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volume 15
august 2012

On the perception of the tonal centre in an ambiguous tonal environment


  The case of Prog-Rock
by Filip Tailor Krejčí
  Song-writers working in the genre of Prog-Rock often excel in creating ambiguous tonal environments where the tonal centre is kept volatile for some length or may repeatedly shift within the space of a only few measures. Do their listeners affirm and perceive these transformations of the tonal centre, and, if so, to which extent? To answer this question Filip Tailor here presents the results of an empirical study in the field of tonal perception.
1 Right: Cover of the Genesis' album Nursery Cryme (1971)

Introduction. The Czech Republic can rely on a long tradition of empirical research in music psychology. In particular J. Luska, M. Franěk, J. Volek and F. Lýsek made significant contributions to the field. The foundations for their studies were laid earlier on by the work of Karel Janeček. It is theirs, and most importantly Janeček's, research that gave rise to the research project at hand at the Music Education Department of the Faculty of Education at the Palacký University of Olomouc. This project not only continues investigating their former findings, but also applies generally described principles of tonal perception to a style of music that up until now has not been explored very well — i.e. Progressive Rock, which is a subgenre of Rock, and as such belongs to the sphere of popular music.

  The target of the current project is an empirical exploration of the quality of tonal perception. Tonality is a matter which is very hard to grasp, especially in respect to individual perception. Already Janeček in his work Základy moderní harmonie (1965) defined the presence of a tonal centre in a composition as the subject of change. The tonal centre, he argued, could be established in a satisfactory or an unsatisfactory way, and could, to some extent, be left open or half-open. A description like this leaves us with a certain vagueness, subjectivity, and even a notion of immeasurableness.
  In the same work Janeček also described the so-called "principle of the clear tonic" which he defines as follows: "A harmonic progression is naturally inclined to a closing consonant tonic provided it is not disrupted by any unabrogated harmonic or tonal imaginary tones, nor by imaginary tones that stand in a tritonic relation to the final tonic." The caveat in this statement implies that the perception of a tonal centre does not merely depend on the direct harmonic characteristics of a composition by themselves. The way we perceive a tonal centre is also determined by many other factors like, for example, interfering imaginary tones. If so, we should also ask whether, in a composition, there are any other factors in play influencing the listener's tonal perception, like latent harmony, melodics, or even the kinetic drive of the musical material and the applied musical patterns. It is this question which will be a focal point for our research.
  Our main objective is therefore an exploration of the way listeners perceive changes in the tonal centre within a composition. We decided to locate this question in the context of some tonally advanced compositional works of authors of the Progressive and Art Rock scene. "Prog-Rock" — the short name by which the genre usually goes — seems a good fit for the job. In fact, right from its start in the late 1960s, the musical practice of Prog-Rock deliberately parted with the paradigm that up until then was held generally valid within the field of rock music. Instead of keeping up with the values and feelings of spontaneity and improvisation (Fukac & Polednák, 2009), it decided to reinstate the "old" or "classical" approach and to return the musical experience to its aesthetically communicative musical value.
  The genre of Prog-Rock openly advocated the standards of artificial music — a fact, demonstrated not only by its numerous quotations of more or less famous music pieces, but also by the way it sought its inspiration in the compositional approach. One of the basic artificial composing principles is traditional motivic and thematic based work. Hence a compositional method which Janeček (1968) often described as a concentrated and well-disciplined flow of musical thoughts mainly using the principle of alliance and the principle of contrast. A compositional method too, which generates tonal ambiguity.
  The phenomenon of tonal ambiguity is not a common feature of the musical material of rock music. On the contrary, in this respect and seen the global context of rock music, Prog-Rock may well be an exception. However, as yet, Prog-Rock has not been the subject of much scientific research. One of the added objectives of this project, therefore, was to fill in this gap, at least partially, by analysing a small number of song fragments of Prog-Rock on the way they treat musical harmony and let their listeners perceive the tonal centre.
2 Left: Cover of the Genesis' album Foxtrot (1972)

Method. For the study five audio-samples of about 40 seconds length each were carefully selected as to provide the phenomenon of the changing tonal centre which is being explored in this project. In most cases the song fragments were diatonical — there were no signs of bitonality or atonality. Four song fragments were catered for by songs of the group Genesis, which in the heydays of Prog-Rock build their compositions around an extremely colourful tonal structure. The four selected song fragments are distilled from "Can-Utility And The Coastliners" (21 measures) from the album Foxtrot (1972), "Firth Of Fifth" (18 measures) from the album Selling England By The Pound (1974), "Seven Stones" (15 measures) from the album Nursery Cryme (1971) and "Supper's Ready" (18 measures) from the album Foxtrot (1972). Next to these songs a track of Mike Oldfield was chosen: "When The Night's On Fire" (18 measures) from the album Islands (1987). This fifth fragment was selected because, from a harmonic perspective, it shows a completely linear development.

  Next, the audio-samples were analysed on harmonic cutting points. These cuts were selected by the researcher on basis of a detailed harmonic analysis of the selected song fragments. There were two criteria according to which these cuts (stops) were made. The first criterion aimed at defining spots that would be as tonally indefinite as possible. Cuts were made in spots where modulation, skewing, or a momentary tonal nebulosity took place. Consequently the amount and positions of cuts differed between the five audio samples. These cuts were made according to, what we may call, musical time (Janeček, 1968)). The second criterion, on the other hand, was firmly rooted in real-world time (ibid.) — to this end each sample was cut into parts of ten seconds length independent of the fact what was happening on a substantive level. Using real-world time the cut could even be made right in the middle or at the end of a measure.
  The data collection took on a stepwise design. After some clear and exact instructions, each respondent had to rate the cuts in the audio-samples. To this end the samples were paused at each subsequent cut at which step the respondent was asked to reproduce (whistle, sing — not play) the tone which s/he at that moment considered to be the tonal centre. The spot where the music was paused was gradually moving towards the end of the examined song fragment. After finishing a sample, the respondents continued with the next one. This way, all respondents rated all five audio-samples successively from the very beginning to the end.
  The whole research was carried out in two phases — in the first phase the respondents rated the subsequent cuts in the audio-samples made according to musical time and in the second phase they rated the cuts made according to real-world time. This implies that the second phase had a rather verifying nature. It tests whether the data collected in the phase of musical time correspond to the data which do not respect the music material. Said otherwise, the second phase to certain extent checks whether the data collected on the basis of musical time are in any way biased by the previous harmonic analysis.
  The stepwise design in combination with the tonally complicated subject matter, makes rating the cuts a very difficult, almost impossible task for people without any musical skills and experience. For this reason only professional musicians, students of the Music Education Department, or other musically active people (conductors, chorus masters, advanced jazz pianists, opera accompanists, soloists or chorister opera singers, orchestral instrumentalists, or musical education lectors) were asked to participate. All in all about 25 respondents participated in the research.
  For the coding of the ratings, the key of C major was represented by the number zero, increased by one for each added ♯ to the key signature or decreased by one for each added ♭ to the key signature. To present the results, we computed the running average of these scores for both phases of each fragment.
3 Right: Cover of the Genesis' album Selling England by the Pound (1974)

Results. Below we offer a graphical presentation of our results. For each song fragment we first discuss the "real" or rather the "most logical" harmonic interpretation of the song fragment as made by the researcher. This interpration is indicated in each graph by the blue curve. The steeper and faster the modulation, the steeper and faster also the curve will be. And vice versa, if the modulation is gradual, the curve will be gradual too. By the time a new tonic is clearly defined, the curve will settle on the number corresponding to the key signature of the new tonic. Next, we present the outcomes for the ratings according to musical time, directly followed by the ratings according to real-world time. These are indicated by the black curves in each graph, presenting the running average of the respondents' ratings. As mentioned above, for the charts presenting the outcomes of the second phase the cuts correspond to ten second segments. In the charts, however, we will hold to the unit of one measure on the x-axis, so that the chart is more transparent and the results are more easily to compare with those of the first phase of our research.

3.1 Genesis: "Can-Utility And The Coastliners" (1972). Chart 1a presents the outcomes of the first phase for the song fragment of "Can-Utility And The Coastliners." In this fragment seven cuts were made by the researcher in measures 4, 6, 8, 10, 11, 15 and 20 respectively.
  Chart 1a: Perception of the tonal centre according to musical time in "Can-Utility And The Coastliners"
  Looking at the blue curve, we see that the song fragment starts with a clearly defined key in B major, which already in measure 4 diverts into F major. In measure 6 it returns for a while to B major. Next, in measure 8 a modulation takes place which in measure 10 leads into D major. D major stays on until measure 17 where the tone centre again returns to the original key of B major.
  The black curve shows that, by and large, the respondents succeed quite well in following the tonal transformations. The respondents do overlook the dive into F major, though, between measure 4 and 6. Remarkable too is the slight delay in the way the respondents pick up a new tonal centre between measure 8 and 12. No less striking is the fact that, at the end of the fragment, the respondents are quick to notice the return to the initial key.
  Chart 1b: Perception of the tonal centre according to real-world time in "Can-Utility And The Coastliners"
  Chart 1b presents the outcomes of the second phase for the same song fragment. Now cuts were made every ten seconds, corresponding to measures 3, 11, 17 and 21. The black curve, illustrating the development in the second phase, basically confirms our findings of the first phase. The main difference is located in the first twelve measures. Due to the fact that the first cut (in measure 3) happened to be made in the middle of the modulation from B major to F major, the respondents were exposed to very subjective ways of answering. Most of them choose to stay with the original key of B major — with value 5 (B major). Quite a few others rated -2 (D minor).
3.2 Genesis: "Firth Of Fifth" (1974). Chart 2a presents the outcomes of the first phase for the song fragment of "Firth Of Fifth." In this fragment four cuts were made by the researcher in measures 5, 9, 13 and 17 respectively.
  Chart 2a: Perception of the tonal centre according to musical time in "Firth Of Fifth"
  Like the first one, this song fragment starts in the key of B major. However, already in measure 2 we can hear an A6/9 chord, which in this context is foreign to the key. It slightly warps the tonic. This phenomenon, though, was only marked as a partial aberration because it is directly followed by a combination of the dominant and the tonic, directing the key back to B major. Next, in measure 5, the tonic becomes the dominant of the following key of E major, which in turn preserves its position until measure 10. Here a slow sliding of the tonal centre over the circle of fifths occurs. In measure 13 this motion finally lands in G major, leaving us with a tonic which is, however, very unstable. After two consecutive diminished chords — G♯halfdim and A♯dim — the tonal centre finally returns to the initial B major.
  Again the respondents prove to be quite able in keeping track of the tonal centre. What sticks out in this fragment, when looking at the black curve, is the fact that the respondents in times of uncertainty (measures 5-10) seem to cling to the initial key. Remarkable, again, is the quick respons to the return of the initial key.
  Chart 2b: Perception of the tonal centre according to real-world time in "Firth Of Fifth"
  Chart 2b presents the outcomes of the second phase for this song fragment. Cuts were made every ten seconds which corresponds to the measures 5, 9 and 16. In this fragment especially measure 16 is worth noticing, showing that none of the respondents took notice of the temporary aberration into the relatively distant key of G major. On the other hand, the return into the original key of B major at the end, though only sounding for a very short period of time, was noticed by everybody and even anticipated by some of them.
3.3 Genesis: "Seven Stones" (1971). Chart 3a presents the outcomes of the first phase for the song fragment of "Seven Stones." In this fragment six cuts were made by the researcher in measures 5, 7, 9, 11, 12 and 14 respectively.
  Chart 3a: Perception of the tonal centre according to musical time in "Seven Stones"
  The third song fragment, spanning fifteen measures, starts with a clearly defined key in G major. In measure 4 tonality very slowly begins to temper into B major by means of several chromatic joints. The pleasant feeling furnished by the key B major is, however, already soon disturbed by a minor dominant, which is illustrated by the slow aberration of the curve in measure 7. From measure 8 to 10 the key stabilises in B major. Yet, in measure 10 it, again, slowly begins to deviate thanks to the common chords of related keys (E♭ major) into keys with greater number of lowered tones. It then settles in the key of A♭ major for one measure. In the end the tonal centre returns to B♭ major.
  The black curve in chart 3a shows that the respondents, again with a small delay, are quite capable in keeping track of the changing tonal centre.
  Chart 3b: Perception of the tonal centre according to real-world time in "Seven Stones"
  Chart 3b presents the outcomes of the second phase for the same song fragment. Cuts were made every ten seconds, corresponding to measures 3, 5, 8, 11 and 14. The curve confirms the pattern seen in the first phase. Although tonally very colourful, this song fragment all in all proved to be quite distinguishable. For that reason the black curve more or less matches the blue one. The chart further illustrates a phenomenon, that is also visible in the previous charts: there seems to be a general tendency in the ratings to displace key changes by levelling them down, as here between the cutting points at measures 3 and 8 and between the cutting points at measures 11 and 14.
3.4 Genesis: "Supper's Ready" (1972). Chart 4a presents the outcomes of the first phase for the song fragment of "Supper's Ready." In this fragment six cuts were made by the researcher in measures 4, 8, 13, 14, 16 and 18 respectively.
  Chart 4a: Perception of the tonal centre according to musical time in "Supper's Ready"
  The fourth song fragment probably offered the most difficult and complicated task in this exercise in tonal analysis. The fragment offers the respondents amply space for ambiguous harmonic interpretation. This was the very reason why we have embodied the fragment into our research. The respondents proved to be quite uncertain in their answers. Many answers were even incorrect. Nevertheless, in particular the most musically experienced responded in accordance with the ascertained findings. Remarkable again, is the delay with which the respondents seem to follow the steep curves of the tonal material.
  Chart 4b: Perception of the tonal centre according to real-world time in "Supper's Ready"
  Chart 4b presents the outcomes of the second phase for the same song fragment. Cuts were made every ten seconds which corresponds to the measures 4, 9 and 15. The resulting curve of this second phase, again, by and large coincides with the curve of the first phase.
3.5 Mike Oldfield: "When The Night's On Fire" (1987). Chart 5a presents the outcomes of the first phase for the song fragment of "When The Night's On Fire." In this fragment all in all nine cuts were made by the researcher always after two measures.
  Chart 5a: Perception of the tonal centre according to musical time in "When The Night's On Fire"
  This excerpt is specific in as far the tonal development proceeds exactly over the circle of fifths, each step always a quarter higher (thus always with one added ♯ in the key signature). The fragment starts in F major, continues in pace of one modulation per two measures and finishes in the sixteenth measure in the key of F♯ major. The evident linearity of modulation provided the main reason for including this song fragment into our survey. With this fragment the respondents were given a clear and unmistakeable tonal development. So if there are any deviations in the collected data, they can not possibly be blamed on the tonal ambiguousness of the song; these deviations have to be caused by the influence of other musical elements (melody, kinetic elements) or constituents (dynamics) or other factors (e.g. imaginary tones). Indeed, in the course of the song fragment, the sound of the guitar changes its effects and at least two melodic lines develop.
  The ratings, as shown by the black curve, indeed, show an irregularity – between measure 7 and 9 the respondents caught up the ongoing delay in determining the key. At these points they correctly rated the keys of D major, repectively A major. This shows that even in the case of a clearly linear harmonic development, tonal perception not necessarily does need to follow track. Tonal perception, so it seems, may be influenced by other factors. In this case the respondents were probably influenced by an interplay of melodies.
  Chart 5b: Perception of the tonal centre according to real-world time in "When The Night's On Fire"
  Chart 5b presents the outcomes of the second phase for the song fragment of "When The Night's On Fire." Cuts were made every ten seconds which corresponds to the measures 5, 9 and 15. The chart asserts the finding from the first phase.
4 Left: Cover of Mike Oldfield's album Islands (1987)

Conclusions and discussion. Having presented our data, now we will summarise our main findings. All findings are evident from all the presented charts. However, some findings are more evident in some charts than in others and that is why, in the following numbered list, we will refer to specific charts as the most illustrating cases.

(1) The human brain is probably able to analyse the key correctly — be it with a little delay — which is apparent from all the charts; see for instance chart 3a as a rather salient example.

(2) The human brain clings for a long time to the key it hears as the initial one even in the case that it has been exposed to it for only a short time. On the other hand, it takes quite long until it accepts a new key. This finding is more or less evident in all presented charts. The best example probably is chart 2a where even in measure 9 respondents still kept to the key of B major, even though the key of E major was already harmonically established and present for a long time.

  (3) On the other hand, the brain picks up a return to the original key almost immediately. In chart 1a only two measures (18, 19) were necessary to let all the respondents recognise the original key of B major.
  (4) The human brain has a global tendency to displace any key changes. It basically endeavours to perform a tonal levelling. This finding is most evident in charts 1b and 2b where the black curve kind of tries to obliterate any tonal changes. This is also apparent from chart 1a where the tonal centre already in the second measure shifts from the key of B major to the key of F major — the most remote keys on the circle of fifths. None of the respondents — even the most skilled ones — were, however, able to recognise such aberration.
  (5) It seems that tonal perception is significantly influenced by all musical elements — i.e. not only harmonic, but also melodic and kinetic elements — and constituents (e.g. dynamics). Of this chart 5a offers an excellent example.
  Given the exploratory character of this research project, these findings are tentative — even more so because we had to make some difficult decisions during the process of data collection. The most complicated, probably, was to decide how to approach incorrect answers. During the playback of the song fragments the respondents made numerous mistakes. Often they were uncertain and, in case of complete and utter confusion, they even took refuge in choosing their answers randomly. These answers were treated as missing values. In several cases, however, we witnessed answers that could be regarded as "interesting." These, for example, concerned parallel keys. Or, the answer sort of reflected a previous established key or anticipated its return. Such results were included into the data set. It proved to be rather difficult, though, to discriminate between "random" and "interesting" answers. Our charts, therefore, should be taken only as visual illustrations with a limited validity. Nevertheless, the findings summarised in our conclusions were so evident that even with regard to the exploratory nature of our research, they may offer a well-grounded and encouraging starting point for further study.

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  This project was realised thanks to the financial support of the Specific Research of the Palacký University Olomouc (Project number PdF_2011_006). Comments and questions can be send to Filip Tailor at the Music Education Department, Faculty of Education, of the Palacký University Olomouc, The Czech Republic.
  The short song fragments on this page are copyrighted. They are used here according to the rules of fair use and academic quoting. The fragment of "Can-Utility And The Coastliners" (0:42 min.) can be found on the album Foxtrot (1972 © Charisma Records), the fragment of "Seven Stones" (0:52 min.) on the album Nursery Cryme (1971 © Charisma Records), and the fragment of "When The Night's On Fire" (0:36 min.) on the album Islands (1987 © Virgin).
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