Talkin' Tone

Sound, especially the tonal aspects of it, is difficult to describe. It seems it's especially difficult for musicians, who oddly enough spend their lives listening to and analyzing it. Guitar makers can be understandably frustrated when multiple musicians, even highly respected ones, not only describe the same instrument's tonal qualities in seemingly contradictory terms, but disagree on whether it is a "good" or "bad" sound. The fact that this is an all too common occurrence points out how different people are, not only in their ability to hear things, but whether what they hear pleases them or not.

Any discussion of tone must define the terms used and put them into a context that the participants can understand in a similar way. For this reason I tend to use very few terms and avoid using undefinable ones. Since I am familiar with graphing the harmonic spectrum of notes (frequency vs amplitude), I try to relate my terminology to a frequency graph. It is also possible to envision the settings of a graphic equalizer, which broadly approximates a frequency graph.

Fig.1 Frequency spectrum (Cubic Spline filter) of the open Low E string (E2, 83Hz) from two Morrison Classic guitars (Y axis:Db, X axis:Hz)

Fig 2. The same frequency data with the X axis as logarithmic scale.

To provide some context to the above graphs, #211 has an Engleman spruce top and a Brazilian Rosewood back. #212 has a Western Red Cedar top and back. The data points have been filtered to make the graphs easier to understand. The entire audible spectrum of 20 - 20,000Hz is shown. Generally, I ignore data points above 10,000Hz as noise. Some guitar makers only concern themselves with points under 1000Hz and many ignore all of them. In the example above, the graphs are very close to identical until 1,000Hz. Listening to both guitars being played, #211 sounds deeper to me while #212 is very bright. See the definitions below.

By envisioning the sound based on the harmonic content of the note, it becomes possible to talk about the same sound, even if one person thinks of it as "sweet" and the other thinks of it as "harsh".  At least the discussion is about the same sound. It is helpful to be able to listen to the instrument that the graph is derived from as a whole (or a recording of it), and not just the single note that the graph depicts, so as to fix the sound with the visual picture.

Let's look at some of the terms I prefer to use and please remember that these are MY definitions and may not match yours, a dictionary, or another builder.

Bright - This refers to the relative amount of treble frequencies present in the notes when the instrument is played. If viewed as a spectrograph of 0 to 20000 Hz with some kind of rounding algorithm (Cubic splines or Bezier)  what is being viewed is the slope of the line, which always declines as the frequency increases. (It always declines because it takes more energy to maintain a high frequency than it does a lower one and there is only so much energy a finger can put into a string by plucking or striking it). The brighter the sound is, the closer the slope of the line will be to horizontal. Which is to say the higher frequencies are relatively loud compared to a less bright sound.

Deep - This term relates primarily to the bass notes and how strong the fundamental harmonic (the one we name the note after) is in relation to the other lower harmonics. This can be a tricky subject because the lowest note (E2) is normally lower than the main air frequency of a guitar, which means that the air column will be less effective for notes lower than itself (usually around G#2 +/-). Often what is heard as E2-G2, is not the fundamental, but the combined effect of harmonics above the fundamental. Our ears translate that for us and we "think" we hear the fundamental. In my universe, a "deep" sound has a fundamental that is equal to or greater than the following harmonics, however that comes into being.

Partials -  All the component frequencies that make up a note above the fundamental pitch.

Harmonic series - The harmonic series is the integral series of partials. This series in plucked strings is the fundamental frequency multiplied by the positive integers. So if the first harmonic is 55 (A1) the second is 55*2 or 110 (A2), the third is 55*3 or 165 (E3) and so on. These tones are produced by the string in motion subdividing into vibrating sections of differing lengths, each "mode" having it's own accompanying frequency.  It's the combination of these frequencies and the relative volume of each that determine what we hear as tone.

Overtones - Harmonics above the fundamental pitch. These are the harmonics that are not octaves and strong enough to induce an audible "beat" to the note. Listening to beats is how we tune notes, knowingly or not, by ear. If a note supplies it's own beats by having a dominant (non octave) overtone, it can be very difficult to tune or play in tune.

Undertones - I alluded to this when defining "deep".  An implied pitch that is lower in frequency than the fundamental. When a pitch (say 110Hz - A2) and the 5th above it (165Hz - E3) sound together (especially at high volume) the note that is the difference (165-110=55 or A1) becomes audible. This trick is useful in Rock and Roll "power chords" and pipe organ music, both of which use this to simulate a lower note than is actually played. In a plucked string, the second and third harmonics have this relationship. For the E2 note, E3 is the second harmonic and B3 is the third harmonic. Doing the math as above, we get the E2 from the combination of E3 and B3. So if the second and third harmonics are well matched, the first  harmonic is re-enforced. This is not as dominant an effect in a guitar as it would be an amplified guitar or pipe organ, but it does come into play and can be heard. During an experiment I encountered a great example of this, I was removing a back while the string were still up to pitch (don't try this at home!) and when I had the back open far enough to get the air cavity pitch up to B2, the low E string became very loud. The second harmonic of the air cavity (B3) aligned with the third harmonic of the low E string (B3) and the result was an strongly enhanced E2 both in volume and a "deeper" tone.

The main Air frequency- The air enclosed in the soundbox functions acoustically as a tube open on one end, similar to a bottle. If you blow across the soundhole you will hear the main air frequency or resonance. You will also hear the harmonic components, which in this case are the odd harmonics.

Looking at this chart, we see the integer based harmonic series. I'm using G#2 as the fundamental which is the most common main air cavity frequency for classical guitars. The air cavity of a guitar is like a tube that is open on only one end, thus it only exhibits (or enforces) the odd harmonics. These are shown in red above and pictured below. 

As an aside, a properly placed "tone port" will transform this into a tube open on both ends and bring the other harmonics into play, although the fundamental pitch will change. This is pictured below.

Coupling - Bass response in Classical/Flamenco guitars is strongly enhanced by harmonic coupling of the top, back and air cavity.

The above information is a short list of terms that help define how I approach tone. There are many more characteristics of sound that I have not covered here (yet). I hope this helps in some way.