# Musical Instrument Frequency Range Analysis in Audio Mixing Tutorial

As shown in the plot, the fundamental frequency of the kick drum is around 55Hz. The maximum is around 100Hz and the minimum is around 30Hz.

The bandwidth in Hz: 100 – 30 = 70Hz
To solve for Q:

Q= fundamental frequency/bandwidth in Hz
Q= 55Hz/70Hz = ~0.8

Therefore if the engineer will be cutting/boosting the kick drum fundamental sound, he will be centering the frequency at 55Hz and using a Q of 0.80.

### Calculating the Minimum and Maximum Frequency of the Instrument based on recommended Q

I received a lot of inquiries (see comments on this post below) on how to estimate the min and max of a certain instrument frequencies in the above spectrum analysis. This is how to do it and how to use this information in your mix using parametric equalizer:

1.) First determine the center frequency. It is clearly explained in the previous section with the use of frequency analysis tool (read the kick drum case study above).

2.) Decide on the Q. In this tutorial on EQ best practices and using parametric EQ, the most recommended Q would be:

Q=1.4 — > 2.0 for cutting frequencies in the audio
Q=0.8 —> 1.0 for boosting frequency range.

3.) Use this Sengpielaudio calculator to estimate the minimum and maximum frequency range given a Q and a center frequency. This is the quantitative method of calculating these values.

4.) Confirm the maximum and minimum values returned by calculator by looking at the musical instrument frequency analysis result plot. Make sure it does make sense. If not, the Q setting you provide is not optimal for your application, try some values near to that.

Example: Let’s use the case study illustrated previously. Supposing the mixing engineer would like to boost the weak kick drum track but doesn’t know the proper center frequency and Q to use for the parametric EQ.

Step1.) Examining the center frequency. Based on the previous frequency spectrum analysis (see screen shots above), the underlying kick drum has a center frequency around 55 Hz where its energy is strongest.

Step2.) However, the maximum and minimum is not clear in the spectrum plot and you will only be guessing. However, since the engineer would like to boost, say for example he uses a Q of 0.8 based on the rule provided previously.

Step3.) Plugging the center frequency of 55Hz and Q of 0.8 in the calculator returns the following results:

Min and Max frequency

Step4.) Looking at the kick drum frequency analysis, the minimum and maximum values (30Hz and 100Hz) seems reasonable. It is because when the mixing engineer boost the kick drum at 50Hz Q=0.8, the change is going to affect most of the kick drum sensitive frequency range (that is cover by musical instrument effective bandwidth and where most of the kick drum sound energy will be found).

Sometimes if the resulting min-max does not correlate with the plot, you might need to adjust and try slightly different Q values to the calculator until the results are sensible. Then use that in parametric EQ in your mix. This technique minimizes the trial and error of setting Q directly in your parametric equalizer to get the most effective EQ adjustment for boosting or cutting. This also reduces ear fatigue associated with frequency changes (as in some applications, this can take some time).

Of course, your ears are still very important to validate all changes in your mix. Don’t forget to use that.

Content last updated on June 20, 2012