Vytautas Germanavičius
Vytautas Germanavičius在研討會的論文發表：
Clearing up Specific Intonations in Lithuanian Folk Songs and their Applications in Composition „L’Astéroïde B-612”for Two Violins (2021)
[SLIDE 1]
My recent study is based on Lithuanian folk songs to determine interval distances in the scale, and to use the results in my recent composition for orchestra. The main source for this research was archival sound recordings from the period between 1930s and 1940s, which could preserve the ancient tunings, unequal pitch distances, microtonality in vocal and instrumental tradition, and possibly change and redefine the structure of the scale in comparison with 12-TET (12-tone equal temperament) and its intervallic relations.
Since the 19th century in the works of Lithuanian, Prussian and other scholars the area of intervallic relations, especially the distances between tones in Lithuanian folk melodies was not considered very important. However, the German educationist, music theorist Friedrich August Gotthold, who studied the folk tradition of the Baltic region remarked about the Lithuanian melodies published in Rhesa’s collection in 1825, that “some tones could have been chromatically altered, and the melodies softened or modified”. Many transcriptions of Lithuanian melodies were made at the turn of the 20th century, during which time ethnomusicologists and researchers relied on the notational system of the 12-tone chromatic scale and tunings of the church organs.
In the interwar period of the 20th century, the famous Lithuanian microtonal composer Jeronimas Kačinskas wrote in his article “Praque – the city of creative musical initiatives” that “according to some famous musicians of Praque, orientalism is closer to Lithuanians than the Western European spirit: it is noticeable in the character of the rhythm and melody of Lithuanian folk music. If we take a look at our ancient instruments (panpipes, small horns, trumpets, etc.), we will find here the intervals smaller than semitones. It can be assumed that the Lithuanians in ancient times did not know the Greek and German major and minor keys. Here will be the most likely influence of later centuries” (Kačinskas, 1932, p. 102).
[SLIDE 2]
Lithuanian music theorists in the 1940s Jadvyga Čiurlionytė, and later Genovaitė Četkauskaitė noted the need to notate smaller intervals than semitones in Lithuanian folk melodies, and recommended using these symbols: by arrows up and down
for notes smaller than a semitone; by a cross – for indefinite pitches, and by a wavy line – for glissando to the first step in the scale.
The other direction besides the scale analyses in the 12-tone chromatic system, refers to the intervallic peculiarities related to the natural harmonic series – the natural simplicity of the frequency ratios between the tones, the musicologist Vytautas Venckus who stated that “the intervals of the perfect fifth and perfect fourth are very important for the construction of the scale. These intervals or the reference tones form the framework for the entire scale in Lithuanian folk music” (Venckus, 1969, p. ???). In the book On the Way of Sutartinės and Skudučiai, the vocal and instrumental music researcher Stasys Paliulis mentions the Lithuanian traditional woodwind instrument daudytė [SLIDE 3], which produces the first five overtones of the natural harmonic series. [SLIDE 4] In the example above we can see 5 overtones produced by two daudytės tuned in G and A respectively. Below you can see a polyphonic Sutartinė melody played in two tunings G and F: from the fundamental tone G it produces 4th, 5th and 6th overtones of the harmonic series and from F – only two the 5th and the 6th overtones.
To begin my study of Lithuanian folk songs and their instrumental versions I needed first to determine the distances between the intervals in the scale. And secondly to compare the collected results with two tempered systems: natural harmonic series (or overtone series) and 12-TET (12 tone equal temperament). About 100 examples of sutartinės and monodies and their instrumental versions were taken to determine each tone distances in the scale. One of the examples with a clearly audible microtone, the monody Lėkįs lėkįs sakalėlis (Fly Fly Little Falcon), recorded in 1937. [SLIDE 5] (we can listen to the song). In this recording which I analysed at the Sibelius Academy of Music in Helsinki, together with the composer Juhani Nuorvala, I used his microtonal instrument Tonal Plexus to identify tones by ear. In this melody we identified the second degree with a deviation of about 30 cents compared to 12-TET. It was a bit surprising to notice that the deviation corresponds to the rast microtone in maqāmāt Arabic scale. (Now we can listen to the song) (LTRF 579.4).
To measure the distances of the notes in the scale I used the computer software Melodyne-5 [SLIDE 6] which can detect sound deviations even in polyphonic music audio samples.
[SLIDE 7]
Here I present a table of overtone series in an octave for comparison with the chromatic 12-TET scale. The microtonal overtones are highlighted in yellow.
Following to the research of contemporary scholars the smallest audible microtones are identified by measuring the distance from the reference tone (or fundamental) usually from 12.5 to 50 cents within a semitone for comparison with 12-TET[1]. In identifying the intervals in the scale I have set a distance limit for detecting microtones of 20 to 80 cents and up to 10-15 cents for overtones compared to the natural harmonic series (quote - However, the choir singers do not hear tone deviations if it does not exceed more than 5 cents singing in unison. The mismatch in 10-15 cents is often felt but still tolerated This is also a standart deviation for solo performers (Ternström and Sundberg 1988, p. 59). Intonation precision of choir singers.” In: Journal of the Acoustical Society of America,.
Using Melodyne, I made the analysis of polyphonic folk instrumental song Sutartinė, on the next slide you can see [SLIDE 8] the collected data: The scale of the song, scale degrees, detected interval distances from the reference tone, and interval ratio. I have calculated interval deviations to compare to 12-TET, tone distances and deviations in the scale, and made an identification of microtones, and harmonics. The numbers in yellow with the asterisk indicate 2 microtonal degrees in the scale, and below numbers in bold with the serial number indicate 2 microtonal overtones in the scale are indicated in blue (No. 13 and No.29). The sonic code of each song was abstracted aurally from the scale generated by Melodyne, and adopted as original tones of the melody. The sonic code and its sequence of tones do not represent a tonic as the tones are arranged from the lowest to the highest with small interval distances in between, to have a clear sonic structure (in this case from C to the lowest F+ in the order in which each horn begins to play). One degree of the scale was taken into brackets as an unsung tone, depending on the algorithm of the computer program (polyphonic or melodic) that is created to detect the scale of each song.
[SLIDE 9] Now we can listen to the song.
In this table you can see the number of overtones with their serial numbers that were detected and calculated when analysing the vocal and instrumental music samples. I identified the most common 9 overtones (Nos. 29, 13, 21, 17, 19, 25, 3, 11, and 5), (B♭+, G#+, -F, C#, E♭, G#+, G, F+, E) and additionally 5 microtonal overtones Nos 29, 13, 21, 25, 11 (B♭+, G#+, -F, G+, F+, ) in vocal music, as well as not so frequently used overtones Nos. 7, 23, and 31 (-B♭, -G, B+),
For instrumental music were identified 3 microtonal overtones Nos 29, 21 and 13 (Bb+, E+,
G#+).
And for all samples commonly used microtonal overtones are Nos 29, 21, and 13 (Bb+, E+,
G#+).
[SLIDE 10]
In this table I have calculated the summary data of the overtones: you can see that vocal music songs have 6 exactly produced overtones to compare with the natural harmonic series, and for instrumental music – it is two. It could be assumed that the number of overtones with exact pitch or slight deviations are common in vocal and instrumental music. Thus, the performers of the Lithuanian folk music tradition partially reproduced the tuning and interval relations of the natural harmonic series. On the other hand, the constant use of microtones in Lithuanian vocal monodies was clearly spotted.
[SLIDE 11]
In Lithuanian vocal and instrumental music samples there are many ornamented, transitional microtones that the program identifies but does not identify as the main tones or recurring sounds but rather summarizes the common intervallic distances ratio of the song. In many cases one finds the same pair of degrees in the scale- tempered and microtonal, for example, two second degrees or two sixth, third, fourth or two seventh degrees in the scale. We can listen to the sound recording
To compare the interval distances between the tones in the scale I have divided all songs into 3, 4, 5 or 7 chord structures, according to the number of tones from 3 to 7 in the scales. I selected three main intervallic distances detected in the ensemble of horns, tunable musical instruments, based on which all examples were compared. [SLIDE 12]
After comparing all the vocal and instrumental music, the scales were divided into two groups. The first group has six subgroups, the first subgroup corresponding to the first interval distance of horn ensembles, which is very common in sutartinės, and monodies. The second group is stable; it corresponds to the second and third interval distances of horn ensembles, and is widely used in all vocal and instrumental music samples.
[SLIDE 13]
In this table you can see identical interval distances of all collected music samples according to the number of tones in the scale. Yellow color indicates sutartinės, pink- monodies, green- horn ensembles, blue – panpipes and red - kanklės.
The dominant interval distances in Lithuanian folk melodies corresponds to the penthachordic structures of the horn ensembles: the interval distance code of the second group is recognized in 22 sutartinės, monodies, horn and panpipes ensembles, and the distance code of the first group A subgroup is recognized in the 16 sutartinės, monodies, and horn ensembles. In the other subgroups the number of samples is lower or 3, 4 and 6.
[SLIDE 14]
From the results of the interval distances in the scale, the general interval distance for all vocal and instrumental music can be determined. It is the formula of the second group - three quarter tones ¾ + 1+1 tone, and the formula of the first group - ¾+tone+semitone.
In the other research angle I identified the recurring or popular tones used in performance of the songs. Thus, in Sutartinės examples the popular or recurring tones are C-F# sharp, then second degree microtones, and second degree tempered tones, and then the intervals are the fourth, fifth and sixth. In monodies - the popular or recurring tones are C-F and Bb. And in all songs – C – F#, F, Bb. So from these examples we can derive a formula for recurring tones: C-F-F#, which correspond to the intervals fourth, tritone and fifth.
To identify the distance between the tones in the scale I have chosen an amplitude of 25 to 75 cents for microtonal deviation.
The formation of the scale for the new piece begins with the analysis of the polyphonic song Sutartinė „ Two Green Little Birtches“ and the identification of the intervallic distances in the scale. [SLIDE 15]
In this table we see three microtonal degrees detected by the computer software Melodyne, the 2nd, the 4th and the 7th of which two pitches assigned to the 4th and the 7th correspond to two microtonal overtones No 23, and No 29. These distict deviations of tones in the scale of sutartinė, are characterized by microtonal alterations, the other tones in the scale correspond to 12-TET (12 tone equal temperament). [SLIDE 16 ] Following the analysis of the sutartine song a quarter tone and a sixth tone alterations are added in this fragment. (We can listen to the recording now).
On the next slide [SLIDE 17 ] you will see two versions of sutartine scales - authentic, with micro alterations, and converted, in 12-equal temperament. Tones in parentheses are unsung pitches, detected by the program. Below is a sonic code of the sutartinė (which I’ve talked about before) for comparison with the modified sutartinė interval structure implemented in multiple episodes in a piece. The difference of these scales is one tone B the sixth tone down instead of up of the original version and F sharp quatertone was eliminated from this scale.
[SLIDE 18]
So to build a new scale for the piece I chose sutartinė‘s 5 tone equal tempered scale, to combine with 5 microtonal overtones from the natural harmonic series, and with the two microtones B and C from sutartinė authentic scale. Red directions demonstrate sutartinės modified structure.
[SLIDE 19]
Now here is the scale of 19 tones with additional tones added. Red line - modified intervallic structure of sutartinė, brown line – sutartinė scale in 12-TET, blue line- 5 microtonal overtones, yellow line – additional tones in 12-TET, and a black marked additional microtone of the IIIrd degree common in Lithuanian folk tunes.
The structure of the piece is based on the projection of a harmonic chord (D-A-D-A-C#-E) [SLIDE 20] which extends the central tone D from the beginning of the piece.
The projection of the harmonic chord forms the central tones along with other tones into microinterval structures. The work begins with the timbre coloring technique on the sound d in the 1st Violin while the 2nd Violin is follows the progression from the notes B-D# tremolo to the noted of the lower octave where two violins meet in unison. Then the 1st violin begins to show the projection of a harmonic chord [SLIDE 21]
The modified interval structure of the Sutartine is incorporated at several points in the piece as part of the 19th tone scale. [SLIDE 22]
The end [SLIDE 23]
[1] Composers and music theorist of Western music culture proposed to divide the octave into 12 equal parts with the distances of 100 cents of the semitone. Thus, quartertone equals 50 cents, sixth tone – 33.3 cents, 12th tone – 16.7 cents, and sixteenth tone – 12.5 cents. In this calculation the octave is divided into 96 equal parts, thereby the semitone h-c consists of eight sixteenth tones.