Fidelity in the Transmission of Music, Part I: Three Possible Paths
Music has always played an important role in my life such as attending concerts in Vienna and spending quite some time listening to recordings, mostly of classical music. What is common to all ways of consuming music is that there is a path in the transmission of a musical concept from its inception to one’s perception at the end of the chain which prompts the questions of fidelity: what is really meant by fidelity in the various paths of transmission, fidelity of what to what by what?
To pre-empt the conclusion of the following deliberation: the key to musical fidelity lies in my opinion in the understanding of the transformation music and all its aspects undergo in all links of various possible chains from producer to consumer, the different paths music can take; this also includes aspects of musical perception and psychoacoustics. As a consequence, musical fidelity also lies in identifying and mitigating the weakest links of any transformation chain, and finally, accepting that once all technical short-comings have been adequately addressed, the weakest link these days is likely to end up to be the matter between the listener’s ears.
The purpose of this story is to gather and articulate my thoughts in and around high fidelity music and audio; it is not a piece of scientific work in audio engineering. I simply wanted to present an abstract view of what matters in this context to gain some understanding which I want to share. My starting point is: there are producers or creators of music on one side, aka composers, and consumers on the other side, aka listeners; and, there are three possible paths or chains with various links between the two as shown in the following diagram (for classical music at least as I do recognise that the flow of information and signals is different for other types of music).
Suppose the creator of music, the composer C, conceives a musical idea, a concept of some sort which is perhaps present in his/her imagination or mind, nearly in a meta-language, even though this might be a rather romantic idea itself. As Engineer, however, I can relate to that in a way as quite often I can see a solution to a problem in a mind, e.g. I can image a machine in all three dimensions and in motion; it is nevertheless quite painful to express this or any concept in an output language, as a sequence of words, or even in diagrams and convey the essence to the consumer or listener. As for music, there are several ways this musical concept can reach the listener L:
- Performance by composer directly to listener,
- Performance by a performing artist directly to listener,
- Reproduction of performance through medium and audio equipment.
Composer → Listener
The closest a listener could get to the perception of a musical idea as conceived by the composer is being present when the composer performs his/her work life. Still, there is the translation of the musical concept through the mind and body of the composer, the musical instrument, the room acoustics, the listener’s ears or hearing and ability to discern musical ideas, idioms and concepts. But that is as good as it gets.
Allegedly, when Beethoven got news that one of his female friends, possibly Countess Josephine Brunsvik, lost a dear person, he hastened to her house, rushed to her room, looked into her eyes; he was unable to speak and express his feelings in words. Instead, he went to the piano and improvised for some time, expressing thus what he felt though his music. At the end of his performance, he looked into the lady’s eyes again and rush out. According to a Beethoven biography, his dear friend is told to have said: I could feel my son going through the gates of heaven as Ludwig finished his improvisation. That said, the musical concept must have been successfully transmitted where language has failed. For some reason, I always think about that story when I hear the last movement of Beethoven’s Piano Sonata No 32 Opus 111.
In terms of musical fidelity, there are two paths here: the feedback path to the composer (shown green above) and the direct path to the listener (shown red above). As for the first, the composer would be able to tell from the feedback loop whether the music produced is a fair representation of the concept in his/her mind. The artist will hence be able to assess the fidelity of the rendition to the concept in his/her imagination. I am sure, that composers need this loop in order to refine the expression of the musical concept or idea and in order to make the composition (written down or not) converge to the musical idea they had in mind. Having said that, Beethoven, in particular in his later years, and certainly other composers, too, could or can “hear” the composition in their minds without the music being performed at all.
With regards to the transmission of music from composer to listener, this direct path is limited by the kind of instruments the composer is able to play at the level the composition demands, and of course limited to both composers and listeners living at the same time in the same place. As a whole, this path is perhaps not the most common one, but one with the highest attainable level of fidelity between the composer’s conceived musical idea and the listener’s perceived musical idea. The composer — listener path, albeit rare, is about expression or concept fidelity.
Composer → Performer → Listener
In order to decouple themselves from the performance, but most importantly in order to make the music available to a wider audience, a composer has to communicate the musical concepts and pour them into a language: sheet music is the most common interface, using an established notation system even though alternative systems are conceivable. Some composers, like Mozart, are said to have been able to simply churn out their musical ideas in a pristine rendering in a single session; others honed the notation until the sheet music appeared to represent what they had in mind. A closed loop, a read-back, which relies on the composers own interpretation of the sheet music (shown as a green arrow in following diagram). If the composer and performer happen to be alive at the same time, another feedback loop (dashed green line) allows a convergence of the representation of the musical idea in sheet music to the original one in the composer’s mind. The result would be a high level of fidelity of the sheet music to the musical idea as both composer and performer can make sure that all subtleties of the music are correctly expressed and conveyed in the sheet music, the common interface.
At a later stage, centuries later even, when the musical ideas and what they represent may not even be relevant any more (for instance I think about a musical idiom of the Viennese Classic which make me think of a courtsy), enter the performing artist, the performer. The latter may study the sheet music, read up on the composer and the composition’s background and try to reverse engineer what the original musical idea may have been about. Performers interpret sheet music. Eventually, the performer will give a rendition of his/her interpretation of the work to his/her best ability, most likely in a suitable surrounding like a concert hall. Then the performer will be able to assess for themselves whether the interpretation delivers a high level of fidelity to his/her understanding of the oeuvre.
On a wider scope, including the audience as well, high fidelity is most likely a reference to the fidelity of the musical rendition by the performing artist or group of artists to the musical concept in the composer’s mind. This, however, is a difficult endeavour because the reference, the ground truth is not known: for most classical music, the composers are not alive any more. What remains is to leave the assessment of musical fidelity to the music critics who can argue about whose interpretation is deemed to be the closest to the unknown reference, the composer’s musical idea.
At a lower, technical level, it should not be so difficult to come up with fidelity metrics between sheet music and the music perceived in the time and frequency domain in a real-time analysis of any performance. Tracking multiple pitches and duration can be automated and used for a comparison with the sheet music. A bum-note detector would be something quite easy to implement as the bottom line for musical fidelity (or performance). Overall, the composer — performer — listener path is about rendition fidelity.
Composer → Performer → Medium -→ Listener
For most people, however, the most common form of consuming music is by playing back recorded music from a medium through some audio equipment as depicted in the next diagram.
While the first leg of the path, from composer to performer and its feedback loops was discussed before, this part is concerned with what happens between performance and listening. What matters here is the frequency or spectral content at three essential probe points in the signal chain: the audible signal (or sound pressure) at the performance, at the location of a concert goer (two ears, i.e. in stereo), Sp, the encoded frequency or spectral content on the medium Sm, also in stereo, and the rendered frequency or spectral content at the listeners room, at the position of listening Sr, in stereo, too. An important aspect in the music perception is the knowledge of the sheet music which can augment the experience and appreciation of music (blue line above).
On the path from performance to listening, the medium that carries the recorded music plays a pivotal role. While it used to be something tangible carrying analogue or digital signals such as a vinyl or a compact disc, respectively, nowadays the medium is a digital music stream. In either case, the medium defines an interface between the performing and consuming side; the information conveyed on modern digital medium is characterised by various properties, most importantly:
- sampling frequency, e.g. 32kHz for digital radio, 44.1kHz for compact discs, 48kHz for digital audio tape, or 96kHz or even 192kHz for high resolution audio;
- sample resolution, 16-bit for normal compact disc, 24-bit for high resolution audio;
- number of channels, mostly two, aka stereo,
- compression and Codex, if applicable.
Before delving into possible interpretations for high fidelity in this context, let’s have a quick look at both sides of the medium. There will be a signal chain transforming the performance spectrum Sp into the medium spectrum Sm, and then another chain transforming the latter to the reproduction spectrum Sr, whereas there are a few essential aspects for each link in both chains:
- the frequency response where every frequency component in the input signal is subject to a change in amplitude and phase imparted onto the output signal, i.e. every frequency present is attenuated or amplified and delayed; ideally, the frequency response should be constant over the frequency range contained, i.e. flat frequency response;
- the total harmonic distortion (THD) where a signal at a given frequency produces artefacts and images onto other frequencies (harmonics), mostly due to non-linearities such as saturation; ideally, there should be none, or at least to an inaudible degree;
- noise at every stage where conceptionally noise is added to the input signal with a signal to noise ratio (SNR); sometimes the noise figure is given together with the harmonic distortion as THD+N.
The view above shows a simplified, linear chain from performance spectrum over the medium spectrum to the reproduced spectrum. In reality, this transformation is fraught with some feedback looks as explained in the following article.
My objective in the following parts is to quantify the frequency response and harmonic distortion in every link and identify the weakest link, i.e. the one that will influence the overall transfer behaviour most and needs to be addressed. The weakest link will determine the level of fidelity in the chain; the composer — performer — medium — listener path is mostly about reproduction fidelity.
