音高和频率

October 28, 2007 1:33 pm UTC | In Study

音高和频率转换表如下(来源

Frequency in hertz (semitones above or below middle C)
Octave→
Note↓
0 1 2 3 4 5 6 7 8 9
C 16.352 (−48) 32.703 (−36) 65.406 (−24) 130.81 (−12) 261.63 (0) 523.25 (+12) 1046.5 (+24) 2093.0 (+36) 4186.0 (+48) 8372.0 (+60)
C♯/D♭ 17.324 (−47) 34.648 (−35) 69.296 (−23) 138.59 (−11) 277.18 (+1) 554.37 (+13) 1108.7 (+25) 2217.5 (+37) 4434.9 (+49) 8869.8 (+61)
D 18.354 (−46) 36.708 (−34) 73.416 (−22) 146.83 (−10) 293.66 (+2) 587.33 (+14) 1174.7 (+26) 2349.3 (+38) 4698.6 (+50) 9397.3 (+62)
D♯/E♭ 19.445 (−45) 38.891 (−33) 77.782 (−21) 155.56 (−9) 311.13 (+3) 622.25 (+15) 1244.5 (+27) 2489.0 (+39) 4978.0 (+51) 9956.1 (+63)
E 20.602 (−44) 41.203 (−32) 82.407 (−20) 164.81 (−8) 329.63 (+4) 659.26 (+16) 1318.5 (+28) 2637.0 (+40) 5274.0 (+52) 10548 (+64)
F 21.827 (−43) 43.654 (−31) 87.307 (−19) 174.61 (−7) 349.23 (+5) 698.46 (+17) 1396.9 (+29) 2793.8 (+41) 5587.7 (+53) 11175 (+65)
F♯/G♭ 23.125 (−42) 46.249 (−30) 92.499 (−18) 185.00 (−6) 369.99 (+6) 739.99 (+18) 1480.0 (+30) 2960.0 (+42) 5919.9 (+54) 11840 (+66)
G 24.500 (−41) 48.999 (−29) 97.999 (−17) 196.00 (−5) 392.00 (+7) 783.99 (+19) 1568.0 (+31) 3136.0 (+43) 6271.9 (+55) 12544 (+67)
G♯/A♭ 25.957 (−40) 51.913 (−28) 103.83 (−16) 207.65 (−4) 415.30 (+8) 830.61 (+20) 1661.2 (+32) 3322.4 (+44) 6644.9 (+56) 13290 (+68)
A 27.500 (−39) 55.000 (−27) 110.00 (−15) 220.00 (−3) 440.00 (+9) 880.00 (+21) 1760.0 (+33) 3520.0 (+45) 7040.0 (+57) 14080 (+69)
A♯/B♭ 29.135 (−38) 58.270 (−26) 116.54 (−14) 233.08 (−2) 466.16 (+10) 932.33 (+22) 1864.7 (+34) 3729.3 (+46) 7458.6 (+58) 14917 (+70)
B 30.868 (−37) 61.735 (−25) 123.47 (−13) 246.94 (−1) 493.88 (+11) 987.77 (+23) 1975.5 (+35) 3951.1 (+47) 7902.1 (+59) 15804 (+71)

一些解释:

  • Octave 0-9 表示八度区。C-D-E-F-G-A-B 为 C 大调七个主音:do re mi fa so la si(简谱记为 1 到 7)。科学音调记号法(scientific pitch notation)就是将上面这两者合在一起表示一个音,比如 A4 就是中音 la,频率为 440 Hz。C5 则是高音 do(简谱是 1 上面加一个点)。
  • 升一个八度也就是把频率翻番。A5 频率 880 Hz,正好是 A4 的两倍。一个八度区有 12 个半音,就是把这两倍的频率间隔等比分为 12,所以两个相邻半音的频率比是 2 开 12 次方,也即大约 1.05946。这种定音高的办法叫做 twelve-tone equal temperament,简称 12-TET。
  • 两个半音之间再等比分可以分 100 份,每份叫做一音分(cent)。科学音调记号加上音分一般足够表示准确的音高了。比如 A4 +30 表示比 440 Hz 高 30 音分,可以算出来具体频率是 447.69 Hz。
  • A4 又称 A440,是国际标准音高。钢琴调音师或者大型乐队乐器之间调音都用这个频率。
  • C4 又称 Middle C,是中音八度的开始。有一种音高标定方法是和 C4 比较相隔的半音数,比方 B4 就是 +11,表示比 C4 高 11 个半音。
  • MIDI note number p 和频率 f 转换关系:p = 69 + 12 x log2(f/440)。这实际上就是把 C4 定为 MIDI note number 60,然后每升降一个半音就加减一个号码。
  • 可以看到 E-F 和 B-C 的间隔是一个半音,而七个主音别的间隔都是两个半音,也叫一个全音。
  • 标准钢琴琴键有大有小,大的白色琴键是主音,小的黑色琴键是主音升降一个半音后的辅音()。一般钢琴是 88 个琴键,从 A0 到 C8。知道了上面这些,看到钢琴键盘应该就马上能找到 Middle C 了,如下
    钢琴琴键图
  • 音高间隔(音程)有各类说法,某些间隔的两个音同时发出来会比较令人身心愉快,比如频率比 3:2 的 perfect fifth 在各类乐曲都会广泛用作和弦。具体音高间隔名称:
    间隔半音数 间隔名 大致频率比
    0 perfect unison 完全一度 1:1
    1 minor second 小二度 16:15
    2 major second 大二度 9:8
    3 minor third 小三度 6:5
    4 major third 大三度 5:4
    5 perfect fourth 完全四度 4:3
    6 augmented fourth 增四度
    diminished fifth 减五度
    45:32
    64:45
    7 perfect fifth 完全五度 3:2
    8 minor sixth 小六度 8:5
    9 major sixth 大六度 5:3
    10 minor seventh 小七度 16:9
    11 major seventh 大七度 15:8
    12 perfect octave 完全八度 2:1
  • 人的听觉和很多音乐设备的频率范围是 20 Hz – 20000 Hz,但是成年人一般只能听到 30 – 15000 Hz,所以上面表格的频率范围已经足够用了。

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9 Comments »

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  1. 介绍的很好,下文怎么没了?
    其实还有个有趣的事情是 和声

    Comment by offall — November 4, 2007 5:10 pm UTC #

  2. 是不是评论不让超过两行啊)
    有那些倍频, 以及各自的频率如何
    都可以影响一个音听起来的效果,
    有空可以讲讲这个啊

    Comment by offall — November 4, 2007 5:12 pm UTC #

  3. 不好意思,贴了几次都贴不上来,是不是评论有什么关键词过滤

    Comment by offall — November 4, 2007 5:12 pm UTC #

  4. 不知道评论是什么问题,也许你需要刷新?

    有空我接着整理,都是我的笔记翻版贴出来的……

    Comment by atppp — November 4, 2007 8:37 pm UTC #

  5. 正想做个WAV to MIDI程序,参考了博主的资料,现在已经可以识别出Note了 :)

    Comment by Raptor — November 12, 2007 4:29 am UTC #

  6. 我能听到17000!

    Comment by chen3feng — December 30, 2007 8:35 pm UTC #

  7. 写得很棒,期待后续文章。

    Comment by 家园 — January 22, 2008 1:35 am UTC #

  8. p = 69 + 12 x log2(f/440)错了,应该是
    p = 9 + 12 x log2(f/440)

    Comment by zjzjtalent — September 4, 2012 8:24 pm UTC #

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