router.js应该这样写吧
//router.js
Vue.use(Router)
import foundMusic from "../compontents/found_music.vue"
export default new Router({
routes:[

{
    path:"/foundMusic",
    component: foundMusic
}

]

})

你试一下 components:{ "left-menu":leftMenu }

看下命名视图 https://router.vuejs.org/zh-c...

我在重新对逻辑进行审查之后发现正常了，下面把正常的代码贴一遍吧，也算是帮助新人了。在此非常感谢回答问题的朋友

//App.vue
<template>
  <p id = "app">
      <music-nav></music-nav>
      <music-content></music-content>
      <music-playing-wapper></music-playing-wapper>
  </p>
</template>
<script>
    import musicNav from "./nav.vue"
    import musicContent from "./music_content.vue"
    import musicPlayingWapper from "./playing_wapper.vue"
    export default {
        name:'app',
        components:{
            musicNav,
            musicContent,
            musicPlayingWapper
        }
    }
</script>
//main.js
import Vue from 'vue'
import App from './App.vue'
import VueRouter from 'vue-router'
import axios from 'axios'
import router from './router/router'

Vue.prototype.axios = axios
Vue.prototype.MUSICAPI = '/api'

Vue.use(VueRouter)
new Vue({
  el: '#app',
  router,
  render: h => h(App)
})
//router.js
import Router from "vue-router"
import content from "../music_content.vue"
import foundMusic from "../compontents/found_music.vue"
import App from "../compontents/found_music.vue"

export default new Router({
    routes:[
        {
            path:"/foundMusic",
            component: foundMusic
        }
    ] 
});
//music_content.vue
<template>
  <p id="music_content" class = "container-fluid">
      <p class = "row">
          <left-menu></left-menu>
          <router-view class="router-view col-md-10"></router-view>
      </p>
  </p>
</template>

<script>
import leftMenu from './menu_content/left_menu.vue'
export default {
  name: 'musicContent',
  components:{
      leftMenu
  }
}
</script>