rhythmisch
rhythmic
Happening in a regular, repeating beat or pattern; having a rhythm.
Die Tänzer bewegten sich rhythmisch zur Musik.
The dancers moved rhythmically to the music.

rhythmic
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rhythmic
Happening in a regular, repeating beat or pattern; having a rhythm.
Die Tänzer bewegten sich rhythmisch zur Musik.
The dancers moved rhythmically to the music.

'Rhythmisch' (rhythmic) is the adjective formed from the noun 'der Rhythmus' (rhythm). The ending '-isch' is often used to form a related adjective from a noun.
Der Sprecher hatte einen sehr angenehmen Rhythmus in seiner Stimme.
The speaker had a very pleasant rhythm in his voice.
'Rhythmisch' (rhythmic/rhythmically) can describe a noun (as an adjective) or a verb (as an adverb). As an adverb, it remains unchanged and describes the manner of an action.
Die rhythmische Musik lud zum Tanzen ein.
The rhythmic music invited people to dance.
'Rhythmisch' (rhythmic/rhythmically) is often used with verbs of movement (dancing, clapping, nodding) or recurring sounds (dripping, pounding). A well-known fixed collocation is also 'Rhythmische Sportgymnastik' (rhythmic gymnastics).
Er klopfte rhythmisch mit dem Stift auf den Tisch.
He tapped the pen rhythmically on the table.
regular
'regelmäßig' and 'rhythmisch' can both mean that something repeats according to a pattern. 'regelmäßig' is more general and works for times, appointments, shapes, or processes. It often simply says that something happens at equal intervals. 'rhythmisch' fits especially well with movement, music, sounds, or a beat. It sounds as if you can hear or feel a repeated pattern. The words can be confused because both describe even repetition. When talking about appointments or habits, you usually use 'regelmäßig'. When a beat or movement is important, 'rhythmisch' fits better.

Beim Training bewegt meine Schwester die Arme rhythmisch zur Musik.
During training, my sister moves her arms rhythmically to the music.
Der Bus fährt am Morgen regelmäßig alle zehn Minuten.
In the morning, the bus runs regularly every ten minutes.