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Period doubling occurences in wind instruments musical performance

机译：吹奏乐器演奏中的周期翻倍

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As a special class of Non Linear Dynamical Systems, self sustained musical instruments can exhibit peculiar behaviours related to bifurcation and chaos theories. While many quasi periodic occurrences in woodwinds and bowed strings have been reported, only a few period doubling scenarios have been observed in musical instruments, and most of the time they have been obtained through numerical simulations or specially designed hybrid experimental set-ups far from musical situations. We present here a set of experimental results, all related to this period doubling scenario and always in direct connection with musical performance on wind instruments and voice. We show that at least three period-doublings can be obtained on a trombone, that the crumhorn and the bassoon can oscillate in the same way and that traditional singers, and in some cases classical singers, exhibit phenomena clearly linked with this scenario. Finally, from the whole set of experimental results available for this particular set of multiphonic sounds we give some hints for a general schema governing their musical production. [References: 43]
机译：作为一类特殊的非线性动力系统，自持乐器可以表现出与分叉和混沌理论有关的特殊行为。虽然已经报道了许多在木管乐器和弓弦中出现准周期性事件的情况，但在乐器中只观察到了几种周期加倍的情况，而且大多数情况下，它们是通过数值模拟或经过特殊设计的混合实验装置获得的，而这些装置远非音乐。情况。我们在这里展示了一组实验结果，所有的结果都与这一时期翻倍的情况有关，并且总是与管乐器和声音的演奏直接相关。我们证明，在长号上可以至少获得三个周期倍增，而长号和巴松管可以以相同的方式振荡，并且传统歌手（在某些情况下还包括古典歌手）表现出与这种情况明显相关的现象。最后，从针对这组特定的多音声音组的全部实验结果中，我们给出了控制其音乐创作的总体方案的一些提示。 [参考：43]

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