The perception of melodic consonance: an acoustical and neurophysiological explanation based on the overtone series

The melodic consonance of a sequence of tones is explained using the overtone series: the overtones form "flow lines" that link the tones melodically; the strength of these flow lines determines the melodic consonance. This hypothesis admits of psychoacoustical and neurophysiological interpretations that fit well with the place theory of pitch perception. The hypothesis is used to create a model for how the auditory system judges melodic consonance, which is used to algorithmically construct melodic sequences of tones

Collaboration between Science and Religious Education teachers in Scottish Secondary schools

The article reports on quantitative research that examines: (1) the current practice in collaboration; and (2) potential for collaboration between Science and Religious Education teachers in a large sample of Scottish secondary schools. The authors adopt and adapt three models (conflict; concordat and consonance) to interrogate the relationship between science and religion (and the perceived relation between these two subjects in schools) (Astley and Francis 2010). The findings indicate that there is evidence of limited collaboration and, in a few cases, a dismissive attitude towards collaboration (conflict and concordat and very weak consonance). There is, however, evidence of a genuine aspiration for greater collaboration among many teachers (moving towards a more robust consonance model). The article concludes by discussing a number of key factors that must be realised for this greater collaboration to be enacted

Syntonets: Toward A Harmony-Inspired General Model of Complex Networks

We report an approach to obtaining complex networks with diverse topology, here called syntonets, taking into account the consonances and dissonances between notes as defined by scale temperaments. Though the fundamental frequency is usually considered, in real-world sounds several additional frequencies (partials) accompany the respective fundamental, influencing both timber and consonance between simultaneous notes. We use a method based on Helmholtz's consonance approach to quantify the consonances and dissonances between each of the pairs of notes in a given temperament. We adopt two distinct partials structures: (i) harmonic; and (ii) shifted, obtained by taking the harmonic components to a given power $\beta$, which is henceforth called the anharmonicity index. The latter type of sounds is more realistic in the sense that they reflect non-linearities implied by real-world instruments. When these consonances/dissonances are estimated along several octaves, respective syntonets can be obtained, in which nodes and weighted edge represent notes, and consonance/dissonance, respectively. The obtained results are organized into two main groups, those related to network science and musical theory. Regarding the former group, we have that the syntonets can provide, for varying values of $\beta$, a wide range of topologies spanning the space comprised between traditional models. Indeed, it is suggested here that syntony may provide a kind of universal complex network model. The musical interpretations of the results include the confirmation of the more regular consonance pattern of the equal temperament, obtained at the expense of a wider range of consonances such as that in the meantone temperament. We also have that scales derived for shifted partials tend to have a wider range of consonances/dissonances, depending on the temperament and anharmonicity strength

Complexity, Consonance, and the Concept of God

Complexity theory has much explanatory power in the scientific community today. The author finds that its bottom-up methodology and some of its concepts can facilitate new understandings of the Christian doctrine of the Trinity

X_System

The X_System makes the playing, writing, and learning of music – even when using unconventional tunings – more intuitive, more logical, more expressive, and better sounding. The X_System allows for: • different temperaments to be chosen at the flick of a switch; • tunings to be dynamically altered at the push of a lever; • the use of a special hexagonal button-field that allows for any given interval or chord always to have the same shape on that button-field; • consonant chords to have their consonance maximised, whatever the tuning actually chosen; • radical changes to be made to the timbral character of tones using a minimal number of controls; • a choice of keyboard mappings, which enable for the balance between number of intervals and octaves to be altered