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13. The law if one did not blow the sets in order: 
- Example: One first blew the sets of Tashat and then Tarat and only then blew the sets of Tashrat. Or one first blew two sets of Tashrat and then blew three sets of Tarat and then blew the third set of Tashrat. Or one blew one set of Tashrat one set of Tashat and one set of Tashat and one repeated this three times.
Blowing the wrong sound is only problematic when one is in the midst of a particular set as explained in the previous Halacha. However blowing the wrong set never invalidates the previous or later sets and even the current set remains valid. Thus in all the above examples as long as there was a total of 30 sounds blown, three times the set of Tashrat, three times the set of Tashat and three times the set of Tarat one fulfills his obligation.
 Based on 590/18; M”A 590/12
In the new Kehos SHU”A footnote 137 they send the reader to Admur 263 KU”A 5 in which Admur states that if one comes in middle of the blows he has to hear the blows in order after they are complete. This statement there does not contradict any part of the ruling here as he simply means to say that he must hear whatever blows he missed. Or if he came in middle of a set he must rehear from the beginning of that set. Certainly however it does not mean that he must hear all the sets over again in the correct order. Upashut!
 The reason this is not considered an interval between sets: As the Torah was only particular that one should not make an interval between the Teruah and the Tekiah that precedes and follows it. However an interval between sets, even of Shofar sounds that do not belong in that grouping, have no Halachic meaning. [ibid] A proof for this is from the fact that originally the blows were established to be heard only in the concluding blessings of Musaf, and in Musaf we make an interval between the sets with the prayers and Piyutim of each blessing. Hence we see that we are not particular against making an interval between the sets. [M”A ibid] Veztaruch Iyun why Admur omitted this proof of the M”A!