This numeric notation is a sort of shorthand for the standard musical notation.  The dot represents a rest.  However the duration of the rest depends on the type of note being represented.

Each number represents a quarter note (crotchet).   This represents a beat in a 4/4 bar. Therefore if you have  1 1 1 1 This means middle C  (using the C major scale) being hit at 4 equal intervals in that bar.  An eight note is or a quaver in standard notation is same as a quater note with a tail.  In the shorthand notation it has a bar underneath it.  So in a 4/4 time signature, 11111111

                                                                                                                   ________

meaning 8 notes hitting in the same time interval ie. double the pace.  This can also be written as

11 11 11 11 

__ __ __ __

简谱 is translated as muscial staff (stave)

The notation,

1.111 means that nothing is played in that dot.  This is different from 1-111 where the dash represent the first note is being held for that duration.  In other words, the first middle C is a half note.  On the piano, 1-111 means that the first C is held for that duration while 1.111 the first C must be lifted up.

Hope this helps.