Research
This is a question worth asking, especially if you've ever played three chords on a guitar and pressed three keys on a piano. And why is the guitar – rightfully so, in my opinion – often referred to as the most flexible and potentially most sonically rich accompaniment instrument in classical music?
To explore this question, I developed a mathematical model that essentially focuses on how the string is set into motion. Whether or not this model fully aligns with physical reality is another matter – but it does provide an idea of where the journey might lead …
So what’s it all about?
The biggest difference between the two instruments lies in how the strings are made to vibrate. A guitar string is plucked, while a piano string is struck by a hammer mechanism. The key point is that plucking happens at a single point (e.g., with the tip of a fingernail), whereas a hammer has a certain width and strikes the string over a broader area.
Naturally, it also matters where on the string the excitation occurs. Striking in the center produces a more harmonious and mellow tone, while striking near the ends results in a brighter sound.
How is a tone actually produced?
A tone is created whenever multiple physical frequencies overlap. For the human perception of pitch, only the so-called fundamental frequency matters – all other frequencies shape the character of the sound. If a guitar and a piano both play the same note, say an A at f0 = 440 Hz, the fundamental frequency is the same (440 Hz), but the overtones differ greatly in number and composition. Overtones can be understood as integer multiples of the fundamental frequency.
The Sound of the Center
When a string (whether on a guitar or a piano) is struck in the middle, only odd multiples of the fundamental frequency appear. Because the even multiples (2*f0, 4*f0, etc.) are missing, no octaves are produced. Instead, the first overtone is a fifth (3*f0). This fifth and the absence of octaves create a particularly harmonious sound experience.
The Sound of the Guitar
When a string is plucked at a single point, the overtones are much quieter compared to the fundamental frequency. However, the further away from the center you pluck, the louder the overtones become. In addition to odd multiples, octaves begin to appear as well – the sound becomes less pure.
The Sound of the Hammer
When a hammer strikes a string, overtones are also produced – but they are much louder than those produced by plucking. The first overtone octave strongly overlaps the fundamental, resulting in a tone that feels less stable or “rested,” and more like the complex frequency spectrum typical of a piano.
Back to the Guitar’s Sound
When you observe the complex motion of a string, it’s easy to imagine what happens when you free it from its mathematical model and place it in physical reality – where the string is not frictionless, massless, or perfectly elastic. Here, temperature, air pressure, humidity, material properties, the guitarist’s virtuosity, and – last but not least – the secrets of the luthier and the instrument itself all play a central role.
(Perry Perreiter | www.perreiter.de)
"Musicality is the innate or acquired ability to perceive and practice music." (Brockhaus 2008) If it were truly innate, there would not be such a wide range of ideas about and expectations of music. In recent years, more and more researchers have been studying music from psychological, neurobiological, and evolutionary perspectives.* (Lorenz Welker, LMU Munich)
Most studies assume a unified concept of music across cultures and historical periods. Although this concept only emerged in 19th-century Europe, it is often applied to all times and cultures. This creates a risk of labeling certain phenomena as universal and evolutionary developments. Sound that is deliberately structured into a musical composition is generally considered music. Music is thus distinguished on one side from speech and on the other from noise—though the boundaries are difficult to define. Are drummers who transmit messages musicians? And aren't orchestral musicians also transmitting messages?
“Music is often perceived as disruptive because it is accompanied by noise.” (Wilhelm Busch)
Music is a heterogeneous, multifaceted bundle of pitch progressions — melody, rhythm, and tone color. These elements are universally valid. Harmony, on the other hand, can only be perceived within specific historical and cultural contexts. In music, harmony refers to the simultaneous sounding of tones. This concept is a Western phenomenon and appeared late in music history. Therefore, there is no universal definition of music that applies to all eras and cultures!
Music must always be evaluated within the context of its function. Marching music, for example, serves a mobilizing function, with aesthetics playing only a minor role. In contrast, the morning song in kindergarten has a unifying effect, where aesthetics are more important. If musicality does indeed have a biological component, why do some find certain music beautiful and of high quality, while others find it unbearable?
Recognizing rhythm or perceiving a melody as harmonious does not require special musical talent. However, the sense of well-being when hearing or creating sounds is shaped by direct cultural experiences — and is by no means universal.
A special feature of music is that there must be an intersubjective agreement between listeners and musicians on what form is perceived as "music." This means that early childhood education already shapes later music perception. It also means that the idea of "divinely gifted musical geniuses" is bound to time and place. Just as some may find certain Arabic music sounds irritating and exhausting, Mozart and Wagner may push the boundaries of auditory comfort in other regions — and are by no means considered geniuses there.
Even here, classical music contributes to well-being for only a select few. Younger people, for example, often find operas just as strenuous and disharmonious as foreign sounds — and vice versa, modern music is not recognized as such by those with “musical understanding.”
The perception of music depends on individual experience:
- through early learning processes
- through culturally and individually shaped listening conventions
- through conscious cognitive processing of melodic and rhythmic patterns
None of this has anything to do with human biology! Music is a culture-specific phenomenon.
(Peggy Seehafer, Anthropologist, www.anthropologen.de)
Intonation of the Classical Guitar
The main idea of this article is to draw the classical guitarist's attention to the aspect of intonation, which is directly related to the tonal beauty of the guitar. The goal is not to delve deeply into complex mathematical music theories, but rather to offer inspiration to explore new horizons in this field.
Do we really still need to worry about intonation today? Didn’t someone already solve this by introducing equal temperament centuries ago?
Virtually all modern guitars are equipped with a fretboard where the fret distances are calculated using the mathematical formula 12√2. This is meant to ensure that the octave is divided into twelve equal semitone steps of 100 cents each.
And that could be the end of the story, …
https://www.guitarfoundation.de/pdf/intonation-der-klassischen-gitarre.pdf
Recording the Classical Guitar charts the evolution of classical guitar recording practice from the early twentieth century to the present day, encompassing the careers of many of the instrument’s most influential practitioners — from the acoustic era to the advent of the CD. A key focus is on the ways in which guitarists’ recorded repertoire programmes have shaped the identity of the instrument, particularly with regard to national allegiances and musical aesthetics.
The book also considers how changing approaches to recording practice have influenced guitarists’ conceptions of the instrument’s ideal recorded representation, and it places these developments in the broader context of classical music recording aesthetics.
As an important addition to the growing field of phonomusicology, the book will be of interest to guitarists and producers, as well as students of record production and historians of classical music recording.
More information:
https://www.routledge.com/Recording-the-Classical-Guitar/Marrington/p/book/9781138554702