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In A Century of WWV, I found this mention of an unusual sounding instrument that may have once been commonplace:

Calibration work was mainly focused on decremeters, instruments designed for measuring the decay, or decrement, of a pulsed radio signal, such as that generated by a spark transmitter typical of the day. Decremeters were essential in minimizing the interference produced as much as possible.

Another (much older) NIST publication titled A Direct-reading Decremeter and Wave Meter describes the motiviation for these devices:

[…] when persistent oscillations of single frequency are emitted from a radio transmitting station much more selective receiving apparatus may be employed with advantage at receiving stations, permitting sharp tuning with consequent minimizing of interference caused by stations other than those with which communication is desired.

These devices were used either in the days of, or during the transition away from, spark-gap transmitters.

Some notes on the Doolittle Decremeter describe that implementation as a "transmitter antenna tuner" and indeed the circuit diagram from the NIST decremeter paper looks to be in that vein as well:

Simple circuit diagram from decremeter paper

Am I right to understand that rather than measuring a signal directly, a decremeter essentially measured what we would now call the "Q" of an antenna, and in that way — indirectly — would determine how long that particular antenna would let a transmitted pulse ring?

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Not only the antenna. It would also include the antenna, the tuned LC circuits, and how tightly the antenna was coupled to the latter.

Spark transmitters produced a damped wave. This edited graph from Wikipedia shows one with desirable longer duration.

The longer the system "rang", the higher the average power --which is what the decremeter measured-- and the better the signal could be copied over longer distances.

Damped wave - courtesy Wikipedia

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