Tonal music theory: A psychoacoustic explanation?

From the seventeenth century to the present day, tonal harmonic music has had a number of invariant properties such as the use of specific chord progressions (cadences) to induce a sense of closure, the asymmetrical privileging of certain progressions, and the privileging of the major and minor scales. The most widely accepted explanation has been that this is due to a process of enculturation: frequently occurring musical patterns are learned by listeners, some of whom become composers and replicate the same patterns, which go on to influence the next “generation” of composers, and so on. In this paper, however, I present a possible psychoacoustic explanation for some important regularities of tonal-harmonic music. The core of the model is two different measures of pitch-based distance between chords. The first is voice-leading distance; the second is spectral pitch distance—a measure of the distance between the partials in one chord compared to those in another chord. I propose that when a pair of triads has a higher spectral distance than another pair of triads that is voice-leading-close, the former pair is heard as an alteration of the latter pair, and seeks resolution. I explore the extent to which this model can predict the familiar tonal cadences described in music theory (including those containing tritone substitutions), and the asymmetries that are so characteristic of tonal harmony. I also show how it may be able to shed light upon the privileged status of the major and minor scales (over the modes)

A psychoacoustic model of harmonic cadences: a preliminary report

This report presents a psychoacoustically derived computational model of the perceived distance between any two major or minor triads, the degree of activity created by any given pair of triads, and the cadential effectiveness of three-triad progressions. It also provides statistical analyses of the ratings given by thirty-five participants for the "similarity" and "fit" of triads in a pair, and the "cadential effectiveness" of three-triad progressions. Multiple regressions show that the model provides highly significant predictions of the experimentally obtained ratings. Finally, it is argued that because the model is based upon psychoacoustic axioms, it is likely the regression equations represent true causal models. As such, the computational model and its associated theory question the plausibility of theoretical approaches to tonality that use only long-term memory and statistical features, as well as those approaches based upon symmetrical geometrical structures like the torus. It is hoped that the psychoacoustic approach proposed here may herald not only the return of psychoacoustic approaches to tonal music theory, but also the exploration of the tonal possibilities offered by non-standard tunings and non-harmonic timbres

New tonalities with the Thummer and The Viking

In this paper we explain the theoretical background of Dynamic Tonality using the Thummer, a new musical interface, and The Viking, a software synthesizer written especially for it. Dynamic Tonality is a musical audio routine that allows for novel tunings and enables the user to relate – to an arbitrary degree – these tunings with the partials of their notes. The Viking features Dynamic Tonality and works with any MIDI instrument, but when paired with the Thummer (or another two-dimensional interface) it creates a system of fingering invariance across chords and tunings. Thus, the Thummer and The Viking render non-standard tunings more physically, pedagogically, and aesthetically accessible

A Computational Model of the Cognition of Tonality

Tonality is the organization of pitches, both simultaneously and across time, so that certain pitches and chords are heard as attracted, in varying degrees, to other pitches and chords. Most art music from the seventeenth to the nineteenth centuries, and popular music to the present day, is heavily steeped in a musical language that makes use of tonality to define a ‘central’ most attractive pitch or chord called the tonic. It is widely thought that the feelings of expectancy and resolution induced by movements towards and away from the tonic allow composers to imbue tonal music with meaning and emotion. In this dissertation, I identify and model some of the innate processes by which feelings of tension, resolution, stability, and so forth, are induced by successions of pitches and chords, irrespective of their harmonic consonance. By innate, I mean processes that do not require the learning of a musical corpus—such processes are important because they provide explanations for why tonal music, and our cognition of it, take the specific forms they do. To do this, I introduce a novel family of mathematical methods—metrics applied to expectation tensors—for calculating the similarity of pitch collections. Importantly, such tensors can represent not just the notated pitches of tones, but also their spectral pitches (their harmonics). I then demonstrate how these techniques can be used to model participants’ ratings of the fits of tones in microtonal melodies, and the fits of all twelve chromatic pitches to an established key centre (Krumhansl’s probe tone data). The techniques can also be generalized to predict the tonics of any arbitrarily chosen scale—even scales with unfamiliar tunings. In summary, I demonstrate that psychoacoustic processes, which are innate and universal, play an important role in our cognition of tonality

Spectral pitch distance and microtonal melodies

We present an experiment designed to test the effectiveness of spectral pitch distance at modeling the degree of “affinity” or “fit” of pairs of successively played tones or chords (spectral pitch distance is the cosine distance between salience-weighted, Gaussian-smoothed, pitch domain embeddings of spectral pitches—typically the first eight to ten partials of a tone). The results of a previously conducted experiment, which collected ratings of the perceived similarity and fit of root-position major and minor triads, suggest the model works well for pairs of triads in standard 12-tone equal temperament tunings. The new experiment has been designed to test the effectiveness of spectral pitch distance at modeling the affinity of tones in microtonal melodies where the partials of the tones can be variably tempered between being perfectly harmonic and perfectly matched to the underlying microtonal tuning. The use of microtonal tunings helps to disambiguate innate perceptual (psychoacoustical) responses from learned (cultural) responses. Participants are presented with a software synthesizer containing two unlabeled controls: one adjusts the precise tuning of the tones; the other adjusts the extent to which the spectrum is tempered to match the tuning (as set by the first control). A selection of microtonal melodies are played in different tunings, and the participants adjust one, or both, controls until they find a “sweet spot” at which the music sounds most “in-tune” and the notes best “fit” together. The results of these experiments will be presented and discussed

Metrics for pitch collections

Models of the perceived distance between pairs of pitch collections are a core component of broader models of the perception of tonality as a whole. Numerous different distance measures have been proposed, including voice-leading, psychoacoustic, and pitch and interval class distances; but, so far, there has been no attempt to bind these different measures into a single mathematical framework, nor to incorporate the uncertain or probabilistic nature of pitch perception (whereby tones with similar frequencies may, or may not, be heard as having the same pitch). To achieve these aims, we embed pitch collections in novel multi-way expectation arrays, and show how metrics between such arrays can model the perceived dissimilarity of the pitch collections they embed. By modeling the uncertainties of human pitch perception, expectation arrays indicate the expected number of tones, ordered pairs of tones, ordered triples of tones and so forth, that are heard as having any given pitch, dyad of pitches, triad of pitches, and so forth. The pitches can be either absolute or relative (in which case the arrays are invariant with respect to transposition). We provide a number of examples that show how the metrics accord well with musical intuition, and suggest some ways in which this work may be developed

Hex Player—a virtual musical controller

In this paper, we describe a playable musical interface for tablets and multi-touch tables. The interface is a generalized keyboard, inspired by the Thummer, and consists of an array of virtual buttons. On a generalized keyboard, any given interval always has the same shape (and therefore fingering); furthermore, the fingering is consistent over a broad range of tunings. Compared to a physical generalized keyboard, a virtual version has some advantages—notably, that the spatial location of the buttons can be transformed by shears and rotations, and their colouring can be changed to reflect their musical function in different scales. We exploit these flexibilities to facilitate the playing not just of conventional Western scales but also a wide variety of microtonal generalized diatonic scales known as moment of symmetry, or well-formed, scales. A user can choose such a scale, and the buttons are automatically arranged so their spatial height corresponds to their pitch, and buttons an octave apart are always vertically above each other. Furthermore, the most numerous scale steps run along rows, while buttons within the scale are light-coloured, and those outside are dark or removed. These features can aid beginners; for example, the chosen scale might be the diatonic, in which case the piano’s familiar white and black colouring of the seven diatonic and five chromatic notes is used, but only one scale fingering need ever be learned (unlike a piano where every key needs a different fingering). Alternatively, it can assist advanced composers and musicians seeking to explore the universe of unfamiliar microtonal scales

Panax ginseng has no effect on indices of glucose regulation following acute or chronic ingestion in healthy volunteers

In the absence of effective pharmacotherapy for diabetes there has been an increase in the use of, and research into, alternative treatment strategies. These include exercise, dietary interventions and the use of supplements including extracts of ginseng. Two separate, placebo-controlled, double-blind, cross-over studies investigating the effects of chronic ingestion of Panax ginseng (study 1 used G115, study 2 used Cheong Kwan Jang) on glycated Hb (HbA1c; study 1, n 18; study 2, n 11), fasting plasma insulin (study 1, n 17; study 2, n 12), fasting plasma glucose and postprandial response (following breakfast) (study 1, n 23; study 2, n 14) in healthy volunteers are reported. In both studies it was found that Panax ginseng had no effect on any gluco-regulatory parameter investigated. These results are not consistent with those reported for a diabetic sample (albeit using slightly different outcomes). These results would suggest that chronic use of Panax ginseng by non-diabetic individuals will have little long-term effect on glucose regulation. The benefits to glucose regulation associated with long-term ginseng use may only be present in populations with compromised glucose control; however, further research is needed to confirm such a speculation

Performance assessment of intravenous catheters for massive transfusion: A pragmatic in vitro study

BACKGROUND: Rapid infusion of warmed blood products is the cornerstone of trauma resuscitation and treatment of surgical and obstetric massive hemorrhage. Integral to optimizing this delivery is selection of an intravenous (IV) catheter and use of a rapid infusion device (RID). We investigated which IV catheter and RID system enabled the greatest infusion rate of blood products and the governing catheter characteristics. STUDY DESIGN AND METHODS: The maximum flow rates of nine IV catheters were measured while infusing a mixture of packed red blood cells and fresh frozen plasma at a 1:1 ratio using a RID with and without a patient line extension. To account for IV catheters that achieved the RID\u27s maximum 1000 ml/min, the conductance of each infusion circuit configuration was calculated. RESULTS: IV catheters of 7-Fr caliber or higher reached the maximum pressurized flow rate. The 9-Fr multi-lumen access catheter (MAC) achieved the greatest conductance, over sevenfold greater than the 18 g peripheral catheter (4.6 vs. 0.6 ml/min/mmHg, p \u3c .001). Conductance was positively correlated with internal radius (β = 1.098, 95% CI 4.286-5.025, p \u3c .001) and negatively correlated with length (β= - 0.495, 95% CI -0.007 to 0.005, p \u3c .001). Use of an extension line (β= - 0.094, 95% CI -0.505 to -0.095, p = .005) was independently associated with reduced conductance in large caliber catheters. CONCLUSION: Short, large-diameter catheters provided the greatest infusion rates of massive transfusion blood products for the least pressure. For patients requiring the highest transfusion flow rates, extension tubing should be avoided when possible

Spectral tools for Dynamic Tonality and audio morphing

The analysis-resynthesis method used by the spectral toolbox allows the independent control of both frequency and amplitude for every partial in a given sound. The spectral toolbox begins by separating the 'signal' from the 'noise' which allows the peaks in the spectrum to be treated differently from the wide-band components. The spectral mapping technology is used to map the input to a fixed destination spectrum G like the SpT.Ntet routine maps all partials of the input sound to scale steps of the N-tone equal tempered scale that can be used to create sounds that are particularly appropriate for use in a given N-TET scale. Spectral morphing generates sound that moves smoothly between a source spectrum F and a destination spectrum G over a specified time t. A Dynamic Tonality synthesizer like Trans-FormSynth has a small number of parameters that enable many musically useful, and relatively, unexplored features like the continuous parameters α,β and γ move the tuning between a number of equal temperaments, non-equal temperaments and circulating temperaments