Variability of Vibrato -A Comparative Study between Japanese Traditional Singing and Bel Canto- Kenji Kojima*, Masuzo Yanagida* & Ichiro Nakayama** *Department of Knowledge Engineering, Doshisha University, Japan **Department of Musicology, Osaka University of Arts [email protected], [email protected], [email protected] Abstract crete examples of vibrato. In western classical singing, “vibrato” or “non-vibrato” is Several styles of vibrato are investigated, comparing those of often specified on score, as appropriate vibrato is usually prefer- Japanese traditional singing with western bel canto from view- able for long notes, but its depth and rate are usually left for points of stationarity, depth, rate, build-up time, and synchro- singers’ freedom. Also in Japanese traditional singing, vibrato nization between ¼ and power. Analyzed as Japanese tra- and melisma (melody on a single syllable in letters) are spec- ditional singing are Noh, Kyogen, Heikyoku(Biwa), Shomyo, ified by putting special marks on letter scores. Preference for Kabuki and Nagauta. Singers of Japanese traditional singing features of vibrato, however, differs depending on regional cul- include living national treasures. Data are taken from a CD ture and taste of individuals. For example excess vibrato and database edited by Nakayama, the last author of this report. too fast (faster than about 10Hz) vibrato are usually not ac- cepted in western classical singing. We can recognize the dif- 1. Introduction ferences of cultural preferences even by simply listening to the songs. Investigated here are stationarity, depth, rate, required Nakayama [1] made recording of Japanese traditional singing time for build-up and synchronization between ¼ and power and the recorded data were published in the end of 2002 as of vibrato in Japanese traditional singing compared with those a database consisting of 18 CDs with a detailed guide. Be- in bel canto. fore completion of recording, the authors began investigating Japanese traditional singing. They investigated Japanese tra- ditional singing from a viewpoint of vowel characteristics and 2. Variability of vibrato vibrato comparing with western bel canto [2] putting emphasis Some examples of vibrato in Japanese traditional singing are on vowel characteristics. It was revieled that formant frequen- shown in Fig. 1, where the abscissa represents the time and cies characteristic to genres are observed both in bel canto and the ordinate, ¼ . Depicted in Fig. 1 are “Noh”, “Kyogen”, Japanese traditional singing and that tendencies of formant shift “Biwa(Heikyoku)”, “Shomyo”, “Kabuki” and “Nagauta”, from within a singer from natural utterance to singing utterance are the above-mentioned CD database [1]. ¼ pattern of Noh be- somewhat different depending on music genres of the singers. gins with a spike-like sharp change, passing through a constant Vibrato, periodic change of fundamental frequency ¼ , was in- pitch part, and reaches a stable vibrato of almost perfect fourth vestigated just from a viewpoint of its depth and required time wide. Shomyo also shows a similar pattern though the starting for build-up. part is not so sharp. Kabuki also shows a similar pattern though Tastes in music may differ depending on culture and also it lacks the sharp change at the beginning on ¼ patterns, and on individuals. By singing a song, the “pitch” (fundamental the vibrato depth in the last half is only a semitone. The rest frequency) and the “note value” (duration on score) of each three show stable vibrato of a semitone or a whole tone wide note is usually prescribed in scores in case of western music starting just after the beginning of voicing. Ó except a few modern songs like ”Pierrot Lunair” by Schnberg, in which singers are specified to change the pitch to any other cents height as soon as she reaches the specified pitch. Temporal in- 300 300 300 tensity of each note is also roughly specified usually by 9 lev- 250 250 250 els, from ÔÔÔ(pianisissimo) to (fortississimo), though the 200 200 200 intensity levels are not quantitatively defined, but just subjec- 150 150 150 tive to singers. So, the prosody, defined as temporal change in 0 1000 2000 3000 0 1000 2000 3000 0 1000 2000 3000 (a) Noh ms (b) Kyogen (c) Biwa ¼ and intensity, in song is regarded as almost specified before- hand and only a few freedom is left for singers. In that sense, 300 300 300 prosody in songs is not spontaneous but highly controlled un- 250 250 250 der strict specifications, however, there is freedom left left for 200 200 200 150 150 150 singers. Vibrato is one of the freedom left for singers. 0 1000 2000 3000 0 1000 2000 3000 0 1000 2000 3000 Singers have freedom in vibrato, that results in varieties of (d) Shomyo (e) Kabuki (f) Nagauta personal vibrato styles. However, there might be ceratin ten- dencies regarded as characteristic to genres. The previous re- Figure 1: Examples of vibrato in Japanese traditional singing. port [2] describes gross features of vibrato in Japanese tradi- Abscissa: time[ms], ordinate: ¼ [Hz]. tional singing together with those of bel canto, without showing any examples. Details are described in this report showing con- Though above-mentioned features of vibrato are described as if those were characteristic to genres, those might not be the Figure 3 shows average vibrato depth, its standard devia- reality because the number of informants for each genre is not tion, maximum and minimum values for each genre including so large, but those features might be characteristic to individual bel canto for comparison [2]. From Fig. 3 we can recognize singers. that the maximum depth of Japanese traditional singing is 500 A typical vibrato pattern of bel canto is separately shown cents, i.e. perfect fourth, while that of bel canto is much smaller in Fig. 2, where vibrato builds up starting at the beginning of than 300 cents, i.e. three semitones. In Japanese singing, per- voicing reaching a stable vibrato of a whole tone wide. Vibrato fect fourth may have important role as it is used as the interval depth and vibrato rate commented in the figure will be explained between the two voice parts in “Shomyo”, a chorus by Buddist in section 3. bonzes at formal ceremonies. Perfect fourth is observed also as melodic jump at chanting “sutras(Buddist scriptures)” and as musical interval between two parts in “sutra”. F0 [Hz] 350 d d 340 1 3 4. Vibrato rate 330 Ø Ø ½´Ø ¿ 320 Instantaneous “vibrato rate” at ¾ is defined as Ø µ Ø ½ ½ 310 [Hz], expressing the average rate of change in ¼ from to d 300 2 2 1/2 Ø D d d d ¿ . Figure 4 shows average vibrato rate, its standard deviation, Vibrato depth v=1200*log2( 1 3/ 2 ) 290 S Vibrato rate Rv=1/(t - t ) the maximum and minimum values for each genre including bel 280 3 1 Build-up time canto for comparison. From Fig. 4 we can see that the average 270 Build-up time S conditioned by d /d < 260 3 1 vibrato rate is within the range from 4 to 5.5 Hz independent of S 250 its genre. t1 t2 t3 16.5 176 336 495 655 815 974 1134 1294 1453 1613 1773 1932 Time [ms] 8 Figure 2: A typical vibrato pattern of bel canto. Vibrato depth is 7 Ô ½¾¼¼ £ ÐÓ ´ £ µ ¿ ¾ defined as ½ [cents] and vibrato rate ¾ 6 ½´Ø Ø µ ½ as ¿ [Hz]. 5 4 3. Vibrato depth 3 2 As observed in Fig. 1 some of Japanese song genres, such 1 as Noh and Shomyo, show a much wider range of change in 0 ¼ ¼ than bel canto. The ratio of the highest to the low- est ¼ within a period reaches 4/3, or perfect fourth higher, for Japanese traditional singing, while that of bel canto is only Noh Biwa Kyogen Shomyo Kabuki Nagauta about 9/8, or one whole tone, though some other Japanese gen- Bel Canto res show very shallow vibrato. To investigate the situation more Ø Ø precisely, instantaneous “vibrato depth” at ¾ in Fig. 2 is Figure 4: Average rate[Hz/s], standard deviation[Hz/s], maxi- Ô ½¾¼¼ £ ÐÓ ´ £ µ ¿ ¾ defined as ½ [cents], expressing the mum and minimum rates[Hz/s] of vibrato for each genre includ- ¾ width of change in ¼ within a period. “Cent” is a unit of mea- ing bel canto for comparison. suring frequency ratio in a logarithmic scale defined as an oc- tave corresponds to 1200 cents or one semitone corresponds to 100 cents. 5. Stationarity of Vibrato 600 By visual inspection or listening the sounds, every vibrato in bel canto seems to be stationary or stable from just after the 500 beginning of voicing up to almost the end of utterance, while that of Japanese traditional siging does not always seem to be 400 so stationary, or rather than that, as shown later in Fig. 6 (b), ¼ 300 of Japanese traditional singing sometimes lacks vibrato even for a long vowel, or its curve often shows nonstationary changes as 200 seen in Fig. 1 (a), (d) or (e). Stationarity can be, in a sense, evaluated by variances in vi- 100 brato depth and vibrato rate. If the both the variances are small 0 for a genre, it can be said that the vibrato of the genre is sta- tionary. As mentioned above, the rate of periodic change in ¼ seems not so different from 5Hz for vibrato parts, that means Noh Biwa variance in vibrato rate is small for both Japanese singing and Kyogen Shomyo Kabuki Nagauta Bel Canto bel canto. So, it would be said that stationarity can be roughly evaluated only by variance in vibrato depth. Allowing that in- Figure 3: Average depth[Hz], standard deviation[Hz], maxi- terpretation, Fig.