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[剧情讨论] 数字与音乐的完美结合---地球的坐标

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发表于 2009-3-25 21:21:12 | 显示全部楼层 |阅读模式
(以下内容节选自Bear McCreary的博客)
My first step was to ask series science advisor Kevin Grazier what kind of coordinates we would need to generate from the music.
He replied:
“When we specify coordinates in astronomy, it’s usually done with two angles – one that ranges 0 to 360 degrees, the other +90 to -90 degrees.  Necessary also is the distance, but for astronomy the distance implied when we’re looking for stars is “infinity.”  We’re collectively used to this.  In geography, it’s latitude/longitude (distance implied – Earth’s radius).  In astronomy it’s Right Ascension / Declination.  In BSG, it’s XXXcaromYYY, distance ZZZ.
‘Now we’ve already established that one unit of measure used by Galactica is the SU, or Stellar Unit (”The Captain’s Hand”), similar to the Astronomical Unit used in our Solar System. It’s reasonable to assume that the Colonials use something similar to a light year as well – we’ll call this a CLY (Colonial Light Year)
‘There are 63495 Astronomical Units in one Light Year.  Irrespective of the absolute sizes of the SU and CLY, the RATIO between those two is likely to be of the same order of magnitude as that of the AU/LY.
‘So as I see it, we will need from the music: XXX carom YYY dist ZZZZZZ”

I was tasked with generating 12 single-digit numbers out of “All Along the Watchtower.”
Since The Final Four Theme had been firmly established as the piece of music Hera draws and the melody that Kara plays, it took a close look at the melody and tried to figure out how go about this unusual assignment:
I emailed everyone involved some possible solutions.
This would be the first time in my television scoring career that the phrase “12-Tone Row” would be necessary in conversations with producers or writers.

(My original sketch for Hera’s dots)

“GRAPHIC INTERPRETATION
You could take this series of dots and plot it on a star chart and have it mean something.  But, we’d have to get enough information out of the notes to derive the relative scale, direction and size of the note heads.
It would be the simplest visually (Kara takes Hera’s drawing, slaps it on a star map and sees the way to Earth) but there are a million variables that could go wrong and it would be, frankly, pretty stupid.

12-TONE THEORY
Borrowing a bit from the post-WWII serialists, we can generate some numbers based on scale degrees.  If you assign each chromatic scale degree in the C#m scale with a number, the melody would be written as such:  1 2 4 9 8 4 9 [8-9-8] 4 2 1.  The parentheses represent the little triplet turnaround, which are the fastest of the notes.
This series, though not a 12-tone row in the traditional sense, could still be inverted, retrograded and then have the inversion retrograded to give us four sets of related numbers:

PRIME: 1 2
4  9 8   4  9  [8-9-8]  4  2   1
RETROGRADE: 1  2  4  [8-9-8]  9  4 8  9   4  2   1
INVERSION: 12 11 9  4 5  9  4 [5-4-5]  9 11 12
RETROGRADE-INVERSION: 12 11 9 [5-4-5]  4  9 5  3   9 11 12

INTERVALIC DIFFERENCES
You can also generate numbers by looking at the spaces between the notes instead of the notes themselves.  For example the space between C# and D is a single step, or “1.”  That series of numbers could also be retrograded, although not inverted since the inversion would be the exact same numbers (’1′ step up = ‘1′ step down):
PRIME: 1 2 5 1 4 5 1 1 1 4 2 1
RETROGRADE:1 2 4 1 1 1 5 4 1 5 2 1

Because the melody is mostly scalar, we see a lot of 1’s and 2’s.
The bigger leaps become visually more apparent.
The 4’s and 5’s seem to really stick out.”


This process became so complicated, I began to empathize with Kara as she maddeningly tried to crack the code in the music.
Series writer and producer Bradley Thompson felt that most of these techniques would be too complex to communicate effectively onscreen.
“These are good thoughts, all great for Kara to wonder about,” Thompson told me. But, when Ron gets to her feeding the coordinates at the last second under the dire circumstances of Episode 21, we’ll probably want an “oh-yeah!” moment that comes as a flash of simplicity.
The jump computer needs input1, input2, and input3 (angular vector1, vector 2 and distance / power). The computer accepts a certain number of digits for these, which Kara determines from the intervals from the tonic (1) in Watchtower’s melody.
I’m sure Ron will have us in white-knuckle drama as the black hole sucks the decrepit Galactica into its hideous tidal stresses – so this won’t be a wonderful time to spend thinking it out.”

As Bradley made his case, I began to understand just little screen time we would have to communicate the abstract idea of Kara deriving coordinates from music.
“Remember, the gods have a hand in all this,”
Bradley explained.
“They took that into account with Kara and which way Galactica’s pointing for the starting point.  Otherwise, we just have to add more digits from the tune as input0 (initial position and heading).  We have only one ship jumping, so we don’t actually need to transmit these coordinates to anybody else.
That, and the audience’s willing suspension of disbelief.”
Bradley’s words sunk in and I re-thought my approach, in search of the simplest solution possible.
Using the 12-Tone method was too complex, and I decided to assign each note in the C# scale a number, excluding the chromatic notes between them. This is a diatonic approach instead of a chromatic one, (basically, I’m talking about the “Do-Re-Mi-Fa-So-La-Ti-Do” scale).


(Steve Bartek and Ira Ingber lay down baritone guitars on “Kara’s Coordinates”)

This approach had several advantages.
It produces only single digit numbers.
It is also the most intuitive solution that someone with Kara’s musical background would arrive at (in fact, my extensive musical training had me pursuing much more complicated ideas, missing the forest for the trees).
“In basic ear training exercises they make you sing melodies with words or numbers corresponding to the notes,”I wrote back to Bradley.
“So, someone like Kara who was taught by a professional musician as a youth could be familiar with thinking of the tonic as ‘1’, the second scale degree as ‘2’ and so forth.  It’s believable that Kara might be humming the tune to herself as the numbers come to her mind.”

With this philosophy in mind, I took a second look at the Final Five Theme.
The melody is either 11 or 13 notes (depending on if you count the little triplet ornament figure that does not consistently appear with the theme).
The easiest way to arrive at 12 notes was to discount the triplet figure and then repeat the first note, which is technically the way the phrase is looped in my arrangement of “Watchtower” anyway.
Assigning numbers based on the diatonic scale system I described earlier yielded the following:

This generated the coordinates: 112 carom 365 dist 365321.

I sent this number to production and they prepared it for the on-camera computer playback.
When I saw the finished cut, I was thrilled to see that my coordinates led them to Earth!
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发表于 2009-3-25 21:30:12 | 显示全部楼层
本帖最后由 taniajiao 于 2009-3-26 01:00 编辑

要将音符转化为数据坐标,首先要知道这种数据坐标应当是什么样子的。科学指导Kevin Grazier的解释是:

在天文学中,确定坐标通常需要确定两个角位——一个是0—360度,一个是(+90)—(-90)度,必要的话还要加上间距。以地球为例,我们确定坐标需要确定经度和维度,这里的隐含间距就是地球的半径。在宇宙中,这种间距其实是“无穷大”,但是既然人们都习惯了,这里的间距实际上表示赤经和偏差间的距离。在BSG中的表达式就应该是:XXX(原点)YYY,间距ZZZ。

单位的话,在BSG中的设定是恒星级单位和殖民地光年,比率大概是63495天文单位等于一个殖民地光年,和我们实际使用的天文单位比率相同。
因此最后的表达式是:xxx(原点)YYY,间距zzzzzz

然后我需要从“All along the watchtower”里抽出12个音来做转换。我为此广散电邮征求意见。自此,我将这段代码称之为“12音阶”。

方案一:图解
直接将音符的排列位置对应星图即可解决。但这样得到的结果将非常不准确,而且看上去傻极了。

方案二:12音理论
将12个音重新排列,像编制密码那样给音符加密。
比如说,将C小调的半音音阶中每个音符对应一个数字,再通过倒置和转位为其加密。
原来的音阶:1 2 4  9 8   4  9  [8-9-8]  4  2   1
将其倒置:1  2  4  [8-9-8]  9  4 8  9   4  2   1
然后转位:12 11 9  4 5  9  4 [5-4-5]  9 11 12
最后再次倒置:12 11 9 [5-4-5]  4  9 5  3   9 11 12

方案三:间隔停顿
也可以对空拍而不是音符本身加密。
如原来的空拍间隔是:1 2 5 1 4 5 1 1 1 4 2 1
经过倒置:1 2 4 1 1 1 5 4 1 5 2 1

以上手法明显太过复杂,很难在屏幕上有效地表达出来。况且编剧兼制片人Bradley Thompson像我解释说,劳模需要星芭在万分紧急的最后关头找出音乐与数字间的对应,这要求我们用一闪的时间做到简单明了。为了营造这种扣人心弦的戏剧效果,当然没时间给星芭思前想后。
接着,Bradley一语点醒梦中人:“要记得,一切的背后都有神的存在。他们已经预料到星芭会在卡舰陷于黑洞之前的一瞬间找到答案……”

为此,我明确了自己的任务,开始重新思考最简单的转换方法,那就是舍弃和声和装饰音,仅仅使用C大调的主音(也就是Do-Re-Mi-Fa-So-La-Ti-Do的音阶)。
这样每一个音只有一个对应的数字。在基础的视唱练耳过程中,人们习惯在哼唱旋律时,用数字来代替相应的音符。按照Kara的音乐背景,在危机时候凭直觉产生这种联想是很正常的(而我过多的音乐训练反倒让我舍近求远不说,只见树木而不见森林)。
带着这样的想法,我又重看了一遍FF的主题曲,发现它们不是13个音就是11个音(这得看你算不算三连装饰音),最后我决定删去三连音,重复一遍第一个音,这样最后的乐谱及数码就对应生成了。


最后的坐标是:112(原点)365(间距)365321


我把数据发送给剧组,在最终的剪辑版出来时,我欣喜地看到我的数码将他们成功地送到了地球!

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发表于 2009-3-25 21:32:35 | 显示全部楼层
本帖最后由 银河 于 2009-3-25 21:33 编辑

我已经不去想bsg里这些了...

多拍几季也许想的更多. 散吧散吧.........  伤感
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 楼主| 发表于 2009-3-25 21:43:49 | 显示全部楼层
我觉得吧这个与XYZ坐标结合起来,很牛啊~~
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发表于 2009-3-25 21:57:10 | 显示全部楼层
就几个音符就能彻底改变人类的命运,真是强大啊.......
星芭已经不是原来的星芭了,而是天使的化身,也只有天使才能行使此神迹........
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发表于 2009-3-25 22:19:36 | 显示全部楼层
塔尼亚,加油!
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发表于 2009-3-25 22:53:58 | 显示全部楼层
介是一个灰常华丽的结合, 看得观众骨头都散了
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发表于 2009-3-25 23:04:34 | 显示全部楼层
这个坐标是以什么为原点的??
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发表于 2009-3-25 23:08:34 | 显示全部楼层
则更想法非常好
艺术也是数字
数字构成世界
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发表于 2009-3-26 01:01:25 | 显示全部楼层
译完鸟~~大家看吧~~

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发表于 2009-3-26 01:07:42 | 显示全部楼层
本帖最后由 银河 于 2009-3-26 01:18 编辑

过来纯水一下,本来说了不想bsg里的东东了

原来还是搞过二次编码的.   我说那歌怎么那么巧和设定的星图还真能扯吻合.
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发表于 2009-3-26 05:25:06 | 显示全部楼层
Bear就是牛啊,喜欢他替BSG写的音乐……
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发表于 2009-3-26 07:17:29 | 显示全部楼层
我们以后编密码可以抄袭这个了
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发表于 2009-3-26 09:03:55 | 显示全部楼层
坐标的对错肯定不是主要问题,BSG这里主要想表现的就是神迹。
Racetrack死了都能正好在发射口对准Cylon殖民地的时候,把手砸下来,发射核弹;
Starbuck最后关头浮想出的一串数字,居然是新的星球的坐标;
歌剧院谜团,最终是为了把Baltar带到1号面前,然后唐僧死他。
排除编剧安排的因素,这些就是神迹!
当然,话也可以反过来说,排除神迹的因素,这就是编剧安排的。

所以坐标的对错与否,真的不重要了!
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发表于 2009-3-26 09:27:52 | 显示全部楼层
这才是宇宙终极奥秘的要义所在  
广普科学和理性艺术的完美结合
我们找到了美好完美的地球家园
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发表于 2009-3-26 10:45:52 | 显示全部楼层
四位数的坐标能提供多大的精度啊,在宇宙中,差一位,都差N光年了,居然能定位到地球
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发表于 2009-3-26 11:54:33 | 显示全部楼层
14# starxt
精辟!!!
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发表于 2009-3-26 13:08:01 | 显示全部楼层
终于明白了
最吸引人的邪恶部分就是地球坐标。。
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发表于 2009-3-26 13:09:22 | 显示全部楼层
Kevin Grazier很强,感谢塔尼亚
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发表于 2009-3-26 16:45:52 | 显示全部楼层
每个天体都有自己的运行轨迹,把轨迹看做是五线谱上的一条条线,以合适时间间隔,记录天体的位置。

用以上办法可以自动生成乐章。
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