Just Intonation, &c

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Group Theoretic Description of Just Intonation

In this paper we present a group theoretic description of just intonation. All possible musical intervals belonging to 5-limit just intonation can be represented by the mathematical group {235|p,q,r ∈Z}. Considering only the intervals within one octave, an isomorphism with the 2-dimensional lattice Z can be made. Plotting the intervals on the lattice according to the isomorphism, we can identif...

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The hayward tuning vine: an interface for just intonation

The Hayward Tuning Vine is a software interface for exploring the system of microtonal tuning known as Just Intonation. Based ultimately on prime number relationships, harmonic space in Just Intonation is inherently multidimensional, with each prime number tracing a unique path in space. Taking this multidimensionality as its point of departure, the Tuning Vine interface assigns a unique angle ...

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Pocket Gamelan: a J2ME environment for just intonation

This paper describes on-going exploration of tuning systems through development of mobile instruments appropriate for tlie audition and performance of music composed in just intonatIon tunmgs. 1he project is a response to a transformation in computer music brought about through the introduction of wireless technologies and is motivated by a desire to enable performance of music based on just in...

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Intonation segments and segmental intonation

An acoustic analysis of a German dialogue corpus showed that the sound qualities and durations of fricatives, vocoids, and diphthongs at the ends of question and statement utterances varied systematically with the utterance-final intonation segments, which were high-rising in the questions and terminal-falling in the statements. The ways in which the variations relate to phenomena like sibilant...

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Charting Enharmonicism on the Just Intonation Tonnetz: A Practical Approach to Neo-Riemannian Analysis

In this study, I propose a theory of voice leading for use with the tonal space of the justintonation Tonnetz. The theory is based largely upon established theories of diatonic voice leading and chromatic harmony, and also draws upon the principles of just intonation within the tonal system. The unambiguous expression of intervals as untempered ratios is dependent upon an established seven-step...

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ژورنال

عنوان ژورنال: Nature

سال: 1877

ISSN: 0028-0836,1476-4687

DOI: 10.1038/015196b0