Science and drumming
The drum serves as a concentration device, enhancing one's capacity to focus attention inward. It stills the incessant chatter of the mind, enabling one to enter a subtle or light-trance state.
This drumming method uses a repetitive rhythm that begins slowly and then gradually builds in intensity to a tempo of three to seven beats per second. The ascending tempo will induce light to deep trance states.
From my own experience and the feedback of past participants, meditation with the drum induces changes in awareness, perception, emotions, and a calm in the mind that is often almost instantaneous.
Meditation and drum-induced trance states have been shown to change brain structure, brain waves, the quality of the thoughts we have (for example enhanced AHA effect or creativity), and even the immune system (for the scientific studies see below).
Most of my workshops entail guided meditation with the drum. From experience and participant feedback, breakthrough experiences tend to happen in those moments.
What are possible scientific explanations for this effect?
A small introduction to brain waves:
All cells in the brain are electrically active. Cells in a particular region of the brain tend to deal with the same function and often end up synchronizing their electrical discharges. This causes the electrical signal coming from that region to magnify so that rather than one minuscule (hence undetectable) electrical signal from a single nerve cell occurring there is a large collective signal coming from a group of neurons that represents the “average” of the electrical activity that’s happening in that region. This signal leaks through the skull, scalp, and hair and can be picked up by electrodes stuck to the skin of the scalp or detected by EEG.
There are five main know types of brain waves, that our brain exhibits when we are in certain states:
Gamma (γ): Concentration
Beta (β): Anxiety dominant, active, external attention, relaxed
Alpha (α): Very relaxed, passive attention
Theta (θ): Deeply relaxed, inward-focused
Delta (δ): Sleep
Our brain can be trained into being (more) in a certain state and techniques for this have been developed, for example for the treatment of ADHD (called neurofeedback).
Periodic sounds and drums have been shown to induce changes in brain waves  and therefore can directly influence the kind of state we are in and foster for example creativity or relaxation.
Which further scientific publications are there on this topic?
Shamanic drum practitioners have significant differences from control individuals in several domains of altered states of consciousness, with scores comparable to or exceeding that of healthy volunteers under the influence of psychedelics.
Drum therapy helps the well-being of students: more awake, relaxed, cheerful, friendly, and clear-headed. 
Drumming treatment influence immune response and the positive psychological effects of shamanic journeying is associated with a decrease in stress, anxiety, and mood disturbance. 
Altered states of consciousness are achieved during drumming rituals. 
Most research has been done on the effect of meditation (drum-induced changes in awareness are similar to the effects of meditation in many ways), see below.
What is meditation?
Meditation is just a game you play within, to alter your state of consciousness and perception. There are different kinds of meditations and not all of them are silent. Meditations can have different purposes: ranging from relaxation and sleep and extreme alertness and creativity. Meditation is used to achieve a greater sense of detachment from your inner processes so you can observe them but also help you to be really aware of all that is going on inside your body (thoughts, bodily perceptions, emotions).
Listening to the drum is also a kind of meditation, its purpose depends on what the practitioner intends to do.
What does science say about meditation?
The remarkable brainwaves of high-level meditators: a youtube video.
Greater brain activity is occurring in people practicing meditation (after only 5 hours) in regions that are speculated to be related to “detecting conflict and breaking mental set”, “ restructuring of the problem representation”, “error detection, problem understanding or general attentive control” and “ ‘Aha’ feeling”.
Meditation enhances mind control. 
Monks’ gamma brainwaves readings, confirm that Zen meditation produces not relaxation but intense though serene attention. Trained musicians also show superior gamma brainwave synchrony while listening to music—another form of calm but intense focus. 
Brain wave types that are arising from the synchronous and coherent (in phase or constructive) electrical activity of brain cells vary depending on the kind of meditation performed: beta, alpha1, and theta/gamma waves are possible. 
Meditation alters the connections in the brain between regions and e.g. leads to a reduction of amygdala size (fear and stress). 
Meditation changes brain structure, brain activity, and brain waves and alters our mood, our immune system, and our well-being. 
Eight brain regions are consistently altered in meditators, including areas key to meta-awareness (frontopolar cortex/BA 10), exteroceptive and interoceptive body awareness (sensory cortices and insula), memory consolidation and reconsolidation (hippocampus), self and emotion regulation (anterior and midcingulate; orbitofrontal cortex), and intra- and interhemispheric communication (superior longitudinal fasciculus; corpus callosum). 
Mindfulness-based stress reduction is associated with a significantly greater reduction in anxiety than alternative programs. 
Brain regions associated with attention, interception, and sensory processing are thicker in meditation. Between-group differences in prefrontal cortical thickness were most pronounced in older participants, suggesting that meditation might offset age-related cortical thinning. 
Short-term meditation induces white matter changes in some parts of the brain. 
Meditation is effective at reducing negative mood, depression, fatigue, confusion, and heart rate. 
Meditation induces changes in brain parts activation and changes in all major neurotransmitter systems. The neurotransmitter changes contribute to the amelioration of anxiety and depressive symptomatology. 
A longitudinal and randomized study documents that brief meditation training improves executive attention, mood, and immune function, and reduces levels of stress hormones. 
Alterations in brain and immune function can be produced by mindfulness meditation.