Tuning Systems for Keyboard Instruments – A Historical Overview

Dan Racoveanu


The article focuses on analysis and reconstruction of tuning systems from 17th- to 18th-century music on the European space. Tempering is the attempt to reach a compromise between the sound’s natural attributes and the “artificial”, chromatic 12-tone octave system. By tempering we negotiate between the fifth’s and the third’s drive toward purity.

Meantone tuning systems must satisfy the requirement that thirds be as close to the natural interval as possible. In the attempt to attenuate the fifth’s narrowness, various divisions of the Syntonic comma were experimented (“French tuning systems”, e.g. Mersenne and Rameau).

The requirements of the well-tempered tunings were the possibility to modulate to all tonalities and a differentiation as refined as possible of the expressivity of each tonality, with a slight preference for the closely remoted. Between the two extremes – Werckmeister and Vallotti – there were numerous well-tempered tuning systems based on the various divisions of the Pythagorean comma. Many musicians attempted, in the last decades, to create new tuning systems in the spirit of those well-tempered, with respect to Bach’s Well-Tempered Clavier, which would at properly highlight the different character of each tonality (e.g. Barnes, Kellner, Lehman).

Contribution to a Future Theory of Supra-Octave Modes. Case Study: Ștefan Niculescu’s Late Works

Mihai Măniceanu


In the present study I attempt an ordering, a systematization of the supra-octave modes, without intending to exhaust the theoretical treatment of this subject, because the combinatorial and expressive possibilities, the compositional processes attached to the supra-octave area are, in fact, infinite. I outline in the first part some classification criteria, according to which I show that the supra-octave modes can be: penta-octave modes, tempered modes, “octave” supra-octave modes, generated by relating each step to the previous step and by the translation of a model, containing the total chromatic, repetitive, homogenous, or artificial. Then, in the second part of the study, I identify and present in detail the complex supra-octave modes used by the Romanian composer Ștefan Niculescu in some of his most important late works (Psalmus, Undecimum, Deisis, and Litanies at the Fullness of the Time).

Aspects of Robert Schumann’s Symphonic Etudes. Semantic Character and Some Performance-Related Implications

Costin Filipoiu


The paper on the semantic character of Robert Schumann’s Symphonic Etudes is structured into three chapters. Chapter 1 describes each etude discursively, Chapter 2 presents a table evaluating the etudes by means of the 5-valued logic and of a list of expressive markings and Chapter 3 compares two recordings of the work, by Sviatoslav Richter and Wilhelm Kempff. From the analysis in Chapter 1 we learn that Schumann successfully describes in this work an entire range of psychological characters, from melancholy, grave, funereal in the theme, to mysterious, pathetic, dreamy, martial, humorous, agitated, bright, energetic, penitent, triumphant in the variations. Chapter 2 represents an attempt to weigh more precisely the character of each variation. To this end, the author compares them to one another, employs a list of 25 expressive markings as different as possible semantic-wise, and evaluates them with the help of 5-valued logic (analytical method developed by Dinu Ciocan). Chapter 3 presents comparatively the recordings by two great pianists, which enable the reader to see how many different interpretations the brilliant Schumannian text is open to, depending on the character of each performer.

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