keystring I read your response here. You seem to be seeing the name "diminished" as some kind of operation or action.
KS. I specifically indicated it. It can depend on perspective though. But you will find in sources a take on that ..... such as a definition of diminished third is a minor third reduced by one semitone.
I did mention that the words diminished third is not to be interpreted to be a type or kind of 'third'. And indeed ... a diminished third is certainly not a type of 'third' or third degree interval in our major/minor system.
If anyone reckons diminished third is a type of third, then they better demonstrate third degree based on 'our' major and minor scale/chord system.
Like some country's language system ... they pack in their rules or conditions ... where it's a case of being taught those conditions or rules, otherwise one can't communicate properly unless those rules are learned ... such as porpoise is not pronounced as porpoys (rhyming with bor boys). And turqoise is not pronounced like porpoise. Etc.
For intervals like major third ... and minor third, I explained various approaches for understanding those intervals, based on workable numbers and patterns. Based on the major and/or minor system.
Yes indeed ... the diminished third interval is defined. It's not a 'type' of third though.
I don't mind if there are multiple 'official' or 'authority' sources specifically showing how their diminished third is third degree in the major and/or minor scale system. But looks like nobody has done that or shown that. Third degree.
And ranjit was pretty much conjuring up a different scale system I think ... which is not our scale system that most people are focusing on. It's like saying a sixth is still a sixth if you reduce it by five semitones ..... which is analogous to anyone thinking that a diminished third is still a 'type' of third interval based on our major/minor system.
If we teach people based on our major/minor system ... then they better show clearly (explain) how their diminished third is truly third degree. Otherwise, they really will get a fail grade here.
Failing is fine though. They can always pass next time around if allowed to resit the test. And for this particular test ... yes ... they are allowed to resit it.
The test question here is ... do you think a diminished third is a type of 'third' (in the major/minor system only)? Yes .... or no. And if yes .... justify your answer by showing how it is third degree in major and/or minor scale system only. That is only to focus on this popular system only, without getting into pseudo-science space, or nested systems - as in getting away from the focus of attention.
Also keeping in mind that 'flatting' is merely a 'construct'. And in a minor scale .... the 'flatting' of the third degree (in minor scale) results in the 'second'. And that still gets people into the rules territory - like how to tweak the system to handle spanners in the works, like perfect fourth and perfect fifths ... (ie. to sort out terms like minor 4th, major 4th, minor 5th, major 5th).