How to pick a different color but with the same perceived luminosity (not by eye)?

Question

Suppose I have a certain shade of violet, like #6727AE. How do I quickly find a different hue (say, greenish) but with the same perceived luminosity (or "weight")? The goal is to have 2 equiluminant colors.

The way I measure perceived luminosity (in Affinity Designer) is with an adjustment layer with a neutral gray solid fill color (#808080) and a blending mode set to "Color". What I get is a certain level of gray. What I need, is to [quickly] find a different hue so that this level of gray remained unchanged.

The way I achieve this currently is "by eye". I enable this luminosity "check layer" and start playing with the sliders until I get the same gray level. And I also overlap objects so that I did not see a transition from one object to another. This does the job but this process slows my creative flow down.

The closest tool that seems like it should do the job is CIELAB color model. But it doesn't (in my case). When I change a/b components of the 2nd object but leave L-component the same, I still get varying levels of gray. I've tried different color models, like, HSB, and change only the H-component but leave out S and B. But gray is different. Same for HSL and any other color model that I've tried. I've even tried mixing, e.g. have some intermediate color model, but I was still unsuccessful.

Is there any tool or process how I can achieve this not "by eye"? Maybe some online tool that I'm not aware of. E.g. one that I use is https://colorizer.org/ . So, it's not necessary that this should be inside Affinity Designer.

[edit] I'm attaching examples of what I'm after. Also, the context is that my designs should contain objects that are colored differently but have the same "weight" (perceived luminosity). The goal is to not give any object a preference over another, they should all appear of "equal". If any color is darker, then it gets emphasis over lighter colors and thus becomes more dominant, which is not what I want.

Answer 1

The next image is in Affinity Publisher. Its color mode is sRGB. I have 2 rectangles. In the bottom rectangle the fill color is your violet RGB(#6727AE). The top rectangle has a quite bright green.

The green rectangle has blending mode = Hue. The intersection of the rectangles is colored with darker green which is got by hue shifting the violet due the blending. That's your wanted green and you can pick it from the image if your color picker is set to global mode. It's RGB(#00790f)

We can test it by inserting a mid grey rectangle with blending mode = Color or Saturation - both of them give the same result:

The grey rectangle removes the saturation from the violet and the green below and changes them to the same grey.

Conclusion: The got green is the right one when checked with your criteria.

You can find more equiluminous colors with the same image by having more colors instead of one solid green.

The sensitivity of the eye varies radically depending on the hue. For ex. yellow which is as luminous as your purple will look much darker than what we generally expect when one says "yellow"

Warnings:

1. If you use a 3rd party screen color picker or take colors from screenshots you have a good possibility to go amiss. If you have used some software monitor color calibration system the screenshot can well contain compensated colors which are distorted to the right ones in the monitor.

2. Layer blending modes and color systems are implemented differently in different programs.In addition one can for ex. in Photoshop select if the blendings are calculated in linear gamma (=1.0) RGB instead of the gamma of the used color space. Thus the "right equiluminous color" can be slightly different in different programs.

ADD due the comment "People should trust Lab color mode"

True. Me too touted the same in my earlier version of this answer (removed). But there's a caveat. If we try the shown hue shift trick in the Lab color mode and check with the grey rectangle, the result is OK:

This is in Photoshop. One can immediately see that the resulted green looks darker than what's got in sRGB mode. Still both are right with the final test????

The reason: The resulted green (=the one with green hue, but colorfulness and lightness taken from your violet) in the Lab mode is actually impossible in sRGB (=out of sRGB gamut). Programs do not show the right green, the shown green is clipped to sRGB range with an unpublished criteria. But inside the program calculations are done with valid Lab colors.

In Photoshop (see NOTE1) it's easy to switch on the Gamut Warning. Only use proofing as set for sRGB:

Colors which are impossible in sRGB are turned grey. If one picks the resulted green and uses it in RGB mode, it surely doesn't work. But working the job in RGB mode gives as good results as the layer blending and color system implementations in the used program allow.

NOTE1: The same gamut check is also possible in Affinity publisher. It's a little trickier. One must insert a soft proof adjustment layer with Gamut Check = ON. The result is the same.

Answer 2

I would go with Lab, with channel manipulation (setting L to the same value) it should be quite easy: