Many people use what is referred to as a "random length" wire antenna for HF, quite effectively. The problem occurs when the wire ends up being a half wave multiple on one of the bands you would like to operate on. Odd number quarter wave lengths work very nicely. Even number quarter wave lengths (half wave multiple) do not.
With eight bands to contend with, how do you find a good "random length"? Well, what I did was to make a table of lengths that you should not use and then extrapolated out from there. Guess what? No longer random, is it?
Look at the table and you can easily see why a true random length will work beautifully on one band and not worth beans on another.
The formula that I used was 300/Freq[Mhz] = 1 wave length in meters . Divide that in half to get 1/2 wave length. Thus 150/F[Mhz]. Take that number, multiply by 39.3701 to get inches in a meter, then divide by 12 to get feet. I used 39.37/12 = 3.2808 rounded to 3.28 to convert from meters to feet.
Final formula is (150/F[Mhz]) * 3.28 = 1/2 wave length in feet. Then multiply by 1, 2, 3, etc. until you exceed my self imposed limit of 125 feet (maximum you can fit on most city lots). Lengths shown are rounded to the nearest one tenth of a foot.
Frequencies (in Mhz) used for the calculations were: 28.6, 24.93, 21.225, 18.11, 14.175, 10.125, 7.150 and 3.928. Yes, I understand that it has its focus on 75M phone and ignores 80M CW, but it also exceeds 125 feet for 75M phone.
Most easily used lengths are: 63', 74', 89' and 111.5'. OR, not very random iffin you want all band coverage (center of band).
Frequencies (in Mhz) used for the calculations were: 28.0-29.7, 24.89-24.99, 21.0-21.45, 18.068-18.168, 14-14.35 10.1-10.15, 7-7.3 and 3.928.
Most easily used lengths are: 63', 74' and 111.5'. 89' is omitted because it would be within about one foot in length of two bands on either side of it.
If you want to cover all of every band with minimum loading problems (that does not imply it will be perfect - only that it should load) 74' is your winner.
Department of redundancy department - Not very random to be able to load all bands.
I have been receiving several E-mails finding fault with the numbers I have posted here. Many of those go on to say (something to the effect) "I can make any half-wave load properly." I'll just bet they can. They can load ONE band or two or maybe even three. Try ALL of them. Anyone miss that last statement? ALL OF THEM. Therein lies the "fly in the ointment". When you are looking for a length that will handle all of the HF bands (and possibly some VHF/UHF [I have not tested those]) you need to be more careful in your thoughts and comments on various boards.