A Research Into the Accords of the Sho by Tadao Osanai

A Research into the Accords of the Sho by Tadao Osanai Synopsis: The sho笙serves as the standard of pitch ih the gagaku雅楽*Japa- Table 1. nese classical court-music, and produces 11 sorts of peculiar accord called aitake fit. The writer desired and endeavoured to know in detail of the tuning of the sh6, and, if pas- sible, to give a reasonable explanation to the aitake. The result is satisfactory, and a very sim- ple method is proposed to express numerical- ly the degree of concordance of not only these 11 aitakes but also of almost any accord. 1. Preliminary Consideration. •˜ The Japanese sh6 V has 17 independent pipes, 2 of which are silent, ", and can give 15 notes as shown in Table 1, pipe and note cor- responding one to one . It is often said" that hese 15 notes are riot tuned in the 12 equallyt tempered scale, but are in the Pythagorean series. If we put aside the difference of octave, the * The eutline of the gagaku is given in European notations: "Cellection of Japanese Musics, 日本音楽集"edited by Mr . Hisao Tanabe田辺尚雄as the Vol.18 of the "Gesammelte Werke der Welt Musik". Shllnju-sha春秋社Publishing Co., 1930. Score of Gagaku, Vol." 1"transcribed by Mr. Sukehiro shiba芝祐泰, published from Ryugin-sha龍吟社; the succeeding volumes have been published or in preparation. 1) L. Traynor and S. Kishibe; "The Four Unknown Pipes of the She", Jour. Soc. Res. Asiatic Music, No. 9, 1951, pp. 26-53; this treats in detail the silent pipes of ancient and modern she. Description on the modern she is given in Mr. Hisao Tanabe's work 5) , which •\1•\ above 15 notes become (in German notation) c g d a eh fis cis gis, the 9 successive notes in the Pythagorean series. As is well known in the theory of pure-intonation, the note of the major third above gis, which is obtained by repeating the perfect fifth eight times above c, is his, and is very near to c, exceeding c only by an interval of a skhisma. Thus, if the sho is tuned in the Pythagorean series, we see that 〔1〕The interval between美 (gis2) and比 (c3) is almost the major third, exceeding the latter only by an interval of one skhisma (1/11 comma) . And, after a little calculation, we see that 2) The intervais between十 (g2) and美 (gis2) , or between比 (c3) and 言 (cis3) are the same, being approximately 5 commas (which is larger than the semitone of the pianoforte) ; and the intervals between工 (cis2) and〓 (d2) , between下 (fis2) and十 (g3) , between美 (gis2) and行 (a2) , betw een七 (h2) and比 (c3) , between言 (cis3) and上 (d3) are the same, being approximately 4 commas (which is smaller than the semitone of the pianoforte) . •˜ 2. On the Tuning of the Sho. The results (1) and (2) may serve to verify the assertion that the sho is tuned in the Pythagorean series. So the writer, in the autumn of 1946, requested Mr. Yoshihire Oku奥好寛, former court-musician3) to examine by his "ears" whether (1) and (2) really hold true. He, an excellent play- er of not only the gagaku-instruments but also of the European flute, who has very good ears, did not give any direct answer, (possibly becau- se he thought his ears were to be tested, or he may have considered that perfectly tuned instruments hardly exist) but gave in detail to the writer the practical method of tuning the sho, as is shown in Table 2, and left the writer to judge from this table. shall be quoted later. 2) Hisao Tanabe; "Theory of Music, 音楽理論"Revised Version, Kyoritsu Publ. Co. 共立出版社t 1956, pp. 69-70, is perhaps the latest work. •\2•\ Table 2. * In Table 2, we see that the Pythagorean series is adopted except in 3. and 15. In the preliminary consideration the result (1] was supposed to serve as a check, when we perform the tuning of the sh6 by the Pytha- gorean series starting from any one of the 15 notes: but 15. of Table 2 reveals that the major third is used for the tuning itself (not merely as a check) , which the writer least expected. If we interpret the words a little in 3. as a skhisma, from Table 2 we at once get Table 3.4) 3) With whom the writer has been in aquaintance in the Pure-intonation Rese- arch Club directed by the late Dr Shohei Tanaka田中正平. 4) The last colurnn of Table 3 shows the frequency of each nete, when we take e2=652.4sec-1 according to A. Ellis.It happens that乞 (a1) becomes very near to one of the European standards of pitch a1=435.0sec-1 •\3•\ Table 3. The result of the above tuning differs from the Pythagorean series only in the three notes c3, g2, d3, and the differences are the same for the three, being equal to just one skhisma. Now, judging from the analogy of the cases of other ordinary musical instruments, it would be rare that the tuning should be carried on in the accuracy of a skhisma. If so or •\ 4 not, we may say that here we have at least an example of tuning which aims at the Pythagorean series within the error of a skhisma. 3. Preliminary Considerations on the Aitake.5' •˜ The ordinary way of playing the shO is to sound 6 or 5 pipes together, 6) thus producing peculiar sorts of accord called aitake. There are 11 sorts of the aitake, which have been used in the court-music since the ancient times. Except in the two cases, the name of each aitake is the same as that of the lowest pipe: examine the left margin of each table (4-1) , (4-2) , 4-11) , whose principal part shall be explained in the ---, (next section, § 4.Among these ll sorts of the aitake, the 6 sorts乞, 一, 行, 〓, 乙, 十双) are accepted as concords i. e. consonant accords, and the 5 sorts比, ( 下, 十, 工, 美as discords i. e. dissonant accords.7) Of course, even the so-called dissonant aitakes are not disagreeable to the ear, although they have some more peculiarity than the so-called consonant ones, as they have been used in actual music from ancient times. The above classification into consonant and dissonant aitakes has been made merely in a meaning somewhat resembling to that of the Europe- an harmony. Therefore, it can be easily foreseen that even when we suc- ceed to give the order of the degree of concordance to the 11 aitakes, probably we can not draw the line of demarcation between consonant and dissonant aitakes, so long as we have no other reason. If we examine the constructions of the consonant aitakes, putting aside the difference of octave, we see that the乞is made up from the 4 successive notes a e h fis of the Pythagorean series; and the-.t行, 九, 乙 are from the 5 successive notes d a g h fis; finally the十 (双) is from 5) For the aitake合竹, detailed descriptions are given by Mr. Hisao Tanabe: "Lectures on the Japanese Musics, 日本音楽講話", published from Iwanami-sho- ten岩波書店1919, pp. 445-450. 6) In the te-utsuri手移り (fingering to change the accords) , several pipes sound successively, i. e. not simultaneously.And, in the fuki-tome吹止め (a sort of Coda er Cadenza}, etc, , only 2 or 3 pipes are sounded tegether, or only l pipe alone sounds. 7) In the work 5) , the aitake行is classified as dissonant, but in thelater work the same author classifies the ll aitakes int。 three kinds, (1) perfectty concordant: 乞, 九, 乙; (2) ) fairly concordant: 一, 行, 十 (双) ; (3) dissenant: 十, 下, 工, 美, 比.Mr. Yoshihiro Oku also informed the writer that the行is accepted as •\5•\ the 5 successive notes g d a e h. Therefore, there occurs no semitone in any of the 5 consonant aitakes. On the other hand, one semitone-interval not putting aside the difference of octave, i. e. semitone-interval ( itself) is always contained in every dissonant aitake; in the工and the美, there are two. From this observation, we are led to the view that the distinc- tion between dissonant—and consonant-aitake may have relation with the existence and nonexistence of semitone-interval. In the European classical music, are sounded sometimes two notes of a semitone-interval simultaneously; I) its result is never disagreeable, but it produces a peculiar "timbre-effect". In modern musics, there are many works which utilize this timbre-effect. Perhaps a cause of this effect is the beat between the two notes, whose frequencies are comparatively near to each other; if two notes in the wholetone-interval are sounded together, this timbre-effect becomes smaller in general, whose amount depending upon the absolute pitches and the kinds of instruments. In the case of the sho, we may say that the limit for this effect lies between semitone and wholetone. The property of the so-called dissonant aitake of the shO may owe greatly to this "timbre-effect" due to the existence of semitone-interval. As we have already seen, the constructions of even the so-called consonant aitakes are afar from those of European major—and minor-chords. However, even in the European classical music, there are cases where 3 or 4 successive notes of the Pythagorean series are sounded simultaneously or successively, in some ways which may be considered as concords; " and it is well known that the similar methods are widely utilized by some composers of modern musics.

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