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1、纯律音阶大 3 度 5/4 小 3 度 6/5 完全 5 度 3/2 完全 8 度 2/1纯律 和弦产生法 12 平均律 1.A4=440 DCEGB 2.C4= A4_C5 =440x 6/5/2=264.00 15cent Am= ACE 261.63 3.E4= C4_E4 =264x 5/4 =330.00 2cent Am= ACE 329.63 4.G4= E4_G4 =330x 6/5 =396.00 17cent Em= EGB 392.00 5.B4= G4_B4 =396x 5/4 =495.00 4cent Em= EGB 493.89 13B=若#F=366.66 则
2、B=488.88-16cent Bm=BD#F 6.F4= A4_F4 =440x 4/5 =352.00 13cent Dm= D#C E 277.18 15=#c=#Fx3/2=371.25x3/2=278.44(7cent) #F=#F#A#C 9.#F4 B_#F =495x3/2/2 =371.25 6cent B = B#D #F 369.99 16= A4_#F4 =440x 5/6 =366.66 -15cent D = D #F#A #C 466.16 #A=#D_#A=309.375x3/2=464.06 18=#A=#Fx5/4=371.25x5/4=464.06(-7c
3、ent) #F=#F#A#C#D4 19= B4_#D4 =495x(5/4)/2=309.375 -8CENT B = B#D #F 311.13 #F4_#D4=366.66x5/6 =305.55 (bEm)#Dm=#D#F#A 10.#G4 #G4_E4 =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= bBDF 466.16 bB4_F5 =352x2x2/3 =469.33 11cent bB= b
4、BDF 466.16 21=bE4_bB4=316.8x3/2 =475.2 34cent bE =bEGbB 466.16 G4_bB4 =396x6/5 =475.2 34cent Gm =GbB.D 466.16 bD4 22=bB_bD5=469.34x(6/5)/2=281.604(25cent)bB=bBbDF 277.18 23=bD4_F4 =352 x(4/5) =281.6(25cent) bD=bDFbA 277.18 bG4 24=bB4_bG4=469.34x 4/5=375.472(23cent) bG=bGbBbD 369.99 bA4 25=bA4_C5 =26
5、4x(4/5)x2= 422.4 (30cent) bA=bACbE 415.3 bD4_bA5=281.6x3/2 =422.4 bD=bDFbA 415.3 bD_bA=281.6x 3/2=422.4 (30cent) bA=bDFbA 415.3 12.bE4 bB4_bE4 =469.33x2/3=312.89(9cent) bEm=bEbGbB 311.13 26=C4_bE4=264x(6/5) =316.8 (32cent) Cm= CbEG 311.13 C_bE 264x(6/5) =316.8 (32cent) bA=bACbE 311.13 bA-bE 422.4x3/
6、2/2=316.8 (32cent) bA=bACbE 311.13 bE4_G4 =396x4/5 =316.8 (32cent) bE=bEGbB 311.13 C #F293.33 - 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 = 1.262.37 x 6.8189 = 16.16 CENT 1.26x4.907975=6.184CENT C264 = 16 CENT #F371.25 =
7、 6 CENT 16cent=264.09720.0972 15cent=263.92990.1875 -13cent=275.14240.1424 17cent=395.93650.0320 -11cent=412.66810.2310 bB469.33=11 CENT F B396 - 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
8、 352 = 13 CENT B495 = 4 CENT 13cent=351.90640.0380 14cent=352.10470.1047 3cent=494.84200.0009 -17cent=366.4531GbB 311.13 )#A bB 黑键有 6 个音 457.8525 458.325 462 467.5 469.33 475.2 1. C261.63 第 7 泛音 bB=457.8525 2. #F366.33 大 3 度#A=458.325 3. C264 泛音纯律第 7 音 bB=462 -13cent C7=1 3 5 b7 4. A440 第 17 泛音 bB=4
9、67.5 4.86cent 5. bB=bE4_bB4=316.8x3/2 =475.2 34cent bE =bEGbB bE=(bE4_G4 =396x4/5 =316.8 32cent bE =bEGbB 311.13 6. bB4_D5 =293.33x4/5x2 =469.33 11cent bB= bBDF 466.16 F352 第 21 泛音 bB=462 ( 同 3) -13cent ( D293.33 第 51 泛音 bB=467.5 同 4)1. A=440 2. F=440x4/5=352 F 和弦 3. C=352x3/2=528/2=264 F 和弦 4. E=26
10、4x5/4=330 C 和弦 5. G=264x3/2=396 C 和弦 6. bB=352x2/3x2=469.33 bB 和弦 7. #C=440x5/4/2=275 A 和弦 8. D=440x2/3=293.33 D 和弦 9. #F=293.33x5/4=366.66 D 和弦 10.#G=330x5/4=412.5 E 和弦 11.B =330x3/2=495 E 和弦 12.bE=469.33x2/3=312.89 bE 和弦1. 纯律应用实例 少女的祈祷 the maidens prayer (t.badarzewska) 本曲 bE 调和弦 bA bB7 bE Fm bA=b
11、ACbE 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) 若 C=264 则 bA=422.4(30cent) bE=316.8 (32cent)bE =bEGbB bE=bE4_G4 =396x4/5 =316.8 (32cent) 若 G=396 则 bB=bE4_bB4 316.8x3/2 =475.2 (34cent)bB7=bBDFbA bB=bB4_D5 293.33x4/5x2=469.33 (11cent)
12、本首曲子 bB 有 2 个音 bB7 和弦 469.33 (11cent) bE 和弦 475.2 (34cent) 本首曲子主调 bE 大调退出故和弦采用 475.2 (34cent)2. 纯律应用实例 大本诗歌 283 首 羡慕-与主交通 本曲 G 调和弦有 G G7 D7 G=396(17cent) B=495( 4cent) D=297 #F=371.25(6cent)3. 泛音纯律乐曲应用实例 给爱丽丝 (贝多芬) for elise (Beethoven) 本曲和弦 C7 F Gm7 C G7 A9 G Cm E7 Am #D7 A9 = A #C E G bB bB=467.5H
13、z (A=440 之 17 泛音 5cent) G391.88 57 泛音- 0.5cent C7 = C E G bB bB=462Hz (C=264 之 7 泛音-12.6cent) G396 3 泛音 17 centC7 和弦之 bB=462 bB 有 4 个音 12 平均律 bB=466.16 528-462=66 bB 和弦 469.33=11cent 200/66=3.0303 bE 和弦 475.2 =34cent 462-466.16=-4.16 C7 和弦 462=-12.6cent -4.16x3.0303=-12.6 A9 和弦 467.5 = 5cent若是 3 度纯律
14、 bB 有 2 个音 bB7 和弦 469.33(11cent) bE 和弦 475.2(34cent) * 在此上述 2 音皆不和谐采用泛音纯律 A9 和弦 bB=467.5Hz (A=440 之 17 泛音 5cent) 也较近 12 平均律传统听觉习惯.G 大调纯律 D=297 4. F 大调 大本诗歌 167 首有 C7 和弦 F 调 当 C=264 C7=C E G bB C264 泛音纯律第 7 音 bB=462 (-13cent)5. 大本诗歌 405 首 F 大调纯律 bB 以 C7 和弦为主=C E G bB 当 C=264 E-330 G=396 bB=462 (-13ce
15、nt)附记:若 D 大调 Dm 和弦 D=293.33 为基音时其 19 泛音的 F=348.33( -4CENT) D 和弦 D=293.33 为基音时其 5 泛音的#F=366.66(-15CENT) 这时音阶分布上有点异样感.因为 G=396(18CENT) #F-G 纯律音阶和 12 平均律音 阶 有 33CENT 之差在音程上有大距离故要特别留意旋律进行时特殊现象.C 大调纯律 C 和弦 C=264(16cent) E=330(2cent) G=396(18cent) Am 小调纯律 Am 和弦 A=440 C=261.25(-2cent) E=330(2cent) Dm 和弦 D=293.33 其 19 泛音 F=348.33(-4cent) A=440结论:最好的调音应该以曲子作和声学的和弦频率分析再来订律制音阶. 和弦纯律 PURE CHORD TEMPERMENT
