I want to begin to break apart the paragraph that holds the appearance of the conductor.
directly social or communal labour on a large scare requires, to a
greater or lesser degree, a directing authority, in order to secure the
harmonious co-operation of the activities of individuals, and to perform
the general functions that have their origin in the motion of the total
productive organism, as distinguished from the motions of separate
organs (Capital, Fowkes trans., p. 448).
The need for a harmonious co-operation of individuals calls forth a directing authority. In English, harmonious bundles a part/whole relationship: "having the parts or elements in accord so a to form a consistent or agreeable whole" (OED). The sociality of labor power requires a directing authority to pull the parts (individuals) into a whole-- "a total productive organism as distinguished from the motions of separate organs." Social labor or communal labor is also geographically imagined in scaler terms -- large scale -- the size (magnitude?) of social labor requires a directing authority. As the parts find themselves belonging to a bigger and bigger whole, the need for a directing authority to secure the agreement, the concordance of the parts, becomes more evident. Why? Because the parts need not co-operate harmoniously. To be harmonious requires agreement in contrast to dischord or dissent (OED). It is the job of the directing authority to secure harmonious interaction between the individual parts./ separate organs of the total productive organism. A sonic quality of being in tune comes as a secondary quality of harmonious reiterating the importance of an agreeable effect: "characterised by harmony of sounds: sounding together with agreeable effect; ... tuneful, sweet sounding." (OED). The binding of part/whole with tuneful-agreeable/dischord-dissent prepares us for the appearance of the the musical metaphor.
A single violin (end p. 448)
player is his [or her] own conductor: an orchestra requires a separate one.
As a single performer, a violin player directs his/her own playing. The violinist is responsible for producing an agreeable sound. A lone violin player retains his/her role as a conductor or directing authority. But once the violin player joins an orchestra, becomes a part in a whole, the sound of the violin requires interaction with the sounds of other players and instruments. To secure this harmony, each musician requires a separate conductor to direct her/his playing with others. To be separate, the conductor externalizes authority from the lone violin player.
work of directing, superintending and adjusting becomes one of the
functions of capital, from the moment that the labour under capital's
control becomes co-operative.
The conductor is to the orchestra what Capital is to social communal labour. In this case, an authority for "directing, superintending and adjusting" the cooperation of social labor. In English, directing embodies a rhetorical history "to write (something) directly or specifically to a person, or for his special perusal; to address" (OED). Directing, superintending, adjusting are rhetorical actions, modes of public address, to create agreement and to limit dissent among the cooperating elements of social labor.
As a specific function of capital, the
directing function acquires its own characteristics." (Fowkes Translation, Vintage Books Edition, 1977, pp. 448-449)
The next two paragraphs of the co-operation chapter explain the specific characteristic of the directing function of capital. In short, the answer is that its form of control/command/rule is despotic. A couple of passages are worth noting for future work:
"As control exercised by the capitalist is not only a special function arising from the nature of the social labour process, and peculiar to that process, but it is at the same a function of the exploitation of a social labour process, and is consequently conditioned by the unavoidable antagonism between the exploiter and the raw material of his exploitation." (Capital, Fowkes tr., p. 449)
Due to capital's directing authority, its ability to externalize its control of the social labor process, the cooperative labor process increases the worker's "resistance to the domination of capital" (p. 449). Social labor needs to be well tuned if it is avoid dissent to its exploitation. Marx argues that the worker confronts the authority of the capitalists "as a powerful will of a being outside them, who subjects their activity to his purpose" (p. 450). This authority "in form it is purely despotic" (p. 450). As we come to understand the Despot as an absolute ruler (as tyrannical), it is worth noting its own rhetorical history as a mode of address: "In Byzantine times, it was used of the Emperor, and, as representing Latin magister, in various official titles, also as a form of address (= domine, n my lord) to the emperor, to bishops, and especially to patriarchs" (OED). Capital as sovereign.
The despotism of capitalist rule generates its own "petty rulers" (OED) as it "hands over the work of direct and constant supervision of individual workers and group of workers to a special kind of wage-labourer ... managers ... foremans ... overseers ... who command during the labour process in the name of capital." (p. 450). A visual rhetoric of supervision and surveillance for the purpose of generating an agreeable sound of workers working for capital.
Capital addresses social labor by directing, superintending, adjusting, supervising it, while social labor's harmonious integration into the whole requires it to address address capital as my lord. Labor's obedience to its conductor is required for co-operation to become the "fundamental form of the capitalist mode of production." (p. 454)