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EN
Consider a finite population. Let qÎ(0,1) denotes the fraction of units with a given property. The problem is in interval estimation of q on the basis of a sample drawn due to the simple random sampling without replacement. In the paper three confidence intervals are compared: exact based on hypergeometric distribution and two other based on approximations to hypergeometric distribution: Binomial and Normal. It appeared that Binomial based confidence interval is too conservative while the Normal based one does not keep the prescribed confidence level.
EN
The novena, one of the forms of popular piety developing in many epochs, consists in turning to God more fervently for a period of nine days, months or years, typically through the intercession of a saint, in order to obtain a favor. This article is concerned with A Novena in Honor of St. Joseph in Songs with a Litany for a Two-Voice Choir contained in a collection of Fr. Franciszek Walczyński, priest of the Tarnów Diocese, musician, and teacher. The cult of St. Joseph flourished especially in the 15th century. In 1870, Pope Pius IX proclaimed him patron of the Universal Church. Four out of the nine analyzed songs were earlier pieces which were given new melodies. The remaining ones were written entirely by Walczyński. The songs are stanzaic, mostly with four-line highly regular stanzas. Most lines have 11 or 8 syllables and exact and paired rhymes. One song has a mid-verse (intra-stanzaic) refrain. The songs have a two-part structure with various components AB retaining strict symmetry or deviating from it. The songs are highly melodious, which stems from the prevalence of seconds and thirds. The meter of the songs, with a few exceptions of 2-note melismas, is syllabic. The tonality is major-minor, with a predominance of the former. The analyzed songs are accessible and have a simple texture.
PL
Przedmiotem artykułu jest interpretacja anonimowego traktatu łacińskiego Mensura instrumenti organici z X w. Tekst jest bardzo zwięzły, ma charakter prostego instruktażu przeznaczonego dla potencjalnego konstruktora organów. Strojenie piszczałek (o jednakowym obwodzie) dokonuje się wyłącznie za pomocą dwóch stosunków liczbowych – epitrytycznego (4:3) i epogdoicznego (9:8). Dokładne wyliczenia potwierdzają, że ta metoda okazała się pewna i daje rezultat w postaci dobrze nastrojonych piszczałek w stroju naturalnym (pitagorejskim) w zakresie trzech oktaw. W artykule przeprowadzono sporo działań matematycznych oraz przedstawiono miarę piszczałek za pomocą rysunków. Szczegółowo wyjaśniono również zagadnienia terminologiczne oraz zaprezentowano teksty greckie i łacińskie niezbędne do właściwej interpretacji traktatu.
EN
The paper is intended to interpret the anonymous Latin Treaty entitled Mensura instrumenti organici written in the X century. The text is very concise and takes the form of a simple instruction intended for a potential constructor of pipe organs. Tuning pipes (of the same circuit) is performed exclusively by means of two ratios – epitritos (4:3) and epogdoos (9:8). The exact calculation confirms that this method proved to be reliable and results in well-tuned pipes using natural Pythagorean tuning in three octave range. Numerous mathematical calculations and the figures of pipes measurements are presented in the paper. The issues of terminology are explained in detail and Greek and Latin texts necessary for the proper interpretation of the treaty are also presented.
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