Did the original reformers believe in a Magisterium? I have seen the original reformers referred to as the "Magisterial reformers" a couple of times over the past few years, and I'm only now wondering what the significance of that phrase is. 

Does it imply that the original reformers (eg Luther and Calvin) believed in a Magisterium? That is, did they believe in an official teaching office of the Church that has the power to proclaim binding dogmas? (In the Catholic system this is the Pope and all the Bishops who are in communion with him)

Another reason I ask is directly related to this: I've read that the original reformers had a very different view of "Sola Scriptura" when compared to modern day protestant evangelicals. Apparently they didn't believe in the "private interpretation" which is common in the protestant church today. This leads me to wonder, if they didn't believe in private interpretation, then did they believe in submitting to official church teachings instead, like Catholics do? 

(Of course if they did indeed believe this, they presumably didn't identify the church with the Catholic church of the day, but instead identified it with their own new and unique denominations)

I've also read that during the reformation, Calvin ruled Geneva theologically and politically, almost as if he were a bishop or Pope of his own new version of Christianity. I understand that he subscribed to sola scriptura, but he was the only person in Geneva who was permitted to actually study the bible and come to theological conclusions  (This is my understanding; I'm open to further information/correction). 

The reason I bring this up is that it seems to indicate that Calvin regarded himself as an alternate, authoritative Magisterium of the church.  

Final note: I have always been utterly baffled by the doctrine of Sola Scriptura as presented by modern evangelical protestants.  It has always seemed fundamentally broken, incoherent and illogical to me. It is impossible to infallibly recognise the canon of scripture when you deny Church authority (This was a deal breaker for me and caused me to convert to Catholicism). 

However I think I'm finally seeing the light. I can understand Christianity following a doctrine of Sola Scriptura provided that there is also an authoritative Magisterium which is operating according to this doctrine. By this I mean, there is still an official church authority who can proclaim dogmas, resolve disputes, recognise the canon of scripture, etc, however this church authority must make sure that everything it teaches can be explicitly proven from scripture.   

In this way you would have a Christianity which embraces both Sola Scriptura and has an authoritative Magisterium. 

Is this what the original reformers were trying to do?
tldr; No - the Reformers disavowed the concept of the Magisterium.

If you read the Wikipedia article on the Magisterial Reformation it is plain to see that the usual usage of the term &quot;Magisterial Reformers&quot; isn't actually related to the concept of a teaching Magisterium:

The Magisterial Reformation is a phrase that &quot;draws attention to the manner in which the Lutheran and Calvinist reformers related to secular authorities, such as princes, magistrates, or city councils&quot;, i.e. &quot;the magistracy&quot;...the Magisterial Reformation argued for the interdependence of the church and secular authorities, i.e. &quot;The magistrate had a right to authority within the church, just as the church could rely on the authority of the magistrate to enforce discipline, suppress heresy, or maintain order.&quot; [Emphases added]

this is contrasted with the Radical Reformation which:

...rejected any secular authority over the Church

So it's actually about the relationship between Church and State, not about the teaching authority within the Church.
When you further consider some of the relevant views expressed, you can see within them explicit disavowals of the concept of the Magisterium:
Luther

…A simple layman armed with Scripture is to be believed above a pope or a council without it.… [N]either the Church nor the pope can establish articles of faith. These must come from Scripture. For the sake of Scripture we should reject pope and councils...I am bound, not only to assert, but to defend the truth with my blood and death. I want to believe freely and be a slave to the authority of no one, whether council, university, or pope. I will confidently confess what appears to me to be true, whether it has been asserted by a Catholic or a heretic, whether it has been approved or reproved by a council. - from the 1519 Leipzig disputation with Johanc Eck, source

Calvin

...Calvin binds the authority of the church to the teachings of scripture. Its structures can claim the power of the Spirit only in that the laws they legislate, the doctrines they teach, and the discipline they enact are consistent with scripture. The church's authority is derivative.
Second, the church's authority is fallible. Though God uses human words and agencies to come near to humanity, these means of grace remain finite and sinful. God accomodates to human capacity; God does not eradicate it. The treasure of the gospel is preserved in an earthen vessel. A distinction is maintianed between the church and God. No claim to infallibility can be made on behalf of any office or person in the church's life.
Third, the authority of the church is dispersed. Since Christ alone is the sole head of the church, Calvin is reticent to place exclusive authority in any single agency or office. He rejects the Roman Catholic argument that the papacy serves as a unifying centre of church life, locating authority in the single head of the church universal. Calvin counters on the basis of Ephesians 4, in which church unity is portrayed as residing in Christ alone. As he puts it, &quot;Do you see how he assigns to each member a certain measure, and a definite and limited function, in order that perfection of grace as well as the supreme power of governing may reside with Christ alone?&quot; As the editors of the Institutes point out, there is a consitent tendency towards &quot;plural authorities&quot; in Calvin's discussions of ecclesiastical and political forms of government. Authority and power are best dispersed throughout the church in order to protect the prerogatives that belong to God alone. - A Teachable Spirit: Recovering the Teaching Office in the Church, Richard Robert Osmer ,pp113-114

Given this, I think you'd have to come up with quite a bit more evidence to justify your claims that &quot;he was the only person in Geneva who was permitted to actually study the bible and come to theological conclusions&quot; and &quot;Calvin regarded himself as an alternate, authoritative Magisterium of the church.&quot;
Although he came much later, Wesley sums up the Reformers' views in this area rather succinctly:

The Church is to be judged by the Scriptures, not the Scriptures by the Church. - Popery Calmly Considered (1779): The works of the Rev. John Wesley,  via wikiquote, [emphasis added]