The cycle is based off of the political cycle, not on a specified time frame. It just doesnt make sense otherwise.
I think the time frame is often more telling than the party ID in many cases, especially since the parties are basically redefined every 24 years. Elaborating on some of my comparisons...
Nixon/Ford = Harding/Coolidge = 2nd-term-Grant/Hayes
8 Years of Excess and Corruption - Nixon, Harding, and Grant each presided over scandal-plagued administrations, and their successors had little impact in restoring faith in government.
Carter = Hoover = Garfield/Arthur
4 Years of Failed Attempts to Return to the Earlier Status Quo - Carter, Hoover, and Garfield each found their appeal as competent outsiders who promised a return to trustworthy governance, but all three (and Arthur) were unable to deal with the economic challenges of their time (Stagflation, The Great Depression, and 1882 Depression, respectively).
Reagan/Bush '41 = FDR = Cleveland/Harrison '23/Cleveland
12 Years of Establishing of the New Dominant Ideological Regime - Bush is basically Reagan's third term if he could have had a third term and, while the differences between Cleveland and Harrison are a bit more stark, both Cleveland and Harrison shifted the national debate away from the sectional and racial arguments of the previous generation and toward finance and industrial policy. The boundaries of the national debate were redrawn in fundamental ways during this period.
Clinton = Truman = McKinley/1st-term-TR
8 Years of Consolidation Holding Back the Reactionaries - Clinton, Truman, and McKinley/TR were all presidents with big plans who failed to substantially alter domestic politics. But while domestically they found themselves in a holding pattern, internationally they redefined America's role in the world. Clinton managed the fall of Communism, Truman managed the fall of Fascism, and McKinley managed the fall of New World (Spanish) imperialism.
Bush '43 = Eisenhower = 2nd-term-TR/Taft
8 Years of Acceptance on the Part of the Opposition - Bush, Eisenhower, and TR/Taft were leaders of the "right" who nevertheless rejected the reactionary impulses of their parties and embraced the ideological status quo...in service of the extremely wealthy. Regressive presidencies, but within limits. Internationally, all three represent periods of America getting entangled in counterproductive pseudo-imperialist boondoggles.
Obama = JFK/LBJ = Wilson
8 Years of Pressing the Limits of the Dominant Ideology - Obama, JFK, LBJ, and Wilson all pushed aggressively to address the problems inherited from their predecessors, but the ideological and political constraints established several steps back in the cycle prevented more from being done. Basically, the limitations of the dominant ideological regime are proven too intransigent during these years. The potential in the cycle is exhausted, which leads us...
Trump = Nixon/Ford = Harding/Coolidge
Back to Excess and Corruption