How can I play one music right after the other ends?

Good day.

You need to check in the updte ifthe audiosource is still playing. When is not, you can plsy the next audio clip

If you want to add fading and other effects, i would recommend using Unity Audio Mixer.
Or you can do this..
adding two game objects to your scene
randomly adding music to their audio source
then decreasing volume of one while increasing volume of other gameobject's audio source.

Looking for the same issue. Bumped into your thread. Thanks for creating it. Looking forward for solution.

MyBalanceNow

The common solution most would recommend is to check isPlaying in the Update() method and play next clip if it's not playing. However there's a very annoying issue: Every time you alt-tab it will consider it "not playing" and start a new piece. So, in addition to that, use the Monobehaviour's OnApplicationFocus(bool b) method. Keep track of it with a variable like

  void OnApplicationFocus(bool b) {
         Debug.Log("application focus: " + b);
         isFocused = b;
     }

If isFocused is false, don't play the next clip.

  // Update is called once per frame
     void Update()
     {
         if(isFocused && !currentAudio.isPlaying)
             playNextMusic();
     }

Solution one: launch your music in a corroutine and wait async for end;

 musicAudio.Play();
 yield return new WaitForSeconds(musicAudio.clip.lenght);
 nextMusic();

Solution two: launch yout music in a corroutine an wait async while is playing

 musicAudio.Play();
 yield return new WaitWhile(() => musicAudio.isPlaying );
 nextMusic();