CakePHP - how should I do these relationships and name my tables?

It's a song and lyrics database. I'm trying to bake an app from my database, which looks like this: (every table does have a primary key 'id', I just left them out..)

    songs
        song_name

    artists
        artist_name

    songs_singers
        artist_id (FOREIGN KEY artists.id)
        song_id (FOREIGN KEY songs.id)

    songs_writers
        artist_id (FOREIGN KEY artists.id)
        song_id (FOREIGN KEY songs.id)

    song_views
        song_id (FOREIGN KEY songs.id)

    videos
        song_id (FOREIGN KEY songs.id)

    video_views
        video_id (FOREIGN KEY videos.id)


Writers and singers both overlap, i.e. some writers sing and some singers write.

When I bake the songs table, I get this error:
   Error: Table singers for model Singer was not found in datasource default.

I think the problem is that CakePHP wants me to create a new model for singers, so I'll have to end up duplicating the names of writers and singers in a new table singers. I just want the names stored in artists and have both song_singers and song_writers link to that table with foreign key IDs.

songs have many:
* views
* videos

videos have many:
* views

both writers and singers have many:
* songs

What should I do?

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