I would like to add another factor to the discussion.
The ratio of 10/1, while ballpark, may not be the only factor if the solid state device uses operational amplifiers in the output stage. Many opamps have output impedances well below 1K, but if you try to drive a 10K load with these (particularly at voltages over 1 V RMS), you can often get flat, lifeless sound performance. Of course, the results also depend on the type of opamp used. Some are better than others.
For opamp driven output stages I suggest an imput impedance of 47K or higher, with output voltages below 1-2V if possible, irrespective of output impedance.
The ratio of 10/1, while ballpark, may not be the only factor if the solid state device uses operational amplifiers in the output stage. Many opamps have output impedances well below 1K, but if you try to drive a 10K load with these (particularly at voltages over 1 V RMS), you can often get flat, lifeless sound performance. Of course, the results also depend on the type of opamp used. Some are better than others.
For opamp driven output stages I suggest an imput impedance of 47K or higher, with output voltages below 1-2V if possible, irrespective of output impedance.