http://www.mayacafe.com/forum/topic1sp.php3?tkey=1109781671
That's one of the questions I'm most frequently asked by nonmusicians: why is the minor
"sad" and the major "glad"? Isn't this proof of the "affective" theory of musical
expression? The answer is no; whatever darkness, or sadness, or passion you feel when you
hear music in the minor mode is perfectly explainable in purely phonological terms. If you
think back to our first lecture when we discussed the harmonic series, or overtones, you'll
recall that one of the earliest overtones of many fundamental is the major third--a strong,
consonant overtone which is clearly heard as part of its fundamental. Along with its
neighboring overtone, the interval of the fifth, it contributes to the basic triad. Now
the minor third, which would turn that triad into a minor one, is a very late and
remote overtone way up here in the series--overtone number 18. So that when it is
emplyed to create music in the minor mode, it is at variance with the major third which is
implicitly present in the fundamental. This creates what is called in acoustics
"inteference", meaning that we are, so to speak, hearing both the major and the minor third
at once.
This interference of the two frequencies causes a phonological disturbance, which we hear
as a "disturbed" quality, a troubled, unstable sound. And so we call minor music
"troubled", "sad", "unstable", "dark", "passionate", or whatever. In other words, we
translate a phonological disturbance into an affective one. We are affected by it,
as in this Chopin Ballade. Now whatever subjective feelings we're going to report
about that, they're going to be "not satisfied"--the very opposite of our Beethoven
symphony (No.6), which is as major as can be.
But now we can explain this opposition in completely phonological terms. So we come to
realize that this so-called "affective" phenomenon of the minor mode is not an extrinsic
metaphorical operation at all; it is intrinsic to music, and its meaning is a purely
musical one...
-- The Unasnswered Question, Six Talks at Harvard, by Leonard Bernstein
- Re: 銆愰煶涔愩�戜负浠�涔堚�滃ぇ璋冩槑鏈楋紝灏忚皟闃撮儊鈥�posted on 06/17/2005
不一定。说调性有点倾向还凑合。各大调不一样，各小调也不一样。除了调性，其他音乐处理也有作用。
音乐的情绪刺激，显然有物理心理基础。 - Re: 銆愰煶涔愩�戜负浠�涔堚�滃ぇ璋冩槑鏈楋紝灏忚皟闃撮儊鈥�posted on 06/17/2005
"God" wrote:
不一定。说调性有点倾向还凑合。各大调不一样，各小调也不一样。除了调性，其他音乐处理也有作用。
音乐的情绪刺激，显然有物理心理基础。
心理学先搁一边。阿珊先讲讲物理学如何？声波的振动频率、能量、稳定性、变化趋势？色彩？跟人声的关系？我在这方面没有常识，但第一感觉是音乐调式的物理学原理一定是有的。 - posted on 06/17/2005
八十一子 wrote:
"God" wrote:心理学先搁一边。阿珊先讲讲物理学如何？声波的振动频率、能量、稳定性、变化趋势？色彩？跟人声的关系？我在这方面没有常识，但第一感觉是音乐调式的物理学原理一定是有的。
不一定。说调性有点倾向还凑合。各大调不一样，各小调也不一样。除了调性，其他音乐处理也有作用。
音乐的情绪刺激，显然有物理心理基础。
不能把心理学先搁一边，挑最简单的说，有的音，人根本就听不见。离开接受主体的学问在这里显然无用。音乐属于PSYCHO-PHYSICAL现像。 - Re: 銆愰煶涔愩�戜负浠�涔堚�滃ぇ璋冩槑鏈楋紝灏忚皟闃撮儊鈥�posted on 06/17/2005
夸张一点，锣鼓敲不出敲不出二泉映月的哀伤，二胡拉不出农民丰收的喜悦。这个也不奇怪。 - posted on 06/17/2005
我也读到了这段，觉得他试图从一个新的角度(大致是将和声构成与语言中语音语句类比的方法，我读得不完全明白)去分析一个大家都知道的现象的原因。
真正的原因，的确是学者也很难说清楚的。我对真正的原因不是很感兴趣，但现象是客观存在。但知道了伯恩斯坦的说法，可以加深一些认识。
至于上面其他各位讲音乐引起情绪和心里变化的原因是多方面的，的确如此，很复杂，也很主观。
谢阿珊分享。
阿姗 wrote:
http://www.mayacafe.com/forum/topic1.php3?tkey=1109781671 That's one of the questions I'm most frequently asked by nonmusicians: why is the minor "sad" and the major "glad"? Isn't this proof of the "affective" theory of musical expression? The answer is no; whatever darkness, or sadness, or passion you feel when you hear music in the minor mode is perfectly explainable in purely phonological terms. If you think back to our first lecture when we discussed the harmonic series, or overtones, you'll recall that one of the earliest overtones of many fundamental is the major third--a strong, consonant overtone which is clearly heard as part of its fundamental. Along with its neighboring overtone, the interval of the fifth, it contributes to the basic triad. Now the minor third, which would turn that triad into a minor one, is a very late and remote overtone way up here in the series--overtone number 18. So that when it is emplyed to create music in the minor mode, it is at variance with the major third which is implicitly present in the fundamental. This creates what is called in acoustics "inteference", meaning that we are, so to speak, hearing both the major and the minor third at once.
This interference of the two frequencies causes a phonological disturbance, which we hear as a "disturbed" quality, a troubled, unstable sound. And so we call minor music "troubled", "sad", "unstable", "dark", "passionate", or whatever. In other words, we translate a phonological disturbance into an affective one. We are affected by it, as in this Chopin Ballade. Now whatever subjective feelings we're going to report about that, they're going to be "not satisfied"--the very opposite of our Beethoven symphony (No.6), which is as major as can be.
But now we can explain this opposition in completely phonological terms. So we come to realize that this so-called "affective" phenomenon of the minor mode is not an extrinsic metaphorical operation at all; it is intrinsic to music, and its meaning is a purely musical one...
-- The Unasnswered Question, Six Talks at Harvard, by Leonard Bernstein - posted on 06/17/2005
八十一子 wrote:
心理学先搁一边。阿珊先讲讲物理学如何？声波的振动频率、能量、稳定性、变化趋势？色彩？跟人声的
关系？我在这方面没有常识，但第一感觉是音乐调式的物理学原理一定是有的。
I think it's a very interesting topic to study! I don't know much yet. In the past I had
always wanted to keep music and physics--two area of my "expertise"--completely separated, as
if the tempering of one with the other will destroy the beauty and the truth in each. These
days I have gained a lot more confidence in everything, in beauty and in truth, in music and
in physics, in arts and in science, and in the truth of Beauty and the beauty of Truth. It
is a good time for me to learn the physics of music and perhaps vice versa. Since I haven't
come across any satisfying theses on this topic, it will be a exciting and possibly rewarding
journey to take.
In fact, I thought about this topic last year when I decided to swtich field to do music. I
was interested in not only the physical aspects of music, but the metaphysical aspects of
it--not only what, how, but also why. OK, I know I am crazy. I am crazy. But only when I'm
crazy I feel a purpose. So let's hope I am kept crazy so I can report to you what I find
along the way.... - posted on 06/17/2005
下面这些刀客论坛的议论抄在这里备查。
独善斋主
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Posted on Tuesday, February 22, 2005 - 02:19 pm: Edit Post Delete Post View Post/Check IP Print Post
BBB，谢谢你的启蒙。
我有个问题，中国古代五音“宫、商、角、徵、羽”(即12356，且不管七音中的4和7)，每个音都构成调式。再结合十二律(黄钟 大吕 太蔟 夹钟 姑洗 仲吕 蕤宾 林钟 夷则 南吕 无射 应钟)，总共合成84种调式。
而西乐中，除了大、小调式之外，是否还有别的调式？因为如果只有大、小，则总共才24种调式。
按照我的理解，大调以(1)为主音，而小调以(6)为主音。那么，像《春江花月夜》为商调式(以2为主音)，《梁祝》徵调式(以5为主音)，在西乐中应该如何分类？
此外，按照中国古人的说法：
正宫、宜调怅雄壮 (等价于C大调)
黄钟宫、宜富贵缠绵 (等价于降B大调)
南吕宫、宜感叹伤惋 (等价于G大调)
道宫、宜飘逸清幽 (等价于F大调)
和你所列举的调式有相近之处，也有些不同之处，老兄是否能谈一些这方面的见解。刘伶借问谁家好，李白还言此处佳。
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guanzhong
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Posted on Tuesday, February 22, 2005 - 04:58 pm: Edit Post Delete Post View Post/Check IP Print Post
职业音乐家也未必能分辨绝对音高的差别。我儿子的钢琴教师则有这个本事，...
When working on an oil field, I was in a band for a while (for Zhi4 Qu3 Wei1 Hu3 Shan1, you know, one of the eight "modern Peking operas"). Our conductor, an amateur singer, was able to find an absolute tone by first going down to the lowest possible note he could sing, and then coming up from there. It turned out to be pretty close to the note played by an instrument.
菊子不能走! 四川饭庄? 同去同去的说!
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guanzhong
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Posted on Tuesday, February 22, 2005 - 05:41 pm: Edit Post Delete Post View Post/Check IP Print Post
Talking about Chinese music, I have some long existing questions as well.
In western music, there are 12 notes in an octave, which are equally separated, i.e., any two consecutive ones are half-step apart. On the other hand, in traditional Chinese music, as 斋主 mentioned above, there are only five notes (without F and B). But the amazing thing is, the five notes precisely match five of the 12 notes in western system (C, D, E, G, A)! That is, these five notes are not equally separated in the frequency range of the octave, as some are one step apart (e.g., between C and D), some are one and a half steps apart (e.g., between E and G), as if they were meant to match the 12 notes in the western system.
The question is, then, were the two music systems really independently developed? If so, what is the chance for the notes in these two systems to match so perfectly? Why don't the five Chinese notes divide the octave evenly? For that matter, do we know any music system in the world history that does not match the 12 tones in the octave? How would such music sound? It must feel very strange, I imagine.
So, does this phenomenon indicate some common human characteristic shared by all cultures?
Anybody, any thought?
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八十一子
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Posted on Tuesday, February 22, 2005 - 06:50 pm: Edit Post Delete Post View Post/Check IP Print Post
管仲所说中国的音阶跟西方的暗合这一点很有意思。
我猜东西方音乐不是独立发展的，大概根子都在印度。这只是自己的感觉，既没有读到过有关论著，自己也没有求过证。
现存的原始部落都有随意的吟唱和节奏，但没有系统的旋律。看来有系统旋律的音乐是文明发展到相当高的程度时的产物。
音乐和语言相通。欧洲的语言发源于印度，音乐的根在印度是有可能的。中国的文化的根究竟在那里？从前认为可能是独立发育的，现在看来，就跟“北京人”化石代表的直立人并不是中国人的祖先一样，中国文化独立发育这个论点有问题。我看有可能是印度古文化的另一个分支。姑且存疑。签名散见于信用卡账单
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BBB
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Posted on Wednesday, February 23, 2005 - 06:21 am: Edit Post Delete Post View Post/Check IP Print Post
斋主，你的国民乐方面的知识真丰富，我在这方面几乎是空白。知道一点五声音阶，据说是中国民乐和日本民乐都用，而且可以用钢琴的黑键来演奏。西方音乐中也有人在其作品中用过，比如肖邦，德彪西等。
大小调式是西方音乐到17世纪最后发展成形。之前有教会调式，先有8种调式，后来加了4种，其中各音都有其的特性和功用，好像各音也都是后来的大小调式中适用的。
“大调以(1)为主音，而小调以(6)为主音”，是在首调唱名法(Tonic Sol-fa)中，无论哪个大调音阶，其第一级音总唱成 doh, 同音阶的小调(关系小调)的主音则总是在这个大调的第六级，所以唱 la。比如C大调，C，D，E，F，G，A，B，中，C唱成doh(简谱中1)，而同音阶的小调(无升降号)为A小调，主音是A，在C大调中唱la (6)，其实A小调音阶应当是A，B，C，D，E，F，G，主音A是音阶中的第一级。这个方法是19世纪中英国人发明的，为了视谱练唱的方便。
老八和关中，
关于西方音乐的起源，我读的东西，大概都追述到地中海文明，古希腊，到基督教教堂音乐(格里高利圣咏等)。地中海是东西方交界处，至于东方的音乐与西方音乐那时或之前，有没有相互影响，没有读到过这方面的东西。我读历史，从近代到古代，越古知道得越少。
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独善斋主
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Posted on Wednesday, February 23, 2005 - 07:40 am: Edit Post Delete Post View Post/Check IP Print Post
我猜东西方音乐不是独立发展的，大概根子都在印度。这只是自己的感觉，既没有读到过有关论著，自己也没有求过证。
老八，有空求证一下。
BBB: 你的国民乐方面的知识真丰富，我在这方面几乎是空白。大小调式是西方音乐到17世纪最后发展成形。之前有教会调式，先有8种调式，后来加了4种，其中各音都有其的特性和功用，好像各音也都是后来的大小调式中适用的。
我是门外汉。只是很感兴趣，尤其中西之比较。看了你的文章后学到不少知识。
管仲说： In western music, there are 12 notes in an octave, which are equally separated, i.e., any two consecutive ones are half-step apart. On the other hand, in traditional Chinese music, as 斋主 mentioned above, there are only five notes (without F and B). But the amazing thing is, the five notes precisely match five of the 12 notes in western system (C, D, E, G, A)!
我觉得管仲在这里有个误解，中国自古(周朝，记于吕氏春秋)就有十二平均律：
黄钟(C) 大吕(#C) 太蔟(D) 夹钟(bE) 姑洗(E) 仲吕(F) 蕤宾(#F) 林钟(G) 夷则(bA) 南吕(A) 无射(bB) 应钟(B)
这十二平均律等价于西乐中的绝对音高。
而中国古代五音“宫、商、角、徵、羽”(即12356，七音中的变徵、变宫，即4和7)，为乐曲中的相对音高。
西方作曲常用七声音阶，而中国古曲常见五声音阶。我们可以用C、#C、bE……的任何一个音高作为宫(1)来构成音阶。 例如，以黄钟(C)为宫(1)，被称为“正宫调”，等价于西乐中C大调；以夹钟(bE)为宫(1)，称为“中吕宫”，即西乐之降E大调。
尽管12律乘7声有84调，而实际上音乐家们只用到很少的一些调式。
ZT 一段：现在我们找一根弦，长度为8.71寸。这根弦发出的音就是黄钟音，我们按住黄钟音的2/3，的地方弹一下，就得到了林钟音，再取林钟音的4/3就得到了太簇，取太簇的2/3就得到了南吕，南吕的3/4就得到姑洗……以此类推，我们可以得到十二律中所有的音。这就是所谓的：“黄钟生林钟，林钟生太簇，太簇生南吕，南吕生姑洗，姑洗生应钟，应钟生蕤宾，蕤宾生大吕，大吕生夷则，夷则生夹钟，夹钟生无射，无射生仲吕”。这种音的生成方法就称为“三分损益法”。而在西洋音乐理论中称之为“五度相生律”。刘伶借问谁家好，李白还言此处佳。
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Lou Lan
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Posted on Wednesday, February 23, 2005 - 08:51 am: Edit Post Delete Post View Post/Check IP Print Post
哇塞，几位蓝银越侃越玄乎了么！对俺们外行真是“公伤觉着愚”，俺还是瞧一眼走人，哼唧俺的“鼻子独奏”，炮制俺的“麻婆豆腐”去咧！
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八十一子
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Posted on Wednesday, February 23, 2005 - 09:50 am: Edit Post Delete Post View Post/Check IP Print Post
现代人类在大约二十五万年前从非洲出走，经西亚，再分两路，分别进入东亚和欧洲。这些移民路线和年代现在大致已经有轮廓了。
从笛子一类定了音的乐器在全世界的分布、沿革和变化，跟移民路线和年代联系起来，大概可以下手研究东西方音乐的关系。谁跟中央音乐学院有联系，请把这个题目给他们。绝对是青史留名的工作。
远古时的移民方向不可能只是单向，也不会是一次性。双（多）向和重复性决定了地域文化完全独立发展是不可能的。
这样看，西亚（印度、波斯）跟中国的联系应该是远在佛教传入中国之前。签名散见于信用卡账单
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guanzhong
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Posted on Wednesday, February 23, 2005 - 01:06 pm: Edit Post Delete Post View Post/Check IP Print Post
"中国自古(周朝，记于吕氏春秋)就有十二平均律："
That is even more amazing, a perfect match between Chinese and western system! There must be a reason!
"ZT一段：现在我们找一根弦，长度为8.71寸。这根弦发出的音就是黄钟音，我们按住黄钟音的2/3，的地方弹一下，就得到了林钟音，再取林钟音的4/3就得到了太簇，取太簇的2/3就得到了南吕，南吕的3/4就得到姑洗……以此类推，...."
This is in terms of wavelength. In terms of frequency (reciprocal of wavelength), multiplying frequency of C by 3/2=1.5 you get the frequency of G, multiplying that by 3/4=0.75 you get D, multplying that by 1.5 you get A, etc.
But note that this is only an approximation. The ratio between the frequencies of two consecutive notes (half step) is the 12th root of 2, 1.059463, so that the 12th note is 12th power of this number, i.e., the frequency is doubled in an octave. The ratio between two notes a full step apart is the 6th root of 2, i.e., 1.12246, but this ratio by 三分损益法 is 1.5 x 0.75 = 1.125, i.e., an accumulated error will be generated when this process is repeated.
There must have been some theory about the relationship between Chinese and western music systems. Hope some one can dig out more. It is really interesting.
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独善斋主
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Posted on Wednesday, February 23, 2005 - 01:27 pm: Edit Post Delete Post View Post/Check IP Print Post
管仲真不愧是个科学家，你是对的。按三分损益法得到的音只是近似，见下面的ZT。
ZT：十二律的名称初见于《国语》，西周编钟已刻有十二律中的一些铭文。以黄钟为标准音高之首，逐次按半音降低，就形成了十二律。最早的乐律计算法见于《管子• 地员篇》中的“三分损益法”，约产生于公元前7～3世纪间，即将主音律的弦（或管）长三等分，取其两份（全管长的2／3，为损一），或增加一份（全管长的 4／3，为益一），依次确定十二律中其他各律的方法。这种以弦长为准的方法，与欧洲当时以频率为准的“五度相生法”是成倒数关系的。16世纪末，朱载堉提出了十二平均律的理论和算法。十二平均律是我国对音乐声学的重大贡献。
按三分损益法得到的音相差不是2^(1/12)倍，而仲吕三分益一后得到得到的竟然不是黄钟的1/2，而是262144/531441=~0.493。也就是说，黄钟音还不了原。关于黄钟音归位的问题一直困绕着中国古代音乐家。直到明代，才由科学家朱载堉在世界音律史上首次建立十二平均律的数理理论，即采用2^(1/12)倍的关系生律，使得黄钟音终于能够顺利的 “归位”。
我在《黄金分割率与人生哲学》一文中写到: 那么我们看看中国最古老的古琴，处处透着黄金分割的神奇。至于古琴发明何时已无考，传说中有伏羲、神农、或是舜帝。琴背两池，左龙右凤。控制琴弦发音的枢纽有三: 轸，凫掌，凤嗉。琴有五弦，音有八度。琴节为徽，“以琴长全体三分损一，又三分益一，而转相增减”，全弦共有十三徽。把这些排列到一起，二池，三纽，五弦，八音，十三徽。多么奇妙的排列，恰是费波那奇数，而两个相邻费波那奇数之比率则越来越接近黄金分割率。是有意还是巧合? 看来，中国古人对黄金分割的领悟与运用，与西方确有异曲同工之妙。
刘伶借问谁家好，李白还言此处佳。
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guanzhong
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Posted on Wednesday, February 23, 2005 - 03:48 pm: Edit Post Delete Post View Post/Check IP Print Post
斋主, 科学家说不上, 只不过好玩罢了. 能不能给个你上面ZT的出处? 中国音乐史我知之甚少, 原来12次方根的关系是中国人发现的, 了不起! 先谢了!
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BBB
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Posted on Wednesday, February 23, 2005 - 08:06 pm: Edit Post Delete Post View Post/Check IP Print Post
< <简明牛津音乐史>>(The Concise Oxford History of Music, by Gerald Abraham 1979)上面对西方音乐之外的音乐作了些非常简略的介绍。其中谈到，中国音乐在六世纪开始受到外来影响，首先是沿着中亚贸易路线，佛教传教士带来了他们自己的礼仪圣歌。。。新的乐器也从西亚传入：波斯的琉特琴是中国的琵琶，波斯的长琉特琴赛特尔琴(字面意思为“三弦”，印度著名的西塔尔琴)就是中国的三弦，波斯的竖琴扬克琴就是中国的箜篌。
也提到上面斋主提到的朱载堉：“明朝的一部不朽著作是大型音乐百科全书<<乐律全书>>，由宗室子弟朱载堉出版于1606年。它包括了一部中国音乐史，不仅保存了大量古老的礼仪旋律，还尝试原有乐队伴奏的重建。这位宗室子弟还是个重要的理论家，在欧洲人之前率先发现了平均律的概念，并用2的12次方根计算出平均律律管的长度。”
这里说的1606 年，也是西方音乐史发展中的最重要的历史时刻之一：意大利作曲家蒙特威尔第(Claudio Monteverdi, 1567-1643)创作第一部歌剧<<奥菲欧>>，第二年初首演。歌剧第一次用完整的乐队为其伴奏，是现代歌剧发展的起点。
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guanzhong
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刚才上网遛狗, 找到不少文章提到朱载堉发明的十二平均律, 现ZT 一篇如下(http://www.chinaschool.org/sgyy/FFFF/fff02/fff01.htm):
苗 建 华
在中国古代优秀的科技成果中，除了广为人知的火药、造纸术、指南针和印刷术这“四大发明”外，还有一门鲜为人知的“千古绝学”——中国古代律学。律学，是运用物理分析、数学验算等科学的分析方法，研究乐音体系中音高体制及真相互的数理逻辑关系的科学。
中国很早便知道了音阶各音之间的关系和生成规律，并称有固定高度的乐音为“律”。律学当然是在音乐实践基础上产生的，但不久便脱离了音乐实践。因为律有 12个，一年也有12个月，由于数字上的相同，早在战国时期，音乐的律和年月的历便被认为是内里一致的事物而被同等看待了。而历又被视为统治者的命脉，是自己的统治“应天承运”的标志，所以一个新朝建立的头等大事就是“定正朔”，新颁历法，与对历的重视和研究、计算一起，律也一直受到重视和研究、计算。因此，一部“廿四史”，除了“乐志”，每朝都立“律志”、“律书”及“律历志”之类的篇章。
明代中国音乐史上出现了一件具有划时代意义的事件——“新法密率”的发明。新法密率即十二平均律，由计算方法求得了12律之间完全平均的音高关系，求得的各律之间最精密的比率。他的发明比西方约早一个世纪。不过由于当时乐器制作的条件限制，他的发明并不能用于音乐实践之中，到后来，连他的学说也或者渐渐给人遗忘了，或者并不能看出它里面深刻的革命意义。但从律学上说，十二平均律的发明是音乐从古代走向近代的基础。这位发明者就是被誉为“东方文艺复兴式人物”的朱载堉。他是一个科学家、律历学家、文学家，也是一个音乐家，是明代的一颗科学艺术巨星，是中国音乐史乃至世界音乐史上的一位伟人。
朱载堉(1536一1611)，字伯勤，号句曲山人，河南怀庆府 (今沁阳)人。朱氏出身皇族，为朱元漳的九世孙，是明宗室郑恭王朱厚烷之子。载自幼聪明过人，“儿时即悟先天学。稍长，无师授，辄能累黍定黄钟，演为象法、算经、审律、制器、音协节和，妙有神解”(《河南通志》)，弱冠之时，即喜读《性理大全》、《律吕新书》、《洪范》、《皇极内篇》等著作，而且“口不绝诵，手不停披，研究既久，数学之旨颇得其要”(朱载堉《进历书奏疏》)。
朱载堉一生经历坎坷，其父厚烷布衣疏食，生活节俭，因上书规谏皇帝和贵族内讧，于嘉靖二十九年被削爵禁锢在安微凤阳。少年遭此变故的朱载备尝世态之炎凉，对封建贵族亲友之间看似仁义道德，实则虚伪残酷的人际关系有了深刻的认识。他在《黄莺儿·求人难》一曲里写道：
“自己跌倒自己爬，指望人扶都是假。至亲人说的是隔山话，虚情儿哄咱，假意儿待咱，还将冷眼观。时下且休夸，十年富贵，再看在谁家?”
跨海难，虽难犹易；求人难，难到至处。亲骨肉深藏远 躲，厚朋友绝交断义。相见时项扭头低，问着他面变言迟。俺这里未曾开口，他那里百般回避。锦上花争先添补，雪里 炭谁青送去。听知!自己跌倒自己起，指望人扶耽搁了自己。”
看破红尘的朱载，痛心于父亲的无故遭难，遂自甘淡泊，筑土室于宫外，“席藁独处者十九年”，潜心学术。其父获释复爵后，载虽重归王室，但仍矢志不移，钻研学问，不惜放弃王位、转让爵位，而以著述终身，最后遂成大业。他一生共写有《乐律全书》、《嘉量算经》、《律吕正论》、《瑟谱》、《醒世词》等著作，其中《乐律全书》代表了他的最高成就。
《乐律全书》是一部划时代的巨著，全书共四十七卷，涉及律学、乐学、舞学、历学、算学等学科，汇集十四种著作而成，包括《律学新说》、《乐学新说》、《算学新说》、《律吕精义》、《操缦古乐谱》、《旋官合乐谱》、《乡饮诗乐谱》、《六代小舞谱》、《小舞乡乐谱》、《二佾缀兆图》、《灵星小舞谱》、《圣寿万年历》、《万年历备考》、《律历融通》等。《乐律全书》文字部分约有六十万字，占全书的一半左右，其余的为乐谱和舞谱。有关新法密率的计算成果在《律历融通》、《律学新说》、《律吕精义》、《算学新说》中都有所见。
过去认为新法密率的计算成果在万历十二年 (1584年)或万历二十四年(1596年)完成，李纯一先生根据《律历融通》的记述，推测出朱载堉应在万历九年(1581年)就完成了计算，将其发明年代提前了数年，订正了旧说。
新法密率的发明是朱载堉在中国律学史上作出的最伟大贡献，它彻底解决了自先秦以来历代律学家所未能解决的黄钟不能还原的历书难题。
中国乐律史上最早产生完备的律学理论，称为“三分损益律”，它大约出现千春秋中期。《管子·地员篇》、《吕氏春秋·音律篇》分别记述了它的基本法则：以一条弦长为基数，将其均分成三段，舍一取二，“三分损一”，便发出第一个上五4度音；如果将均分的三段再加一段，“三分益一”，便发出第一个下4度音，用这种方法继续推算下去，可得12个音，称“十二律”，每律有固定的律名，即：
黄大太夹姑？仲林夷南无应
钟吕簇钟冼吕宾钟则吕射钟
因为这种“生律法”是一步步推算5度音，所以又叫“五度相生律”。
“三分损益”虽然推演出“十二律”，但计算到最后一律时却不能循环复生，它是一种不平均的“十二律”，各律之间含有大、小半音之别。因此，为了寻求一种可以自由地旋宫转调的平均律制，就成了两千多年来乐律学家们孜孜以求的理想。
汉代著名律学家京房（前77一37）沿着五度相生的方法连读推算下去，至第53“色育”律时，己基本还原到出发伟“黄钟”（欧洲在16世纪时也出现过53平均律）。
他最后算到60律，后世称“京房律”。表面上看，京房推算60律的繁复律制，与简练的十二平均律理想南辕北辙，但如果抛开它神秘主义的外衣，他在运算过程中得到的许多律高，都可以在曾侯乙编钟所体现的“钟律”上予以印证。南朝的钱乐之、沈重在京房60律的基础上继续按“二分损益法”推演生律，直至更为周密的360律。他们把还生黄钟本律的音差数缩小到最少程度，从而为从其中选择十二平均律各音提供了更大的可能性。但同时沿此途求解十二平均律的探索也步入 “山穷水尽”的困境。
不无巧合的是，与钱、沈同时代的乐律学家何承天（370一447）大胆提出一种“新律”。他的作法是把第十二律不能还原所剩的误差数，分作十二份，每律增补一份。
十二次相生后，正好回归黄钟律。这可以说是天才的十二平均律构想，何承天在当时几乎就要叩开这一高深莫测的律制的大门了，可惜他不是按频率比计算，而是依弦长计算，难题再度搁浅。 隋代刘焯（581一618）摆脱“三分损益律”的羁绊，以振动体长度桐邻律之间的差数相同，推算出“十二长度等差律”。王朴（905一959）于959年又提出一种“新律”，以倍半关系的八度音程硬性调整各律。他清楚地认识到，解决不平均律的矛盾只能在12律范围内进行，但他的基本方法还是在“三分损益法”上修修补补。
经历乐如此漫长的探索和徘徊，至明朝中时，皇族世了朱傤堉（1536一1611）终于成为登上律学的宝塔顶摘取“十二平均律”明珠的第一人。他以珠算开方的办法，求得律制上的等比数列，第一次解决乐十二律内自由旋宫转调的千古难题，实现了千余年来无数律学家梦寐以求的理想。
朱载堉在《律吕精义》一书里详细记述了新法密率的计算方法和成果：
度本起于黄钟之长，即度法一尺。命平方一尺为黄钟之率。东西十寸为句，自乘得百寸为勾幂；南北十寸为股，自来得百寸为股幂；相并共得二百寸为弦幂。乃置弦幂为实。开平方法除之，得弦一尺四寸一分四厘二毫一丝三忽五微六纤二三七三0九五0四八八0一六八九，为方之斜，即圆之径，亦即蕤宾倍律之率；以句十寸乘之，得平方积一百四十一寸四十二分一十三厘五十六毫二十三丝七十三忽0九五o四八八0一六八九，为实，开平方法除之，得一尺一寸八分九厘二毫0七忽一微一纤五00二七二一0六六七一七五，即南吕倍律之率；仍以句十寸乘之，又以股十寸乘之，得立方积一千一百八十九寸二百0七分一百一十五厘00二毫七百二十一丝0六十六忽七一七五，为实，开立方法除之，得一尺0五分九厘四毫六丝三忽0九纤四三五九二九五二六四五六一八二五，即应钟倍律之率。……是故各律皆以黄钟正数十寸乘之为实，皆以应钟倍数十寸0五分九厘四毫六丝三忽……为法除之，即得其次律也。
上述记载显示朱载堉利用了“勾股术”、“开平方术”、“开立方术”等算术成就来完成自己的运算，他先求出八度的二分之一即蕤宾律之长( ２＝1．414213……)，次求八度的四分之一即南吕律之长( 1．414213＝1．189207……)，再求八度的十二分之一即应钟律之长( 3 1．189207＝ 1．059463……)。十二律中黄钟为始，应钟为终，周而复始，循环无端。应钟之数既得，欲求十二律中某律的数值，以比其律高一律的数值乘以黄钟正律十寸，再除以应钟倍律数10．59463……寸即可得，其详细结果如下：
黄钟倍律＝2 (c)
大吕倍律＝1．887748……(#c)
太簇倍律＝1．781797……(d)
夹钟倍律＝1．681792……(#d)
姑洗倍律＝1．587401……(e)
仲吕倍律＝1．498307……(#f)
蕤宾倍律＝1．414213……(f)
林钟倍律＝1．334839……(g)
夷则倍律＝1．259921……(#g)
南吕倍律＝1．189207……(a)
无射倍律＝1．122462 (#a)
应钟倍律＝1．059463……(b)
黄钟正律＝l (c)
朱载堉新法密率的发明使中国在明代居于世界律学领域的先导地位，其成果在西方产生了强烈反响，引起了欧洲学术界的赞叹。德国人赫尔姆霍茨说道：“在中国人中，据说有一个王子叫朱载堉的，他在旧派音乐家的大反对中，倡导七声音阶。把八度分成十二个半音以及变调的方法，也是这个有天才和技巧的国家发明的。” 英国李约瑟博士也说“朱载堉对人类的贡献是发明了将音阶调谐为相等音程的数学方法”，“平心而论，在过去的三百年间，欧洲及近代音乐确实有可能曾受到中国的一篇数学杰作的有力影响，……第一个使平均律数学上公式化的荣誉确实应当归之中国”。由于朱载堉的发明在欧洲影响巨大，半个多世纪以来，很多人提出朱氏理论启示了欧洲十二平均律的产生。
朱载堉的新法密率尽管在国外引起人们的赞叹，而在国内却备受冷落，并因受到当时诸多主观、客观条件的限制，一直未能付诸实践。其成果进献宫廷后，不但被“宣付史馆，以备稽考，未及实行”，而且还遭到一些人的攻击。清《律吕正义后编》就曾罗列了新法密率的十大罪状，《四库全书总目提要》也对新法密率作出了不公正的评判。朱载堉的新法密率于东方开花而在西方结果，不能不说是我国音乐史上一件令人倍感遗憾的事情。
朱载堉在律学上的又一贡献是“异径管律”的首创。我国晋代律学家荀勖曾制十二支同径的笛来寻求管口校正数，而朱载堉则认为“律管修短既各不同，则其空围亦当有异”，另辟蹊径，提出了“异径管律”系统的管口校正方法。其结果是使按半音依次排列的各律管的管径构成以为比率的等比数列。朱载堉“异径管律”的发明也引起世界注目，比利时声学家马容就因朱氏的成果说道：“在管径大小这一点上，中国的乐律比我们更进步了，我们在这方面，简直一点还没有讲到。”
朱载堉的异径管律和他提出的“新法密率”，是中国古代科学技术对世界文明的一大贡献。它通过严密的数理计算，大量的实验探索以及巧妙的工艺设计，一举解决了十二平均律制下全套律管的系统管口校正这一物理难题，确立了制作十二平均律音高标准器的基本规范，并成功地提供了第一个实际可行的制作方案、实物模型和测音结果。
1986年9 月，为纪念朱载堉诞辰四百五十周年，国内举行了隆重的纪念活动，在学术讨论会所发的函告中，对朱氏有以下评价：“他第一个提出十二平均律的理论原理——比欧洲早半个世纪；第一个创造出按照十二平均律原理发音的乐器——弦准；第一个发现‘异径管律’的规律；第一个在算盘上进行开方计算；第一个得出求解等比数列的方法；第一个创立‘舞学’一词，并为这一学科规定了内容大纲。”从这六个第一看来，朱载堉的发明创造涉及科学、艺术领域。作为近代科学和音乐理论的先驱，他的发明代表了明代自然科学与艺术科学的最高成就。他不愧为我国明代的科学与艺术巨星，无愧于“东方文艺复兴式的人物”的称号。
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LiaoKang
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Posted on Wednesday, February 23, 2005 - 09:17 pm: Edit Post Delete Post View Post/Check IP Print Post
问题是，朱载堉对中国后世的影响有多大呢？
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独善斋主
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Posted on Thursday, February 24, 2005 - 05:14 am: Edit Post Delete Post View Post/Check IP Print Post
廖康： 问题是，朱载堉对中国后世的影响有多大呢？
不大。关键是，中国历代都把科学当作雕虫小技。
管仲：能不能给个你上面ZT的出处?
你叼来的那篇更详细！刘伶借问谁家好，李白还言此处佳。
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BBB
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Posted on Thursday, February 24, 2005 - 06:28 am: Edit Post Delete Post View Post/Check IP Print Post
不大。关键是，中国历代都把科学当作雕虫小技。
昨晚读到那段，看到同时间西方音乐发展，我也这么想。在此之前，15世纪，甚至更早的一些西方音乐(古乐)，近十多年来在西方演出很热，国内的西方古乐爱好者也愈来愈多。我前面讲，这两年也受影响，接触了不少。
谢斋主找来这篇，非常受益！
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guanzhong
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Posted on Thursday, February 24, 2005 - 09:52 am: Edit Post Delete Post View Post/Check IP Print Post
"中国历代都把科学当作雕虫小技"
That is an old but also very sad topic. For thousands of years, Chinese culture has always emphasized philosophy, literature, and poetry, mostly based on abstract thinking, interesting but impractical. Even if there were some individual efforts and inventions in technology and science, they were mostly treated as unworthy (奇技淫巧) and disgarded. Occasionally we see a few important scientific and mathematical sparks shining here and there in the long civilization, but China has never really had any systematic development in science and technology. While science and technology has been studied and taught in the west over many hundreds of years, China did not have such education in any form as recent as one hundred years ago. I agree with those who say Chinese culture, when compared with western cultures, is a premature one, which skipped much of the young age with strong curiosity in the objective world (science and technology), but jumped into the old age of abstract and subjective thinking (philosophy and literature) too fast too soon. Very unfortunately, the brain of Chinese culture seems to have much too weak a left hemisphere compared to the right one.
As much as I appreciate and enjoy the ancient Chinese philosophy and poetry, I can't help but think just because of such out-of-proportion advancements, China was very much behind in science and technology, and, consequently, beaten badly too many times by much younger but more practical civilizations during the last two hundred years. After taking over the entire domain of science and tochnology, the west may look back at some ancient Chinese philosophy and literature, and enjoy a few thoughts here and there, over a few beers. But we know only too well none of those thoughts helped us in any way avoid being beaten. We may appreciate the thoughts like "庄生梦蝶或蝶梦庄生", "子非我安知我不知鱼之乐", we may also enjoy the poems praising the beauty of the spring flowers and autom moon, do they actually matter?
Also I don't really appreciate those ancient poems (way too many of them) that glorify personal sadness (愁), although they may be very beautifully written. If you feel sad, why don't you just go figure something else out in science or math and be happy? Too many such sentimental but useless intellectuals will only harm the country.
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78级
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Posted on Friday, February 25, 2005 - 06:19 am: Edit Post Delete Post View Post/Check IP Print Post
"That is an old but also very sad topic. For thousands of years, Chinese culture has always emphasized philosophy, literature, and poetry, mostly based on abstract thinking, interesting but impractical."
Hi Guanzhong and everyone,
Very intriguing topic.
I see what you are trying to say, but I am not sure if I can agree with you completely. Is philosophy itself to blame? I know very little about Western history, it may be out of place for me to talk about this. But I believe, after medieval, there was a period of time during which the enlightenment philosophy had an enormous and profound influence on just about every aspect of Western culture – music, art, literature, let alone politics. Even the Russian empress Catherine the Great self-claimed to be an “enlightened monarch”. And it may not be a great exaggeration that all the modern music, art, literature, as well as science, are developed from the ground of enlightenment philosophy.
It is also interesting to notice the impact of Christianity on the development of Western culture. No need to talk about music and art, just think about architecture, the cathedrals. I wouldn’t be surprised that the advance in architecture stimulated mechanics, which in turn stimulated math. Perhaps even the discovery of calculus can be attributed to Christianity in an indirect way.
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LiaoKang
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Posted on Friday, February 25, 2005 - 08:32 am: Edit Post Delete Post View Post/Check IP Print Post
当然不该指责哲学，哲学实际上就是“热爱知识”，到了近代才与自然科学分野。但我越来越觉得我们传统文化没有这种对知识的热爱。个人的热爱当然有，但始终没有形成气候，几千年的才华精力多花在人伦关系上了。三大宗教也反映了求知，反映对绝对理念的追求。甚至我们认为的很多意外或自然发生的事情，他们都要说出个道道来。
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guanzhong
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Posted on Friday, February 25, 2005 - 09:42 am: Edit Post Delete Post View Post/Check IP Print Post
Welcome class 78! Glad you are finally here!
Actually I totally agree with you in terms of the importance of philosophy, and personally, I enjoy this kind of profound thinking about both the objective and subjective worlds. Actually there was an interesting discussion about some issues in logic and philosophy on CND a while ago
(http://my.cnd.org/modules/newbb/viewtopic.php?topic_id=30160&forum=2&start=0&viewmode=flat&order=0) I think you may be interested in reading some of the posts there.
However, the point I was trying to make in my post above is that in traditional Chinese culture, philosophy, and more generally, abstract thinking, is out of proportion, out of balance, and out of order. There always seemed to have a lot of philosophical thinking in the early stage of any civilization (e.g., ancient Greece), when little was known about the objective world around. However, while such thinking was closely associated with the early development of science and math in the west, it does not seem the case in Chinese civilization (except there may be some primitive chemistry in the practice of Taoism, which didn't lead to anywhere). Moreover, when math, science and technology gradually grew out of the early stage of philosophy and became independent fields of study in the west, no similar process took place in Chinese history. While the West studied the objective world in great details, scholars in Chinese turned more inward to study the subjective world such as literature, poetry, and some social and moral issues.
Western and Chinese paintings may serve as a typical example. From the Medieval Christian paintings to the Renaissance paintings, one can see clearly a maturing process, during which more accurate observation of the world and more skillful painting techniques were developed. Only during the 19th and 20th century did other styles of painting deviating from the tradition of accurate representation of the objective world became more popular, such as the impressionism and expressionism paintings which emphasize more of the subjective feelings. But in Chinese painting, from the beginning to the end, the emphasis has always been the capture of the spirit rather than the form (写意, 神似 not 形似). Portrait painting may be the most illustrative example of this difference between Western and Chinese paintings. Traditional Chinese painters could never even paint a human figure in the right proportion, let alone the resemblance of the face, as they never cared to try to record the objective world based on careful observation. They just enjoyed painting as a process to express their feelings from the inner world, poetically, maybe, but arbitrarily. (I don’t know whether it is the cause or consequence of my little appreciation of Chinese painting that I have never developed a good taste of it.)
There is therefore no surprise at all that no modern science and technology could ever be possible to grow out of such culture and civilization. Sigh!
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78级
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Posted on Friday, February 25, 2005 - 02:18 pm: Edit Post Delete Post View Post/Check IP Print Post
Guanzhong,
You have a very good point. The Western art pursued 神似 after they reached the pinnacle of 形似, while Chinese art never attempted 形似, they just used 神似 to cover up their weakness, meanwhile 贬低形似 (A Q?). As a sharp contrast, Leonardo not only is one of the greatest artist of all time, but also an important pioneer in science.
That may be related to another point both you and Liao Kang have raised: 我们传统文化没有这种对知识的热爱. In that sense, Chinese文人 are more “practical”, but in a different way: they pursued education simply because 书中自有黄金屋，书中自有 颜如玉。The pure joy and thrill from discovery rarely seemed to be a motivation for the pursuit of education in Chinese culture, and the intellectual curiosity rarely seemed to bring any joy to 中国文人.(Sigh).
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78级
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Posted on Friday, February 25, 2005 - 02:32 pm: Edit Post Delete Post View Post/Check IP Print Post
我猜东西方音乐不是独立发展的，大概根子都在印度。这只是自己的感觉，既没有读到过有关论著，自己也没有求过证。
That brings up another interesting topic, the“relationship” between different civilizations. I remember people talked about the “invention” of chess game, whether it’s imported from India or home-grown. I am convinced that chess must be originated from India and then 流传 to China. The most convincing evidence, to me, is the piece 象. Had it been home grown, we could have 相, but never 象.
A related question. I am always puzzled why all the other civilizations ended up with a spelling language, only Chinese is an exception? Does it indicate some of our characteristics? Any thought?
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八十一子
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Posted on Friday, February 25, 2005 - 02:36 pm: Edit Post Delete Post View Post/Check IP Print Post
A related question. I am always puzzled why all the other civilizations ended up with a spelling language, only Chinese is an exception? Does it indicate some of our characteristics? Any thought?
也不尽然。埃及、玛雅、印加等古文化跟中国一样，都用的象形文字，只是它们过早消亡了。签名散见于信用卡账单
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guanzhong
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Posted on Friday, February 25, 2005 - 02:44 pm: Edit Post Delete Post View Post/Check IP Print Post
Hah, class 78, I see you have been sucked in! Your boss is not around?
Yes, what you said is totally agreed.
I am still unable to find the URL of the discussion on CND regarding some philosophic issues. I should be able to do this tonight, I hope, and I will put it in my post above. I think you will enjoy and even join the discussion.
BTW, 椅子, just wonder, what is the policy of inviting new members? I think it would be great to have 变形金刚 and 青, two extremely intelligent and nice people on CND to join us here. 青is also a philosopher, and a poet. I am sure they will make very positive contributions to this site.
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LiaoKang
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Posted on Friday, February 25, 2005 - 03:45 pm: Edit Post Delete Post View Post/Check IP Print Post
I had very pleasant and educational experiences exchanging posts with Transformer. Guan Zhong, can you invite him? Our Chair Dok is no Wang Lun. He and all of us welcome all heroes and heroines.
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guanzhong
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Posted on Friday, February 25, 2005 - 04:00 pm: Edit Post Delete Post View Post/Check IP Print Post
Who is Transformer? Do you mean 变形金刚? I didn't know he writes poems. I only knew 青 was a poet. Wonderful. I am trying to get him ...
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LiaoKang
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Posted on Friday, February 25, 2005 - 04:09 pm: Edit Post Delete Post View Post/Check IP Print Post
变形金刚, I believe, is the Chinese translation of Transformer, a kind of toys popular in the late 80's. See the picture under his name. He is a philosopher and a music lover and expert, too. I don't know if he is a poet.
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guanzhong
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Posted on Friday, February 25, 2005 - 04:23 pm: Edit Post Delete Post View Post/Check IP Print Post
" He is a philosopher and a music lover and expert..."
I think he is a mathematician by training. I also had some interesting conversations with him.
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石头
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Posted on Saturday, February 26, 2005 - 03:18 pm: Edit Post Delete Post View Post/Check IP Print Post
从最近一期的National Geographic抄几段下来:
Music is native to the human mind. There is not a culture on Earth that does not have it, and our brains are wired to apprehend and be moved by its magic. By contrast, absolute or perfect pitch--the ability to identify a specific musical tone without hearing it in relation to another one--is an exceedingly rare gift, found in as few as one in 10,000 individuals in Western societies.
People who possess the trait can identify the sound of an E flat or G sharp as effortlessly as anyone else can see that a fire engine is red or the sky is blue. Not surprisingly, it is more common among musicians. Mozart had it, and so did Beethoven. But what accounts for this peculiar faculty?
Some research suggests the phenomenon may not be so unusual after all. Investigators at the University of California, San Diego, found that many people who speak tonal languages, such as Mandarin Chinese and Vietnamese, possess a form of absolute pitch, speaking words and repeating them days later at the same pitch. Another study found that 7 percent of non-Asian freshmen at the Eastman School of Music in Rochester, New York, were endowed with absolute pitch, as opposed to fully 63 percent of their Asian counterparts at the Central Conservatory of Music in Beijing.
But the relationship between absolute pitch and language cannot be the whole story. Not all tonal language speakers have absolute pitch, and not all absolute pitch possessors speak tonal languages. In Japan the trait is relatively common compared with the west, and Japanese is not a tonal language. Perhaps a genetic predisposition for absolute pitch is more common among Asian populations. But a more likely explanation for its prevalence in Japan may be the value the culture places on early music training, exemplified by these young violinists undergoing Suzuki Method training.
(本来想把计算机译文也放在这里。惨不忍睹。哪位有好点的网站，帮黎京翻译一下。)
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LiaoKang
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Posted on Saturday, February 26, 2005 - 06:18 pm: Edit Post Delete Post View Post/Check IP Print Post
黎兄正在酝酿大作，也许用得着《国家地理》杂志这一段。还是看愚弟的人工智能吧：
人类的大脑天然能够接受音乐。世上没有任何文化没有音乐，我们的头脑天生能够了解音乐并为其魔力所打动。与此相反，绝对音高或者完美音高—即不必与其它音调相比就能够断定某一特定音调的能力—却是一种非常罕见的天赋，在西方社会一万个人中才有一个。
具有此能力者，就象你我能够看出救火车是红色，天是蓝色一样，他们能够轻而易举地识别降E调和升G调的差别。毫不奇怪，音乐家中此种奇才较为多见。莫扎特和贝多芬都具有此才能。但怎么会产生这种特殊功能呢？
有研究表示此现象其实未必罕见。加州大学圣地亚哥分院的调查者发现，许多说具有声调的语言者，比如说中国话和越南语的人，具有识别绝对音高的能力，能够在几天后以同样声高重复以前说过的话。另一项研究发现，在纽约州，罗切斯特市伊斯曼音乐学院的非亚裔新生（译注：不是说非裔和亚裔，而是说亚裔之外的新生）只有百分之七具有识别绝对音高的能力，而北京中央音乐学院的新生中百分之六十三都有此能力。
但绝对音高和语言之间的关系并不能说明全部问题。说有声调的语言者并非人人具有识别绝对音高的能力，具有识别绝对音高的能力者并非人人都说有声调的语言。在日本，此种能力与西方相比较为普遍，而日语并非有声调的语言。也许亚洲人的基因里有识别绝对音高的特质。但对此现象的更好解释也许是日本重视早期音乐教育，受过玲木教学法培训的年轻小提琴手是这种解释活生生的范例。
译注：有声调的语言是指通过声调，如中国话的四声，来决定语义的语言。欧洲语言的声调和语义没有太大关系。据说广东话、越南语有九种声调，请会说者指教。
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BBB
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Posted on Saturday, February 26, 2005 - 08:44 pm: Edit Post Delete Post View Post/Check IP Print Post
上面这段关于对“绝对音高或者完美音高—即不必与其它音调相比就能够断定某一特定音调的能力—却是一种非常罕见的天赋，在西方社会一万个人中才有一个。”正是我想找的一个依据。前段时间在一个古典音乐论坛问这个问题(www.classical.net.cn)，就有人告诉我，一般音乐爱好者，甚至一般音乐工作者，只凭听是听不出一段音乐的调性的：因为听不出绝对音高。
我也很喜欢上面关中和廖康兄提到的变形金刚和青两位CND上的网人。
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BBB
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Posted on Sunday, February 27, 2005 - 08:44 pm: Edit Post Delete Post View Post/Check IP Print Post
关于大调和自然小调的形成：
钢琴上的88个键基本上包括了西方音乐中的全部音。这88个音是如下12个从低到高的音的循环：
C，C#，D，Eb，E，F，F#，G，Ab，A，Bb，B，(C)
从C 到(C)称为一个八度，其中相邻两个之间的音高相差半音(semitone)。大小调式是七声音阶，由上面12个音中的七个音构成。其中每一音都可以是大小调式音阶的主音(tonic)。构成大调式的规则是：每相邻两音之间的音程为：全音，全音，半音，全音，全音，全音，半音，这样可以构成：
C大调：C，D，E，F，G，A，B， (C)
D大调：D，E，F#，G，A，B，C#，(D)
类似可以构成另外10个大调。
如果相邻的两个音之间的音程为：全音，半音，全音，全音，半音，全音，全音，就构成小调音阶：
A小调 A，B，C，D，E，F，G， (A) (与C大调音阶相同)
B小调 B，#C，D，E，#F，G，A，(B) (与D大调音阶相同)
类似可以构成另外10个自然小调。因为小调有不同变种，所以这样的小调称自然小调。
当有升(#)或降(b)，的音构成的调，比如上面D大调中所有的F和C音都要升高半音，无论在哪个八度上。所以，在五线谱上，看调号(Key Signature)，就能知道在哪个大调或小调上：D大调和B小调有两个#号。C大调，A小调则没有升降号。下面是另外几个常用调的Key Signature：
Eb(降E)大调：Eb，F，G，Ab，Bb，C，D，(Eb)，与C小调相同，三个降号：C，D，Eb，F，G，Ab，Bb，(C)
F大调：F，G，A，Bb，C，D，E，(F)，与D小调相同，一个降号：D，E，F，G，A，Bb，C，(D)
G大调：G#，A，B，C，D，E，F，(G)，与E小调相同，一个升号：E，F，G#，A，B，C，D，(E)
调号相同，但主音不同的两个大小调互为关系调：G大调是E小调的关系大调，D小调则是F大调的关系小调。
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闲云野鹤
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Posted on Monday, February 28, 2005 - 11:03 am: Edit Post Delete Post View Post/Check IP Print Post
在龙坛讨论德沃夏克第八交响乐的时候，我贴过一张调性图。再贴这里给大家参考。
The Circle of Fifths - Major and Relative Minor Keys
The Circle of Fifths is an easy way to learn the key of a given musical composition. The Circle of Fifths tells you how many sharps or flats are in a given key. C has no sharps or flats. The diagram below is called the Circle of Fifths because as you go clockwise you go up a fifth. For example, the fifth note of the C major scale is G. The fifth note of the G major scale is D, and so on.
Notice that every other note is succeeded by the one before. C, skip G, D, skip D, A, etc. Also notice how there are twelve notes corresponding to twelve numbers on a clock. C is in he 12 noon position. G is in the 1 o'clock position (likewise has one sharp; F in the 11 o'clock position.) D is in the two o'clock position (likewise has sharps; F and C). A is in the 3 o'clock position (likewise has 3 sharps; F, C, G). E is in the four o'clock position and has 4 sharps (F, C, G, D). B is in the 5 o'clock position and has 5 sharps (F,C,G,D,A). F# is in the 6 o'clock position and has 6 sharps (F,C,G,D,A,E; everything is sharp except B; notice also how this corresponds with the key of F in which it has one flat, Bb). These are just some memory tags that can help you remember. Also, notice that G through E, each letter has as many pen strokes in writing the letter as it does sharps. G is made with one pen stroke and has one sharp. D is made with two pen strokes and has two sharps. A is made with three pen strokes and has three sharps. E is made with four pen strokes and has four sharps.
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BBB
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Posted on Monday, February 28, 2005 - 01:39 pm: Edit Post Delete Post View Post/Check IP Print Post
闲云野鹤好！这张图对记住调号很有帮助，我上周末刚好在女儿的钢琴老师那里见过。
在龙坛讨论德沃夏克第八交响乐的时候
我也比较喜欢这部G大调作品，特别是他的D小调第七交响曲。当然还有“新世界”，太熟悉，。。。
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Gang He
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Posted on Monday, February 28, 2005 - 02:49 pm: Edit Post Delete Post View Post/Check IP Print Post
欢迎闲云野鹤!
闲云野鹤, BBB能否用中文简要介绍此图？温柔一刀
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闲云野鹤
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Posted on Monday, February 28, 2005 - 04:36 pm: Edit Post Delete Post View Post/Check IP Print Post
guanzhong,
C大调和D大调上了一个调，还比较容易明白，就像BBB说的，其和弦组成不同，效果就不同了。
更极端的例子，B double flat 与 A 虽然都是enharmonic，可是由於其和弦组成不同，却不是完全一样的。
Gang He，
这图主要是用于记忆，
G在一点钟的位置，可以一笔写完，只有一个sharp。
D在两点钟的位置，可以两笔写完，就有两个sharp。
A在三点钟的位置，可要三笔写完，就有三个sharp。
BBB，
很高兴你也喜欢这几部交响乐。无影大师在龙坛详细解剖分析了德八德九的所有乐章，带着音乐讲解了各章主题，呈示部展开部再现部。欢迎你来参加讨论。
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guanzhong
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Posted on Monday, February 28, 2005 - 08:28 pm: Edit Post Delete Post View Post/Check IP Print Post
"C大调和D大调上了一个C调，还比较容易明白，就像BBB说的，其和弦组成不同，效果就不同了。 "
你这么一说我又不明白了. 我原来的问题是: 如果把C大调乐曲中的每一个音符都提高一度(C>D, C#>D#, D>E, D#>F, E>F#, F>G, F#>G#, G>A, etc.), 其中所有和弦的相对关系都并无变化(比如C调大三和弦 CEG 变成D调大三和弦 DF#A), 而只是绝对音高稍有提高(每个音符的频率都乘以 2^(1/6)=1.122462), 为什么"其和弦组成不同"?
"更极端的例子，B double flat 与 A 虽然都是enharmonic，可是由於其和弦组成不同，却不是完全一样的."
什么是 B double flat? 你是说B降调两次变成A? 为什么"和弦组成不同"?
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guanzhong
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Posted on Monday, February 28, 2005 - 11:22 pm: Edit Post Delete Post View Post/Check IP Print Post
这两天找了本杨荫浏的“中国音乐史”恶补, 又上网到处遛古狗, 想发掘出些有关早期中西音乐关系的资料. 先把刚挖出来的这点放在这与大家分享.
中国的十二律(黄钟, 大吕, 太蔟, 夹钟, 姑洗, 仲吕, 蕤宾, 林钟, 夷则, 南吕, 无射, 应钟)最早出现于东周(400 BC), 吕氏春秋最早提到其三分损益算法: “黄钟生林钟, 林钟生太蔟, 太蔟生南吕, 南吕生姑洗, 姑洗生应钟, 应钟生蕤宾, 蕤宾生大吕, 大吕生夷则, 夷则生夹钟, 夹钟生无射, 无射生仲吕. 三分所生, 益之一分以上生; 三分所生, 去其一分以下生. 黄钟, 大吕, 太蔟, 夹钟, 姑洗, 仲吕, 蕤宾为上, 林钟, 夷则, 南吕, 无射, 应钟为下.”
几乎在同时, 古希腊毕达哥拉斯(Pythagoras)也提出他的十二律. 他根据不同弦长对应不同音调的实验, 找出几个和谐音之间的基本比例关系 1:1 (Unison), 1:2 (Octave), 2:3 (Fifth), 3:4 (Fourth), 并用这些数的最小公倍数十二来表达: 12:12, 6:12, 8:12, 9:12, 由此产生出他的十二律.
另外, 早在周代出现的五音(宫-dou、商-rei、角-mi、徵-sou、羽-la)和七音(变徵-降sou、变宫-降dou,xi)也与西方后来的音阶系统基本相符(仅差 fa 和降sou).
至于毕达哥拉斯与中国的十二律有什么关系, 就没有任何资料可以证实了. 因为这两种文化是各自独立发展的, 两种十二律由互相启发产生的可能性不大. 为什么两种文化都不约而同地用十二这个magic number, 为什么都各自产生七音的音阶系统, 大概就只能从人类共同的感知系统来解释了. - posted on 06/18/2005
81, I read all the discussion at dok's forum. Although I'm not an expert yet,
I can tell there are just too many misunderstandings and confusions about the
theory of music sound. It is not a very easy concept to grasp at first,
because there are many different concepts that are not clearly defined in our
everyday speech. Try to read the following two articles carefully, and ask me
any questions you may encounter. The second article is not well-written. Try
your best.
http://en.wikipedia.org/wiki/Harmonic_series_(music) http://en.wikipedia.org/wiki/Physics_of_music
I haven't read this next article yet, but might clarify the confusion about
musical tuning.
http://en.wikipedia.org/wiki/Equal_temperament
After this, read about Bernstein's explanation on major/minor and glad/sad
relationship I posted previously. After we understand Bernstein's argument,
we will begin our exploration on how different keys might affect us
differently.... - posted on 06/18/2005
Bernstein here explains musical differences in terms of phonological differences, which is no help at all. Phonological differences are themselves differences in sound. Dissonant and consonant sounds have different emotional impact, simple.
Bernstein tried to be chic wherever he could. His Norton lecture was no exception. That borrowing Chomskian linguistics didn't help his cause is obvious to critical readers of "Unanswered Question".
I read the book ten years ago and bought and watched his lectures on DVD. What's valuable is everything minus his "theoretical" effort. - posted on 06/18/2005
伯恩斯坦是试图强调音乐本身没有情感，这是一个可“自圆其说”的理论。
但音乐确实会引起人的联想-情感反应，这也是“不证自明”的事实。
伯恩斯坦用minor偏离major引起的心理反应来涵盖所有所谓minor引起的whatever
affect，不够严密。因为，偏离并不必定就是unsatisfied，就好像surpise
有delighted ones。
心理和物理在这里不能分开讲，因为听觉本身就是一个心理物理现象，而不是
一个物理现象或心理现象。
至于minor本身能引起的affect到底应该还原到那个层次，这是引起混乱的一个
问题。
音乐可以没有expression，但音乐可以有expressiveness。
"God" wrote:
Bernstein here explains musical differences in terms of phonological differences, which is no help at all. Phonological differences are themselves differences in sound. Dissonant and consonant sounds have different emotional impact, simple.
Bernstein tried to be chic wherever he could. His Norton lecture was no exception. That borrowing Chomskian linguistics didn't help his cause is obvious to critical readers of "Unanswered Question".
I read the book ten years ago and bought and watched his lectures on DVD. What's valuable is everything minus his "theoretical" effort. - posted on 07/01/2005
见到有这么一本书。不过 amazon 上的书评好象不是很好（3/5星，43人评）。
Temperament: How Music Became a Battleground for the Great Minds of Western Civilization
by STUART ISACOFF
Editorial Reviews
Amazon.com
Involving mathematics, philosophy, aesthetics, religion, politics, and physics, Stuart
Isacoff 's Temperament invokes the tone of a James Burke documentary. However, the focus is
not on a modern invention, but rather a modern convention: that of tuning keyboards so that
every key is equally in tune--and equally out of tune.
With the existing literature tending to bog down in mathematical theory or historical
tuning methods, Isacoff bravely attempts to make this seemingly arcane topic interesting to
the general reader. He distills the mathematics and music theory into their simplest
essences, and draws apt analogies from the everyday. He also generously peppers the text
with the quirks and escapades of its more flamboyant central characters; the relevance of
the information is often tenuous at best, but Isacoff has obviously done his homework, and
he can be forgiven some frivolity.
Less forgivable is his neglect of "well-temperament." Namesake of Bach's masterful
collection of 24 pieces (one each in all the major and minor keys), the well-tempered
keyboard liberated composers from the howl of badly tuned keys in the way equal temperament
did, while preserving the distinct quality of each key. It was a pragmatic and
aesthetically rich solution that captivated composers and theorists for decades. Yet
Isacoff reserves less than two pages for its description. (Perhaps he deliberately
overlooked the topic since it doesn't fit well with his casting of equal temperament's
opponents as rigid, dogmatic, and impractical.)
Despite its flaws, Temperament is an accessible guide to a fascinating topic seldom
discussed outside musical circles. Though the book may not invigorate hard-core theorists,
the amateur musician, armchair scientist, history buff, or plain old curious can glean
plenty from it. The advent of digital keyboards--some of which can be tuned to historical
temperaments at the flip of a switch--makes this an ideal time for the topic to be
rejuvenated. --Todd Gehman
From Publishers Weekly
Isacoff, editor-in-chief of Piano Today magazine, tells the worthy tale of how musical
temperament the familiar, seemingly fixed relationships between notes on an instrumental
scale came to be taken for granted. After centuries of an accepted belief in the
mathematical and divine governance of music, the 17th century saw the growth of a fierce
debate over experimental new tuning methods. In the 18th century, the modern keyboard
allowed for a new kind of tuning, known as equal temperament, whereby each pitch is equally
distanced. New musical possibilities opened up, changing composition forever. Isacoff
traces music theory contributions by da Vinci, Newton, Descartes, Kepler and Rameau.
Unfortunately, he sometimes clumsily attempts to keep his audience's attention with
irrelevant, if salacious, gossip e.g., philosopher Robert Hooke "recorded his orgasms in a
diary," and King Louis XIV refused to eat with a fork. Meanwhile, he gives relatively short
shrift to Kepler and Galileo. His ambitious historical canvas uses extensive secondary
sources, but there are research gaps, such as his outdated portrait of Isaac Newton as a
total "ascetic." Nevertheless, this harmonics drama will excite music geeks and music
historians. (Nov. 24)Forecast: Knopf's prestige guarantees sales to major music
collections, and Isacoff's national media appearances (NPR, etc.) may mean good general
sales.
http://www.amazon.com/exec/obidos/tg/detail/-/0375703306/qid=1120152526/sr=8-1/ref=sr_8_xs_ap_i1_xgl14/002-0977440-2001660?v=glance&s=books&n=507846 - Re: 銆愰煶涔愩�戜负浠�涔堚�滃ぇ璋冩槑鏈楋紝灏忚皟闃撮儊鈥�posted on 07/14/2005
I read this too. What haven't I read? ;)
The book is much hoopla, a little substance, which is very controversial. The musical fanatics could literally kill each other over the subject. - posted on 07/15/2005
这本书呢？
Harmonic Experience: Tonal Harmony from Its Natural Origins to Its Modern Expression by W. A. Mathieu
Amazon review:
Reviewer: The Philosophical Musicologist (Cambridge, MA)
As an undergraduate music major interested in music theory, I happened upon this book by
accident while browsing through the theory section of the music library looking for a good
book on harmony. All I can say is that the book impressed me so much that I ordered my own
copy three days later.
What impressed me so much? Well, for more than a year now I've been trying to sift through
music theory texts (as well as acoustics and other math-heavy texts) trying to understand
why music sounds good. Why did music develop the way it did? Why did tonality and other
parts of classical music break apart in the early twentieth century? Is it purely
explicable by artistic means, or is there something about the physical world of acoustics
(or psychoacoustics) that effected the development of Western music?
My search led me to the area of tuning, in particular, and to numerous other areas of
musical acoustics and theory. In any case, this book explains the basics of everything that
I've distilled out of scores of books. Most theorists and general musicians have no clue
about how music really works--it took me a full year of reading to get some clue. But, this
book presents the basics in such a way that the beginner feels at home, but also puts
everything together for an advanced reader in such an incredible way that all I could say
was, "Why didn't I find this book last year? It puts together everything I've learned in 18
months to produce the theory that I always knew had to exist!"
Mathieu has written a different kind of music theory book, and one that more theorists
should read. He systematically derives Western harmony, starting from simple improvised
melodies against a drone, and ending with a theory that encompasses jazz theory as well as
traditional tonal harmony. Along the way, you learn more than you ever need to know about
the tuning problems that led to modern equal temperament (and without the endless
mathematics that scares many musicians away).
But, more importantly, you learn to sing intervals--in tune and pure. The beginning (and
most important part) of "Harmonic Experience" is about singing--it is about FEELING why
music makes sense to our ears, and slowly figuring out how that evolved into modern Western
music.
I recommend this book to three groups:
(1) People who want to know why and how music works (i.e., beginners in music theory) - you
won't be able to digest everything in this book in one gulp, but, studied along with
traditional harmony, this book will enrich your understanding of music in so many ways.
It's written at a level that anyone with the ability to read music and play keyboard a
little will understand.
(2) More advanced musicians who have some theory background - if music theory always turned
you off, or if you ever wanted to understand more of the "why" rather than the "how" that
most harmony courses focus on, this is the book for you.
(3) Music theorists - Even if you have a Ph.D. in music theory, I think you can learn
something from this book. There are a few places where the author goes a little far out in
his way of explaining things, but you often have to do that when presenting an alternative
viewpoint. WARNING: this book may change the way you think about theory. I'm not saying
this is a new Bible for theorists--but I think it addresses issues that are not adequately
considered in current theoretical research. It provides a fresh perspective in a simple,
constructive way. Also, it provides a new set of analytical tools based on some already
used in theory--but the background the book gives allows you to use the tools in new ways.
It is not so much a new theory as it is a new basis for theory and a new way of THINKING
about theory.
In general, if you are a musician and want to understand why music is structured the way it
is, this will start you off on the right track. - Re: 銆愰煶涔愩�戜负浠�涔堚�滃ぇ璋冩槑鏈楋紝灏忚皟闃撮儊鈥�posted on 07/15/2005
Not this one. But the word "natural" in the title tells me something. Someone could have written an "unnatural origin of ..." and here lies the controversy.
I do believe the great classical composers were no mere flukes. You know what I mean? - posted on 07/20/2005
Harmonic Experience: Tonal Harmony from Its Natural Origins to Its Modern Expression by W. A. Mathieu
I read a few chapters of this book in the last couple of days. This book is truly
insightful. I want to recommend this to all music lovers who want to understand the
experience of music. The author is patient and clear in explanation, and rich and
wise in metaphors. He guides the readerd not in the direction of learning more knowledge
of music, but of tuning in with the experience of music. For example, one does not learn
what "perfect fifth" means, but how a perfect fifth feels..... remarkable!
八十一子, I belive this book will answer all your questions and more.
It's an expensive book.... But how I wish to have someone to share it with! - Re: 銆愰煶涔愩�戜负浠�涔堚�滃ぇ璋冩槑鏈楋紝灏忚皟闃撮儊鈥�posted on 07/20/2005
About $30 bucks on Amazon. Not too expensive for a life-saving book. His "The Musical Life" might be a stand-in for poorer and lazier folks.
- Re: 銆愰煶涔愩�戜负浠�涔堚�滃ぇ璋冩槑鏈楋紝灏忚皟闃撮儊鈥�posted on 07/21/2005
阿姗 wrote:
It's an expensive book.... But how I wish to have someone to share it with!
Let me read the book you bought. Does that count as "sharing"? :) - posted on 07/21/2005
灵魂的七个咏叹瞬间
江山如画
一直以来， Material乐队在实验音乐领域意味着永无止境的探索，它的领军人物就是号称“全能实验大师”的纽约地下音乐殿堂级人物Bill Laswell，此公尤其擅长将来自不同文化背景的各种音乐形式进行杂交，混制出全新面貌的作品，还特别注重文化内涵——与NEW AGE式的混杂有着全然不同的境界。
Seven Souls就是选取威廉·巴洛斯（William S. Burroughs）作品经典片段的概念专辑（SEVEN SOULS的朗诵词附后）。The Western Lands（SEVEN SOULS的特别版）是更具颠覆性的混搭专辑，巴洛斯式的拼贴、碎切和混音，世界音乐与实验音乐盛大的赤裸午餐，包括Talvin Singh、印度小提琴家Shankar、电子怪杰DJ Spooky，从电子音效、舞曲节拍到带电的西塔琴，乃至土耳其古琴Saz、希腊二弦古琴Baglama……全都被招至巴勒斯麾下，向西方乐土进军，而哪怕面对来势汹汹的音乐重围，巴洛斯的声音仍是统帅，如孤舟稳行于惊涛骇浪。
巴洛斯除了是实验音乐家和贝司演奏家，并且由他参与制作的唱片超过两百张的Bill Laswell。在Bill Laswell最为出名的乐队Material的作品中，有《Seven Souls》和《The Road to the Western Lands》两张伟大的专辑都有巴勒斯的声音混入其中。前者是1989年巴勒斯和Bill Laswell合作的朗诵与配乐，后者是1998年为了怀念巴勒斯逝世出版的混音专辑，打造这张专集的有来自伦敦的世界节拍缔造者Talvin Singh，有可以用唱机转动世界的DJ Spooky，还有地下舞界的新贵Spring Heel Jack，专辑的七个音轨不就是巴老爷带去的那Seven Souls么。用专辑内页的一句话向音乐中的巴勒斯致敬，显然这些是远远不够的：“声音可以感知痛苦，我们何时才能真正拥有这种力量，即使不用武器。”
Seven Souls 来源于古埃及，和中国民间传说中的“三魂七魄”有相似的地方，但到底是怎么回事，俺还没来得及仔细研究……就着冻啤酒或者冰冻绿茶，在夏天有繁星的夜晚，我们一起来聆听他的《Seven Souls》！
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