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Musical Settings (XXI): “Yangguan san dié” 陽關三疊

This entry is part 43 of 43 in the series Chinese Art Song

Air of Weicheng/Send-off for Yuan’er on his mission to Anxi
渭城曲/送元二使安西
Wang Wei 王維

渭城朝雨浥輕塵
[wei4 cheng2 zhao1 yu3 yì4 qing1 chen2]
ㄨㄟˋ ㄔㄥˊ ㄓㄠˉ ㄩˇ ㄧˋ ㄑㄧㄥˉ ㄔㄣˊ
Mists, after the morning rain in Weicheng, dampened the light dust.

客舍青青柳色新
[kè4 shè4 qing1 qing1 liu3 sè4 xin1]
ㄎㄜˋ ㄕㄜˋ ㄑㄧㄥˉ ㄑㄧㄥˉ ㄌㄧㄡˇ ㄙㄜˋ ㄒㄧㄣˉ
The guest house is irradiated by verdant willows, all pristine.

勸君更盡一杯酒
[quan4 jun1 geng4 jin4 yì4 bei1 jiu3]
ㄑㄩㄢˋ ㄐㄩㄣˉ ㄍㄥˋ ㄐㄧㄣˋ ㄧˋ ㄅㄟˉ ㄐㄧㄡˇ
I urge you, my friend, to drain another cup of wine:

西出陽關無故人
[xi1 chu1 yang2 guan1 wu2 gu4 ren2]
ㄒㄧˉ ㄔㄨˉ ㄧㄤˊ ㄍㄨㄢˉ ㄨˊ ㄍㄨˋ ㄖㄣˊ
For west of Yangguan, you will find no old friends.

__Yangguan san dié 陽關三疊, qinge 琴歌

Since ancient time, qin 琴 (or guqin 古琴—ancient qin) , a fret-less plucked seven-string instrument, has been a symbol of spiritual and cultural refinement for Chinese scholars. Among qin repertoire, pieces to be played and sung by the players in a heterophonic manner are called qinge 琴歌 (qin-song). Yangguan san dié 陽關三疊, one of the most important works in this category, is based on Weicheng qu 渭城曲 (air of Weicheng) by Wang Wei 王維 (699-759). Wang has written the poem as a send-off for an old friend on his way to a remote post. Yangguan 陽關, a frontier pass near Dunhuang symbolizing the geographical and emotional boundaries in the poem, soon becomes the namesake of the qinge. The second part of the title—san dié 三疊, means “three folds” literally. In music, it is often translated as three repetitions.

Su Shi 蘇軾 (1037-1101) of the Song Dynasty in his essay “Ji Yangguan sì sheng 記陽關四聲” (an account of the fourth phrase of Yangguan) documented the performance practices of Yangguan san dié:[1]

舊傳陽關三疊，然今歌者，每句再疊而已，通一首言之，又是四疊。皆非是。或每句三唱，以應三疊之說，則叢然無復節奏。余在密州，有文勛長官，以事至密，自雲得古本陽關，其聲宛轉淒斷，不類向之所聞，每句皆再唱，而第一句不疊。乃知唐本三疊蓋如此。及在黃州，偶讀樂天《對酒》詩云：「相逢且莫推辭醉，新唱陽關第四聲。」註：「第四聲：『勸君更盡一杯酒。』」以此驗之，若第一句疊，則此句為第五聲矣，今為第四聲，則第一不疊審矣。

Three folds of Yangguan were circulated in the old days. Today, however, singers would perform each verse twice only. Taking the entire song into account, there would be four repetitions. Neither would match the “three-fold” tradition. Others sing each verse three times to fit the term “three-folds.” There would be, however, no longer any rhythmic organization. When I was in Mizhou, my superior Wen Xun came for a business visit. He said that he obtained an old version of Yangguan. It sounded melodious and forlorn, unlike what one usually heard. [In which], every verse was repeated except the first one. Hence, I understood that this would have been the three-hold practice of the Tang Dynasty. Also, when I was in Huangzhou, I came across [Bai] Letian’s “Duei jiu”. It read: “As we encounter each other, do not use inebriation as an excuse. Let’s sing the fourth phrase of Yangguan again.” The poet noted: “The fourth phrase is: ‘quan jun geng jin yi bei jiu’” Based on this note, if the first verse were repeated, the quoted verse would have been the fifth phrase. With it being the fourth, the first verse would not have been repeated.[2]

From these commentaries, we can be certain that

  • Yangguan san dié was already a popular song in the Tang Dynasty, decades after Wang Wei’s death.
  • It was passed down both orally and in written form.[3]
  • Structurally and musically, it continued to evolve.

Zhe yin shi zi qin pu 浙音釋字琴譜 (1491), one of the first tablature collections pairing song texts and notes, contains an eight-part version of Yangguan san dié. Only the initial sectionuses Wang Wei’s verses.[4]

Zhe yin shi zi qin pu 浙音釋字琴譜, Wiki commons, scanned pages 140 (right column)-141 (left)

The opening motif set to the first verse of Weicheng qu becomes a closing refrain in the later sections pairing with the text “wu shan gao song shui dong liu 吳山高聳水東流” (Wu Mountain towering, water flowing eastwards).

A later version of Yangguan appears in Xin kan fa ming qin pu 新刊發明琴譜 (1530).[5] Largely following the structure in the Zhe yin version with some new texts, it combines the first two parts into one and added a repetition of Weicheng qu as the conclusion.

Xin kan fa ming qin pu 新刊發明琴譜, vol. 2, Wiki commons, scanned page 29.

Today’s performances are mostly based on the notation found in Qinxue rumen 琴學入門 (1864).[6] Written and compiled by Zhang Hè 張鶴 as a rudimentary method book, it is divided into two parts: Part one, introduction to the instrument and performance technique; part two, tablature of essential works. Without the pairing of lyrics, this collection added gongche notation 工尺譜 to aid the pitch recognition and the appreciation of rhythmic flow.

Qinxue rumen 琴學入門 (1864)_ Two parts 二卷_Volume 6, 12 -13 : Tianjin Library, Wiki commons

This version of Yangguan consists of three parts with a coda. Each of the main parts begins with a complete statement of Weicheng qu and continues with added melodies and texts.[7] A recurring five-note bridge marks the division of the melodies. In a revised edition of 1873, the complete lyrics along with gongche notation were provided following the qin tablature.[8]

Since oral tradition always plays an important role in the performance practice of Chinese music, characteristic details vary from performer to performer. In 1949, Wang Zhengya 王震亞 adapted the interpretation of Yangguan by the twentieth century virtuoso Xia Yifeng 夏一鋒 into a choral arrangement with piano accompaniment. This arrangement is frequently performed in recitals as a solo art song. Below is a transcription of Yangguan san dié based on Qinxue rumen and interpretations of modern performers. Wang Wei’s verses are presented in bold; additional texts, regular font. The words in parenthesis, mostly pairing with the bridge, were omitted in Wang Zhengya’s choral adaptation.

__Setting of Yangguan san dié by Huang Yongxi 黃永熙 (1917-2003)

Born on July 1, 1917, in Hankou 漢口 of Cantonese heritage, Huang Yongxi grew up in Shanghai where his father owned a construction company. Devoted Christians, the Huangs participated in church choirs and music groups passionately. At age twenty, Huang Yongxi became the director of the church orchestra. He later studied conducting and theory with Theodore Urbach and Stokowski. During the Japanese occupation, he stayed behind and did musical work in the International Settlement.

He left for America in 1947, studying engineering at Bob Jones University. After graduation, he settled in New York and continued pursuing musical studies while working as an engineer. For three summers, he trained with renowned conductor Pierre Monteux. In 1961, he received a Ph.D. in Music Education at Columbia University. Six years later, he gave up a successful career in engineering and returned to Hong Kong, dedicating his time and effort on church music. As an art-song composer, Huang rendered works with melodious vocal lines and eloquent piano accompaniment.

His setting of Yangguan san dié begins with an extended piano solo carrying the entire melody, which would be repeated three times. Throughout the introduction, the melodic line is doubled in the soprano and the bass, as two voices sing in unison. Arpeggios derive from the melodic notes flow in between the voices without a “functional” structure. Dissonant intervals in mm. 6 to 8 are clearly symbols of intoxication and parting sorrows.

__ 一疊 (The first fold)

In the first repetition, the last three words of verse one—yì qing chen 浥輕塵 (dampened the light dust)—are sung twice: the second time, in a melismatic manner. The two-bar melody for verse one turns into a four-part imitation in the piano accompaniment, which continues polyphonically. The section ends on a fully functional authentic cadence in m. 19.

__ 二疊 (The second fold)

In the second fold, the last three words of verse two—liu sè xin 柳色新 (irradiated by verdant willows)—are repeated, with the second time being a melismatic variation (mm. 25-26) which moves along with the piano line like the weeping willow. The piano part opens with an ostinato consisting of a sustained open c chord in the left hand and staccato chords in the right hand. The three-note motif c-d-c, taken from the second measure of the vocal part, is repeated in the middle voice. Polyphonic texture returns in m. 25 and culminates in m. 29 where the same motif is layered in three different note values, emphasizing the words xi chu yang guan (west of Yangguan). A downward cadential movement gives a heart-broken ending.

__ 三疊 (The third fold)

In the third fold, the final three words of verse three—yì bei jiu 一杯酒 (another cup of wine) are repeated. The piano accompaniment becomes dramatic with solid chords and syncopated lower parts, extending to the lowest register of the instrument. The low c octaves are marked with “gong.” The second statement of yì bei jiu is intensified by the buildup of tremolo. The dissonances in the piano introduction recur in the last verse.

In Zhongguo yishu ge baiquji 中國藝術歌百曲集 (Collection of one hundred Chinese art songs) of 1975, orchestration shorthand was given throughout the entire song.[9] These markings reflect the composer’s ideas for tone colors and articulations as well as the possibility of an orchestrated version of the setting. Performers, especially pianists, should take these markings into consideration while preparing the work.

Words of sadness are not found in Wang Wei’s Weicheng qu. The profoundness of emotions, nevertheless, is palpable. These verses have become the embodiment of parting sorrows in the Chinese psyche over the centuries. Saying farewell once is never enough. Thus, let the words and songs be repeated once, twice and more times.

[1] 三蘇全集_第三十九册_Wiki common, scanned page 3.
[2] The verses are taken from the fourth of five seven-word jueju on wine, “Duei jiu wu shou 對酒五首,” by Bai Letian (Juyi) 白樂天 (居易).
[3] Traditional guqin tablature, jianzi pu (減字譜), uses symbols combining elements of characters to indicate the playing technique and the position of the string.
Guqin_notation_Wiki, https://blog.nyl.io/guqin-part-3-tablature-old-and-new/
[4] 浙音釋字琴譜_朱權原題臞仙_刻本_Wiki common, scanned page 140-143. The last section is incomplete.
See www.silkqin.com/02qnpu/09zysz/zy13ygsd.htm#music for details on this version of Yangguan san dié including the complete texts and performance notes. A transcription and performance by John Thompson can be found at https://www.silkqin.com/07play/staff/1505/revzy13ygsd.pdf and https://www.silkqin.com/06hear/myrec/1505/zy13ygsd.mp3
[5] 新刊發明琴譜_第2冊_Wiki common, scanned pages 29-34.
[6] Many contemporary sources cited the date 1867. A preface by the compiler Zhang Hè 張鶴 was dated the third year of Tongzhi 同治三年 (1864).
琴學入門_二卷_第1冊_Wiki common, scanned page 4.
[7] 琴學入門_二卷_第6冊_Wiki common, scanned pages 12-13.
Yangguan san dié, played and sung by Hu Ruyin 胡如茵_YouTube.
[8] Texts on the first page of Part two indicated that the collection was revised in Tongzhi kweiyo 同治癸酉 (1873) by Li Shifang 李士芳. 琴學入門二卷_清張鶴輯_清陸琮校刊_清李士芳重較_清吳嗣昭訂_清光緒刻本_Wiki common, scanned pages 83-88.
[9] Liang Rongling 梁榮嶺, ed., Zhongguo yisu ge baiquji 中國藝術歌百曲集 (Collection of one hundred Chinese art songs), Taipei, Tiantong Publication 天同出版社, 1975, 73-75.

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Musical Settings (XX): Sang Tong’s Accompaniment for Hongdou ci

This entry is part 42 of 43 in the series Chinese Art Song

__Sang Tong 桑桐 (1923-2011)

Born Zhu Jingqing 朱鏡清 in Shanghai, Sang Tong was a composer, music educator, and theorist. His ”Ye Jing”(夜景, Night scenery) for solo violin and piano (1947) was the earliest implementation of twelve-tone series by a Chinese composer. Sang credited his mentors Wolfgang Fraenkel (1897-1983), Julius Schloss (1902-1973) and Tan Xiaolin 譚小麟 for his work.

In 1941, he entered the National Music Conservatory, studying composition under Fraenkel, a Jewish musician escaping Nazi oppression in Shanghai.[1] Sang recalled being introduced to works of Debussy, Stravinsky, Vaughan Williams, Kodály, Bartok, Scriabin and Mahler.[2] In addition to analyses of standard repertoire by composers such as Bach, Beethoven, Schubert, Brahms and Richard Strauss, Fraenkel’s teaching materials included Arnold Schoenberg’s Harmonielehre (Theory of harmony) and Ernst Kurth’s Grundlagen des linearen Kontrapunkts: Bach’s Melodische Polyphonie (Foundation of linear counterpoint: Bach’s melodic polyphony).

For health reasons, Sang dropped out of the Conservatory in 1943 but re-enrolled three years later, continuing his study with Julius Schloss, a colleague and friend of Alban Berg. He also audited classes taught by Tan Xiaolin, a young professor who had studied with Paul Hindemith at Yale.[3] In 1947, Sang composed “Ye Jing” and a piano piece “Zai na yaoyuan de difang” (在那遙遠的地方, In the land far, far away) based on a folk tune from the Qinghai 青海 Province. Both explored modern compositional techniques and were premiered in 1948 in Shanghai.[4] He also collaborated with Qu Xixian 瞿希賢 on the film music for Ye Dian (夜店, Night Inn) and Yian Yiang Tian (艷陽天, Bright Sunny Days) during this period.

Frequent participant in demonstrations held by students with progressive ideology, Sang began his training by CCP in 1948. As the conflicts between CCP and KMT intensified, he relocated to Northern Jiangsu Liberated Area 蘇北解放區 and changed his name to Sang Tong. In March 1949, he became a CCP member officially and was sent back to Shanghai. In June 1949, Sang Tong assisted Shanghai Municipal Military Control Commission of the Chinese People’s Liberation Army 中國人民解放軍上海市軍事管制委員會[5] in taking control of the Music Conservatory. A few months later, he began his long teaching career there. In addition to teaching theory and composition, he held various administrative positions. From 1986 to 1991, he served as the President of the Conservatory.

Sang Tong’s writings include “Heshengxue zhuanti liu jiang” (和聲學專題六講, Six lectures on harmony), “Hesheng de lilun yu yingyong”(和聲的理論與應用 , The theory and application of harmony), “Wusheng zonghexing hesheng jiegou de tansuo”(五聲綜合性和聲結構的探索, Investigations of the structure of integrated pentatonic harmonies)[6], and “Duodiaoxing xiezuo shoufa jianjie” (多調性寫作手法簡介, An introduction to polytonal writing techniques). He passed away on July 24, 2011, in Shanghai at the age of 88.

—Integrated Harmonization of Pentatonic Melodies

In Wusheng zonghexing hesheng jiegou de tansuo (五聲綜合性和聲結構的探索, Investigations of the structure of integrated pentatonic harmonic), Sang Tong indicated that pentatonic melodies could be harmonized using basic western tonal harmonic structure—triads in major and minor tonalities—三度結構性和聲方法. Other possibilities include using parallel motions (planing) 平行進行, polychordal 複合和聲, and polytonal 複合調式structures. He believed that, in practice, harmonizations of pentatonic melody were often restricted by three notions:

  • Emphasizing that the tonality of the harmony must match that of the melody
  • Using only tertian chords—stacking thirds—as the structural foundation
  • Relying on functional harmony

To break away from these restrictions, he explored the implementation of integrated harmonization of pentatonic melodies, based on the methodology developed by Paul Hindemith.

The key component of Hindemith’s theory is “interval,” as he wrote in his seminal treatise Craft of Musical Composition:[7]

. . . The motion from one tone to another, the bridging of a gap in space, produces melodic tension, while the simultaneous juxtaposition of two tones produces harmony. Thus the Interval, formed by the connection of two tones, is the basic unit of musical construction.

He ranks the intervals by their acoustic stability to a fundamental tone. The strength of intervals, in turn, governs the harmonic progressions, freed from the traditional functional harmonic structure.

Like Hindemith, Sang Tong builds his theory around the interplay of melodic and harmonic intervals. He explains that all the notes of a pentatonic scale could be combined into three-note, four-note, and five-note chords. Each group is subcategorized by their intervallic organization.[8] He systemizes these chords using Hindemith’s conception of intervallic strength and root identification. He emphasizes that, in integrated pentatonic harmonization, chords can be linked without hierarchical restrictions. Nevertheless, the movements of roots need to be organized around a tonal center. Harmonic intensity and colors need to be distributed orderly.

Finally, Sang prescribes methods of tonal expansion:[9]

  • Expansion from five tones to six or seven tones can be created by layering multiple voices with different tonalities.
  • Adding modified tones, such as qing-jue 清角 (raised-jue), bian-zhi 變徵 (lowered-zhi), qing-yu 清羽 (raised yu), and bian-gong 變宮 (lowered gong), without changing the mode and the pentatonic nature.[10]
  • Modes based on the same tonal center can be combined to expand the tonality.

Sang uses these additional tones to enrich the tonalities and to balance the harmonic fluctuations.

__Sang Tong’s piano accompaniment for Hongdou ci*
*The following transcription and analysis use C as the tonal center—C minor key signature and C as yu 羽.

Although Sang was setting accompaniment to a song written by another composer, he was not hindered by the existing melodies. Instead, he used the pentatonic tones as constituents of harmonies—harmonic cells in Hindemith’s term. According to Hindemith, harmonic movements were felt by the increase and decrease of harmonic tensions—fluctuations. As he categorized chords into six groups by the existence or absence of tritone, the presence of second and seventh, and the root positions, he ranked them by their intervallic strength. The harmonic tension would increase with movements from lower-number groups, the more stable harmonies, to higher ones, the less stable ones. Combinations of pentatonic tones often contain seconds and sevenths but without tritones. Therefore, most of these chords would be placed under group III in Hindemith’s chord analysis. If the majority of the chords were in the same group, there would be very little fluctuation.[11] Sang solved this dilemma by implementing tonal expansions.

Sang opened his piano introduction with a four-note chord, c-f-g-c, resonating from the extreme ends of the keyboard. Without the interval of third, he established a non-western sonority immediately. Structurally, this chord contained the fifth and the fourth, two of the strongest intervals according to Hindemith. Acoustically, he utilized the rich overtones from the lower range of the instrument to achieve a colorful but open sound. This chord structure would be moved up a fifth in m. 3 and return to the first position in m. 5.

Liu Xue’an’s piano introduction, based on the thematic melody, was only two measures long and fully cadenced. Sang Tong quoted the first two vocal lines and linked them to the vocal entrance with an added measure of chords and arpeggios. The familiar syncopated repeating chords in the left hand broke the solemness created by the opening chord. They also brought in two tones outside of the pentatonic C-yu mode: The a-flat in mm. 1-2 and b-natural in m. 3. Although they could be interpreted as modified tones within the pentatonic system, a more comprehensive explanation would be that Sang overlapped the C-pentatonic melody with C harmonic minor scale.

More outside tones appeared in mm. 4-5 in the right-hand parts. The two Ds in m. 4 were auxiliary bian-gong 變宮 included in the original melody. They led to the d-flats in measure 5, a completely foreign tone.  Tracing the voice-leading in these two measures, a melodic movement of D-C-D-flat-C became clear. In the final beat of m. 4, a double-neighboring tone group—d-flat & b-flat—moved to the octave Cs in m. 5.

As the melody ended in m. 4, the underlaying harmony, a composite chord of minor third-perfect fifth-minor sixth, sounded an inconclusive tone. The tritone formed by the d-flat and g-jue 角 furthered the uneasiness. Structurally, this tritone was stabilized by two sets of perfect fifths: the D-flat-A-flat in the upper piano part and the rooted C-G in the bass.

The first two phrases of the vocal line (mm. 6-9), covering verses one and two of the poem, were the most straightforward section of the entire song structurally. Worth noticing, however, were the unique use of downward arpeggios in the upper register of the piano. They produced an effect reminiscent of the sliding tones on the guzheng 古箏 or the guqin 古琴. Set an octave above the vocal line, they became a phenomenon of their own.

The other distinctive feature in this opening section is the descending bass line from  m.6 to m. 9. Doubling the melodic line in the first measure as in Liu’s version, it continued to descend on a C-natural minor scale (or its Chinese counterpart qing-jue mode 清角調). Here, Sang again overlayered pentatonic and heptatonic scale. Freed from functional harmonic progression, Sang was able to take this feature further. Starting with f/F in m. 10, a descending E-flat major scale was formed, with a chromatic embellishment –B-flat-A-natural-A-flat in mm. 12-13. Without the presence of tertian or traditional seventh chords, there was no clear sense of “modulation.”

Sang matched the increasing anxiousness in verses three to six and the agitated dotted-three-note motif in mm. 10, 12, 14, and 16 with syncopated chords of denser texture and accented jumping chords in the right hand. A-natural, a foreign tone, appeared frequently throughout this section. Instead of fitting it into any tonal pattern, it might be best to observe its descriptive function here. It first took place in the piano right-hand part in m. 11, coinciding with the words huang hun 黃昏 (dusk), a time when the fading of daylight obscured the scenery. Then, with the chromatic movements in the bass, it marked the words xin chou 新愁 (new sorrow) and jiu chou 舊愁 (old sorrow). It generated two palpable tritones with octave-E-flats in mm. 15 and 16, manifesting the suffering of choking and sad reflection of a waning face. These back-to-back tritones caused a ripple in the harmonic movement.

Sequential bass lines in mm. 18 to 21 brought in a sense of relentlessness. The two A-naturals should simply be treated as passing tones. The onomatopoeic chords in the final beat of each measure should be handled carefully.

With the upper piano parts doubling the melodic lines, the final section of Sang Tong’s arrangement of Hongdou ci was marked by frequent occurrences of tritones. The A-natural-D combination in m. 23 stirred up a quick III-V-III harmonic movement stressing the pains in the vocal cries. A longer and less stable harmony with an F-B tritone in m. 26 was eased in the first ending but went unresolved onto another tritone chord in the second ending. While most composers sought smooth and conclusive endings, Sang chose to, in the penultimate measure, circle back to the open-ended harmony linking the introduction and the initial vocal line. He then evoked the opening c-f-g-c chord yet added a seventh, the least stable interval. The message of the never-ending longing could not be clearer.

In his piano accompaniment for Hongdou ci, by combining traditional and western musical practices, Sang Tong cracked open a field of possibilities for Chinese composers. By exploring the acoustic boundaries and performing techniques, he also elevated the role of the piano in an art song. Given the fact that Liu Xue’an’s works were banned in China until early 1980s, it could only have become popular in the final decades of the twentieth century. It represented the result of deeper western influences during the late 1940s, directly and indirectly, to a generation of composers.

[1] Christian Utz, “Cultural Accommodation and Exchange in the Refugee Experience: A German-Jewish Musician in Shanghai,” Ethnomusicology Forum, vol.13, no. 1, January 2004, 119-151.
[2] Sang Tong 桑桐, “Jinian Fulanke’er yu Xu Luoshi” (紀念弗蘭克爾與許洛士, In memory of Wolfgang Fraenkel and Julius Schloss), Yinyue Yishu (音樂藝術, The Art of Music: Journal of the Shanghai Conservatory of Music), 12, no. 1 (1990): 10-15
[3] https://en.wikipedia.org/wiki/Tan_Xiaolin
[4] Utz, Musical Composition in the Context of Globalization: New Perspectives on Music History of the 20th and 21st Century, trans. Laurence Sinclair Willis (Bielefeld: Transcript-Verlag, 2021), 182. https://doi.org/10.14361/9783839450956.
[5] Qian Yiping 錢亦平, “Sang Tong Xiansheng’” 桑桐先生, 17, quoted in Cheong Wai-Ling, “Reading Schoenberg, Hindemith, and Kurth in Sang Tong: Modernist Harmonic Approaches in China,” Acta Musicologica 88, no. 1 (2016), 7.
中國人民解放軍上海市軍事管制委員會_zh.Wiki/zh-tw/
[6] Sang Tong, “Wusheng zonghexing hesheng jiegou de tansuo, Yinyue Yishu, 2, no. 1 (1980): 20-44. This title is somtimes translated as “The Vertical Structure of Pentatonic Harmonies.” Since Sang’s discussion included both the horizontal and vertical applications of pentatonic scales, the terms “integrated” or “composite” (綜合性) are much more comprehensive than “vertical” (綜向性).
[7] Paul Hindemith, The Craft of Musical Composition, Book 1, Theoretical Part,trans. Arthur Mendel, (Associated Music Publisher, 1942): 57
[8] Sang, Ibid., 23-24.
[9] Ibid., 34-40.
[10] Xiao Yomei 蕭友梅 in “Gujin zhongxi yingjie gaishuo 古今中西音階概說” (Survey of ancient and modern Chinese and western scales) traced the historical development of Chinese heptatonic scales. He also listed the eight-four possible heptatonic scales (seven modes on twelve tones), using the Western church mode comparison. Yueyi, 1930: 14-25
See also 七聲調式_zh.Wiki/zh-tw/
[11] In Hindemith’s chord group, III 1 and III 2 differ only in their root positions. III 2 chords can be considered as inverted III 1. Thus, the movements back and forth between the two are subtle.