Tuning Capacitors - Some Theory From classic radio texts, Tuning capacitors were classified 3 ways, namely:

 SLC SLW SLF Straight Line Capacity Straight Line Wλvelength Straight Line Frequency
The "straight-line" description refers to the linearity between shaft rotation and change of either,
capacitance (SLC), oscillator wavelength (SLW ) {λ} or oscillator frequency (SLF) {f}.
The shape of the moving plates is such that:
equal angular incremental shaft rotation produces an identical change in tuning frequency (or wavelength).
e.g. each 10º rotation makes say 50 KHz change (uniform across full tuning range)
The reason for this being that a dial type scale (attached to the tuning shaft)
becomes uniformley "linear" in presentation.
If say, an SLC capacitor were to be used; scale calibrations -
in frequency (or wavelength) would be compressed at one end,
and expanded at the other end of the tuning dial.
From the theoretical analysis below; a graphical curve defines the shape of the moving plates,
to give a so-called "straight line" action!

Superhetrodyne Tracking using ganged tuning capacitors.

The signal and oscillator circuits must resonate at frequencies which exhibit a constant difference
(the IF frequency) with a ganged capacitor.
The MW band is 530KHz to 1600Khz and the oscillator circuit will have to cover a range of
530 + 455 (985) to 1600 + 455 (2055) KHz (normal high side LO injection)
The ratio of the band-edge signal frequencies is 1600:530 or 3.02 whilst the ratio of the
corresponding local oscillator frequencies is 2055:985 or 2.08
Since frequency of resonance is inversley proportional to square root of resonating capacitance

Thus the range of maximum to minimum capacitance to cover the bcst band will be 3.02 2 = 9.12
and the oscillator circuit will need a ratio of 2.082 = 4.33
By adding the correct amount of fixed capacity in parallel with the tuning capacitor
and choosing the correct value of inductance, it is possible to obtain the same frequency difference
at each end of the tuning range.
However this will not give the correct difference at intermediate points.
The error in tuning will be:-

C1 is a trimmer
C2 is the tuning capacitor (gang)

In general the padder capacitor is equal to the maximum value of the tuning capacitor.
The above circuit does not give perfect tracking but can be made to give
the required frequency difference at 3 points
and the error in tracking can be kept
to within 0.5 % of the signal frequency.

A second method is to used a ganged capacitor in which the shape (and/or number)
of the moving plates in the oscillator section
differ from the signal section such that
the two different tuning ranges are acheived.
These are sometimes called "padderless gangs"

Reference:
Marconi School of Wireless Text: stage 3 Reception (c 1970)
Click on any image to enlarge.