The Double Bass低音提琴
The double bass, also called bass Viol or contrabass, is the largest and lowest-pitched member of the orchestral string section. The standard double bass has four strings and a range from E just over an octave below the bass staff, upwards for nearly three octaves, although some instruments may have five strings in order to extend the range downward. The strings are tuned a fourth apart at E1(41.2 Hz), A1, D2, G2(98 Hz). For the double bass, the string tensions of the four strings are essentially equal, implying that the mass per unit length of the strings must be adjusted close to 9/16 ratios for successive strings. This is to achieve the musical fourth 4/3 pitch intervals since the string frequency is proportional to the inverse square root of the mass per unit length. Tables of string tension show tensions in the range 60 to 80 lbs for different compositions and manufacturers, but in all cases the tensions for the four strings are about the same. This is in contrast to the other members of the classical string family for which the tensions in the lowest pitch strings are significantly higher. 低音提琴,也称为低音提琴或低音大提琴,是管弦乐中弦乐部分中体积最大、音域最低的乐器。标准的低音提琴有四根弦,其音域从E音(比低音谱号低一个八度以上)开始,向上延伸近三个八度,尽管有些乐器可能有五根弦以扩展低音域。四根弦的音高间隔为纯四度,即E1(41.2 Hz),A1,D2,G2(98 Hz)。对于低音提琴来说,四根弦的张力基本上相等,这意味着为了实现纯四度的音高间隔(4/3),四根弦的单位长度质量必须调整接近9/16的比例。这是因为弦的频率与单位长度质量的平方根成反比。弦张力表显示不同型号和制造商的张力范围在60到80磅之间,但无论如何,四根弦的张力大致相同。这与古典弦乐器家族中的其他成员形成对比,后者最低音弦的张力显著更高。
String instruments characteristically produce a fundamental resonance plus all the string harmonics. 弦乐器通常会产生基频共振以及所有弦的泛音。
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A good description of the interaction of the 关于低音提琴弓与琴弦相互作用的良好描述,可以参见新南威尔士大学的网站。低音提琴的弓通常由黑色马鬃制成。马鬃会粘附在琴弦上,并将琴弦向一侧拉一定距离,然后释放它,形成重复的粘滞-滑动模式。对于低音弦的低频,粘滞-滑动重复的频率可以等于琴弦的频率,这种条件与乐器产生丰满、丰富的音色有关。这种条件被称为“亥姆霍兹运动”或“亥姆霍兹节点”,以赫尔曼·冯·亥姆霍兹(1821-1894)命名。 bow with the string on the bass may be found on the University of New South Wales site. The bow for the bass is typically made of black horsehair. The horsehair sticks to the string and pulls it to the side a certain distance and then releases it in a repetitive stick-slip pattern. For the low frequencies of the bass strings, the frequency of the stick-slip repetition can be equal to the frequency of the string, a condition associated with a full, rich tone for the instrument. This condition is referred to as the Helmholtz motion or "Helmholtz node" after Hermann von Helmholtz (1821-1894).
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