单元 6

Notice that there is considerable 增 in 响度 because the two 正弦 波 have a 时间 关系 描述 as being in 相位

Because the two 音 are in 相位 they add constructively and the resulting 组合 has twice the 振幅 of either 音 alone Those knowledgeable in 电子 will recognize this as producing a 6-dB 增 in 信号 级

Now let’s see what happens if the same two 500-Hz 正弦 波 are 合并 out of 相位 or in 相位 对立 that is when one 波形 goes positive the other goes negative and vice versa

That four-second 死 点 in the middle was caused by adding the second 相等 500-Hz 音 out of 相位 When the two 信号 are in 相位 对立 one cancels the other out and the resultant 输出 is zero

The 频率 of the 拍（音） is 确定 by the difference between the 频率 of the two 音 which are 拍音 together

As the difference between the two 音 is 增 so that the 拍（音） 频率 增 to about 20 赫兹（he zi） the 耳 becomes unable to discern the individual 拍（音）

As the 拍（音） 频率 is 增 beyond 20 赫兹（he zi） a 刺耳（粗糙） rattling 声波 is 听

音符 this 粗糙 well! It is the secret ingredient of what we consider to be 不爽 樂/乐 效果

As with so many other 因素 of 人类 听觉 the 批判 带/乐队 seems to be involved in how we 听 two 音 which are 声/听起来 together If the two 音 are a 批判 频带宽度（带宽） apart they are 听 不 as 拍（音） or 粗糙 but resolved 悦耳 as two separate 音

To 避免 the distraction of the 拍（音） and the 区域 of 粗糙 and for the 耳 to separate the two 音 they must be at least a 批判 频带宽度（带宽） apart

All this leads us to the conclusion that when 几个 音 are 声/听起来 simultaneously the result may be considered as either 宜人 or 不爽 Another way of 描述 these 感受 is with the 术语 辅音 and 刺耳 In this 心理声学 语义（上下文） when we say 和协 we 中项 音 or 感官 和协 This is distinguished from the musician’s 用 of the 词 which is dependent on 频率 比率 and 樂/乐 理论

Here we are referring to 人类 感知 Of course in an ultimate 感觉 the two 定义 must come together The 清晰度 of these 粗糙 效果 does 不 depend on 樂/乐 训练

This puts the 效果（效应） of 合并 two 音 in proper 透视 If their 频率 are separated by a 批判 频带宽度（带宽） or more the 效果（效应） is 辅音 If less than a 批判 带/乐队 离 the 音 变化 度 of 不和协 are 听 The most 刺耳 that is the least 辅音 spacing of two 音 is about one-fourth of a 批判 频带宽度（带宽）

音乐家 定义 an 倍频程（八度） as a 樂/乐 间隔（音程） whose two 音 are separated by eight scale 音

音 separated by an 倍频程（八度） have an essential similarity 识别 by everyone There is a very good reason for the octave’s 和协 which directs our attention once more to the 批判 带/乐队

An 倍频程（八度） represents a 频率 比 of two to one

This 中项 that the 谐（泛音） of both are either well separated or coincident up through the 可听 频谱 when the two are played together

In fact the 声波 of the 较高 音符 reinforces that of the 较低 one The result is consonance- full rich and complete

The 纯/完美 fifth is only slightly less 宜人 than the 倍频程（八度） 间隔（音程）

we 音符 that they are either separated more than a 批判 频带宽度（带宽） or they are at essentially the same 频率 both 因素 contributing to 和协

对比 the 频率 of the 基（础） and 谐（泛音） of middle C and B-flat we fail to find coincident pairs as we did with the 纯/完美 fifth 间隔（音程）

For a minor seventh 间隔（音程） we find numerous 谐（泛音） of C and B- 平（坦） close enough together to result in some 粗糙 Evaluating the separation of 谐（泛音） we find many near misses which are 不 coincident but less than a 批判 频带宽度（带宽） apart contributing to the 粗糙

We see that the 纯/完美 fifth is close to perfect-that is close to the 和协 of the 倍频程（八度） 间隔（音程） The minor seventh has some 间隔（音程） separated less than a 批判 频带宽度（带宽） hence somewhat 刺耳

We 结论 that the 批判 带/乐队 approach has 值 in explaining or even predicting the 度 of 和协 an 间隔（音程） exhibits

不和协 can be considered another 维度 of 樂/乐 创造性 to be explored

Our purpose in this 分析 is only to relate 和协 and 不和协 to the 批判 频带 of the 人类 听觉 系统