Repetitive Transcranial Magnetic Stimulation (rTMS) is increasingly used to treat stroke, Parkinson's disease and depression (Fregni et al., 2005; Loo and Mitchell, 2005; Hallet, 2007; O'Reardon et al., 2007; Ridding and Rothwell, 2007). rTMS uses bursts of magnetic pulses to change the excitability and connection strengths of cortical neurons. However, the evidence to inform clinical application is highly inconsistent (Thut and Pascual-Leone, 2010; Hamada et al., 2013) and substantially based on trial and error. Systematic theory is lacking. Typically, in rTMS research, measurements of motor-evoked potential (MEP) are made, often in terms of the strength of the MEP and the length of the cortical silent period that follows. However, the MEP is probably a poor and certainly an indirect measure of changes in the brain (Nicolo et al., 2015), clouding our understanding of rTMS mechanisms. In practice, therefore, particular amplitudes and timing of pulses in an rTMS sequence are selected because they show promise in small subsets of people. However, even basics such as the sign of any change in the outcome measure (e.g., does the MEP increase or decrease?) is debated. Many results show a wide spread in responses. It has become common to talk about “responders” and “non-responders” although evidence for a binary distinction in these two groups is lacking—in reality there is usually a continuum of response often including potentiation in some and depression in others (Nettekoven et al., 2015). Moreover, Heroux et al. (2015) provide evidence that the irreproducibility of results may be due to small sample sizes, unscientific screening of subjects and data, and selective reporting of results. In rTMS a regular train of pulses is applied. There is considerable variation in possible stimulation sequences, leading to many parameters that could potentially affect the results. Pulses are applied at a particular amplitude (normally recorded as percent motor threshold, (%RMT), or sometimes percent machine output, themselves imprecise measures), at a given rate (pulses per second, or hertz, Hz), until a particular number of pulses have been applied. There are three numerical parameters here. Additionally, one can consider variation in coil shape, orientation and place of application. Different waveforms for the magnetic pulse are also available. Thus, for an ostensibly straightforward pulse sequence such as non-bursting rTMS, the parameter space is considerable. Fitzgerald et al. (2006) carried out a comprehensive review of rTMS effects. They concluded that low frequency (0.9–5 Hz) stimulation generally results in a decreased MEP, while high frequency stimulation (5–20 Hz) results in an increased MEP. Very low frequency stimulation gave no effect. The “ 5 Hz, potentiation” mantra is now well established in rTMS literature. More recently, bursting protocols have become popular. The quadripulse protocol (Tsutsumi et al., 2014) is one example—four pulses are applied in quick succession, with this pattern repeated at regular time intervals. Theta-burst stimulation (TBS) is another; bursts of pulses are applied at theta-band (4–8 Hz) frequency. A continuous theta-burst stimulation (cTBS) protocol adds two more parameters, the number of pulses in a burst and the burst frequency. Intermittent theta-burst stimulation (iTBS) protocols require a further two parameters. Here, the bursting protocol is applied for a given time (denoted ON time, often 2 s), then removed for a given time (denoted OFF time, often 8 s) before being active for another 2 s period, etc. Thus, the parameter space for describing intermittent bursting pulse sequences becomes vast. Experiments performed to date do not come close to spanning it.