Frequencies, Frequencies, and More Frequencies

Introduction

The intent of this discussion of frequency is to explain the definition of frequency, and to resolve some of the confusion with frequency and the harmonic content of musically-related signals. Also, the application of frequency equalizers on such harmonic content will be addressed.

Frequencies

Sound is made up of pressure waves or vibrations. The vibrations are referred to as “cycles”. The number of cycles per unit time are called “cycles per second”. One thousand vibrations per second would be called 1,000 cycles per second or 1 kilocycles per second.

The term “cps” (cycles per second) was commonly used in the industry for many years. The more recent term “Hertz”, abbreviated “Hz”, was substituted as the unit of frequency (cycles per second). When frequencies greater than 1000 Hz are discussed, the metric prefix “kilo” is used (designating thousand) prior to the symbol Hz. Therefore 15,000 Hz would be indicated as 15 kHz..

Harmonics

Musical sounds are comprised of a fundamental frequency and harmonic frequencies. The fundamental frequency is the lowest and usually the most predominant part of the harmonic series for the musical note. Harmonics are integer multiples of the fundamental. The 1st harmonic is the fundamental frequency, the second is two times the fundamental, the third harmonic is three times the fundamental, etc. The amount of harmonic frequency levels in a sound is the perceived sound characteristic, usually called timbre.

The waveshape of an audio signal may be determined if the harmonic levels are known. The Fourier Series shown in the equation below can be used to create periodic wave functions, using discrete sine-wave components for the fundamental and the harmonic. The amplitude of the sinusoidal component of each harmonic frequency is algebraically summed.

An audio signal that has relative harmonic levels similiar to a wound guitar string, somewhere in time after the inital strike and before the final sustain, is shown below, plotted with 5 terms of a Fourier Series.

Audio Frequency Range

The average human with good hearing can hear frequencies from 20Hz to 20 kHz. Frequencies below 20 Hz may be felt when they are at high pressure levels. Thunder and earthquakes contain this range of frequencies.

Even though most audio equipment is designed to handle and produce up to a 20 kHz frequency response, a listening audience with hearing above 10 kHz as well as any available musical program content in that range is rarely available.

Application for Frequency Equalizers

Although the vibrating string, reed, or other mechanism has a fundamental or “tuning” frequency of the values below, this does not mean that its frequency spectrum is limited to that tone only. The musical note is filled with harmonic content that is usually the most significant portion of the instrument’s sound. The chart below depicts the harmonic frequency range of most instruments.

Musical Note Frequencies (Hz)

The following table shows the pitch frequencies for an equal tempered scale based on the geometric progression of the twelfth root of 2. These are the frequencies used by a chromatic tuner to display the tuning of the guitar. A 24-ret guitar ranges from E3 to D7. Notice on the chart above that the harmonic frequency range extends almost ten times higher in frequency than the pitch of the instrument’s highest note.

Equal Tempered Scale

It is obvious that most instruments like the guitar, having the highest string on the last fret played, represents a frequency equally significant to the harmonic content of the lowest string (E) played open. The highest note playable on a 24-fret guitar is a (D octave 7) note. This has a fundamental frequency of 1175 Hz. If you played the lowest frequency string of a guitar (E octave 3) at 82 Hz, you would find that the setting of an equalizer at the 1175 Hz would dramatically alter the sound of the low note, especially with bright new strings. 1175 Hz is just below the 4th octave of the 82 Hz E string.

In summary, the frequency equalization settings that affect the quality and shape of an instrument’s sound far surpass the fundamental or tuning pitches of the instrument.

Using the Equalizer Effectively

One of the biggest mistakes to make when using an equalizer is to boost or cut frequencies above or below the dominant energy of the instrument. As mentioned earlier, these ranges extend far past the fundamental frequency of the instrument.

The following paragraphs outline specific equalization applications for various instruments as well as some settings that should be avoided.

Vocals

Low frequency boosts are almost never effective for female vocals, but may be effective on male vocals to a limited extent. Boosting of lower frequencies from 500 Hz to 800 Hz will add body and warmth to the vocal.

The most distinct vocal clarity range is from about 3.5 to 6 kHz. This range will enhance breath effects as well as increase the overall intelligibility of singing and speech. This boost does not come without penalty. Excessive boost in this range increases the sibilant [pronounced sib·i·lant (sīb¹e-lent)] effect of the voice. Sibilance occurs when the vocalist pronounces words with the letter “s”. If a vocalist naturally has this problem, cutting the 3.5 kHz to 6 kHz range can cure the problem. Beware that this is the presence range of intelligible speech and too much cut will make the vocal sound muddy. Also, presence may be added in the 1 kHz to 3 kHz range; although, the 3.5 kHz to 6 kHz range is generally better suited for overall clarity. The other problem with boosts in this range is vocal microphone feedback. Directional cardioid dynamic microphones are almost always used for live vocal performances. The cardioid pickup pattern created by the design of the microphone is quite effective. The overall pattern of the mic and monitor or main speaker tend to be less directional and predictable at the 3.5 kHz to 6 kHz region. It is unfortunate that this vocal clarity range must have the inherent pitfalls of transducer physics. Feedback will inherently occur freely at this range.

Bass “Kick” Drum

It is hardly ever effective to boost frequencies of a kick drum below about 60 Hz. There are applications on some modern dance music where synthesized drum patches will have dominant energy below 50 Hz. These 20 to 40 Hz fundamentals are the type that easily propagates through the closed windows of automobiles and other structures. These low frequency waves encounter little acoustical attenuation in materials and may be heard from great distances.

For the generalized kick drum application, the “thump” is usually realized in the 60 Hz to 100 Hz range. The definition or “slap” of the kick drum is very essential for its relationship to the bass guitar. Boosting the kick drum at 60 to 100 Hz for the “thump” and boosting 1.5 kHz to 3 kHz for the “slap” will provide a “spectral saddle” for the bass guitar to reside. Boosting bass drum frequencies from 100 Hz to 2 kHz in excess will often cause the kick drum and bass guitar relationship to be very boomy and muddy. Letting the kick drum initial attack in the 1.5 kHz to 3 kHz region start off the event, and letting the bass guitar fresh string harmonics provide the sustaining clarity, provide a pleasing spectral combination.

Snare Drum

Older audio references will refer to snare drum dominant frequencies being in the 1 kHz to 2 kHz region. If you are mixing sound for modern rock or country music, you will find a potpourri of snare drum frequencies. Starting with disco in the 70’s and the urban cowboy country craze of the early 80’s, snare drum became spectrally similar with a bass drum. Experiment with a multi-octave equalizer on a stereo system with an early to mid 1980’s country record, like George Strait, and you will find very dominant snare drum spectral content in the 150 to 200 Hz region. Mixes of that era, as well as today, use caution in not having the snare and the kick drum both being dominant in the mix since it would be difficult to tell the difference between the two drums. This often results in a “double time” effect. There are no general rules to the equalization of the snare drum with one exception. When using a real snare with a microphone, be aware that if the drum is tuned very high like a marching band snare, excessive low frequency boosts will not create a fat snare. Listen to the real drum sound up close and realize that fundamental frequencies that are not available from the drum cannot be created or synthesized by equalization. Excessive boost at low frequencies will cause pickup of other drums undesirably.

Generally, if a trigger snare patch or drum has energy in the 150 Hz range and you desire a fat snare, then use it accordingly. Some crisp quality can be added in the 2 kHz to 5 kHz region. Remember, however, that excessive boosting of any frequency of a snare drum means you are probably trying to get a sound that is not available from the source and you are likely picking up extraneous sounds from other nearby sources.

Snare drum reverb is a diverse topic alone. The reverb usage will greatly affect overall equalization used.

Toms

Depending on the tuning of the toms, most of the effective range is from 150 Hz to 2 kHz. The lows are good for deep percussive effects, but definition that cuts through the mix is usually about 1 kHz to 3 kHz. One advantage of toms, particularly in a country or contemporary mix, is that they are only played occasionally. That means their level and occupancy of spectral space may be loud and wide. They don’t need to repetitively compete with other instruments like kick drum and bass guitar. The application of reverb also effects equalization as mentioned in the snare drum topic.

Cymbals

Fortunately, cymbals remain fairly constant and predictable over many types of music. Their dominant energy lies in the 2 kHz to 5 kHz region. Cymbal harmonics extend beyond the range of human hearing. Boosting of cymbals in the 10 kHz to 12 kHz region results in a very brittle sound. Usually, boosts in the dominant area of 2 kHz to 3 kHz makes the overall mix less “wet” or “noisy” than boosting in the upper region.

Electric Bass

As with the discussion of drums, boosting lower frequencies to try to create more depth than what is available is a common mistake. Most bass guitar energy lies around 100 Hz with definition in the 1 kHz to 2 kHz region. Boosting of very low frequencies will result in a “muddy” clash with the kick drum. Letting the kick drum make the fundamental, and the bass guitar rounding out the low midrange just above the kick drum results in a more clear discernible mix. The kick drum can have high definition attack for the initial hit while the bass guitar string harmonics can provide the sustaining definition for the sound.

Electric Lead or Steel Guitar

The most important rule for equalizing guitars is to realize that harmonic series content not available at the source cannot be generated or synthesized at the mixer. Most guitar and steel guitar energy lies between 80 Hz and 5 kHz.

Acoustic Guitar

The same frequency range applies to the acoustic guitar as the lead electric guitar. One common mistake is to listen to the acoustic guitar too much by itself rather that with the entire band. One common mistake with the solo acoustic guitar is to add too much bass. A solo acoustic guitar seems to need more low-frequency boost to round out the sound than it does when played with a set of other instruments. If the low frequencies are excessively boosted, this results in a very muddy relationship with the overall mix. Remember that the acoustic rhythm guitar is as much a percussive timing component as a melodic component. Its high-frequency spectrum is most essential to the “sizzle” of the program material.

Overall Equalization

Excessive boosts or cuts in the main system EQ will drastically effect the decisions made at the individual channel EQ. One method of enhancing vocal clarity is to make sure that all other instrument mixer-channel equalizations do not occupy the 3.5 kHz to 4 kHz band so much. The perception of presence of vocals and instruments can also be simulated by restricting other instruments to have dominant energy in that band. One common mistake for a sound engineer to make by listening to each instrument individually is to make each instrument sound very clear and present. It is easy to boost all instruments in this 3 kHz to 4 kHz range. The separation of sounds is more often achieved by spacing their dominant energy in bands not significantly occupied by others.

The most obvious mistake is excessive amounts of equalization. Experimentation with an equalizer in a home stereo system is a valuable tool to recognition of the various frequency bands. In summary, live or recorded mixing is very subjective, and remember not everyone will have the same opinion.

©1996 Terry Downs Music™