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)

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 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

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

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

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

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

RAG-induced DNA double-strand breaks signal through Pim2 to promote pre-B cell survival and limit proliferation

Interleukin 7 (IL-7) promotes pre–B cell survival and proliferation by activating the Pim1 and Akt kinases. These signals must be attenuated to induce G1 cell cycle arrest and expression of the RAG endonuclease, which are both required for IgL chain gene rearrangement. As lost IL-7 signals would limit pre–B cell survival, how cells survive during IgL chain gene rearrangement remains unclear. We show that RAG-induced DNA double-strand breaks (DSBs) generated during IgL chain gene assembly paradoxically promote pre–B cell survival. This occurs through the ATM-dependent induction of Pim2 kinase expression. Similar to Pim1, Pim2 phosphorylates BAD, which antagonizes the pro-apoptotic function of BAX. However, unlike IL-7 induction of Pim1, RAG DSB-mediated induction of Pim2 does not drive proliferation. Rather, Pim2 has antiproliferative functions that prevent the transit of pre–B cells harboring RAG DSBs from G1 into S phase, where these DNA breaks could be aberrantly repaired. Thus, signals from IL-7 and RAG DSBs activate distinct Pim kinase family members that have context-dependent activities in regulating pre–B cell proliferation and survival

The landscape model: a model for exploring trade-offs between agricultural production and the environment

We describe a model framework that simulates spatial and temporal interactions in agricultural landscapes and that can be used to explore trade-offs between production and environment so helping to determine solutions to the problems of sustainable food production. Here we focus on models of agricultural production, water movement and nutrient flow in a landscape. We validate these models against data from two long-term experiments, (the first a continuous wheat experiment and the other a permanent grass-land experiment) and an experiment where water and nutrient flow are measured from isolated catchments. The model simulated wheat yield (RMSE 20.3–28.6%), grain N (RMSE 21.3–42.5%) and P (RMSE 20.2–29% excluding the nil N plots), and total soil organic carbon particularly well (RMSE 3.1 − 13.8 %), the simulations of water flow were also reasonable (RMSE 180.36 and 226.02%). We illustrate the use of our model framework to explore trade-offs between production and nutrient losses