Well, for one thing, Nietzsche, as far as I know, never uses the phrase “master slave morality”. Where did you get that phrase anyway - Wikipedia? But Wikipedia writes “master-slave morality”, which we could rewrite as “master/slave morality”. And indeed, you Initially do write it this way. I suppose that what is meant by this phrase is “the interplay between master morality and slave morality” - a dynamic. But then you say:
“Ive also been reading that he views nihilism as a situation which has come about through the master slave morality.”
If you mean “through the master/slave dynamic” or “through the interplay between master and slave morality”, I think you’re wrong: it has come about through slave and herd morality - which are not one and the same! George Morgan says of these two moralities:
“The flock [die Heerde], needing leaders, was seduced by decadents, its morality perverted in the direction of decadence ideals. But in the course of time herd instincts proved more powerful: the decay of ascetic Christianity and the rise of democratic humanitarianism was a return of Flock Morality to its natural form. Nietzsche believed that Flock Morality is the most important element in present morals, and that this fact threatens ultimate stagnation for humanity.”
[Morgan, What Nietzsche Means, page 161.]
The ascetic priest, too, was too extreme for the herd (and of course he was himself a kind of nobleman: a “spiritual nobleman”, a person closer to God than most people, than “laymen”).
Anyway, this is how Nietzsche ultimately describes nihilism:
"Supposing that what is at any rate believed to be the “truth” really is true, and the meaning of all culture is the reduction of the beast of prey “man” to a tame and civilized animal, a domestic animal, then one would undoubtedly have to regard all those instincts of reaction and ressentiment through whose aid the noble races and their ideals were finally confounded and overthrown [that is, slave instincts, not herd instincts] as the actual instruments of culture; which is not to say that the bearers of these instincts themselves represent culture. Rather is the reverse not merely probable—no! today it is palpable! These bearers of the oppressive instincts that thirst for reprisal, the descendants of every kind of European and non-European slavery, and especially of the entire pre-Aryan populace—they represent the regression of mankind! These “instruments of culture” are a disgrace to man and rather an accusation and counterargument against “culture” in general! One may be quite justified in continuing to fear the blond beast at the core of all noble races and in being on one’s guard against it: but who would not a hundred times sooner fear where one can also admire than not fear but be permanently condemned to the repellent sight of the ill-constituted, dwarfed, atrophied, and poisoned? And is that not our fate? What today constitutes our antipathy to “man”?—for we suffer from man, beyond doubt.
Not fear; rather that we no longer have anything left to fear in man; that the maggot “man” is swarming in the foreground; that the “tame man,” the hopelessly mediocre and insipid man, has already learned to feel himself as the goal and zenith, as the meaning of history, as "higher man"—that he has indeed a certain right to feel thus, insofar as he feels himself elevated above the surfeit of ill-constituted, sickly, weary and exhausted people of which Europe is beginning to stink today, as something at least relatively well-constituted, at least still capable of living, at least affirming life.
[…]
“Here precisely is what has become a fatality for Europe—together with the fear of man we have also lost our love of him, our reverence for him, our hopes for him, even the will to him. The sight of man now makes us weary—what is nihilism today if it is not that?— We are weary of man.”
[Nietzsche, Genealogy of Morals, 1, 11-12.]
The part I have made bold describes the herd type. As you can tell, Nietzsche ranks this type higher than the slave type. Indeed, Nietzsche believed in the desirability of “a strong and healthily consolidated mediocrity” [The Antichrist(ian), section 57]. Such a mediocrity is the foundation of the culture pyramid (“culture” not in the sense used above, though…):
“A high culture is a pyramid: it can stand only on a broad base; its first presupposition is a strong and healthily consolidated mediocrity.”
This mediocrity would consists of “slaves”, it is true; but not resentful slaves, but rather like the serfs of medieval times:
“The third [and bottom] layer of the social structure is that of the rural peasantry, this is the function of fecundity and prosperity, this class can be associated with the class of slaves - although this class is very different to the slave class of the early modern era and is probably best thought of as an underclass.”
[Philip Quadrio, Odhinn and Tyr.]
The dropouts of the social structure (from all three layers), those who rank below the bottom, are what Nietzsche calls the chandalas: the pariahs, outcasts, the truly hated (for the mediocre are just despised: despised and loved). It is from these dropouts that slave morality, the slave instinct of resentment, arises:
“Whom do I hate most among the rabble of today? The socialist rabble, the chandala apostles, who undermine the instinct, the pleasure, the worker’s sense of satisfaction with his small existence—who make him envious, who teach him revenge… The source of wrong is never unequal rights but the claim of “equal” rights… What is bad? But I have said this already: all that is born of weakness, of envy, of revenge.— The anarchist and the Christian have the same origin…”
[Nietzsche, ibid.]
This origin is shared by Marx and Paul.