Mechanisms of absolute pitch: I. Acoustical beating

Abstract

Musicologists and philosophers have commonly attributed distinctive qualities to individual musical pitches, and absolute pitch (AP) possessors recognize and recall notes and keys with immediacy and accuracy, leaving little doubt that they are aware of such characteristics. Bachem proposed that these distinct tonal qualities underlie the rapid and accurate judgments that he identified as genuine AP, and he defined the qualities as tone chroma (TC). The TCs of notes and keys, and of notes separated by a musical octave (pitch class) are frequently expressed in visual terms, and studies of synaesthesia, the association of intersensory stimuli, provide clues to the systematic variation of TC qualities. The historical literature relating to note and key characteristics is commonly overlooked in the study of AP, however, and the article seeks to address this problem. Long-standing conclusions are reviewed, leading to the hypothesis that TC sensitivity can derive from an awareness of variations in the acoustical beats that occur in the tuning of instruments to equal temperament and which are perceived with particular clarity in organ tuning. This acoustical hypothesis is supported by modern neuroscientific findings and was predicted by theoretical observations in the literature as long ago as three centuries. In a follow-up article, Thurlow and Baggaley discuss the role of synaesthesia-type judgments in musical skills not previously regarded as absolute: for example, a perfect touch capacity observed in keyboard players.

The idea that individual musical notes and keys have distinctive characteristics has been debated for millennia. Plato and Aristotle wrote about qualities associated with the Greek modes, the seven arrangements of tones and semitones in the musical octave (Steblin, 1996). Plato argued against the use of five of these modes owing to their allegedly weak and immoral qualities, which he considered likely to endanger “the whole fabric of society” (Welty, 1973, p. 281). The Pythagoreans went into detail about color associations between musical notes and colors (Hall, 2010), and Newton, in Opticks (1704), presented a color wheel indicating a direct correspondence between the color spectrum and the Greek Dorian mode. As Babbit (1878) noted, however, these ancient theories shared no fixed consensus of opinion about modal characteristics in general, being based on different and often arbitrary rationales, some political and geographical, others aesthetic and emotional. Only two of the original Greek modes remain in common usage in today’s Western music—the Ionian, corresponding to the major key, and the Aeolian mode or minor key. Plato would hardly approve of this outcome, for to him the Ionian mode denoted sloth and drunkenness rather than the generally upbeat qualities associated with it in Western music today (Monro, 2020).

Individual notes and keys began to be identified with specific pitches in the 18th century. The invention of the tuning fork by the British musician John Shore in 1711 (Watkins Shaw, 2004) brought a new level of consistency to pitch naming and identification, and the Stuttgart Congress of Physicists’ 1834 decision to adopt A above middle C, tuned to 440 cycles per second, as the central reference point for concert pitch tuning established that notes and keys could henceforward be tuned to consistent frequencies throughout the audible range (Hollander, 2015). Today, there is still incomplete consistency in this, with the A440 concert pitch existing alongside the A415 standard of Baroque music and A466 in German church music (Chorton pitch), and the idea that each note and key can have a distinctive, consistent, and widely shared quality is commonly denied.

A further argument against the key characteristics notion arose from the 17th-century adoption of the equal temperament (ET) tuning system (Clark, 2013), replacing the traditional just intonation system that allows fixed-pitch instruments (e.g., the piano) to play satisfactorily in one key only. ET tuning overcomes the limitation of instruments to a single key by deliberately mistuning their notes and distributing the tuning errors among them. In the view of theorists including von Helmholtz (1863) and Külpe (1901), this eradicates all distinctive characteristics perceived in the keys except those relating to their structural composition (e.g., major or minor). The current article counters this conclusion, citing historical observations that ET tuning is fallible and involves errors that accumulate systematically as the tuner proceeds around the musical circle of fifths. The article proposes that this build-up of tuning error causes different musical notes and keys to obtain characteristic qualities, and that the influential view expressed by von Helmholtz fails to account for a major anomaly of musical psychology: absolute pitch (AP, or perfect pitch).

AP and tone chroma

AP, as is well known among musicians, is the rare ability to identify a note or key instantly and without apparent use of a reference note (Bachem, 1937; Baggaley, 1974; Levitin, 2019). Reports of AP date from the same 17th-century period as the European adoption of ET. Notable composers of that era considered to have AP were Bach and Handel, and subsequently Mozart, Beethoven, and Chopin (Deutsch, 2002). The phenomenon has been documented in the scientific literature for over a century (Abraham, 1901; Stumpf, 1883), although opportunities to study it formally have been limited in view of its rarity. In the Western population, the incidence of AP is commonly cited as 1:10,000, an estimate that has not been confirmed empirically (Levitin, 2019). Contrary estimates have been wide-ranging. For example, based on a survey of 1,156 professional musicians, Sergeant and Roche (1973) concluded that AP manifests in early childhood with an incidence in musicians of approximately 7:100, and the increasing evidence for AP’s early learning is discussed by Miyazaki and Ogawa (2006), Deutsch (2013), and Levitin (2019). Carden and Cline (2019) indicate that the inconsistency of AP incidence estimates is due in large measure to the wide range of cultural and musical sub-groups on which they have been based.

As in the discussion of key characteristics, academic views about the nature and origins of AP have been contentious. Meyer (1899) argued that AP is merely a well-practiced relative pitch ability, a view preserved to this day by commercial interests such as Musical-U.com (2021a, 2021b) that claim to be able to train AP in adulthood. Particular confusion concerns whether or not AP’s development requires the ability to identify notes/keys by name, as discussed by Levitin and Zatorre (2003) and Rogenmoser et al. (2015). While accurate pitch naming facilitates the ability to communicate and verify AP possession, however, this does not necessarily identify pitch naming as the actual mechanism on which AP sensitivity is based (Schellenberg & Trehub, 2003). Pitch recognition and recall tasks can each be designed to dispense with the need for pitch naming, as when a subject is presented with an unnamed recorded note and successfully reproduces it on an instrument (recognition). Recall tasks can avoid a pitch naming requirement similarly, as when a subject is asked to sing a popular tune and does so in its usual key. High levels of accuracy in the latter task have been found among AP and non-AP musicians alike (Levitin, 1994; Terhardt & Seewann, 1983). Commonly referred to as the Levitin effect, this finding suggests that AP can be latent in individuals who are unaware of it, and Levitin (2019) acknowledges that this latency indicates the possession of cortical “representations of pitch that are more stable and accurate than previously recognised” (p. 372). Such cortical representations may enable AP judgments with or without the assistance of pitch naming, and a substantial body of opinion supports the view that AP is facilitated by an internal template of memorized and distinctive pitch sensations of this type (Bachem, 1937, 1948, 1950, 1955; Baggaley, 1974; Frieler et al., 2013; Ward, 1963; Ward & Burns, 1982). A detailed comparison of the nature/nurture views of AP is provided by Steblin (1987).

In general, however, the AP phenomenon still raises the question: if ET tuning has eradicated the existence of note/key characteristics as suggested by von Helmholtz (1863), what is the physical property in notes and keys that many AP possessors memorize and are able to recognize instantly and accurately? Bachem (1937), in proposing a taxonomy of AP types, reasoned that immediate and accurate pitch judgments indicate a genuine AP capacity facilitated by rapid comparisons of incoming pitches with memorized tonal sensations on two dimensions, tone height (TH) and tone chroma (TC). Pitch identifications resembling AP but actually based on relative pitch judgments were labeled in Bachem’s taxonomy as quasi-AP. Use of the term genuine AP in the article from this point onward refers to Bachem’s definition of the AP capacity that enables instant and accurate judgments without the use of relative pitch judgments. His two-dimensional analysis of pitch sensation was supported by Shepard (1964). Bachem (1948) also proposed the notion of chroma fixation to illustrate the fading of TC toward the extremes of the audible range. He did not intend the TC term to imply that incoming musical stimuli necessarily generate physical sensations of color, and as an AP possessor himself, he made no claim to perceive pitch in colored terms.

Other musicians frequently describe the qualities of notes and keys in colored terms, however (Ishiguro, 2010; Steblin, 1996). Cross-modal associations of this type are known as synaesthesia (Millet, 1892), from the Greek term sun-aisthesis describing the “feeling together” of the senses. McKellar (1968) considered synaesthetic reports of tone/color associations that are not physically experienced to be uses of metaphor, and a similar view has been expressed by Nikolić (2009) in proposing the concept of ideaesthesia whereby intersensory qualities are associated with the qualities associated with a stimulus rather than being triggered by the stimulus directly. Synaesthetic sensations may be induced indirectly in this way in some individuals and by direct sensory stimulation in others, as in the wide spectrum of possible synaesthesia rationales discussed by Curwen (2020). The TH quality of a given note/key as it recurs at different octave levels is referred to in the current literature as its pitch class (Temperley & Marvin, 2008).

A range of studies has considered whether tone/color synaesthesias can be consistent and shared. Carroll and Greenberg (1961) reported that they shared color associations with notes and keys that varied systematically around the musical circle of fifths (i.e., the cyclic progression of the diatonic notes/keys by intervals of a fifth, returning to their starting point after passing through the 12 items in turn), and they felt that their awareness of these qualities underlaid their AP abilities. The composer Alexander Scriabin also based his work on synaesthetic key characteristics varying systematically around the circle of fifths (Myers, 1914), and the same trend was observed in an analysis of 80 historical reports of tone/color synaesthesia by Baggaley (1972) involving 630 tone/color associations. Baggaley noted a statistically significant consensus in relation to associations between the 12 major keys and yellow/blue and found an extremely high consistency between the two trends when the colors were quantified on a brightness scale from yellow (bright) to blue (dark). This brightness trend occurred in the reports of the AP and non-AP possessors alike and was confirmed by Fourier analysis as varying systematically around the musical circle of fifths. The view that pitch–color associations are based on corresponding perceptions of auditory and visual brightness had previously been proposed by Drobisch (1852) and von Hornbostel (1927), and the primary role of brightness in cross-modal associations generally was later stressed by Marks (1978). More recently, the synaesthetic associations of AP possessors have been examined by Petrović et al. (2012), and many of the tone/color associations reported in their study are the same as those observed by Baggaley (1972). Studies using other rationales for tone/color associations (e.g., non-brightness rationales and incomplete sets of notes/keys) have reported different associations. Extensive current reviews of the AP and synaesthesia literature, including studies of their genetic and cultural determinants, are provided by Baggaley and James (2020, pp. 23–58) and Glasser (2021).

Tone chroma and ET tuning

The repeated observation of brightness qualities in note/key associations, and their trends in relation to the musical circle of fifths, suggest that TC may have an acoustical basis. A few months before the publication of Bachem’s initial 1937 article about AP, the physicist Herrenden Harker (1937) published conclusions in the same journal suggesting that the distinctive characteristics of musical notes/keys were not eradicated by the adoption of ET tuning as argued by von Helmholtz (1863) but may actually have been created by it. Harker suggested that the long-standing goal of tuning to ET to render all musical intervals precisely the same is rarely if ever achieved. He pointed out that tuning practices from the Renaissance onward make the questionable assumption that the tuner is capable of subtle judgments of pitch that are significantly beyond the human ear’s capability, and that even a first-class tuner is unlikely to achieve more than an approximation to ET. In this, Harker was echoing the 18th-century composer de Laborde (1780), who went further by suggesting that, for the trained musical ear, even a small level of mistuning between notes separated by a third or fifth interval can give individual keys a distinctive quality. De Laborde, in turn, was echoing the suggestion by Rameau (1722) and D’Alembert (1752) that variable acoustical beating sensations originate in the harmonic overtones of notes and keys (Plomp, 1967; Roederer, 2008) and the statement by an even earlier theorist, Johann Mattheson (1719), that “even though ET should be introduced everywhere today through royal ordination, one does not have to fear that one key will sound like every other key and nothing be gained thereby” (Mattheson, 1719, p. 101). Steblin (1987) observes that Mattheson’s statement of 300 years ago “reads like a description of tone chroma” (p. 149).

Keyboard tuners are well aware that errors accumulate during ET tuning, and they have a standard procedure for minimizing it: that is, deliberately mistuning the notes according to assessments of the frequency of the acoustical beats that it emits when in near-perfect consonance with notes separated from it by the interval of a fourth or fifth (Plomp, 1967; Roederer, 2008). Tuning instruments to ET traditionally begins at the A440 above middle C with the tuning of notes separated from it by the interval of a fifth (i.e., D below and/or E above). After each interval has been tuned to perfect consonance, it is slightly mistuned until a pulsing sound is heard, described by Plomp as second-order beating, distinguishing it from the first-order beats that occur between mistuned notes in almost perfect unison. (Descriptions and audio illustrations of first- and second-order acoustical beats are provided by Stanford University’s Correlogram project, 2019.) The notes separated by a fifth from the D and/or E are then tuned in the same way, and the procedure continues around the musical circle of fifths until all the notes in the central TH range have been (mis)tuned and the errors, to the limits of the tuner’s ability, equally distributed among them. At this point, the notes in the high and lower ranges are tuned to perfect consonance with their equivalent mistuned notes in the central range. As de Laborde (1780) and Herrenden Harker (1937) indicated, however, the precisely equal tuning of all intervals requires judgments of which even the best tuners may be incapable.

While the assessment of beating rates during ET tuning minimizes the error build-up, it is therefore unlikely to cancel it completely. If the tuner proceeds consistently in one direction around the full circle of fifths, an appreciable amount of error is likely to be found in the form of a clash between the initial A440 and the new A generated along the way. Tuners commonly avoid this build-up of tuning error and of the second-order beats relating to it by proceeding in one direction as far as the circle’s midpoint (E flat) and then returning to the A440 starting point to tune the remaining notes in the other direction. When the process is complete, the second-order beating rates between the E flat at the circle’s midpoint and both of its neighboring fifths (A flat and B flat) are likely to be comparable. On this basis, the tuning errors and their associated second-order beats can be predicted to increase around the circle of fifths as far as the E flat midpoint, with the slowest beating occurring among the D, A, and E notes and the fastest in the A flat, E flat, and B flat range.

Modern musicology is beginning to confirm the connection between acoustical beating, temperament, and key characteristics. Francis (2005), for example, has provided calculations of the acoustical beats arising from Johann Sebastian Bach’s use of various temperament systems. He indicates that Bach selected particular temperaments for the performance of specific works based on “an explicit decision to adopt an unequal beating temperament with the consequence that each key has its own colour” (Francis, 2005, p. 2). The possibility therefore arises that awareness of ET tuning errors as they vary around the circle of fifths can underlie TC perception and the AP judgments that it enables. This notion is consistent with the conclusion of theorists since Bachem (1937) that AP is facilitated by an internal cortical template of distinctive TC sensations memorized in a logical series. Block (1983) noted the particular readiness of AP possessors to attribute distinctive qualities to organ notes and the greater consistency of their associations compared with those of musicians who base them on relative pitch judgments. Pianists are normally unaware of the acoustical beats that occur between notes owing to the fact that a piano note decays rapidly within a few seconds of striking the note’s string. A note emitted by an organ pipe, however, persists for as long as its key is depressed and provides clear and continual evidence of the harmonic beats generated by the pipe in its mistuned consonances with other pipes. For the purpose of illustration, the next section provides a detailed look at the mechanics of the organ tuning process.

Acoustical beating in organ tuning

Each pipe on an organ produces a single note via either a flue stop or a reed stop. In flue stops, the sound is produced by the pipe itself as in a recorder, while in reed stops (oboe, clarinet, trumpet, and other quasi-orchestral timbres), it is made by air setting a (brass) reed into vibration, with the pipe above acting purely as a resonator. Reed pipes work like a clarinet, although the reed is housed inside what is termed the boot of the pipe rather than externally as on a clarinet mouthpiece. Flue pipes generally remain fairly true in pitch, whereas the pipes of reed stops are notably less stable. Pipe organs are usually professionally tuned at regular intervals, but reed pipes can go badly out of tune between the tuner’s visits. When this happens, as in a cathedral where the instrument is in daily public use, the organist has the difficult choice of whether to continue using the out-of-tune notes or to avoid using them altogether until they have been attended to during the tuner’s next visit. An alternative is for the organist to tune the pipe, although while this is a common practice in mainland Europe it is often not encouraged by organ builders in Britain.

The co-author A.T., during his career as the organist of Chichester Cathedral, conducted a weekly tuning process to ensure that any pipe which had deviated to a noticeable degree from its ET pitch was restored to its intended tuning. The moderate-sized Chichester organ has 3,667 pipes and adjusting them requires the tuner to go inside the body of the organ, to climb ladders to the first or second stage of the building frame, and then to regulate each pipe individually. The tuning of a reed pipe is effected by tapping a rigid steel wire called the tuning spring upward or downward with a flat-ended metal rod known as a reed knife. The tuning spring passes vertically through the roof of the boot of the pipe, having its lower end within the boot and its upper end outside it. Both ends finish with a short section of the wire fashioned horizontally at right angles to the vertical. The horizontal bottom end of the spring inside the boot is held firmly across the surface of the reed, thus determining its vibrating length and consequent pitch. Rising vertically, the tuning spring then passes to the outside of the pipe through a hole of the exact diameter required in the top of the boot. The tuner uses the reed knife to tap the short horizontal end of the external section of the spring, an upward motion flattening the pitch and a downward one making it sharper.

If the tuner has no one at the console to hold each note down as the pipe is being tuned, this is a complex routine. First, on a different stop (usually a flue), A.T. would identify a pipe of the same pitch as the one to be adjusted, played from the same note on the keyboard and that was well in tune. He would then use the pointed end of a pencil to wedge the required note down on the keyboard. When the respective flue and reed stops were pulled out to initiate the sound, fast acoustical beating could immediately be heard between the two pipes that were producing marginally different pitches albeit intended to be in unison with each other. The next stage was to climb the internal ladders up to the soundboard on which the two pipes stand and to identify the location of the pipe to be tuned. A.T.’s practice was to start by tapping the tuning spring upward, flattening the pitch of the reed to around a tone below its target pitch, and then tapping it gently downward again, slowly raising the pitch until it reached a perfect unison consonance with the flue pipe that was sounding the required note. As happens on organs, both pipes had been sounding their notes continuously from the moment the key was wedged down at the console. Throughout the tuning process, the near-perfect consonances generated strong and fast (first-order) beats which, as they slowed in the approach to the point of complete consonance, were joined by a low-pitched buzzing sensation apparently generated within the ear (second-order beats) rather than externally. As the perfect consonance drew closer and the first-order beats slowed, the pitch of the second-order buzzing rose quickly and seemingly proportionately, both sensations disappearing when perfect consonance was attained. An illustration of the near-consonance points at which second-order beats emerge and disappear is given by Trulla et al. (2018, Figure 6), and estimations of beating rates are provided by Francis (2005): that is, one to two beats per second in perfect ET (p. 2) and up to five beats per second in non-ETs (p. 4).

At this point, the consonance was deliberately mistuned as in the ET tuning procedure on the piano and harpsichord (see previous section). During this final stage of the process, the first- and second-order beats were simultaneously audible and were available as a guide to the extent of the mistuning required. The flue pipe against which the reed pipe had been brought into consonance was sounding at the mistuned pitch that the professional tuner had assessed as indicating the ideal ET pitch for that interval. The task completed, and with the two notes still sounding, A.T. climbed back down the ladders, removed the wedge from the keyboard, and then repeated the procedure for the next note and pipe on his list. He might typically retune 10 or 12 pipes in each weekly session.

To the best of our knowledge, the prediction that the second-order acoustical beats generated in ET tuning vary systematically around the circle of fifths has not been confirmed empirically. Baggaley (1972) tested it in theory by applying the stochastic (random) drift principle of probability statistics to determine whether tuning error and beating rates are likely to vary systematically in relation to individual notes and keys, and he observed that they can be predicted to wax and wane around the musical circle of fifths in a logical linear fashion. The lowest levels of beating in this trend were found to be associated with the musical keys having the brightest synaesthetic qualities (see section “AP and tone chroma,” above) and the highest beating levels with notes/keys with the darkest associations. These observations support the hypothetical relationship between TC awareness and the perception of distinctive beating rates in the notes and keys generated by ET tuning. Baggaley (1972) proposed that the varying acoustical qualities generated during the tuning process are likely to be duplicated in each note and in the major key (tonality) identified with it owing to the identical beating rates that arise within the harmonic series of individual notes and in the third and fifth intervals of the corresponding key. (The terms note, tone, and key tend to be used interchangeably in the current article for this reason.) Baggaley (1974) reported laboratory evidence for this conclusion, indicating that AP possessors’ assessments of piano notes are usually the same as those of pure tones though are more instantaneous owing to their clearer harmonic beats. Similar results were obtained by Marvin and Brinkman (2000), with AP possessors’ judgments found related in different situations to key color and timbre, and with the fastest judgments made in identifications of the white keys on the piano keyboard as opposed to the black ones.

Conclusion

Based on conclusions in the literature dating back to the 18th century, it is proposed that the TC qualities reported by genuine AP possessors (Bachem, 1937, 1948, 1950, 1955) can arise from the second-order acoustical beats that accumulate around the musical circle of fifths in the tuning of musical instruments to ET. This acoustical hypothesis is consistent with observations about tuning error by Mattheson (1719), Rameau (1722), D’Alembert (1752), de Laborde (1780), and Herrenden Harker (1937) and with Plomp’s (1967) analysis of the second-order beats between mistuned consonances. The hypothesis counters the view expressed by von Helmholtz (1863) that ET has eradicated all distinctive note and key characteristics. With beating rates of less than 5 per second (Francis, 2005, p. 2), second-order beats are likely to occur in the low-frequency theta wave range found related to associative memory (Clouter et al., 2017; Elmer et al., 2015; Leipold et al., 2019). It is not supposed that acoustical beating is the only mechanism underlying AP sensitivity, nor that its hypothetical effects are exclusive to any one of the AP types defined in the classical literature by Bachem (1937) nor to any given area of the pitch identification continuum described by current researchers (Glasser, 2021; Leite et al., 2016). Part II of this article (Thurlow & Baggaley, 2022) places the acoustical beating hypothesis in the context of other physical rationales for TC, each of which may have synaesthetic effects that differ between individuals and from note to note/key to key.

The varying qualities of TC are confirmed by anecdotal and questionnaire reports of tone/color synaesthesia. Baggaley (1972) observed that tone/color associations quantified on a brightness scale follow a systematic trend containing the same high and low points as those noted in the calculation of random drift in ET tuning. He concluded that bright tonal qualities are associated with low beating levels and dark ones with high ones. The linkage between AP and synaesthesia is supported by modern neuroscience research. While non-AP pitch perception in AP is associated with the right side of the brain’s planum temporale area, AP processing is located separately on the left side (Deutsch, 2013; Keenan et al., 2001; Schlaug et al., 1995; Zatorre et al., 1998). AP possessors and synaesthetes exhibit enhanced activity in the superior temporal gyrus associated with auditory associations, suggesting that AP and synaesthesia are “two sides of the same coin” (Loui et al., 2012), a view confirmed by the observation that AP and music-related synaesthesia are related genetically (Gregersen et al., 2013).

It is concluded that the second-order acoustical beats underlying TC sensations occur within the harmonic series of individual notes, and specifically between the harmonics separated by the third and fifth intervals. The same levels of beating can be predicted to occur between (a) notes separated by the third and fifth intervals in the major triad of a given key and (b) the harmonics of the note or tone after which the key is named (the tonic). This explains the ability of genuine AP possessors to identify notes presented in isolation as well as in relation to beats occurring between multiple notes sounded simultaneously. It also accounts for the fact that AP possessors can identify individually sounded notes/keys without needing to compare them with others separated from them by a given interval. On this basis, genuine AP and TC perceptions underlying judgments of notes as well as keys can be described as arising from a high level of sensitivity to musical tonality. Whereas tonality variations are usually defined in terms of the structural characteristics of musical keys—for example, major versus minor (Dahlhaus, 1990)—the key characteristics created by second-order beating represent an added criterion for tonality (Bibby Preston, personal communication, 1971) of which only AP possessors and synaesthetes may be fully aware. As Glasser (2021) points out, studies to date have largely overlooked “aspects of music-induced forms of synaesthesia such as timbre, tonality and context. This may in part explain why the important gap of linking AP to synaesthesia has not to date been adequately explored” (p. 703).

The hypothetical connection between TC and acoustical beating can be explored empirically by the following procedures:

• (a) The random drift hypothesis predicting the accumulation of beats around the circle of fifths in ET tuning can be tested by identifying the precise frequencies and second-order beating rates generated by a sample of ET piano tuners. The frequencies may be measured by use of pitch recognition software available on standard cellphones, and the systematic progression of their cps levels around the circle of fifths may be checked by Fourier analysis. The build-up of error around the circle and the degree of mistuning for each note should be compared with those of tuners who use more up-to-date electronic methods. The findings should be compared with the conclusions by Reymore and Hansen (2020) that AP may occur in different, instrument-specific forms, and perceptions of acoustical beating and note/key characteristics based on the tuning of instruments to different non-ETs should be examined as per the research of Francis (2005).

• (b) The ability of AP and non-AP musicians to distinguish between varying levels of second-order beating should be compared to determine whether or not these perceptions are likely to underlie AP judgements.

• (c) In view of the observation by Block (1983) that AP possessors attribute more distinctive qualities to organ notes, these tests should be replicated with the help of a sample of organ tuners. To avoid influencing their tuning accuracy and that of tuners with whom they may be in contact, the participants in these samples should not be alerted to the studies’ acoustical hypotheses before or after their participation.

• (d) Ultimately, the conclusion that TC varies systematically around the musical circle of fifths should be tested in relation to the music of different cultures. The importance of this step is indicated by the high incidence of AP in non-Western cultures (Deutsch, 2013). The acoustical hypothesis offered for note/key characteristics in this article is not expected to be fulfilled in musical cultures that do not apply ET tuning. Jacoby et al. (2019) have opened up this field of study in their investigation of the pitch singing of the Tsimané people in the Bolivian Amazon. They observe that, unlike Western musicians, the Tsimané neither observe octave equivalence nor fixed positions for TCs within separate octaves. Whether or not musicians with this type of pitch sensitivity develop forms of AP should be checked. The cultural and biological reasons for different tuning temperaments may also help to explain the manner in which pitch sensitivity varies among AP and non-AP possessors in ET cultures.

The subjective analyses of pitch perception and synaesthesia by classical composers are also a potentially rich source of insights into these phenomena. The suggestion that Bach selected particular tuning temperaments for specific works based on the temperaments’ acoustical beating qualities (Francis, 2005) implies a dimension of musical perception which few musicians have probably ever perceived. Further studies of Bach’s rationale for connecting acoustical beating and temperament tuning, and of the glyph designs by which he appears to have encoded his tuning instructions (Sparschuh, 1999), may cast new light on the notion that acoustic beats generate characteristics recognized by at least one type of AP possessor. Unfortunately, researching these studies will be a bumpy ride, for both Sparschuh and Francis have been subjected to highly antagonistic comments in the musicological literature (Lehman, 2005–2014) in a manner similar to the way that explanations of AP have been dismissed by skeptics who are unequipped to test them against their own musical experiences.

The often denigrated artistic and theoretical contributions of the composer Alexander Scriabin to AP and synaesthesia studies merit particular re-evaluation. Scriabin’s music was totally dominated by his synaesthetic imagery, which he regarded as triggered by tonality characteristics of the notes and keys, and the continuum underlying the systematic key color characteristics that he reported a century ago was the circle of fifths (Baggaley, 2012; Myers, 1914). Each of these subjective conclusions by Scriabin is consistent with those of the current study. The mystical beliefs that he used to explain his synaesthesia, however, have caused his ideas to be dismissed during the past century as suspect and fanciful. Dann (1998), for example, claims that there is no evidence that Scriabin was a genuine synaesthete, and that his color associations follow the circle of fifths “too neatly . . . No true chromaesthete has such a systematic arrangement of color-tone equivalences (p. 71).” Similarly, the synaesthesia scholars Cytowic and Eagleman (2011) have described Scriabin’s account of his circle of fifths associations as a “deliberate contrivance rather than a manifestation of perceptual synaesthesia” (p. 191). The current article argues that sufficient evidence is available to suggest that Scriabin’s imagery was not contrived but had a logical and highly systematic acoustical basis which deserves wider recognition. It is to be hoped that with the increasing fusion of psychological, musicological, and neuroscience scholarship, acoustical explanations of AP and tonality/colour synaesthesia will be more widely recognized and subjected to empirical testing.

Part II of the article (Thurlow & Baggaley, 2022) continues this review of the AP literature in discussing the theoretical implications of paracusis musicalis, the deterioration of AP ability with advancing age. It also considers a form of pitch perception not previously described as absolute: perfect touch.