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One Vietnamese gong set of nine flat and six bossed gongs was acoustically studied. Main partial (primary pitch) for the flat gong was estimated by human hearing sense, suggesting that the primary ...

This paper presents Tarsos, a modular software platform used to extract and analyse pitch organization in music. With Tarsos pitch estimations are generated from an audio signal and those estimations are processed in order to form musicologically meaningful representations. Tarsos aims to offer a flexible system for pitch analysis through the combination of an interactive user interface, several pitch estimation algorithms, filtering options, immediate auditory feedback and data output modalities for every step. To study the most frequently used pitches, a fine-grained histogram that allows up to 1200 values per octave is constructed. This allows Tarsos to analyse deviations in Western music, or to analyse specific tone scales that differ from the 12 tone equal temperament, common in many non-Western musics. Tarsos has a graphical user interface or can be launched using an api—as a batch script. Therefore, it is fit for both the analysis of individual songs and the analysis of large music corpora...

The aim of this article is to present an octave error optimized pitch detection algorithm based on spectral analysis. The proposed algorithm is effective for signals with strong harmonic content, as well as for nearly sinusoidal ones. In addition, as an extension to the presented octave error optimized algorithm, a method of estimating instantaneous pitch is described. Experiments and estimation accuracy tests in terms of octave errors were performed on a variety of musical instruments (i.e., 567 sounds played on acoustic instruments with various articulations and dynamics, with fundamental frequencies ranging from 34 Hz up to 1700 Hz, were processed). Fine pitch error tests of the instantaneous pitch estimation algorithm were performed for 4,000 different synthetic signals, with frequencies ranging from 50 Hz to 4000 Hz, including both clean signals and signals contaminated with noise. Results exemplifying the main issues of both engineered algorithms are shown. In addition, a performance compar...

Auditory displays with the ability to dynamically spatialize virtual sound sources under real-time conditions enable advanced applications for art and music. A listener can be deeply immersed while interacting and participating in the experience. We review some of those applications while focusing on the Helical Keyboard project and discussing the required technology. Inspired by the cyclical nature of octaves and helical structure of a scale, a model of a piano-style keyboard was prepared, which was then geometrically warped into a helicoidal configuration, one octave/revolution, pitch mapped to height and chroma. It can be driven by MIDI events, real-time or sequenced, which stream is both synthesized and spatialized by a spatial sound display. The sound of the respective notes is spatialized with respect to sinks, avatars of the human user, by default in the tube of the helix. Alternative coloring schemes can be applied, including a color map compatible with chromastereoptic eyewear. The graphical disp...

Temporal codes and neural temporal processing architectures (neural timing nets) that potentially subserve perception of pitch and rhythm are discussed. We address 1) properties of neural interspike interval representations that may underlie basic aspects of musical tonality (e.g. octave similarities), 2) implementation of pattern-similarity comparisons between interval representations using feedforward timing nets, and 3) representation of rhythmic patterns in recurrent timing nets. Computer simulated interval-patterns produced by harmonic complex tones whose fundamentals are related through simple ratios showed higher correlations than for more complex ratios. Similarities between interval-patterns produced by notes and chords resemble similarity-judgements made by human listeners in probe tone studies. Feedforward timing nets extract common temporal patterns from their inputs, so as to extract common pitch irrespective of timbre and vice versa. Recurrent timing nets build up complex temporal expectations over time through repetition, providing a means of representing rhythmic patterns. They constitute alternatives to oscillators and clocks, with which they share many common functional properties.

During the past centuries a great many ways have been proposed to divide the octave into smaller units. The twelve semitones have been by far the most often proposed and used, but many systems with sometimes much more steps in the octave have been developed as well. There are basically two ways to construct these systems with multiple steps: either subdividing the octave into an arbitrary number of equal steps (the ensuing systems are often called multiple divisions), or building intervals by addition from basic intervals. The basic intervals then follow the order of prime numbers in their frequency ratios: 2:3 (perfect fifth), 4:5 (just major third), 4:7 (‘harmonic seventh’), etc. This method lies behind the just intonations. In this paper it will be shown that in both cases the various systems can be most efficiently described in terms of the circle of fifths. Methods are given to derive from the basic premises of the systems one or more circles of fifths, which encompass all the notes of the systems an...

On April 1994 in New York city, I introduced subharmonics as a musical element to extend the violin's range by a full octave below the open G string without changing the tuning. Since then, I am now able to play not only an octave below, but also almost all the chromatic intervals below the fundamental notes by applying different amount of bow pressure (Kimura, 1997). This article explains the empirical data and elements for producing subharmonics including bow location and pressure on the string and the age of strings. This article also introduces a curious method; it was found that a ''twisted'' string works better. These different subharmonics for string players will also afford composers broader possibilities in creating their works. This article is also accompanied by sound examples, as well as excerpts from my compositions using subharmonics.

Unlike traditional alternative tunings, expanded tunings are not based on any equal or unequal division of the octave into any integral number of scale steps. Expanded tunings equally divide what has been called “super‐consonant intervals”, that is, the main intervals of the harmonic series, with the exception of the octave and its multiples, into a variable integral number of scale steps. In the absence of the octave as a point of reference, and given certain musical conditions, the ear might perceive some of the aforementioned super‐consonant intervals — here referred to as “morenoctaves” — as a kind of expanded octaves, thus creating a strange and unexpected expansion of the known tonal space. The possibility of this unexplored musical phenomenon is explained, and empirical research proposed.