
einstimmig
unanimous
With no opposing vote or objection; with the agreement of everyone involved.
Der Vorstand hat den Beschluss einstimmig gefasst.
The board passed the resolution unanimously.
unanimous / monophonic
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unanimous
With no opposing vote or objection; with the agreement of everyone involved.
Der Vorstand hat den Beschluss einstimmig gefasst.
The board passed the resolution unanimously.

monophonic
In music: consisting of only a single melodic line, without harmonic accompaniment. The opposite of polyphonic.
Gregorianische Choräle sind eine Form des einstimmigen Gesangs.
Gregorian chants are a form of monophonic singing.
The word is made up of 'ein' (one), 'Stimme' (voice/vote), and the ending '-ig'. It literally means 'with one voice'. Both meanings are derived from this: a shared opinion (everyone has one voice) or a single melody (one musical voice).
Die Entscheidung für das neue Projekt war einstimmig.
The decision in favor of the new project was unanimous.
This meaning is often combined with nouns that express a decision or election. Typical phrases are 'ein einstimmiger Beschluss' (a unanimous resolution), 'eine einstimmige Entscheidung' (a unanimous decision), or 'eine einstimmige Wahl' (a unanimous election).
Der Kandidat wurde einstimmig zum neuen Vorsitzenden gewählt.
The candidate was unanimously elected as the new chairperson.
You can easily tell which meaning is intended from the context. If it is about politics, clubs, or group decisions, 'ungeteilt' (undivided/unanimous) is meant. If it is about music, especially early music or singing, 'mit nur einer Melodie' (with only one melody) is meant.
Der Ausschuss hat den Vorschlag einstimmig angenommen.
The committee unanimously accepted the proposal.
agreed / united
Einig generally refers to the participants being in agreement. Einstimmig emphasizes that no one objects or votes against something when agreeing to or making a decision. Einig is suitable for a shared opinion; for a decision approved by everyone, einstimmig is more precise.

Die Mitglieder nehmen den Antrag einstimmig an.
The members unanimously approve the motion.
Die Mitglieder sind sich über den Antrag einig.
The members agree on the motion.