I've allways thought the octave was the unit of measurment of bandwidth. With this in mind, a Q of one equals one octave at any frequency (40Hz, 800Hz, 4kHz, 12kHz, etc...).

Actually a Q of 1 equates to 1.3885 octaves.

And the bandwidth is the same for any frequency, whether you express it in Q or in octaves.

If you express the bandwidth in Hz, then its proportional to frequency (double the frequency, double the bandwidth).

Q

Q is actually the slope of the curve of a filter's response characteristic, and is measured in db per octave, or portion of octave. Its quite often mistaken for the bandwidth of the filter, though they are directly proportional.

Q is the slope average at the half power (-3db) points of the curve. Generally, the higher the Q number, the steeper the slope, and the narrower the bandwidth. The actual numerical relationship depends on the filter design.

Q

Q is actually the slope of the curve of a filter's response characteristic, and is measured in db per octave, or portion of octave. Its quite often mistaken for the bandwidth of the filter, though they are directly proportional.

Q is the slope average at the half power (-3db) points of the curve. Generally, the higher the Q number, the steeper the slope, and the narrower the bandwidth. The actual numerical relationship depends on the filter design.

Pennies,
By "Q . . . is measured in db per octave", are you suggesting that a gain of 1 db with Q set to 1 affects a bandwidth equal to one octave, and that a gain of 7.5 db with Q set at 7.5 also affects a bandwidth equal to one octave? In other words, that the size of the bandwidth affected is a function of both Q and gain (or cut)?

No. First, the slope is usually not identified by the knob. Its just a general diagram, if you look close, of a bell curve, which on the left looks like a bell, and on the right looks like a spike. I don't know about the big expensive boards, but most mid priced boards (and other processors, including alot of EQ plug-ins) you have to look at the manual to get the actual specs of the filters, if they are even published there (A luxury). The numbers on the left and right that accompany these "icons" are general also. That means that a "1" to the far left is (without knowing the specs) general-speak for the longest db/octave slope, and to the right side of the knob, whatever the value, stands for the steepest slope. You have to play around with it to get an idea of what the filter is actually doing by ear. (even if the specs say a "1" is a ---db per octave slope, unless you hear it that way the spec means squat)

Yes to the second part though. The "cut-gain" knob of a parametric EQ does indeed affect the slope, or "Q" of the filter, and unless you are into extreme exactness don't worry about that. It does not, however, affect the bandwidth (or negligably anyway).

I am sure that equipment is made where the numbers on the "Q" knob actually mean 1db/octave slope, or maybe "a slope such that adjusting the gain will affect one octave" where it says "1", etc, but years ago I learned how to analyze EQ filters by ear unless, like I said, precission is needed, and then I don't trust the knobs, I bench test it. (who does that anymore?) The gear user manual should explain it.

This subject is a specialty and requires alot of study, and at the rate of your initial question you may want to take up some electronics classes. "Q" is rather ellusive at times, and it is difficult to know what the equipment engineer really meant, because in transister design it means one thing and in filters it means something else, and in tube guitar amps it is again something else.

I would be happy to continue this in more detail if anyone is interested. There are plenty of web sites with graphs and charts but I have to look them up, maybe later.