Just a hint for the experiments. I am not really answering this question, as I do not like to compare little tiny piece of the algorithm inside the camera, but rather end to end result, and I am a fun of constructive and creative learning.
I think except automatic programs no one cares about 1/3 ISO increase. Important is how much noise you have when you are making bigger steps. In the links below you will find great shots done using big ISO (not very big, but quite big).
Look at images done with Nikon 610 at: ISO from 1600 to 3200 and compare them with e.g. ISO from 6400 to 12800 or e.g. Canon EOS 5D mark IV ISO 1600 - 3200 and ISO 6400 - 12800
When you had a closer look some of them are of similar quality.
But anyhow I recommend to make yourself the following experiment.
Use RAW images and no JPGs. Use rather Manual, Aperture, Shutter speed or Program mode and not any kind of Auto, to avoid uncontrolled ISO changes.
Take tripod. And in good lighting conditions shot photo of the light object in the ISO 3200, then increase it by 1/3 and shot again, and then again 1/3 - shot, and then take ISO 6400. Then take the same object and made the same session in the dark place with poor lighting (do not use flash). Poor for me means e.g. object lightened by candle or some ambient light reflected by the light wall. Additionally copy of the images convert to BW.
If you are patient you can repeat photo session with dark object. The result will be interesting. As shooting light object in the light environment is more like shooting edges. Light object in dark place is shooting contrasts. Dark object in light environment is like catching contrasts and dark in dark is again about edges.
You will get your photos and compare them in sense of noise. Do not post process images. Observe them in RAW in full size. JPGs and any kind of scaling will change noise.
Get your feeling not how "big" is nose, but rather how equally distributed is it. What do you think when you look at images. It is like nice image with few damaging oversaturated places or evenly distributed noise which gives a bit perception like you look at old photo or some fuzzy memories or almost forgotten dream.
At the end you will have a full table of ISOs and you will see how your camera is working and how your mind is interpreting results.
At the second and later end - the photography is not about ISO, it is about the final perception of the image.
Completely another story is how to post-process images to change influence of the noise made by increased ISO or how to bring the noise to the low ISO images to make them looking like old photos.
Have a fun with shooting and less care about technical interiors of the camera :-).