Eckard
Sound is considered different, but my essay exposes the moot similarities. The common error is here;
There is a remarkable difference between the Doppler effect in sound waves and the Doppler effect in light waves. For light waves there is no preferred frame of reference, no material \medium" in which the waves travel... One consequence is that, unlike a sound wave, the speed of a light wave is the same to all receivers regardless of their velocities. The details are left to a careful derivation elsewhere. (SR). http://www.physnet.org/modules/pdf_modules/m204.pdf
Ref the RKN essay Fig 1. showing velocity in the medium n as c/n wrt the medium. you say "This is obviously wrong. The velocity of a wave does not depend on emission but only on the medium." I think you only need to read that again more carefully to see your error. You are only taking an 'anthropocentric' view, assuming somehow your own state of motion is relevant to some other medium. I hate to say this but you have NO effect on light propagation speeds wrt media!!
You forget you must first visualise yourself at rest wrt that medium, so you can use 'Proper Time' to measure speed. You will then find, (when at rest in or with the medium) that it's propagations speed is c/n. Any remaining confusion you have is due to confusing the secondary scattered light travelling from the charged medium particles to your eye (at c) with the original 'charge' propagation speed. i.e. Apparent c+v is allowable, but don't confuse that with real speed through the medium.
You claim 'one medium is definitely enough' to describe waves. I agree, but only in terms of one AT A TIME! If you claim there is only one 'globally' (your word) then you are claiming that nobody in Concord ahead of another can hear them speak!
You would be denying that sound travels within concord at c wrt concord. Or that those on another concord flying past the other way can also converse.
There are of course as many spaces/frames in relative motion as there are collections of matter particles in relative motion. You were simply forgetting you allow for your own variable observer states of motion.
The 'matter' may be hollow, or a solid medium, and big or small, the effect is the same. The important inverse 'shift' in lambda and f comes when a wave sequence move from one frame to another over non zero time.
Yet I agree. You will be entirely unfamiliar with this truth because, as you say in your own essay, we have all become too familiar with other assumptions.
Peter
(PS. Judy. Are you related to Richard Kingsley-Nixey?)