PHYS341/2023/Project7

Timbre Variations Within a Guitar

Author: Adil Habib

Fig 1.1. Spectrum Graph Illustrating Timbre. (Raamsdonk, 2023).

Fig. 2.1. First Position - Standard. Diagram by Author.

Fig. 2.2. Second Position - Bridge. Diagram by Author.

Fig 2.3. Third Position - Twelve-Frets Above. Diagram by Author.

Timbre is defined as the tone quality of a note. Timbre is what gives each note its unique flavour. It’s why a C-major chord sounds much warmer on a solid mahogany acoustic guitar than a C-Major chord on a laminated spruce guitar. In this article, I will explore timbre variations within a guitar. To understand why that is, we must first understand what harmonics are.

Harmonics and Timbre

A harmonic is a sound wave whose frequency is an integer multiple of its fundamental frequency. For example, if we take the note A4, whose frequency is 440 Hz, the harmonic frequencies would be 880 Hz, 1320 Hz, 1760 Hz, and so on. We could notate these harmonics as f, 2f, 3f, 4f,...

This is also referred to as the harmonic, or overtone, series. This series is as follows: fundamental frequency (root note), the second harmonic (octave), third harmonic (perfect fifth above second harmonic), fourth harmonic (perfect fourth above third harmonic), and so forth. Understanding that harmonics resonate when playing any acoustic instrument is vital in the understanding of timbre, as timbre is caused by aptitude combinations of these harmonics. A fundamental frequency with a note of 100 Hz may sound different to a note with the same frequency played on a different instrument because both of these played notes produce different volumes or amplitudes of their respective harmonic frequencies. This can be better understood on a spectrum graph.

Spectrum Graph

Figure 1.1 is a spectrum graph illustrating the varying amplitudes of the harmonic frequencies, where 100 Hz is the fundamental frequency and the subsequent frequencies are the subsequent harmonics of this fundamental frequency. This note at 100 Hz has a specific sound, or tone, quality due to the unique amplitudes of the harmonics.

Timbre Variation Within a Guitar

Now that we understand what timbre is and how it works, we can move on to the example of this exploration: timbre within a guitar. This experiment is carried out by playing a G5 chord (consisting of the notes G2, D3, & G4) three different ways. The first way is going to be the most common way people play their guitars, and that's in between both pickups or somewhere over the pick-guard. The second way is going to be over the bridge, and the third way is going to be 12-frets above the fretted notes. If you try this experiment at home with a guitar, you will notice that each position produces a different sound. The standard position is the sound that is associated most with clean-tone guitar playing, as the sound is quite full. The bridge position yields a sharper, twangy sound, which is especially useful when playing fast-tempo staccato melodies. Lastly, the third position results in the warmest of the three tones, with a very pure and almost muffled sound.

Analyzing the Spectrum Graphs

Fig 2.4. Spectrum Graph of Standard Position. Diagram by Author.

Figures 2.4-2.7 are spectrum graphs for their respective positions and chords. Figures 2.4-2.6 are the three different positions and figure 2.7 is the spectrum graph of a G-major chord. Figure 2.4 has its most notable spikes at around 98 Hz ($\approx$ G2), 145 Hz ($\approx$ D3), 194 Hz ($\approx$ G3), 392 Hz ($\approx$G4), 586 Hz ($\approx$ D5), 777 Hz ($\approx$ G5). The fundamental frequencies for this G5 chord are, 98 Hz (G2), 146.83 Hz (D3), and 196 Hz (G3). This follows the harmonic series of f, 2f, 3f, 4f... as if we look at the fundamental frequency of the G2 note and multiply that by integer multiples, we would get the following frequencies: 1 x 98 = 98 Hz (fundamental), 2 x 98 = 196 Hz (second harmonic), 3 x 98 = 294 Hz (third harmonic), 4 x 98 = 392 Hz (fourth harmonic), and so on. Comparing the spikes to the harmonic series, we can see that the second, fourth, sixth, and eighth harmonics of the G2 note are spiking the loudest, and that the latter (7th and onwards) harmonics of the D3 are spiking as well. If we compare the spectrum graph of the standard position to that of the bridge position, we will notice that the spectrum graph for the bridge position has a lot more spikes and seemingly more harmonics. Figure 2.5 has similar spikes in the fundamental frequencies compared to figure 2.4, but interestingly, figure 2.5 has notable spikes at 123 Hz ($\approx$ B2), and at 987 Hz($\approx$ B5). This is interesting because the relationship between a G note and a B note is a major third, therefore, by playing a G5 chord (which contains no major third) on the bridge position, you can get a resulting phantom third (producing the sound of the third without physically the note), making the G5 chord sound more similar to a G-major chord without playing the B, or the major third. This can be understood further by comparing the figure 2.5 and figure 2.7, the bridge position and the G-major chord spectrum graphs respectively. Both graphs have similarities in their attacks and in the overall shape of the spectrum graph, with spikes around 987 Hz ($\approx$ B5). This may suggest that the tone-quality of a G5 chord (or any power chord) played at the bridge position sounds more similar to a G-major chord than a G5 chord. Lastly, if we examine figure 2.6, we will notice that there aren't many decibel spikes other than the fundamental frequencies, this is indicative of the warmer tone that is achieved when playing at this position. What's interesting about this spectrum graph is that the most notable decibel spikes are at frequencies of 98 Hz ($\approx$ G2), 193 Hz ($\approx$ G4) , 498 Hz ($\approx$ B4), and 987 Hz ($\approx$ B5). This is interesting because other than the fundamental G2 note, we are not hearing a clear fundamental frequency for the D3 note. The spectrum graph for third position (fig. 2.6) suggests that the tone-quality of a G5 chord played in this position is a dyad that implies a G-major chord.

Applications

Fig 2.5. Spectrum Graph of Bridge Position. Diagram by Author.

Fig 2.6. Spectrum Graph of Third Position. $\approx$Diagram by Author.

Fig 2.7. Spectrum Graph of G-Major Chord. Diagram by Author.

Understanding the concept of timbre can pose many practical applications when playing an instrument - specifically the guitar. By understanding that different strumming positions yield different sounds, musicians are able to vary their tone physically, without the use of any additional EQ or effects. This could be especially useful for acoustic players as they will be able to alter their tone with just their hands rather than with technology.

Conclusion

Timbre is a crucial concept in understanding how we perceive sound. It's what gives notes they're unique flavours and what differentiates instruments from each other. Timbre is not something that is just perceived when listening to different instruments, but is also perceived when the same instrument is played in different ways. This was explored through the example of the electric guitar and strumming positioning. We discovered that playing a G5 chord in the first position results in a warm and full sounding tone, which could possibly be caused by the clear spikes in the harmonics (which followed the harmonic series), the longer attack, and/or the smoother and more regular decay. Perhaps this yields the most in-tune sound as the harmonics produced by the G5 chord follow the harmonic series. The timbre of the bridge position resulted in a more twangy sound, containing harmonics which followed the harmonic series and an array of harmonics that did not. This position yielded a sound that loosely emulates a G-major chord. The final position is what seemed most interesting as the fifth (the D3 note) was not clearly spiking, rather, the root note (G2) and octave (G3) had spiking decibels alongside the major-third (B4 & B5) although the major-third was never fretted and strummed.

Having a vague understanding of timbre can pose practical benefits as it can aide guitar players in the creation of their own unique tone and sound print. It can help studio musicians get different tone-qualities for their sessions, and it can help amateur musicians experiment create different sounds with their instrument.