half-hourly \half"-hour`ly\ -our`ly^, a.
   done or happening at intervals of half an hour.
   1913 webster

cyclic \cyc"lic\ s?k"l?k or s?"kl?k, cyclical \cyc"lical\
   s?k"l?-kal, a. cf. f. cycluque, gr. kykliko`s, fr. ky`klos
   see cycle.
   1. of or pertaining to a cycle or circle; moving in cycles;
      as, cyclical time. --coleridge.
      1913 webster

   2. chemistry having atoms bonded to form a ring structure.
      opposite of acyclic.

   note: used most commonly in respect to organic compounds.

   note: narrower terms: bicyclic; heterocyclic;
         homocyclic, isocyclic

   syn: closed-chain, closed-ring.
        wordnet 1.5

   3. recurring in cycles2; having a pattern that repeats at
      approximately equal intervals; periodic. opposite of
      noncyclic.

   note: narrower terms: alternateprenominal,
         alternatingprenominal; alternateprenominal, every
         otherprenominal, every secondprenominal;
         alternatingprenominal, oscillatingprenominal;
         biyearly; circadian exhibiting 24-hour
         periodicity; circular; daily, diurnal;
         fortnightly, biweekly; hourly; midweek,
         midweekly; seasonal; semestral, semestrial;
         semiannual, biannual, biyearly; semiweekly,
         biweekly; weekly; annual, yearly; biennial;
         bimonthly, bimestrial; half-hourly; half-yearly;
         monthly; tertian, alternateprenominal;
         triennial
         wordnet 1.5

   4. marked by repeated cycles2.
      wordnet 1.5

   cyclic chorus, the chorus which performed the songs and
      dances of the dithyrambic odes at athens, dancing round
      the altar of bacchus in a circle.

   cyclic poets, certain epic poets who followed homer, and
      wrote merely on the trojan war and its heroes; -- so
      called because keeping within the circle of a single
      subject. also, any series or coterie of poets writing on
      one subject. --milman.
      1913 webster
see also:
cycle acyclic bicyclic heterocyclic homocyclic, isocyclic noncyclic 
alternateprenominal, alternatingprenominal alternateprenominal, every otherprenominal, every secondprenominal alternatingprenominal, oscillatingprenominal biyearly circadian exhibiting 24-hour periodicity 
circular daily, diurnal fortnightly, biweekly hourly midweek, midweekly 
seasonal semestral, semestrial semiannual, biannual, biyearly semiweekly, biweekly weekly 
annual, yearly biennial bimonthly, bimestrial half-hourly half-yearly 
monthly tertian, alternateprenominal triennial cyclic chorus cyclic poets 

half-hourly
     adj : occurring every half hour
     adv : every thirty minutes, every half hour