The oscillogram to the upper right shows the 13560 kHz signal at TP1, i.e. you see the signal
directly at the output of the first stage. As you see, it is not a sinusoidal wave, but more
or less you see inverted-U-shaped pulses, or in other words, the sinus is cut off at the bottom.
In order to show the harmonics which are hidden in this signal, I used the little high-pass
filter. With this filter between TP1 and the oscilloscope, you get the harmonics on the scope
as demonstrated with the oscillogram at the bottom. The counter shows double frequency
(27120 kHz) and the signal consists of pairs of one larger and one smaller wave.
This means, that unwanted harmonics exist to an important amount at TP1. Furthermore, you see
that the distortion is mainly due to the second order harmonic at 27120 kHz.
The buffer stage roundabout transistor T2 together with several RC and LC low-pass filters, act
to inhibit 27120 kHz and higher order harmonics. As a result, at TP2 which is the output of 
the oscillator, there are no more distortions and no more harmonics.
To demonstrate this, I show the oscillogram to the upper left. Here again the little high-pass
filter in between TP2 and the oscilloscope is used in order to enhance visibility of any
harmonics. As you see, there are none. Or to be accurate, none visible. The 27120 kHz is
sufficiently suppressed but still existing, as you can demonstrate with your radio tuned to 
the frequency of 27120 kHz. If my Grundig satellite 3400 professional's meter indicates
correctly, 27120 kHz is supressed by about 60 dB, or in other words, in 
comparison to the 13560 kHz signal, the signal strength of 27120 kHz is 1000 times lower.