On the formula, I give an example, my KEF Q100 5.25" coaxials. Weeks ago I changed in the tweeter first order filter the cheap NOS styroflex capacitor that acted as a bypass
(added by me) by other and the resistor.
The sound improvement was spectacular and it sure has not changed the frequency response or impedance /phase curve.
If I had not made the change it would cost me a lot to believe it if someone else told me.
If you actually did measure the frequency, impedance and phase response before and after and found no change, what you're experiencing is 100% expectation bias. But you don't need to take my word for this, you can prove it to yourself relatively easily by doing a double-blind listening test with the help of a friend. You'll need two coins, some post-it notes, and a blindfold (nothing kinky, don't worry).
1. If you use the speakers with stands, place one of the stands in front of your listening position. If not, place a marker in the form of a blank post-it note in the middle of where you usually place the speakers (e.g. on a desk/cabinet).
2. Change one of the speakers back to the original state you bought it in, without your friend seeing which one, and stick one post-it note with a square drawn on it to the bottom of the original speaker, and another note with a triangle on it to the one you modified. Tell your friend to make sure the notes stay on, but obviously don't tell them what the symbols mean.
3. Write down the meaning of each symbol for this trial just for yourself (this is important).
4. Leave both speakers next to each other, and tell your friend to flip a coin after you walk out of the room and shut the door - heads they connect up the speaker that's on their left to the left channel of your source, and place it on the stand / desk marker; tails they choose the speaker on their right, and connect it to the same source channel (left), and put it in the same place.
5. While out of the room, blindfold yourself so your vision is completely obscured (in case there are slight visual differences in the speaker cabinets), then call your friend to guide you to your listening position in the other room.
6. Instruct your friend to play your favourite music. Listen for as long as you want, then once you've decided which speaker you think it is, tell your friend to write this down ('original' or 'modified') under 'guess' for this trial.
7. Tell your friend to disconnect the speaker, get them to check what symbol is written on the note underneath it, then they should write this symbol next to the guess for this trial they wrote down in the previous step.
8. Take off your blindfold and tell your friend to go out of the room and shut the door.
9. Flip a coin - if it's heads, keep the post-it notes as they are; if it's tails, swap them.
10. Repeat steps 3-7 nine times. This is very important, as we need to be statistically confident you are definitely able to distinguish which speaker is which - too few trials, and they could have just been lucky guesses.
11. Once you've done all ten trials, decode the symbols on your friend's results list using your symbol meaning 'key' for each trial from step 3, then count up how many times you guessed correctly.
If, as you claim, the sound improvement of the modified speaker is "spectacular", you should easily be able to distinguish it from the original in all ten trials, and this will be the beginning of a whole new revolutionary paradigm for physics and psychoacoustics. If not, then you've learnt a valuable lesson about the scientific method and the power of expectation bias. Win-win.