My title describes something most of us have known about all our lives without realising it.
Why do 'hip hop' and 'ding dong' sound right, but 'hop hip' and 'dong ding' sound wrong somehow? It's not just familiarity, there is a rule at work, as we shall seen. If I invented a new expression 'squop-squip' it wouldn't sound as satisfactory as the alternative 'squip-squop', because the first version doesn't follow the rule, whereas the second does.
Reduplication is when a word is repeated two or more times. In English there are several kinds of reduplication, for example it can be used to amplify the sense of a word, so 'very very' is stronger than simple 'very' and 'big big' is stronger than just 'big'.
Rhyming reduplication is also very common: higgledy piggledy, silly billy, willy-nilly, Humpty Dumpty, raggle-taggle, easy-peasy (lemon squeezy), teeny-weeny, fuddy-duddy and so on.
Ablaut reduplication is a form of reduplication following a pattern called ablaut, in which semantically related words coming from the same root keep the same consonants but vary the vowel sounds in a predictable way. A classical example in English is sing, sang, sung. Notice that if you say these words aloud, you say the first at the front of the mouth, the second further back, and the third at the back of the mouth.
We have many expressions like; tip-top, tick tock, flim-flam, pitter-patter, jim-jam, and they pretty well all follow the ablaut pattern, with the first part being a higher vowel from front-of-mouth, and the second a lower vowel from further back. We even have some examples with three elements, such as tic-tac-toe and bish bash bosh.
This ablaut pattern is thought to be inherited from the ancient and lost language that is the ancestor of moist European and West Asian languages today. This language had no written form that we know of, and no longer exists, but has been extensively reconstructed from its more recent descendants.
The name cyclamen goes back to Greek kyklos, "circle", and we have related words like circus and cycle etc. These words may even be related to ring, the common PIE root being something like *sker-, "turn", with kyklos being a reduplicated form skersker. "ring" is from the same PIE root, so I suppose "circus ring" could be consider a triplication.