Can somebody explain autotransformer impedance-matching volume controls?

More specifically I'd like to know how the 1X2X4X8X jumpers work. I can see how coil taps and a multi position switch can change volume, but the jumpers are beyond me right now. They seem to be connected to the winding somehow, and I think that makes sense. Do they add in or remove parts of the winding to/from the circuit? If somebody can give me a quick sketch of the circuit or point me to where I can find one, I'd be most grateful.

thanks
 
An autotransformer has a single ("auto" is Greek for "self", the single coil acting alone) winding with two end terminals and one or more terminals at intermediate tap points.

https://en.wikipedia.org/wiki/Autotransformer

A transformer has primary and secondary windings.
Tap points on the primary winding can allow for suitable power levels, secondary winding tap points can offer different impedances to match the loudspeaker nominal impedance rating.

https://www.electronics-tutorials.ws/transformer/audio-transformer.html

Can't be more specific without a specific model number of your transformer.
 
As the currents in an autotransformer are common or shared along part of the winding, it has a larger coefficient of coupling or K factor.

Those autotransformers usually has much less leackage inductance, and for the same power are physically smaller than a true transformer. This is because the current in the common part of the winding to pri and sec are always in opposite direction resting them in place of adding. Thus, the common part can be filled with thinner wire, ocupping less core window.

During the TV era of tube sets, several manufacturers used them to couple output tubes of the deflection circuits to the corresponding coil of the yoke. This lead to a great simplification of the circuits mainly in horizontal output stages, meaning less capacitance intra-windings and less leackage inductance, with large benefits in the design and performance of such tubes. Imagine that transformer coupled in firsts sets used the 807 for HOT while lasts were using the smaller 6DQ6 and similar although the CRT deflection angle passed from 70° to 110° and the high voltage for anode of CRT also was taken autotransforming the flyback pulse at the final tube anode and rectifying it whilst in the earlier sets was taken from iron trafo from line frequency (50/60Hz).