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The purpose of this study is to describe the character of melody by means of numerical and statistical analysis of melodic intervals. The objects of analysis consist of four groups: Gregorian chants, secular monophonies of the middle ages, soprano parts of J. S. Bach's two-part inventions, and melodies from F. Schubert's " Winterreise."
These melodies are coded for computer processing, and the frequency of melodic intervals are calculated by computer. The results are then statistically investigated, and the four groups are analysed by means of discriminant analysis. (Variables used are the frequency of melodic intervals) .
It is apparent from the results that the frequency of melodic intervals, most importantly major/minor seconds and major/minor thirds, are effective as criterion to distinguish one group from the other.
It is widely known that the tonal structure of Gregorian or plain chant is founded on church modes. There do exist, however, some chants which shows close resemblance to the music using the pentatonic scale.
In this study, three dorian or hypodorian chants, i.e. Kyrie IX, Sequentia "Victimae paschali laudes", and Introitus "Dominus dixit", are analyzed based on the scale theory for Japanese traditional music proposed by Fumio Koizumi.
In these chants, the typical pentatonic motives such as D-F-G or A-c-d often appear. At the same time, in some phrases, the Japanese folk song scale D-F-G-A-c-d can also be found. Some European scholars explain this phenomenon as "Germanic dialect", which dates back to around the year 1000. This explanation, however, is not satisfactory because the neumatic notation before the 11th century was not so precise. Furthermore, even if the phenomenon had been observed exclusively in Germany, it would not still eliminate the possibility that this type of dialect had been inherited from older traditions.
It may not be possible to resolve the question of whether or not these chants were actually based on the pentatonic scale. It can still be pointed out, however, that people accustomed to pentatonic music, e.g. Japanese, may hear the pentatonic framework in these chants.