ALGORITHMIC COMPOSITION AS A MODELOF CREATIVITY

Bruce L Jacob University of Michigan BLJ@umd.eduTranslator: Briquz Email: hn@bz-inc.com

2016年9月29日至10月10日

There are two distinct types of creativity: the flash out of the blue (inspiration? ge-nius?), and the process of incremental revisions (hard work). Not only are we years awayfrom modeling the former, we do not even begin to understand it. The latter is algorithmicin nature and has been modeled in many systems both musical and non-musical.

有两种截然不同的创造力:一种是突然的那么一瞬间(灵感?天才?),另外一种是不断的学习自我修正的过程(努力)。我们不仅常年没有建模,我们甚至都不曾理解过它。而后者是一个自然而然的算法,并且在很多音乐性和非音乐性的系统中已经被建模。

Algorithmic composition is as old as music composition. It is often considered a cheat,a way out when the composer needs material and/or inspiration. It can also be thoughtof as a compositional tool that simply makes the composer’s work go faster. This articlemakes a case for algorithmic composition as such a tool. The ‘hard work’ type of creativityoften involves trying many different combinations against each other and choosing oneover others. This iterative task seems natural to be expressed as a computer algorithm.The implementation issues can be reduced to two components: how to understand one’sown creative process well enough to reproduce it as an algorithm, and how to programa computer to differentiate between ‘good’ and ‘bad’ music. The philosophical issuesreduce to the question who or what is responsible for the music produced?

算法作曲和音乐作曲一样久远。当作曲家需要素材或者灵感的时候,算法作曲通常被认为是作弊,是一种摆脱困难的方法。它也可以被认为是仅仅使作曲家工作更快的一个创作的工具而已。本文就以算法作曲作为一个工具来阐述。“努力”类型的创造力往往涉及尝试许多不同的相互组合,然后在其中选择一个。这种反复的操作很自然的被表示为电脑算法。执行度的问题可以简化为两个部分:一、如

何足够理解一个人的创作过程以至于可以将这个过程作为一种算法复现;二、以及如何编程使得计算机能够区分音乐的“好坏”。从哲学层面上讲,问题就是谁或者什么对音乐创作负责?

1 Introduction 简介

The question what is algorithmic composition is analogous to the question what is arti-゙cial intelligence. Both are hotly debated. Neither are answered easily. Both ask funda-mental questions about the authorship of ideas.

什么是算法作曲就类似于问什么是人工智能。两者都被激烈的讨论着,并且都不是很容易解释。都是询问一个基本的问题——作者的思想。

Algorithmic composition is the application of a rigid, well-de゙ned algorithm to theprocess of composing music. It is frowned upon by ‘traditional’ composers because itis often used as a means to expand one’s musical palette. The explicit message is thatalgorithmic composition is invalid as a methodology, but the implicit message is that themusic produced is in some sense unlike what the composer would have produced withouthelp. In other words, music produced by algorithmic composition is considered somehowinferior not because it was produced by an algorithm, but because it is someone else’smusic–it belongs to the designer of the algorithm, and not to the user of the algorithm.One can avoid this criticism merely by implementing one’s own algorithm.

算法作曲是一个在严格,定义良好的情况下,用于音乐作曲过程算法的应用。算法作曲被“传统”的作曲家看不惯,因为它通常被用来作为增长一个人的音乐创作直觉的一种手段。表面意思就是算法作曲作为一个方法是无效的,但是含蓄的讲,音乐创作某种意义上不像是作曲家创作中没有任何帮助。换句话说,通过算法作曲创作的音乐在某种程度上是低级的,不是因为它是通过算法创作的,而是因为它是别人的音乐——它属于算法的设计者,而不是这个算法的用户。仅仅只是为了避免这种批评,人们可以通过实现自己的算法。

To further support the algorithmic approach, the only difference between a com-poser’s creative methodology and some algorithm that approximates it is that the com-poser can exhibit much more ゚exibility. An algorithm by de゙nition is rigid, whereas cre-ativity often breaks rules. But there is something to be said for following the rules throughto completion. This is what the algorithm does quite easily but what a human composerwill often avoid–we like to break rules in the name of creative license. Though it isdif゙cult to follow the rules through to completion, there is a reason why well-de゙nedstructures are used to create music, art, sculpture, dance, poetry: in order to follow therules, one will often devise creative solutions that might not otherwise have been chosen.Therefore, a computer is well suited to the task of creativity-through-hard-work, as it isincapable of stepping outside of the well-de゙ned structures.

为了进一步支持算法的方法,作曲家创作的方法和一些类似的算法的唯一的区别在于作曲家可以表现出更大的灵活性。被定义的算法是死板的,而创造性又常常打破规则。但是也有一些被形容为遵循规则完成作曲。这点对于算法是很容易办到的,但是人类作曲家往往会避免——我们更喜欢以创作的名义打破规则。虽然通过遵守规则完成很难,这也是为什么一个定义良好的结构常常被用来创造音乐,艺术,雕塑,舞蹈,诗歌:为了遵循规则,对于那些可能无法被选择的方式,人们常常会设计出创造性的解决方法。因此,计算机是非常适合“通过努力的方式的创造力”,因为计算机在已经被定义好的结构之外,无法进行下一步。

However, we are still left with the question of authorship. To return to the arti゙cialintelligence theme, if an algorithm faithfully represents an artist’s creative process, what isthe difference between music produced by the artist and music produced by the algorithm?

然而,我们依然遗留了作者的问题。回到人工智能的主题,如果一个算法如实地表现了艺术家的创作过程,那人工作曲和算法作曲又有什么区别呢?

2 The Goal of Algorithmic Composition 算法作曲的目标

Creativity sometimes arrives in a sudden warm embrace, leaving one with a giddy sense ofinspiration, vision, and purpose–resulting in a moment of clarity that is both inexplicableand undeniable. Other times, one starts with a vague creative seed to spend countlesshours of revision and rethinking to hammer out a work of blood, sweat, tears, but mostlyfrustration.

创造力有时候像个突然的温暖拥抱般的抵达,留下让人眼花缭乱的灵感,视野和目标——导致当我们清醒时即让我们费解又不可否认。又有时候,创造力始于一个模糊的创意种子,然后花费无数小时的修改和重新思考敲定,这份工作中包含着我们的心血,汗水,眼泪,但是更多的是沮丧。

In short, creativity comes in two ゚avors: genius and hard work. While the formermay produce more ‘inspired’ music, we do not fully understand it and therefore have aslim chance of reproducing it. The latter resembles an iterative algorithm that attemptsto achieve some optimal function of merit, and is therefore more easily realizable as acomputer program.

简而言之,创造性有两种形式:天赋和努力。前者可能会产生更多的“启发”式音乐,我们不能完全理解它,所以再现这样的音乐的可能性很渺小。而后者就像一个迭代算法,试图获得一些最优化的函数,因此更容易让计算机实现。

We therefore have de゙ned a clear goal for an algorithmic composition system: to re-5

produce the composer’s creative methodology when the composer is in ‘hard work’ mode.The result is a system tailored for that particular composer (call him A); if another personwere to use the system to produce music, they would be composing A’s music, not theirown.

因此,我们给算法作曲系统设立了一个明确的目标:重现作曲家在“努力”模式下的创作方法。结果是一个为特定作曲家(A)量身定做的系统;如果另外一个人使用这个系统 去创作音乐,他将会作出A的音乐,而不是他自己的。

3 Philosophical Digression 哲学层面的题外话

This brings us to an interesting digression on the difference between music compositionand music recognition. When an algorithm written by a composer produces music thatis not exactly what the composer would produce, the composer ゙lters it–he culls outthe parts that con゚ict with his own personal tastes. (We will assume for the momentthat we are not dealing with Cage here.) Is this composition? How minimal must thechanges be in order for the algorithm-produced music to be considered composed (bythe algorithm or the composer)? How extensive must the changes be before one’s roleas algorithm-designer moves from composer to editor? At what point is the composermerely recognizing music that he likes? Is there a difference?

这给我们带来了一个有趣的题外话:音乐作曲和音乐鉴赏有什么区别。当一个作曲家写的算法创作的音乐确切的说不是作曲家创作的,作曲家只是过滤作用——他精心剔除了与自己个人喜好有冲突的部分。(在这里我们暂时假设不讨论Cage)这是创作么?为了让算法产生的音乐被认为是创作(通过算法或者作曲家的作曲),最小的必要更改是什么?如何大量的改变使一个算法设计者的角色从作曲家到编辑的转换? 什么是作曲家喜欢一个音乐的点?有何区别?

To take this a step further, suppose the ‘algorithm’ is a machine devised by the com-poser that beats on piano keys more or less randomly. The composer records key-bangingsessions to edit them later and stitch together the portions that make up a good piece (inhis estimation). What is the role of the composer here? Is the composer composing musicor merely recognizing music? Again, is there a difference?

借此更进一步,假设“算法”是一个在钢琴键上或多或少的随机演奏的作曲家设计的机器。作曲家纪录key-banging时段然后编辑它们,并且将它们整合各个部分成为一个好的模块(在他的估计中)。作曲家在这里的作用是什么?这是作曲家创作音乐还是仅仅是鉴赏音乐?再问一次,这有什么区别呢?

One step further: here, the composer travels to the nearest algorithmic compositionstore and purchases a machine that beats on piano keys more or less randomly, as well asa nice tape deck for recording and editing the session. He takes the machine home, recordsa session, and edits it down to a piece he calls Rhapsody in absentia. Whose music is this?To whom can we attribute the results? To the piano-punching machine? To the designerof the machine? To the user of the machine who recognized that certain passages wereviable compositions? Or is the Rhapsody merely non-music, sounds that do not countas music because no human actually envisioned them before they were heard–althoughthis de゙nition would seem to be a categorical cop-out.

进一步来说:在这里,作曲家就如前往最近的算法创作商店并且购买一个在钢琴键上或多或少随机按键的机器,以及一个超棒的录音机录制并且编辑会话。他把机器带回家,纪录一个会话,然后将它们编辑进一个被命名为“狂想曲”的模块中in absentia。这是谁的音乐呢?是我们认为造成结果的人?是属于钢琴机器么?还是机器的设计者?还是意思到某些段落是可行的作品的机器使用者?或者是“狂想曲”仅仅是非音乐,声音不算是音乐,因为实际上在他们听之前,没有人期望是这样的——尽管这个定义似乎是无条件的逃避问题。

If we simply look at the two diametrically opposed viewpoints we unearth much of theissue. One viewpoint is that art is communication and so anything one communicates toanother is art; art is the physical equivalent of “hey–look at this.” A piece of driftwoodfound on the beach, once recognized as interesting to the beholder, is art, even thoughthe person who takes the driftwood home and mounts it on the wall is not responsiblefor any of its characteristics, including its shape, its color, its texture, etc. This person didnot stand at the seaside and dangle the wood in saltwater for several decades in order toget the desired results, he merely discovered the wood and said, “hey–look at this.”

如果我们简单的看看通过大量问题挖掘出来的这两个截然不同的观点。其中一个观点是艺术是一种交流,所以任何从一方到另一方的交流都是艺术;艺术是物理的相当于“嘿,看看这个”。一个在海滩被发现的浮木,一旦有旁观者认为有趣,那就是艺术,即使把这个浮木带回家并且挂在墙上的人对它的任何特征,包括外形,颜色,纹理等等完全不负责。这个人并没有站在海边,将木头悬挂在盐水中几十年就为了得到想要的作品,他只是发现了这个木头,并说“嘿,看看这个”。

The other viewpoint is that only what comes directly from the hands of the artistis of the artist. This is the viewpoint that has caused many of the world’s Rembrandtsto devalue (to name just one of many artists) because some of the work was done byassistants, not by the master. Where the other viewpoint considers vision more importantthan toil, this viewpoint considers toil more important than vision.

另一个观点是艺术只有直接来自艺术家之手。这个观点导致世界上很多伦勃朗7

的作品被贬值(这里只是指出众多艺术家之一)因为有一些工作都是助理完成而不是艺术家本人。其他观点认为想象比工作更为重要,而这种观点认为辛苦比想法更重要。

One viewpoint discounts all algorithmic composition, another embraces it. There areno answers here, this is merely an aside to suggest that the more closely an algorithmre゚ects a composer’s methodology, the less question there is that the work is authenticand of the composer.

一个观带贬低算法作曲,另一个拥簇。这里并没有什么答案,这里仅仅是题外话建议算法在真实的工作和作曲家中,更接近地表现作曲家的创作方法,更少的问题。

4 Evolution of the Role of the Computer 电脑作用的演变过程

Computers are not new to music composition; Max Mathews was developing sound syn-thesis programs at AT&T in the 1950’s [1]. For decades, the computer has been usedto compose music, typically via probabilistic or stochastic methods .[2][3][4] Articles byLorrain and Jones [5][6] provide excellent descriptions of the mathematics involved. Untilthe mid-eighties, much of the attention was focused on timbres, rather than the structureof the music composed (e.g. [Truax 1982, Risset 1985, McNabb 1981, Vaggione 1982]).This is understandable, given the state of the art–the computational limits of the com-puters and the relative lack of rich sound sources. Also, given the limits of early comput-ers, it seems reasonable that much of the composition algorithms were centered aroundnotes, e.g. Markov chains giving next- note probabilities, rather than around higher-levelstructures such as phrases or thematic material. Note-based composition is much lesscomputationally intensive, but with its simplicity comes an organizational tradeoff. Anote-based method works at the level of trees and is hard-pressed to create a forest, ex-cept as a collection of trees.

对于作曲而言,电脑作曲以及不是什么新的话题;马克斯·马修斯在20世纪50年代于AT&T开发声音合成程序。几十年来,计算机通常是通过概率或者随机的方法用来作曲。Lorrain and Jones 的文章提供了优秀的数学描述。直到80年代中期,大部分的注意力集中在音色,而不是作曲的结构。这是可以理解的,给定的艺术形态——计算机的计算限制和相对缺乏丰富的声音来源。由于早期计算机的局限性,算法作曲主要是围绕着音节就合情合理了,例如马尔可夫链提供了下一个音节出现的概率,而不是围绕像乐句或者主题这种高层次的结构展开。以音节为基

础的作曲计算量要少得多,但是简单带来的组织上的权衡。基于音节的方法的工作是树木级别除了树的集合是很难创造一个森林的。

Today, with samplers, sample-based synthesizers, and orders of magnitude more com-pute cycles readily available, more attention can be placed on structured composition.There are many examples of complex composition algorithms which produce ‘correct’music, most of them centered around databases of style descriptions or rules [7][8][9][10].On the other side, the computer is still often used as a fast randomizing agent; populargeneration programs M and Jam Factory both use Markov chains to create lines whichare statistically close to what the user inputs [Rowe 1993, Walker 1994, Zicarelli 1987].Another tendency is to use the computer as an accompanist who listens to what is beingplayed and responds appropriately in real-time. Here, the human input is used to gen-erate rules on which the machine will base its output. This is seen in such programs asCypher [11] and IBL-Smart [12].

如今,随着采样,基于采样的合成器和容易获得的数量级更大的计算速度,我们可以把更多的精力放在结构作曲上。有许多产生“正确的”音乐的复杂作曲算法,其中大部份是围绕风格描述或者规则的数据库。另一方面,计算机依然经常被用于快速随机化的工具;流行一时的程序M和Jam Factory都使用了马尔可夫链去创造统计上接近用户输入的水平线。另一个趋势是使用计算机当作伴奏,当他听到正在演奏的音乐并且即时的作出回应。在这里,人们输入创作规则,机器就会基于规则进行创作输出。这类的程序可以参考 Cypher和IBL-Smart。

As computers get more powerful, they become capable of handling increasingly com-plex tasks. Accordingly, as time goes on, composers have used computers to more closelymodel the creative process. This has happened not just in music composition, but in anentire range of creative pursuits from analogy-making to the creation of typefaces [Hofs-tadter 1995]. This is an inevitable trend, but it is also vital to the validation of algorithmiccomposition and computer-generated art in general. The more closely we can model ourcreative processes, the more the computer becomes a simple tool for artistic creation, andless a replacement for inspiration.

随着计算机越来越强大,他们变的能够处理日益复杂的任务。因此,随着时间的推移,作曲家可以用计算机更准确地模拟创作的过程。这不仅仅发生在音乐创作,而是在整个富有创造性的范围从类推制作到字体的创造。这是一个必然的趋势,但是算法作曲和一般意义下的电脑创作艺术的验证也是至关重要的。我们的模型越接近创作过程,电脑越容易成为一个简单的艺术创作工具,就有更少的灵感替代品。

5 The variations System Variations系统

While this article is a generic argument for algorithmic composition, it uses examples thatcome from a speci゙c system. In order to better understand the examples, this sectiondescribes the system brie゚y. For a more complete description, see [Jacob 1995] or theauthor’s webpage.

虽然本文是对算法作曲一个通俗的讨论,但是它来自一个特定的系统使用例子。为了更好地理解例子,本节先简单的描述一下系统。详情见Jacob或者作者的网站。

5.1 System Overview 系统综述

variations is an algorithmic composition system that attempts to model the ‘hard work’ethic of creativity. The system was designed to reproduce very closely the creative pro-cess that this author uses when composing music, which is very similar to writing a canon,except that the variations on themes need not be isomorphisms. The human creative pro-cess allows one to ‘make up’ new themes whenever they are needed or wanted. Creativityis dif゙cult to de゙ne, let alone program into a computer, so the system makes no attemptat thematic generation–it only produces variations on existing material. However, sincethe themes can be variations upon variations, the net result is often indistinguishablefrom creating new, barely related thematic material.

Variations是一个试图模拟“努力”型创作理论的算法作曲系统。系统被设计用来再现接近作者创作音乐时的创作过程,这很类似于写一首卡农,除了主题不需要同构。人类在创作的过程允许在任何它们需要或者想要的地方可以“制造”新的主题。创造力很难被定义,更不要说编程化了,所以该系统没有尝试初代主题——它只是在现有的素材进行改动。然而,由于主题可以不断的更新,最终的结果往往是不能辨别新创建的主题,几乎没有主题联系的资料。

The system works at the level of motives, which simpli゙es the organization of themusic. It is much easier to create structure in a piece when one works at a higher levelthan it is when working at the level of notes–it is hard to force a next-note-probabilitymodel into creating structured pieces riddled with thematic development. In the varia-tions system, order is imposed on the music produced by de゙nition; by ensuring that allof the notes used in the resultant piece belong to phrases related to each other throughtransformation, a certain amount of thematic development is inherent, almost inevitable,in the music. This allows the system to pay more attention (and computer cycles) to har-monic progression.

该系统在动机层面工作,这简化了音乐的组织。工作在比音节层次更高的层次,更容易在一个模块中创建结构——很难迫使一个“下一个音节的可能性”的模型区创建充斥着主题发展的结构化模块。在Variations系统中,命令通过定义被强制执行与音乐创作中;通过确保所有在结果中属于乐句的模块中被使用的音节彼此通过的变化,在音乐中,一定量的主题发展是内在的,几乎不可避免。这使得系统更关注(和计算机周期)于调和级数(和声的发展)。

The compositional algorithm:作曲算法:

1. De゙ne a number of primary themes (motives) to be used in the composition.定义一定数量的主要主题(动机)用于作曲。

2. Compose phrases by creating motives and adding them one by one to the phrase.At each step, judge the quality of the resultant phrase and remove the last motiveif the combination is unsuitable.通过创建动机和添加一个又一个的乐节构成乐句段。在每个步骤中,判断产生乐节的质量并且如果组合是不合适的,则删除最后一个动机。

3. Create motives by selecting at random from the primary themes and motives al-ready in the phrase, and producing variations upon the selection.通过从主要主题和已经在乐节中的动机中随机选择创造动机,并且产生变异的选择。

4. Once there are a large number of phrases, join them together into larger frame-works.

     一旦有大量的乐句,则将它们加入到更大的框架中(乐段)。
   

The primary software components are the composer and ear modules. The composerproduces material and the ear ゙lters out whatever is ‘bad.’ It is a producer-consumerparadigm, popular in music composition systems. One side produces music, the otherside consumes it and critiques it, affecting the future output of the producer.

主要的软件组件是作曲家和听力模块。作曲家组件产生音乐素材,听力组件过滤“坏”的部分。这是生产-消费的范式,流行于音乐作曲系统。边生产音乐边欣赏并评价它,从而影响之后生产的音乐。

Figure 1 illustrates the process. The composer takes as input a number ofmelodies,and composes aphrasefrom them motive by motive. The composer creates music byproducing a variation on a previous motive and layering and sequencing it with the othermotives. Each motive is either a copy of a primary motive, a variation upon a primary

motive, a copy of a previous motive, or a variation upon a previous motive. At each step,the resultant phrase is tested by the ear and given a yes/no grade. If the ear likes thepiece, the composition process continues. If the ear does not like the piece, the composerdeletes the motive and tries a different variation.

图一 说明了这个过程。作曲家奖作为一系列输入的旋律,并且从旋律动机到动机中生成乐汇。然后作曲家系统通过产生原有动机的变异体并且与其他动机分层测序从而创造音乐。每一个动机是主要动机的复制品,主要动机的变异体,先前动机的复制品或先前动机的变异体之一。而在每一步中,合成乐汇与否是由听力系统打分yes/no来决定的。如果听力系统喜欢这个组合,则作曲过程继续下去,如果不喜欢,则作曲系统则会删掉这个动机并且尝试一个不同的变化。

5.2 Motive-Oriented Organization of the Composer 以动机为目标的作曲组织

The system organizes and manipulates material at the level of motives, so thatthematicdevelopmentis inherent in the music produced. A motive-oriented internal representa-tion forces an implied structure on the compositional process; it allows for easy coherentmanipulation of the material so that the resultant thematic variations are neither trivialnor unrecognizable.

该系统在动机层次上组织和操作素材,所以主旋律的发展在音乐制造中是固有的。以动机为目的的内部表征在作曲的过程中强迫一个隐式结构?;它允许简单连续操作素材使得合成的主旋律的变化既不琐碎也无法识别。

Each motive contains the following:每一个动机包含如下内容:

• a list of pitches, where the possible values are 1 (tonic), 2, 3, 4 (subdominant), 5(dominant), etc.一个音高的列表,其中可能的值为1(基音),2,3,4(次属音),5(属音),等等

• corresponding lists of rhythms andarticulations相对应的有节奏和发音的清晰度列表

  音调信息:基音(包括八度音阶在内),其中音调是大调还是小调

• keyinformation: the tonic (including which octave it is in), whether the key is majoror minor

• timinginformation:offsetin measures from previous motiveTiming信息:在之前的动机中适度地获取offset修正值(关于BPM)

• partinformation: which instrument声部信息:使用了何种乐器

The chosen form encourages transformation:transpositionis a simple matter ofchanging the tonic or adding the same number to every member of the pitch list. Chang-ing the rhythm is just as simple: dividing the elements of the rhythm list by 2 turns everyquarter note into an eighth note, every eighth into a sixteenth and so on. Similarly chang-ing the numbers in the articulation list will make alegato phrasesound morestaccato.

选择的形式鼓励转换:改变基音或者向音高列表中每个项增加相同的值,移调是一件简单的事情。改变节奏一样简单:将节奏列表中的元素用2个turns分割出来从而将每个四分音符变成八分音符,每个八分音符变成十六分音符等等。同样的改变发音列表的值将会使一个连音乐汇听起来更不连贯。

Since the system begins with a small number of de゙ned motives, resultant composi-tions will consist entirely of motives closely related to each other. Each phrase containsself-similar components, and all phrases based upon the same primary motives are re-lated to one another. The component motives are all related by transformation, and therelations span from the obvious, such asechoor transposition, to the very subtle.

自从系统从一些很少数量的被定义的动机开始运作,合成的作品将会完全的由彼此密切相关的动机组成。每一个乐汇都包括自相似的部分,并且所有基于相同的基本动机的乐句彼此也是相关的。构成的动机都是相关的,通过变形和显性的关系跨度,如echo或者转调,非常微妙。

5.3 The Composition Process as an Algorithm 作曲过程的算法描述

The goal of this section is to demonstrate through examples that composing-by-hard-work is inherently algorithmic. The composition process described in the previous sectionis not speci゙c to a computer program; the process is quite similar to the creative processesof a human. Phrases are built up from motives one by one. Motives are composed byarbitrarily picking from a few themes, modifying them slightly, and adding them to thework-in-progress. For example, we start with the following well-known theme (typeset byDaniel Taupin in his MusicTeX manual):

本节主要目的是通过实例表明努力型作曲是一个内在的算法。在之前的章节已经描述的作曲过程并不针对于电脑程序;这个过程和创造人类的过程很相似。乐句是通过一个又一个的动机组成。而动机则武断的从少量的主题中挑选,再轻微的修改他们并将它们加入半成品中。例如,我们从下列我们熟知的主题开始(DanielTaupin排版于他的MusicTeX手册):

’((8 10 12) (7 8 9 8)) ’((1/2 1/4 1/4)(3/8 1/16 1/16 1/2))themes1.mid

If the length of the variation is to be seven notes, then the following would be apossible result: (Please note that the inclusion of a time signature is simply to make therhythms of the phrases easier to read. Some phrases will not ゙ll out the last measureexactly, but do not have implicit rests at the end.)

如果变化的长度是七个音节,则下一个的可能结果如下:(请注意包含时间信号仅仅使乐句的韵律更容易阅读。有些乐句在最后的单位了并不能准确的填满,但是最后没有隐式休止。)

’((12 7 8) (13 12 12 10)) ’((1/2 1/4 1/4)(3/8 1/16 1/16 1/2))themes121.mid

The following would be just as viable:以下是同样可行的:

’((8 10 12 7) (7 8 9 8)) ’((1/16 1/16 1/2 3/8)(1/8 1/4 1/4 3/8))themes122.mid

If the length is to be longer or shorter than seven, we can get simple variations suchas this:

如果长度比7还长或短,我们可以简单的这样变化:

’((7 8 9) (8 8 10 12)(7 8 9)) ’((1/2 1/4 1/4)(3/8 1/16 1/16 1/2)(1/2 1/4 1/4))themes2.mid

or this:或者这个

’((12 7 8)) ’((1/4 3/8 1/8))themes3.mid

We can also see more dramatic changes. We can choose to run pitches forward andrhythms backward:

我们可以看到更多戏剧性的变化。我们可以选择音高forward和韵律backward:

’((12 7 8)(9)) ’((1/4 1/4 1/2)(1/2))change1.mid

We can change the key:我们可以改变调:

bbb’((8 10 12) (7 8 9 8)) ’((1/2 1/4 1/4)(3/8 1/16 1/16 1/2))key1.mid

We can transpose (note the lack ofaccidentals):我们可以转调(注意缺失临时记号):

’((6 8 10) (5 6 7 6)) ’((1/2 1/4 1/4)(3/8 1/16 1/16 1/2))transpose1.mid

We can multiply all pitch values by 1.5 and round:我们可以把所有的音高值乘以1.5并四舍五入:(应该是指变化音阶的1.5)

’((8 11 14) (6 8 10 8)) ’((1/2 1/4 1/4)(3/8 1/16 1/16 1/2))multiply1r5.mid

We can multiply all pitch values by 1.5 and truncate:我们可以把所有的音高值乘以1.5并循环并去尾:

’((8 11 14) (7 8 10 8)) ’((1/2 1/4 1/4)(3/8 1/16 1/16 1/2))multiply1t5.mid

We can multiply the pitch values by -2.0:我们可以把所有的音高值乘以-2:

’((8 3 -1) (9 8 5 8)) ’((1/2 1/4 1/4)(3/8 1/16 1/16 1/2))multiplyn2.mid

We can choose to use just a subset of the pitches (maintaining order):我们可以选择使用音高的子集(保持顺序):

’((8 10 12) (8 10 12 8)) ’((1/2 1/4 1/4)(3/8 1/16 1/16 1/2))subsetp1.mid

We can choose to use just a subset of the rhythms (also maintaining order):我们可以选择韵律的子集(依然保持顺序):

’((8 10 12) (7 8 9) (8)) ’((1/2 1/4 1/4)(1/2 1/4 1/4) (1/2))subsetr1.mid

When we start combining the changes with each other, we get more complex behav-ior. The variations begin to look less like the original theme and more like the weighted-probability characteristics of Markov processes for the choice of notes, rhythms, and ar-ticulations. However, it is still clear that there is a relationship between the motivesproduced.

当我们开始结合互相的变化,我们能够获得更多复杂的行为。变奏曲的开始更不像原始的主旋律反而更像选择音节,韵律,发音的加权概率特征的马尔可夫过程。然而,我们依然清楚,所产生的动机彼此之间是有联系的。

For instance, we can multiply the pitch values by 3 and change keys:举个例子,我们可以将音高值乘以3并且改变调:

b’((3 9 15) (-1 3 6 3)) ’((1/2 1/4 1/4)(3/8 1/16 1/16 1/2))multiply3key.mid

We can choose a shorter list, multiply the rhythm values by 2, choose different subsetsof pitches and rhythms, and transpose:

我们可以选择一个更短的列表,节奏值乘以2,选择音高和韵律的不同的子集,并且转调:

b’((3 9 15) (-1 3 6 3)) ’((1/2 1/4 1/4)(3/8 1/16 1/16 1/2))multiply3key.mid

We can choose a longer list, translate within C major, and mismatch the rhythms:

我们也可以选择一个更长的列表,转译到C大调上,并且不匹配韵律:

‘((0 1 0) (0 2 4) (0 2 4 -1)) ’((1/2 1/4 1/4)(1/2 1/4 1/4) (3/8 1/16 1/16 1/2) )translateCmr.mid

Things get very interesting when we perform variations on the variations. Each vari-ation on a theme is akin to a poor-quality photocopy or musical recording–with eachiteration, the resemblance to the original fades. After several iterations the original isalmost indistinguishable. If we only consider the last three examples, which were fairlynormal variations to begin with, we get motives that barely resemble the original theme.

当我们在变异体上进行变化的时候,事情就变的更有趣了。每一个主题的变化类似于低质量的复印件或者音乐纪录片——随着每一次迭代,与原始的主题的相似处就越来越淡。经历数次迭代,原作几乎不能被区分。如果我们只考虑最后三个例子,都是以正常的变化作为开始,我们得到了仅仅类似于原始主题的动机。

For instance, we can modify the ゙rst theme by dividing the pitch values by 4, selectinga subset of the pitches, selecting a different subset of rhythms, and transposing:

举个例子,我们可以通过音高值除以4对第一个主题进行修改,选择音高列表的一个子集,选择节奏列表的一个不同的子集,并且更换:

b‘((7 6 5 6 7 6 5 6 7)) ’((1/16 1/16 1/16 1/16 1/16 1/16 1/16 1/16 1/8 ))

We can modify the second theme by repeating the entire theme while mismatchingthe pitches and rhythms:

当没有匹配音高或者韵律的时候,我们可以通过重复整个主题对第二个主题进行修改:

‘((-2 -1 1)(1 3)(-2 -1 1)(1 3)(-2 -1)) ’((1/4 1/4 1/2) (1/4 3/4) (1/4 1/4 1/2) (1/4 1/4))

We can modify the third theme by repeating subsets of the pitches and rhythms:我们可以通过重复音高和韵律的子集对第三个主题进行修改:

‘((0 2 4 -1 0 2) (4 -1 0)) ’((3/8 1/16 1/16 3/8 1/16 1/16) (3/8 1/16 1/16))

These modi゙cations are all classic variations used in canons and fugues to vary the-matic material. There is nothing special or inspired about the examples–they are merelyprovided to demonstrate that there is an extremely large number of possible modi゙cationsthat can be done to a piece of music, many more possibilities than a human would wantto explore, or even could explore in a reasonable time. The beauty of using a computer isthat it can explore the space.

这些修改都是传统的变奏曲使用于卡农和赋格音乐产生不同主题的素材。这里没有什么特别活着有灵感的例子——它们只不过是被提供证明了极多的可能的修改可以做成音乐的一个乐汇(音乐的一个片段)。

5.4 Algorithmic Compositions: Variations on a Theme by Mozart 算法音乐作品辑:莫扎特主题变奏曲

There is a search space that is composed of all possible variations on a theme; the sizeof this space cannot be overestimated. To give a feel for its extent, a dozen examplesof phrases that have been derived from the original theme are presented. They havenot passed any sort of quality test, they are merely presented as they were generated bythe algorithmic composition system variations. (They happen to be sections of piecesthat neither broke MIDI2TeX nor required extensive editing of the generated MusicTeXmacros.)

含有一个由所有主题变化的可能性的搜索空间;空间的大小不能被高估。为了让大家有一个这个空间大小的概念,下面列出关于由原始主题衍生出的12个乐句例子。它们还没有通过任何种类的质量测试,它们仅仅是被作为算法作曲系统变奏曲被提出来。(它们变成一个个部分,无论是通过broke MIDI2Tex还是需要大量的编辑生成MusicTex宏)

这些例子只展示了由仅仅一个互相对立的主题并列的变奏创造的空间的极小部分。空间中加入的主题是以指数级别的增长。重复性的执行程序函数这点电脑比人类在行,所以把所有变奏的可能性的工作分配给电脑是很恰当的;我们已经重新定义了我们的问题:现在,作曲的“智能”部分,不再是定义如何进行音乐创作;而是如何能够区分什么是“好的”素材,什么是“不好的”。虽然这并不是一件轻松的事情,但是仍然是在正确的方向上迈出了一步。

6 Conclusions 总结

Algorithmic composition is a methodology for allowing a human composer to work morequickly. Its success depends very heavily upon two things:

算法作曲一种能够让人类作曲家工作更迅速的方法。它的成功很大程度取决于两件事:

1. A close match between a composer’s creative methodology and the implementedalgorithm.

   作曲家创作的方法与应用的算法的紧密匹配。(就是说算法是否完整描述了该作曲家的作曲方法)

2. An accurate mechanism for quickly determining the viability of a speci゙c phrase.有一个准确的机制能够迅速地确定一个特定的乐汇的可行性。(筛选的标准)

The problem of computer-aided music composition is thus reduced from answeringthe nebulous how do I create music to answering two slightly more concrete questions:what steps do I use to compose music and what types of harmonic movement do I like.

电脑辅助音乐作曲的问题因此被减少到从回答模糊的我如何创造音乐到两个更具体的问题:我作曲的过程是怎样的;我喜欢什么哪种和声乐章?

This is neither a trivialization of the compositional process nor a vague speci゙cationfor an algorithmic composition system. These are the questions one must successfully an-swer before one can use algorithmic composition in a manner that escapes mudslinging.Each composer has a unique compositional process and therefore one algorithmic toolcannot hope to satisfy the demands of many different composers. Algorithmic composi-tion is perhaps a little bit like religion or politics; one must ゙nd one’s own path. The moreclosely one can match an algorithm to one’s own creative process, the more the computerbecomes a simple compositional tool, and the less it appears to be a compositional crutch.

这既不是对创作过程的轻视,也不是对算法作曲系统模糊的描述。These are thequestions one must successfully answer before one can use algorithmic composition in amanner that escapes mudslinging. 每一个作曲家都有独一无二的作曲过程,因此一个算法工具并不能被期望用来满足大量不同的作曲家。算法作曲有点宗教或者政治的味道;每个人只有发现他们自己的路。一个人能够写出的算法越接近他自己的创作过程,那么电脑就更加成为一个简单的作曲工具,并且作曲的支持就会更少。

References

1. [1]  Roads, C.1989. An interview with Max Mathews. In Roads, C., editor, The MusicMachine. The MIT Press, Cambridge MA.

2. [2]  Hiller,L.1981.Composingwithcomputers:Aprogressreport.ComputerMusicJour-nal , 5(4):7-21.

3. [3]  Laske, O. 1981. Composition theory in Koenig’s Project One and Project Two. Com-puter Music Journal, 5(4):54-65.

4. [4]  Englert, G. 1989. Automated composition and composed automation. In Roads, C.,editor, The Music Machine. The MIT Press, Cambridge MA.

5. [5]  Lorrain, D. 1980. A panoply of stochastic ‘cannons’. Computer Music Journal, 4(1):53-81.

6. [6]  Jones,K.1981.Compositionalapplicationsofstochasticprocesses.ComputerMusicJournal, 5(2):45-61.

7. [7]  Cope, D. 1987. An expert system for computer-assisted composition. Computer Mu-sic Journal, 11(4):30-46.

8. [8]  Cope, D. 1992. Computer modeling of musical intelligence in EMI. Computer MusicJournal, 16(2):69-83.

9. [9]  Friberg, A. 1991. Generative rules for music performance: A formal description of arule system. Computer Music Journal, 15(2):56-71.

10. [10]  Widmer, G. 1992. Qualitative perception modeling and intelligent musical learning.Computer Music Journal, 16(2):51-68.

11. [11]  Rowe, R. 1993. Interactive Music Systems. The MIT Press, Cambridge MA.

12. [12]  Widmer, G. 1994. The synergy of music theory and AI: Learning multi-level expres-sive interpretation. Technical Report OEFAI-94-06, Austrian Research Institute forArti゙cial Intelligence.