=E=330 2cent
9.Di=B=495 4cent
10.Soi=#F=371.25 6cent
11.Ri= #C=278.44 8cent
12.Li= #G=417.66 10cent
(¤T)bE¤j½Õ¯Â«ß­µ¶¥ ¥D©M²Í bE G bB ¤UÄÝ©M²Í bA C bE ¤WÄÝ©M²Í bB D F
1.do=bE=312.89 10cent bE=bBx2/3=312.89 ¥D©M²Í bE G bB
2.Re=F=352 14cent
3.Mi=G=391.11 -4cent G=bEx5/4=391.11 ¥D©M²Í bE G bB
4.Fa=bA=417.19 8cent bAx3/2 /2=bE bA=417.19 ¤UÄÝ©M²Í bA C bE
5.So=bB=469.33 12cent bB=bEx3/2=469.33 ¥D©M²Í bE G bB
6.La=C=260.74 -6cent bAx5/4=C=260.74 ¤UÄÝ©M²Í bA C bE
7.Si=D=293.33 -2cent
8.Fi=
9.Di=
10.Soi=
11.Ri=
12.Li=
(¥|)C¤j½Õ¯Â«ß­µ¶¥ §t¦³¥D©M²Í C E G ¤UÄÝ©M²Í F A C ¤WÄÝ©M²Í G B D
1.do=C=264 16cent
2.Re=D=297 20cent
3.Mi=E=330 2cent
4.Fa=F=352 14cent
5.So=G=396 18cent
6.La=A=440 0cent
7.Si=B=495 4cent
8.Fi=#F=371.25 6cent
9.Di=#C=278.44 8cent
10.Soi=#G=417.66 10cent
11.Ri= bB=469.33 12cent (bBx3/2=F bBx3/2=352 bB=469.33)
12.Li= bE=312.89 10cent (bEx3/2=bB 469.33x2/3=bE=312.89)
(¥|-1) E¤j½Õ¯Â«ß­µ¶¥ ¥D©M²Í E #G B ¤UÄÝ©M²Í A #C E ¤WÄÝ©M²Í B #D #F
1.do=E=330 2cent
2.Re=#F=371.25 6cent
3.Mi=#G=412.5 -12cent
4.Fa=A=440 0cent
5.So=B=495 4cent
6.La=#C=275 -14cent
7.Si=#D=309.375 -10cent #C #D #F #G #A
-14 -10 6 -12 -8
8.Fi=#A=469.86 -8cent C D E F G A B
2 0 4
(¤­)G¤j½Õ¯Â«ß­µ¶¥ ¥D©M²Í G B D ¤UÄÝ©M²Í C E G ¤WÄÝ©M²Í D #F A
1.do=G=396 18cent
2.Re=A=445.5 22cent
3.Mi=B=495 4cent
4.Fa=C=264 16cent
5.So=D=297 20cent
6.La=E=330 2cent
7.Si=#F=371.25 6cent
8.Fi=#C=278.44 8cent
9.Di=#G=417.66 10cent
10.Soi=#D=313.245 12cent
11.Ri= #A=469.86 14cent
12.Li= #E=352.40 14cent .
(¤») D¤j½Õ¯Â«ß­µ¶¥ ¥D©M²Í D #F A ¤UÄÝ©M²Í G B D ¤WÄÝ©M²Í A #C E §t¦³G D A ©M²Í
1.do=D=293.33 -2cent
2.Re=E=330 2cent
3.Mi=#F=366.66 -16cent
4.Fa=G=391.11 -4cent
5.So=A=440
6.La=B=488.88 -18cent
7.Si=#C=275 -14cent #C bE #F #G bB
-14 10 -16 -12 12
8.Fi=#G=412.5 -12cent
9.Di=#D=309.34 -10cent C D E F G A B
10.Li=#A=469.86 -8cent 16 -2 2 14 18 0 -18
11 F=352 14cent
12 C=260.74 -6cent
(¤C) A¤j½Õ¯Â«ß­µ¶¥ ¥D©M²Í A #C E ¤UÄÝ©M²Í D #F A ¤WÄÝ©M²Í E #G B
1.do=A=440 0cent
2.Re=B=495 4cent
3.Mi=#C=275 -14cent
4.Fa=D=293.33 -2cent
5.So=E=330 2cent
6.La=#F=366.66 -16cent
7.Si=#G=412.5 -12cent
(¤C-1)B¤j½Õ¯Â«ß­µ¶¥ ¥D©M²Í B #D #F ¤UÄÝ©M²Í E #G B ¤WÄÝ©M²Í #F #A #C
B¤j½Õ¯Â«ß#F=371.25«h B=495 #D=309.38 #F=371.25= 6cent
1.do=B=495 4cent
2.Re=#C=278.44 cent
3.Mi=#D=309.375 -14cent
4.Fa=E=330 2cent
5.So=#F=371.25 6cent
6.La=#G=412.5 -12cent
7.Si=#A=464.06 cent
(¤C-2)¦N¥LC¤j½ÕA¤p½Õ¥D­µ¯Â«ß­µ¶¥ ©w©¶¤§­µ E A D G B E
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C¥D¤j¤T©M²ÍC=261.25 E=330 G=391.88
-2cent 2cent 0.5cent
Am¤p¤T©M²Í A=440 C=261.25 E=330
0cent -2cent 2cent
Dm¤p¤T©M²Í D=293.33 F=348.33 A=440
-2cent -4cent 0cent
G¥D¤j¤T©M²ÍG=391.88 B=495 D=293.33
-0.5cent 4cent -2cent
12¥­§¡«ß
C4=261.25 ¤ñ­È -2cent C 261.63
#C2=68.75 ¤ñ­È -14cent #C277.18
D3=A3x2/3=73.33(D4=293.33) ¤ñ­È 9/8 -2cent D293.66
#D=Bx5/4=122.22x5/4=152.78(#D4=305.56) ¤ñ­È -25cent #D311.13
E4=330 ¤ñ­È 2cent E329.63
F=²Ä19¤À­µ440x2/3 x19=5573.3/16=348.33 ¤ñ­È 76/57 -4cent F349.23
#F3=183.33(#F4=366.66 ) ¤ñ­È -16cent #F369.99
G4=391.88 Cx3/2=G A²Ä57¤À­µ(G4=391.11) ¤ñ­È 3/2 -0.5cent G392.00
#G=97.775 =412.50 -12cent #G415.30
A4=440 ¤ñ­È 96/57 0 cent A440.00
#A2=#Fx5/4=366.66x5/4 x1/4=114.58 ¤ñ­È -23cent #A466.16
B4=495 ¤ñ­È 4cent B493.89
(¤K)D¤p½Õªx­µ¯Â«ß­µ¶¥+ bE__bB_D__F_A_C_E_G=¥D­µ¯Â«ß
bE=309.63=-8cent bB=464.44=-6cent D=293.33=-2cent
F=348.33=-4cent A=440 C=261.25=-2cent E=330=2cent G=0cent
#A4
528 - 458.33=69.67
200 /69.67=2.87CENT
458.33-466.16=-7.83
-7.83x2.87 = -22.47
#A458.33 = -23 CENT
¹Ï¤K ¾A¦X G D A B #F ¤j½Õ
-25cent -23cent
305.56 458.33
#D4 #A4 #C #D #F #G #A
-18cent /\-16 /\ -14cent -14 -25 -16 -12 -23
244.44 / \ / \550 825
A E B3/___ #F4___#C5___#G5 C D E F G A B
/\ /\ /\ /\ /\ /\ -6 -2 2 -8 -4 0 4
/ \ / \ / \ / \ / \ / /____\/____\ /____\/____\/____\/____ F4 C4 G3 D4 A4 E5
260.74 195.55 293.33 440.00 660.00
-6cent -4cent -2cent -0cent 2cent
¹Ï¤E ¾A¦X C G D A B #F ¤j½Õ
-25cent -23cent
305.56 458.33
#D4 #A4 #C #D #F #G #A
-20cent -18cent/\-16 /\-14cent-12cent-10cent -14 -25 -16 -12 -23
325.93 244.44/ \ / \550 825 309.34
E B3/___ #F4___#C5___#G5 #D C D E F G A B
/\ /\ /\ /\ /\ /\ /\ -6 -2 -20 -8 -4 0 -18
/ \ / \ / \ / \ / \ / \ / /____\/____\ /____\/____\/____\/____\/____ F4 C4 G4 D4 A4 E4 B4 #F4
260.74 391.11 293.33 440 330 495 371.25
-6cent -4cent -2cent -0cent 2cent 4cent 6cent
¹Ï¤Q
-25cent -23cent
305.56 458.33
#D4 #A4
-20cent -18cent/\-16 /\-14cent-12cent-10cent
325.93 244.44/ \ / \550 825 309.34
E B3/___ #F4___#C5___#G5 #D
/\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\
/ \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / \ / /____\/____\ /____\/____\/____\/____\/____\/____\/____\ /____\/____\/____\/____\/____\/____\/____\/____ bG bD bA bE bB F C G D4 A4 E4 B4 #F4 #C #G #D #A #E
417.18 312.89 469.33 347.65 260.74 391.11 293.33 440 330 495 371.25 278.44 417.66 313.245 469.86 352.4
10cent -6cent-6cent -6cent -4cent -2cent 0cent2cent 4cent6cent 8cent 10cent 12cent 14cent 16cent
¤j´£µ^©w©¶ C2 G2 D3 A3
12¥­§¡«ß 65.406 98.000 146.83 220.00
A©¶A4=442 65.705 98.445 147.505 221.00
2cent 4cent 6cent 8cent

¤­«×¬Û¥Í«ß65.185 97.775 146.66 220.00
-5cent -4cent -2cent 0cent
¤j3«×¯Â«ß 66 99 148.5 222.75
16cent 18cent 20cent 22cent
¥D­µ¯Â«ß 65.3125 97.9688 146.665 220.00
-2cent 0 cent -2cent 0cent
¤j´£µ^C¤j½Õ¤­«×©w©¶¤§¯Â«ß­µ¶¥
12¥­§¡«ß
C2=Ax2/3 x2/3 x2/3=65.185(c4=260.74) ¤ñ­È -6cent C 261.63
#C2=68.75 ¤ñ­È -14cent #C277.18
D3=A3x2/3=73.33(D4=293.33) ¤ñ­È 9/8 -2cent D293.66
#D=Bx5/4=122.22x5/4=152.78(#D4=305.56) ¤ñ­È -25cent #D311.13
E2=65.185x5/4 =81.49 (E4=325.96) ¤ñ­È -20cent E329.63
F=²Ä19¤À­µ440x2/3 x19=5573.3/16=348.33 ¤ñ­È 76/57 -4cent F349.23
#F3=183.33(#F4=366.66 ) ¤ñ­È -16cent #F369.99
G2=Ax2/3x2/3=97.775 (G4=391.11) ¤ñ­È 3/2 -4cent G392.00
#G=97.775 =412.50 -12cent #G415.30
A2=110.00(A4=440) ¤ñ­È 96/57 0 cent A440.00
#A2=#Fx5/4=366.66x5/4 x1/4=114.58 ¤ñ­È -23cent #A466.16
B2=G2x5/4=97.775x5/4=122.22(B4=488.89=391.11x5/4)¤ñ­È -18cent #B493.89
¹Ï¤Q¤@. ¤j´£µ^¤­«×¬Û¥Í«ß©w©¶ ¹Ï
-20cent -18cent -16cent
81.49 122.22 183.33 #C #D #F #G #A
E2 B2 #F3 -14 -25 -16 -12 -23
/\ /\ /\ C D E F G A B
/ \ / \ / \ -6 -2 -20 -8 -4 0 -18
/____\/____\/____ C2 G2 D3 A3
65.185 97.775 146.66 220
-6cent -4cent -2cent 0cent


-20cent -18cent-16cent-14cent-12cent
81.49 122.22 183.33 137.5
E B3 #F4 #C5 #G5 #D
/\ /\ /\ /\ /\ /\ /\ /\ /\
/ \ / \ / \ / \ / \ / \ / \ / \ / \
/....\/....\/....\/____\/____\/____\/....\/....\/....bE bB F C G D A4 E4 B4 #F4
117.33 86.912 65.185 97.775 146.66 220 330 495 371.25 278.44
10cent -8cent -6cent -4cent -2cent 0cent2cent 4cent 6cent 8cent
¾A¦X C G D ¤j½Õ E4=325.96(-20cent) B4=488.89(-18cent)
¦bG¤j½Õ®É(G=391.11)¤j¤T«×B­µ¬° 488.89 (-18cent)
¦ý¦bA.E¤j½Õ®É(E=330.00)¯Â¤­«×B­µ¬° 495.00 ( 4 cent)
©¶¼Ö¯Â«ß©M12¥­§¡«ß¤ñ¸û
©¶¼Ö©w©¶1 5 2 6 3
-6cent -4cent -2cent 0cent 2cent -18cent
c260.74 g391.11 d293.33 a 440 e 330 b488.89
-14cent -16cent -12cent
#c275 #f366.66 #a458.33 #d311.13 #g412.5
1.A4=440 ¯Â«ß 12¥­§¡«ß
2.D4= A4_D4 440x 2/3 =293.33 -2cent 220.00
3.G4= D4_G4 293.33x2/3 =391.11 -4cent 261.63
4.C4= G4_C4 391.11x2/3 =260.74 -6cent 329.63
5.E4= A4_E4 440x 3/4 =330.00 2cent 392.00
6.B4= G4-B4 391.11x5/4 =488.89 -18cent 493.89
7
8
9
C #F
293.33 - 264 = 29.33 Hz 412.5 - 366.66 = 45.84
200 /29.33 = 6.8189 CENT 200 / 45.84 = 4.37 CENT
264 - 261.63 = 2.37 Hz 366.66 - 369.99 =-3.33
2.37 x 6.8189 = 16.16 CENT -3.33x 4.37 =-14.56CENT
C264 = 16 CENT #F366.6 =-15 CENT
#C G
305.55 - 275 = 30.55 440 - 396 = 44
200 / 30.55=6.5466CENT 200 / 44 = 4.54
275 - 277.18 = 2.18 396 - 392 = 4
6.5466x2.18 = 14.27 CENT 4 x 4.54 = 18.16 CENT
#C275 = 14 CENT G396 = 18 CENT
D #G
330 - 293.33=36.67 458.33 - 412.5 = 45.83
200/36.67= 5.45 CENT 200 / 45.83 = 4.36 CENT
293.33-293.66=-0.33 412.50 - 415.30 = -2.8
-0.33x5.45 =-1.79 CENT -2.8 x 4.36 = -12.2 CENT
D293.33=-2 CENT #G412.50 = -12 CENT
#D A
352 - 309.375 = 42.625 A = 440
200 / 42.625= 4.672 CENT
309.375 - 311.13 =-1.755
4.672x -1.755=-8.2ENT
#D305.55 =-8 CENT A440 = 0 CENT
E #A
366.66 - 330 = 36.66 528 - 458.33=69.67
200 / 36.66 = 5.45 CENT 200 /69.67=2.87 CENT
330 - 329.63 = 0.37 458.33 - 466.16 = -7.83
0.37 x5.45 = 2.21 CENT -7.83x 2.87 = -22.47
E330 = 2 CENT #A458.33 = -23 CENT
F B
396 - 352 = 44 550 - 495 = 55
200 / 44 = 4.54 CENT 200 / 55 = 3.63 CENT
352 - 349.23 = 2.77 495 - 493.89 = 1.11
2.77 x 4.54 = 12.57 CENT 1.11 x 3.63 = 4.02 CENT
F352 = 12.57 CENT B495 = 4 CENT
¡¹½Õ©Ê¡]Tonality¡^
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¥Ñ¥D­µ©Î¥D©M²Í¶}©l¡Aµ²§ô®É¤S±N¦^¨ì¥D­µ©Î¥D©M²Í¡C¦¹ºØ¼Ò¦¡³Ì­«­nªº·N¸q¦b
©ó¨Ï­µ¼Ö¶i¦æ¨ã¦³±j¯Pªº¤è¦V·P¡C¥H¤U±N­µ¶¥¤¤¦U­µ¦WºÙ¶¶§Ç¦C¥X¡G
¥D­µ(tonic).¤W¥D­µ(supertonic)
ÄÝ­µ(dominant).¤WÄÝ­µ(up dominant).¤UÄÝ­µ(sub dominant).
¤¤­µ(mediant).¤W¤¤­µ(up mediant).¤U¤¤­µ(sub mediant).¤p¤¤­µ(small mediant)
¾É­µ(leading tone)¡B¤K«×­µ(octave)¡C
¥Ñ¦¹¥iª¾¤Q¤G­Ó­µ¦U¦Û¯à¦¨¬°¤@­Ó½Õªº¥D­µ¡A¦p¦¹±N±o¨ì¤Q¤G­Ó¤j½Õ»P¤Q¤G­Ó¤p
½Õ¡AÁ`¦@«K¬O©ÒºÙªº¤G¤Q¥|­Ó¤j¤p½Õ¡C
¤j¤T«×¯Â«ß©M12¥­§¡«ß¤ñ¸û (30­Ó°ò­µ) ³Å°êÅv 1991µÛ 2007.12.11­q

¯Â«ß ©M²Í²£¥Íªk 12¥­§¡«ß
1.A4=440 D<F< A >C>E>G>B
2.F4= A4_F4 =440x 4/5 =352.00 13cent F= F>A>C 349.23
3.C4= F4_C5 =352x 3/2/2=264.00 15cent F= F>A>C 261.63
4.E4= C4_E4 =264x 5/4 =330.00 2cent C= C>E>G 329.63
5.G4= C4_G4 =264x 3/2 =396.00 17cent C= C>E>G 392.00
6.B4= G4_B4 =396x 5/4 =495.00 4cent G= G>B>D 493.89
13B=­Y#F=366.66«hBx3/2=366.66 B=488.88-16cent Bm=B>D#FF

7.D4= A4_D4 =440x 2/3 =293.33 -2cent D= D>#F>A 293.66
14.D4=G4_D5=396x3/2/2 =297.00 19cent G= G>B>D
8.#C4 #C5_A4 =440x(5/4)/2 =275.00 -14cent A= A>#C E 277.18
15.#c4=#Fx3/2=371.25x3/2 =278.44 7cent #F=#F>#A>#C
9.#F4 B4_#F5 =495x3/2/2 =371.25 6cent B= B>#D #F 369.99
16.#F4= A4_#F4 =440x 5/6 =366.66 -15cent D= D #F<A 369.99
17.#A4= #A4_#F =366.66x5/4 =458.33(-23cent)#F=#F>#A #C 466.16
#A=#D_#A=309.375x3/2=464.06
18.#A4=#Fx5/4=371.25x5/4 =464.06(-7cent)#F=#F>#A>#C
27.#A4=#D_#A=310x3/2=465
19.#D4= B4_#D4 =495x(5/4)/2 =309.375 -8CENT B= B>#D #F 311.13

10.#G4 E4_ #G4 =330x 5/4 =412.50 -12cent E= E> #G B 415.30
20=#C_#G=278.44x 5/4 =417.66
11.bB4 bB4_D5 =293.33x4/5x2=469.33 11cent bB= bB>D>F 466.16
bB4_F5 =352x2x2/3 =469.33 11cent bB= bB>D>F 466.16
21=bE4_bB4=316.8x3/2 =475.2 34cent bE =bE>G>bB 466.16
G4_bB4 =396x6/5 =475.2 34cent Gm =G>bB.D 466.16
bD4 22=bB_bD5=469.34x(6/5)/2=281.604(25cent)bB=bB>bD>F 277.18
23=bD4_F4 =352 x(4/5) =281.6(25cent) bD=bD>F>bA 277.18
bG4 24=bB4_bG4=469.34x 4/5=375.472(23cent) bG=bG>bB>bD 369.99
bA4 25=bA4_C5 =264x(4/5)x2= 422.4 (30cent) bA=bA>C>bE 415.3
bD4_bA5=281.6x3/2 =422.4 bD=bD>F>bA 415.3
bD_bA=281.6x 3/2=422.4 (30cent) bA=bD>F>bA 415.3
12.bE4 bB4_bE4 =469.33x2/3=312.89(9cent) bEm=bE>bG>bB 311.13
26=C4_bE4=264x(6/5) =316.8 (32cent) Cm= C>bE>G 311.13
C_bE 264x(6/5) =316.8 (32cent) bA=bA>C>bE 311.13
bA-bE 422.4x3/2/2=316.8 (32cent) bA=bA>C>bE 311.13
bE4_G4 =396x4/5 =316.8 (32cent) bE=bE>G>bB 311.13
27=bA bA-bE bAx3/2=bE bAx3/2=312.89 bA=417.1866(7cent)
28=bD bD-bA bDx3/2=bA bDx3/2=417.18 bD=278.1244(5cent)
29=bG bGx3/2=bD bGx3/2=278.1244 bG=370.83(3cent)
30=F=bBx 3/2/2=469.33x 3/2/2=351.99 bB=bB>D>F
¯Â«ß­µ¶¥ ¤j2«×9/8,10/9 ¤p3«×19/16,6/5 ¤j3«×5/4 §¹¥þ4«×5/4 §¹¥þ5«×3/2
¤j7«×15/8 §¹¥þ8«×2/1


C 2 #F 9
293.33 - 264 = 29.33 Hz 412.5 - 371.25 = 40.75
200 /29.33 = 6.8189 CENT 200 / 40.75 =4.907975
264 - 261.63 = 2.37 Hz 371.25-369.99 = 1.26
2.37 x 6.8189 = 16.16 CENT 1.26x4.907975=6.184CENT
C264 = 16 CENT #F371.25 = 6 CENT
16cent=264.0972>0.0972
15cent=263.9299<0.0701
C264 = 15 CENT
#C=275Hz 8 G 4
305.55 - 275 = 30.55 440 - 396 = 44
200 / 30.55=6.5466CENT 200 / 44 = 4.54
275 - 277.18 =-2.18 396 - 392 = 4
6.5466x -2.18 =- 14.27 CENT 4 x 4.54 = 18.16 CENT
#C275 = -14 CENT G396 = 18 CENT
-14cent=274.9608<0.0392 18cent=396.1875>0.1875
-13cent=275.1424>0.1424 17cent=395.9365<0.0635
#C275 = -14 CENT G396 = 17 CENT
D 7 #G 8
330 - 293.33=36.67 458.33 - 412.5 = 45.83
200/36.67= 5.45 CENT 200 / 45.83 = 4.36 CENT
293.33-293.66=-0.33 412.50 - 415.30 = -2.8
-0.33x5.45 =-1.79 CENT -2.8 x 4.36 = -12.2 CENT
D293.33=-2 CENT #G412.50 = -12 CENT
-12cent=412.5320>0.0320
-11cent=412.6681<0.1681
#G412.50 = -12 CENT
bE 12 A
352 - 312.89 = 39.11 A = 440
200 / 39.11 = 5.11 CENT
312.89 - 311.13 =1.76
5.11 x 1.76 =8.993CENT
bE312.89=9 CENT A440 = 0 CENT
E 3 bB 11
366.66 - 330 = 36.66 528-469.33 =58.67
200 / 36.66 = 5.45 CENT 200 /58.67=3.409 CENT
330 - 329.63 = 0.37 469.33 - 466.16 = 3.173
0.37 x5.45 = 2.21 CENT 3.409 x 3.173 = 10.816
E330 = 2 CENT bB 469.33= 11 CENT
11cent=469.2083<0.1217
12cent=469.5610>0.2310
bB469.33=11 CENT

F 6 B 5
396 - 352 = 44 550 - 495 = 55
200 / 44 = 4.54 CENT 200 / 55 = 3.63 CENT
352 - 349.23 = 2.77 495 - 493.89 = 1.11
2.77 x 4.54 = 12.57 CENT 1.11 x 3.63 = 4.02 CENT
352 = 13 CENT B495 = 4 CENT
13cent=351.9064<0.0936 4cent=495.0380>0.0380
14cent=352.1047>0.1047 3cent=494.8420<0.1580
F352 = 13 CENT B495 = 4 CENT
#A4 18
523.23-464.06=59.17
200/59.17=3.38
464.06-466.16=-2.1
-2.1x 3.38=-7.1
#A464.06=-7CENT
#C4 8 #G
#D4-#C4=311.13-277.18=33.95
200/33.95=5.89
278.44-277.18=1.26
5.894x1.26=7.42
#C4=7cent
#D4 19-1 (12¥­§¡«ß­µ®t)
349.23 - 311.13=38.1
200/38.1=5.2493cent
309.375-311.13=-1.775
-1.775x5.2493=-9.21
#D309.375 =-9 CENT
---------------------------------------------------------
#D4 19 (¯Â«ß¥­§¡«ß­µ®t) #A4 17
352 - 309.375 = 42.625 528 - 458.33=69.67
200 / 42.625= 4.672 CENT 200 /69.67=2.87CENT
309.375 - 311.13 =-1.755 458.33-466.16=-7.83
4.672x -1.755=-8.2 -7.83x2.87 = -22.47
#D309.375 =-8 CENT #A458.33 = -23 CENT
bD4 22 bA4 25
316.8-281.604=35.196 469.34-422.4=46.94
200 / 35.196 =5.68246 200 / 46.94 =4.26
281.604-277.18=4.424 422.4-415.3 =7.1
4.424 x5.68246=25.1 7.1 x 4.26 =30.24
bD281.604=25 CENT bA422.4=30 CENT
bE4 26 bB4 21
352-316.8=35.2 528-475.2=52.8
200 /35.2=5.681818 200/52.8=3.78787
316.8-311.13=5.67 475.2-466.16=9.04
5.67x5.681818=32021 9.04x3.78787=34.2423
bE316.8=32CENT bB475.2=34CENT
#F4 16
bG4 24 412.5 - 366.66 = 45.84
422.4-375.472=46.928 200 / 4 .84 = 4.36 CENT
200 / 46.928 =4.2618 366.66 369.99 =-3.33
375.472-369.99=5.482 -3.33x .36 =-14.5 CENT
5.482x4.2618=23.363 #F366.6 =-15 CENT
bG4 375.472 =23 CENT -16cent=366.6675>0.0009
-17cent=366.4531<0.2135
#F366.66 = -16 CENT
D4 14-1 D4 14
329.63-293.66=35.97 330-297=33
200/35.97=5.56 200/33=6.06
297-293.66=3.34 297-293.66=3.34
3.34x5.56=18.57 3.34x6.06=20.24
D297=19cent D297=20cent
G©M©¶B©M©¶¤£¾A¥Î«eµÛ¥i¥ÎG7©M©¶¥N´À
D¦³2­Ó­µ G©M©¶g b d D=297 ¤£±Ä¥Î
Dm ©M©¶d f A D=293.33 ªñAªx­µ¯Â«ß293.25
#F¦³2­Ó­µ B©M©¶b #d #f #F=371.25 ¦PAªx­µ¯Â«ß»P12¥­§¡«ß­µ¶Z¸ûªñ
D©M©¶d #f A #F=366.66¤£±Ä¥Î.¥u¥Î¦bD¤j½Õ
------------------------------------------------------------------------
¯Â«ß ¯Â5«×(3/2) +¤j3«×(4/5)
F©M©¶
_____440_______
F - A C
352 528
bB©M©¶ C©M©¶
__________ ________
bB - D F C - E G
469.33 330 396
D©M©¶ A©M©¶
__________ ________
D #F - A -#C E
293.33 366.66 440 275 330
bE©M©¶ E©M©¶ B©M©¶
________ ___________ ___________
bE-G bB E - #G B B - #D- #F
312.89 469.33 412.5 495 495 371.25
(bE=bE4_G4 =396x4/5 =316.8 (32cent) bE =bE>G>bB 311.13 )
#A bB ¶ÂÁ䦳6­Ó­µ 457.8525 458.325 462 467.5 469.33 475.2
1. C261.63²Ä7ªx­µbB=457.8525
2. #F366.33¤j3«×#A=458.325
3. C264ªx­µ¯Â«ß²Ä7­µbB=462 -13cent C7=1 3 5 b7
4. A440 ²Ä17ªx­µbB=467.5 4.86cent
5. bB=bE4_bB4=316.8x3/2 =475.2 34cent bE =bE>G>bB
bE=(bE4_G4 =396x4/5 =316.8 32cent bE =bE>G>bB 311.13
6. bB4_D5 =293.33x4/5x2 =469.33 11cent bB= bB>D>F 466.16
F352 ²Ä21ªx­µbB=462 ( ¦P3) -13cent
( D293.33²Ä51ªx­µbB=467.5 ¦P4)
1. A=440
2. F=440x4/5=352 F©M©¶
3. C=352x3/2=528/2=264 F©M©¶
4. E=264x5/4=330 C©M©¶
5. G=264x3/2=396 C©M©¶
6. bB=352x2/3x2=469.33 bB©M©¶
7. #C=440x5/4/2=275 A©M©¶
8. D=440x2/3=293.33 D©M©¶
9. #F=293.33x5/4=366.66 D©M©¶
10.#G=330x5/4=412.5 E©M©¶
11.B =330x3/2=495 E©M©¶
12.bE=469.33x2/3=312.89 bE©M©¶
1. ¤j3¯Â«ßÀ³¥Î¹ê¨Ò ¤Ö¤kªº¬èëthe maidens prayer (t.badarzewska)
¥»¦±bE½Õ©M©¶ bA bB7 bE Fm
bA=bA>C>bE bA=bA4_C5 =264x(4/5)x2=422.4 (30cent)
bE=C_bE =264x(6/5) =316.8 (32cent)
bE=bA-bE 422.4 x3/2/2 =316.8 (32cent)
­Y C=264«h bA=422.4(30cent) bE=316.8 (32cent)
bE =bE>G>bB bE=bE4_G4 =396x4/5 =316.8 (32cent)
­Y G=396«h bB=bE4_bB4 316.8x3/2 =475.2 (34cent)
bB7=bB>D>F>bA bB=bB4_D5 293.33x4/5x2=469.33(11cent)
¥»­º¦±¤l bB¦³2­Ó­µ bB= bB7©M©¶ 469.33 (11cent)
bB= bE ©M©¶ 475.2 (34cent)
¥»­º¦±¤l¥D½ÕbE¤j½Õµ²§ô¬G©M©¶±Ä¥Î 475.2 (34cent)
2. ¯Â«ßÀ³¥Î¹ê¨Ò ¤j¥»¸Öºq283­º ¸r¼}-»P¥D¥æ³q
¥»¦±G ½Õ©M©¶¦³ G G7 D7
G=396(17cent)
B=495( 4cent)
D=297
#F=371.25(6cent)
3. ªx­µ¯Â«ß¼Ö¦±À³¥Î¹ê¨Ò µ¹·RÄRµ· (¨©¦hªâ) for elise (Beethoven)
¥»¦±©M©¶ C7 F Gm7 C G7 A9 G Cm E7 Am #D7
A9 = A #C E G bB bB=467.5Hz (A=440¤§17ªx­µ5cent) G391.88 57ªx­µ-0.5cent
C7 = C E G bB bB=462Hz (C=264¤§7ªx­µ-12.6cent) G396 3ªx­µ 17 cent
C7©M©¶¤§bB=462 bB¦³4­Ó­µ 12¥­§¡«ßbB=466.16
528-462=66 bB©M©¶469.33=11cent
200/66=3.0303 bE©M©¶475.2 =34cent
462-466.16=-4.16 C7©M©¶462=-12.6cent
-4.16x3.0303=-12.6 A9©M©¶467.5 = 5cent
­Y¬O¤j3«×¯Â«ß bB¦³2­Ó­µ bB7©M©¶ 469.33(11cent) bE©M©¶ 475.2(34cent)
* ¦b¦¹¤W­z2­µ¬Ò¤£©M¿Ó±Ä¥Îªx­µ¯Â«ßA9©M©¶bB=467.5Hz (A=440¤§17ªx­µ5cent)
¤]¸ûªñ12¥­§¡«ß¶Ç²Îťı²ßºD.
G¤j½Õ¯Â«ßD=297
4. F¤j½Õ ¤j¥»¸Öºq167­º¦³C7©M²Í F½Õ ·íC=264 C7=C E G bB
C264ªx­µ¯Â«ß²Ä7­µbB=462 (-13cent)
5. ¤j¥»¸Öºq405­º F¤j½Õ¯Â«ßbB¥HC7©M©¶¬°¥D=C E G bB
·íC=264 E-330 G=396 bB=462 (-13cent)
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