@rjduncan - great question and one that involves a lot of learning.
EDUCATION: I'd suggest reading Dr Toole's book "Sound Reproduction" which is about acoustics and psychoacoustic stuff. A base of knowledge and common sense will take you far.
TOOLS: While others here have recommended REW, I found that it has a steeper learning curve than OmniMic from Dayton Audio and which I prefer to use. I also prefer it's graphical user interface but both tools should give you the same measurement results.
While REW/OmniMic come with lots of different measurement charts, my analytical background has me importing the OmniMic measurements into Microsoft Excel spreadsheet for further data manipulation and additional calculations and added Charts. For example, decibels are logarithmic values that should not be added or divided or multiplied together, so they need to be converted into linear energy first, then perform your arithmetic on them, and finally convert the result back to decibels; this is needed for frequency response and early reflections analysis primarily. While subtracting a log value from another log value is fine (e.g. take the difference between L and R speakers to quantify their loudness variance across the frequencies), you'll need linear energy values for creating averages or sums such as to calculate "Error Rates" which represents the distance the measured frequency response for a channel is from your Target curve. Another area of applying linear energy is with Energy Time Curve data for early reflections of 0-10ms which impacts tonal balance and imaging strength with the goal of having acoustical energy symmetry from 1st order and other reflections especially important in unsymmetrical shaped rooms. More can be found in this article I wrote here: https://pmamagazine.org/early-reflections-101-the-first-10-milliseconds-that-make-or-break-stereo-imaging/ Please excuse the shameless plug.
WORKFLOW SEQUENCE: Acoustically Treating a Room - Is there a Work Flow that works best?
Many of us spend a lot of time (and money!) curating the perfect stereo or home theatre setup — reading reviews, visiting shops, asking trusted audiophile friends. Eventually, we piece together a system that should sound amazing…but then we bring it home, and it doesn’t sound as good as it did in the store. The problem might not be your gear — it might be your room.
Acoustics play a huge role in how your system sounds. In fact, many pros say the room contributes about 50% of the final sound quality. That’s massive. So we start exploring acoustic treatments. Maybe we try a few DIY absorption panels, or maybe we're lucky enough to have a dedicated room where WAF isn't a factor and we can really experiment.
But here's the big question:
Is there a “right” order for treating a room?
Yes — and following a proper sequence makes a big difference.
Over the years, I’ve refined this workflow for both my room and my clients’.
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Early Reflections (0–10ms)
Start with the floor, ceiling, sidewalls, front and rear walls — focusing on first-order reflections. These reflections arrive just after the direct sound and have the biggest impact on imaging and tonal balance.
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Bass Decay
Use bass traps to reduce overly long decay times. Why? Bloated bass can mask midrange detail, so this step is crucial for clarity.
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Mid/High Decay Times
Add diffusion and/or reflectors to maintain liveliness. Over-absorbing these frequencies can leave the room sounding dull and lifeless. You want a balance — not an anechoic chamber.
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Frequency Response EQ (the very last step)
Once the room’s reflections and decay are under control, then (and only then) consider gentle EQ. Aim for each channel to be within ±3dB across the range. Doing EQ first often masks deeper acoustic issues — it’s like painting over a cracked wall.
Most people start with EQ… but trust me, it’s better saved for last.
Here are 2 articles I wrote about taking and deciphering measurements:
https://pmamagazine.org/analyzing-a-stereos-frequency-response-and-decay-times/
https://pmamagazine.org/deciphering-stereos-acoustical-measurements-and-taking-corrective-actions/
Hope this helps . . .