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In musical tuning, deviations from the simple frequency ratios of pure consonant intervals are often necessary. These deviations are called temperings. They result in beats in the sounding interval. Rules are developed according to which the beat frequencies can be determined, both exactly and by way of easy integer approximations. Beat frequencies of consonant intervals are most easily expressed as relative beat frequencies, the quotient of the beat frequency and the lower fundamental frequency of the interval. The relative beat frequency is a constant for a certain interval in a certain tuning, whereas the absolute beat frequencies vary with fundamental frequencies. Also described are the relationships between the beat frequencies of the three intervals that make up a consonant triad. Numerical data are given for five model tunings: Pythagorean, equal, Silbermann, meantone, and Salinas.
In musical tuning, deviations from the simple frequency ratios of pure consonant intervals are often necessary. These deviations are called temperings. They result in beats in the sounding interval. Rules are developed according to which the beat frequencies can be determined, both exactly and by way of easy integer approximations. Beat frequencies of consonant intervals are most easily expressed as relative beat frequencies, the quotient of the beat frequency and the lower fundamental frequency of the interval. The relative beat frequency is a constant for a certain interval in a certain tuning, whereas the absolute beat frequencies vary with fundamental frequencies. Also described are the relationships between the beat frequencies of the three intervals that make up a consonant triad. Numerical data are given for five model tunings: Pythagorean, equal, Silbermann, meantone, and Salinas.
No abstract
The present article is aimed at collecting and organising the knowledge about harpsichords and similar instruments which were made on the territory of today’s Italy between the 16th and the 18th centuries. The analysis of the instruments from the Italian Peninsula will cover their exterior (instrument as a work of art) and typically technical features (disposition, rage, tuning, etc.). An addition to the text are the illustrations presenting construction-related and decorative details. The article is addressed to both harpsichordists and early music performers. Harpsichords, virginals and Italian spinets are a sort of exception as compared to the instruments from other European centres. Italy-made instruments had a relatively short period of evolution before they achieved their final form – it nowadays causes a significant problem in terms of assigning the right date when a given model was created. The key for understanding the uniqueness of Italian instruments is their unusual structure and sound. Both features are important for a performer in order to ensure the best performance possible. The construction of the harpsichord is what influences its sound the most, so the knowledge about the differences between Italian, French or German instruments translates directly into the style of the aesthetics of performance. The article also presents the harpsichord as a unique work of art. Intricately ornamented, carved and painted, clavicembali were meant to please the eye and blend with the room interior like a beautiful piece of furniture. The practical interpretation of this issue are the descriptions of a few instruments and the techniques used by artists working on the territory of today’s Italy.
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