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Wavelet introduces a novel family of directed-acyclic-graph (DAG)-based consensus protocols. It is designed to alleviate the numerous scalability dilemmas predicated in decentralized ledgers, such as those that utilize either the longest chain rule or some variant of stake delegation or committee election scheme. Wavelet guarantees irreversibility of transactions, and consistent total ordering of transactions without any compromise on safety, performance or liveness; enabling features such as transaction graph pruning and Turing-complete smart contract execution. The safety and liveness of Wavelet are solely dependent on the safety and liveness of any arbitrarily chosen Byzantine fault-tolerant binary consensus protocol executed within the Wavelet framework. Unlike prior works, Wavelet requires minimal configuration of a minuscule set of system parameters to work in a large range of practical network settings where communication is only partially synchronous.