{"id":8049,"date":"2023-04-16T22:33:42","date_gmt":"2023-04-16T22:33:42","guid":{"rendered":"https:\/\/theory.esm.rochester.edu\/integral\/?page_id=8049"},"modified":"2023-05-31T00:42:55","modified_gmt":"2023-05-31T00:42:55","slug":"zhang","status":"publish","type":"page","link":"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/","title":{"rendered":"Hope to Grief: An Analysis of Dvo\u0159\u00e1k\u2019s <i>Moravian Duets<\/i>, op. 38"},"content":{"rendered":"\n\n\n\n\n<script type=\"text\/x-mathjax-config\">\nMathJax.Hub.Config({\n messageStyle: \"none\"\n});\n<\/script>\n\n\n<style>\n.wp-block-table table tr td {white-space: nowrap;}\n.wp-block-table table tr td {font-size: 90%}\n<\/style>\n\n\n\n<p><strong>Xieyi (Abby) Zhang<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Abstract<\/h3>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p>Despite being considered some of his most pivotal compositions, Dvo\u0159\u00e1k\u2019s <em>Moravian Duets, <\/em>op. 38, have long been analytically overlooked. The present essay uses neo-Riemannian methods to understand the final set of Dvo\u0159\u00e1k\u2019s <em>Moravian Duets<\/em> and demonstrates that these parsimonious voice-leading techniques\u2014ones that came to dominate Dvo\u0159\u00e1k\u2019s compositional style\u2014play against descending fifths progressions to create a tragic narrative across the duet cycle.<\/p><p><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/36-zhang\/\" data-type=\"page\" data-id=\"8872\">View PDF<\/a><br><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/\">Return to Volume 36<\/a><\/p><\/blockquote>\n\n\n\n<p><strong>Keywords and Phrases:<\/strong> Dvo\u0159\u00e1k, neo-Riemannian, nineteenth century, art song, octatonic cycles, narrative, song cycles<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Introduction<\/strong><\/h2>\n\n\n\n<p class=\"has-drop-cap\">Anton\u00edn Dvo\u0159\u00e1k\u2019s <em>Moravian Duets<\/em>, opp. 20, 32, and 38, composed between 1875 and 1877, have long been considered some of his most pivotal compositions.<span id='easy-footnote-1-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-1-8049' title='On the history of Dvo\u0159\u00e1k\u2019s Moravian Duets, see D\u00f6ge (2001) and \u0160ourek (2004).'><sup>1<\/sup><\/a><\/span> They earned him recognition by the likes of Johannes Brahms and Fritz Simrock, spurred numerous similar compositions, and ultimately gave him the international recognition to be invited by Jeannette Thurber to the United States, where he composed other iconic works like the \u201cNew World\u201d Symphony and the \u201cAmerican\u201d String Quartet.<span id='easy-footnote-2-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-2-8049' title='One of the primary motivations for Dvo\u0159\u00e1k\u2019s invitation to the United States was to build up American music. On this issue, Thurber invited Dvo\u0159\u00e1k because he had been \u201cso successful in taking Bohemian music into the mainstream\u201d (Beckerman 2003, 4).'><sup>2<\/sup><\/a><\/span> Analytical discussions of such formative compositions, however, have been virtually nonexistent in the literature. This neglect might give the impression that, despite their importance to Dvo\u0159\u00e1k\u2019s life, the analytical aspects of the compositions are somewhat uninspired. On the contrary, these duets exhibit a rich and unique musical language that not only enhances the narrative of the song cycles, but also influences much of Dvo\u0159\u00e1k\u2019s later harmonic-compositional style.<span id='easy-footnote-3-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-3-8049' title='For example, Dvo\u0159\u00e1k\u2019s use of frequent modulations is a trait seen in these duets. For more on these modulations in his symphonies, see Jaroslav Volek (1984).'><sup>3<\/sup><\/a><\/span>\n\n\n\n<p>This paper analyzes the third set of <em>Moravian Duets<\/em>, op. 38 through a neo-Riemannian perspective and sheds light on the narrative implications of these songs. I begin with an overview of the set and devise a formal model for analyzing the main harmonic gestures in the duet cycle. Following this, I analyze each song in order, illuminating a narrative of hope to grief that weaves across the four songs.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>1. The <em>Moravian Duets<\/em>, Op. 38: A Summary<\/strong><\/h2>\n\n\n<p>The <em>Moravian Duets<\/em>, op. 38 are the third and final set of <em>Moravian Duets<\/em> and the only one to remain unchanged from its original publication. All three sets of duets were commissioned by Jan and Marie Neff and are based on the texts of Moravian folk songs compiled by Franti\u0161ek Su\u0161il.<span id='easy-footnote-4-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-4-8049' title='On Dvo\u0159\u00e1k\u2019s interactions with and relationship to Moravia, see Bul\u00ed\u0159 (1990).'><sup>4<\/sup><\/a><\/span> The texts and translations of the four poems are provided in Table&nbsp;1.<span id='easy-footnote-5-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-5-8049' title='Translations are mostly my own, with occasional consultation against that in Adams (2003). Given the poetic nature of the original text, I opt here for a literal translation that preserves the ordering of words. However, in places where the meaning is obscured by the literal translation, I provide an idiomatic translation in square brackets.'><sup>5<\/sup><\/a><\/span> The textural profile of the four duets remains remarkably consistent throughout. Each duet features the soprano and alto singing homophonically with the piano doubling both voices. The only two moments where this pattern is broken are used to paint the image of separation and loneliness.<\/p>\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Title<\/td><td>Key<\/td><td>Text<\/td><td>Translation<\/td><\/tr><tr><td>Mo\u017enost (Possibility)<\/td><td>E major<\/td><td>Zakukala zezulenka sed\u0148a na bo\u0159e, <br>zaplakala m\u00e1 panenka cho\u010fa po dvo\u0159e. <br>Ja co pla\u010de\u0161 a na\u0159ik\u00e1\u0161, dy\u0165 ty bude\u0161 m\u00e1, <br>a\u017e zezulka na v\u00e1noce t\u0159kr\u00e1t zakuk\u00e1! &nbsp; <br><br><br>Jak pak bych j\u00e1 neplakala, \u0161ak nebudu tv\u00e1, <br>dy\u0165 zezulka na v\u00e1noce nikd\u00e1 nekuk\u00e1t! <br>P\u00e1n B\u016fh mocn\u00e9, P\u00e1n B\u016fh dobr\u00e9, on to<br>m\u016f\u017ee d\u00e1t, <br>\u017de zezulka na v\u00e1noce m\u016f\u017ee zakuk\u00e1t!<\/td><td>Calls the cuckoo [the cuckoo calls] sitting on a pine tree, <br>cries my darling [my darling cries] walking about the<br>yard. <br>\u201cAlas, what are you crying about, that you will be mine, <br>as the cuckoo on Christmas three times calls out.\u201d &nbsp; <br><br>\u201cHow would I not weep, since I would not be yours, <br>indeed the cuckoo on Christmas never calls!\u201d <br>\u201cGod almighty, God the good, he can provide it, <br>that the cuckoo on Christmas can call.\u201d<br>&nbsp;<\/td><\/tr><tr><td>Jablko (Apple)<\/td><td>G major<\/td><td>Svi\u0165 m\u011bs\u00ed\u010dku, vysoko, a\u017e j\u00e1 povandruju, <br>aby mil\u00e1 vid\u011bla, ker\u00f3 cest\u00f3 p\u016fdu! <br>P\u016fduli t\u00f3 vrch\u0148\u00e9\u0161\u00ed a nebo spod\u0148\u00e9\u0161\u00ed, <br>bude plakat, na\u0159ikat moja n\u00e9mil\u00e9\u0161\u00ed. &nbsp; <br><br><br>K\u00f3lelo se, k\u00f3lelo \u010derven\u00e9 jabli\u010dko, <br>nemohlo se dok\u00f3let k m\u00e9 mile na l\u016f\u017eko. <br>A kdy\u017e se dok\u00f3lelo, odpoved&#8217; j\u00ed dalo: <br>s P\u00e1nem Bohem tu b\u00e9v\u00e9, moja mil\u00e1 panno.<br><\/td><td>Shine, moon, high, as far as I wander, <br>so that my dear sees where I am going! <br>I will go, if either by high road or low road, <br>will cry and lament my most loved. [my most loved will<br>cry and lament.] &nbsp; <br><br>Rolled, rolled, the little red apple, <br>it could not roll to my love in bed. <br>And when it was done rolling, it gave her a response: <br>\u201cwith the Lord God here you stay, my beloved.\u201d<\/td><\/tr><tr><td>V\u011bne\u010dek (Garland)<\/td><td>B$$\\flat$$ major<\/td><td>Jid\u00fa \u017eenci z rol\u00ed, p\u0159ikr\u00fdvajte stoly, <br>stoly jaborov\u00e9, u\u017ei\u010dky klenov\u00e9. <br>Kdo mn\u011b pro n\u011b p\u016fjde, ten m\u016fj mil\u00fd <br>bude. &nbsp; <br><br>\u0160el mn\u011b pro n\u011b synek, bylo mu Martinek, <br>j\u00e1 sem mu sl\u00fabila sv\u016fj zelen\u00fd v\u00ednek. &nbsp; <br><br>Vinku m\u016fj, v\u00ednku m\u016fj, co ti m\u00e1m ud\u011blat? <br>M\u00e1mli \u0165a opustit? A lebo \u0165a nechat? &nbsp; <br><br><br>M\u00e1 panenko kr\u00e1sn\u00e1, nestrhaj mia z <br>jasna, <br>trhaj mia na podzim, a\u017e sa j\u00e1 zhotov\u00edm!<\/td><td>Ride reapers from the field, cover the tables, <br>maple tables, sycamore legs. <br>Who will go for me to fetch them, that my love will be. &nbsp; <br><br><br>My son went for me, he was Martinek, <br>I have promised him my green garland. &nbsp; <br><br>My garland, my garland, what am I supposed to do with <br>you? <br>Should I forsake you? Give you up? &nbsp; <br><br>\u201cMy darling beautiful, don\u2019t pluck me in the spring, <br>pluck me in the fall, when I\u2019ll be ready.\u201d<br>&nbsp;<\/td><\/tr><tr><td>Ho\u0159e (Grief)<\/td><td>B major<\/td><td>Zr\u00e1lo jabko, zr\u00e1lo, jak dozr\u00e1lo, spadlo, <br>\u017ee moje srdenko, do \u017ealosti vpadlo. &nbsp; <br><br>Ne tak do \u017ealosti, do velk\u00e9ho ho\u0159e, <br>\u017ee moje srdenko, no\u017eem kr\u00e1ja\u0165 mo\u017ee. &nbsp; <br><br>Ne tak no\u017eem kr\u00e1ja\u0165 ale pil\u00fa \u0159eza\u0165, <br>dy\u0165 tebe nemo\u017eu, m\u016fj syne\u010dku, dosta\u0165.<br>&nbsp;<\/td><td>Ripened apple, ripened, as it matured, it fell, <br>as my heart fell into mourning. &nbsp; <br><br>Not just into grief, [but] into great sorrow, <br>that my heart has been cut with a knife. &nbsp; <br><br>Not just sliced by a knife but cut by a saw, <br>indeed to you I cannot, my son, to get. [indeed I cannot <br>get to you, my son.]<\/td><\/tr><\/tbody><\/table><figcaption>Table 1: <em>Moravian Duets<\/em>, op. 38, keys, texts, and translations of the four songs.<\/figcaption><\/figure>\n\n\n<p>Harmonically speaking, the duets combine a globally octatonic soundscape realized using neo-Riemannian P and R transformations with a locally diatonic vocabulary generated by functional diatonic harmonies and progressions by fifth.<span id='easy-footnote-6-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-6-8049' title='The relationship between octatonic collections and neo-Riemannian PR cycles has most explicitly been described by Plotkin (2019, [3.1.4]). Several recent authors have noted on the role of octatonicism in works by early twentieth century composers such as Edward Elgar (Chandler 2020), Sergei Prokofiev (Bazayev 2018), and Maurice Ravel (Bl\u00e4ttler 2022). These entries add to the use of octatonicism by composers such as Igor Stravinsky (Burger 1968), Claude Debussy (Forte 1991), and B\u00e9la Bart\u00f3k (Cohn 1991). The earliest composer thus far whose music has been analyzed as octatonic is Nikolai Rimsky-Korsakov. Both Sylvia Kahan (2005) and Richard Taruskin (2011) have described the role of the octatonic in Rimsky-Korsakov\u2019s music.'><sup>6<\/sup><\/a><\/span> Example&nbsp;1 illustrates the interactions between these two harmonic profiles.<span id='easy-footnote-7-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-7-8049' title='These duets are, generally speaking, globally octatonic while remaining locally diatonic, much like Richard Cohn\u2019s (2012, 195\u2013199) observations of double syntax in the music of Schubert. As such, the present analysis will couple neo-Riemannian P and R transformations with surface-level diatonic features such as cadences. Example&amp;nbsp;1, for instance, draws heavily from Cohn\u2019s (1999) star-cluster analyses of Schubert\u2019s work.'><sup>7<\/sup><\/a><\/span> The three unique octatonic collections parse the collection of keys into three closed tonal cycles, each encompassing a complete set of PR-related triads. Progressions by fifth, on the other hand, are used to traverse between the three collections.<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-01-pr-and-fifths-cycles\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-01-PR-and-Fifths-Cycles.png\" alt=\"\" class=\"wp-image-8074\" width=\"256\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-01-PR-and-Fifths-Cycles.png 1546w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-01-PR-and-Fifths-Cycles-262x300.png 262w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-01-PR-and-Fifths-Cycles-895x1024.png 895w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-01-PR-and-Fifths-Cycles-768x878.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-01-PR-and-Fifths-Cycles-1343x1536.png 1343w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>Example 1: Relationship between neo-Riemannian PR cycles, their octatonic collections, and progressions by fifth.<\/figcaption><\/figure><\/div>\n\n\n<p>Interactions between PR cycles and descending fifths portray the textual narrative across the duet cycle. As Table&nbsp;1 demonstrates, the song cycle begins with hope for the narrator to be reunited with the object of her desires. As the song cycle progresses, the protagonist becomes increasingly worried, until hope ultimately dies in the final song. Tonal centers for the first three songs occupy the OCT<sub>1,2<\/sub> PR cycle (or PR<sub>1,2<\/sub>).<span id='easy-footnote-8-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-8-8049' title='Given the interchangeability of the OCT collections and their generated PR cycles, the rest of this essay will refer to PR cycles generated by their respective OCT&lt;sub&gt;x,y&lt;\/sub&gt; collections as PR&lt;sub&gt;x,y&lt;\/sub&gt;. For example, the PR cycle contained within OCT&lt;sub&gt;1,2&lt;\/sub&gt; will be referred to as the PR&lt;sub&gt;1,2&lt;\/sub&gt; cycle.'><sup>8<\/sup><\/a><\/span> Within this cycle, increasing voice-leading distance from the key of the first song represents increasing distance from hope, and the final song begins in PR<sub>0,2<\/sub> to depict the new unattainability of hope. Throughout the duet cycle, PR transformations gradually give way to fifth-related ones. For the most part, PR-related voice-leading supports the hopeful atmosphere established at the outset of the song cycle. The subject of the text then becomes increasingly mournful, and the descending affect of the fifths begins to settle in as the narrator confronts the reality of loss.<\/p>\n\n\n<h2 class=\"wp-block-heading\"><strong>2. Harmonic System of the <em>Moravian Duets<\/em>: Analytical Model and Criteria<\/strong><\/h2>\n\n\n<p>The harmonic motions in these duets are most effectively modeled using Julian Hook\u2019s (2002) uniform triadic transformations. Under this model, the set of all chords related by P and R can be generated using &lt;\u2013,9,0&gt; and its inverse, &lt;\u2013,0,3&gt;, whereas those related by fifths are generated through &lt;+,7,7&gt; and &lt;+,5,5&gt;, its inverse.<span id='easy-footnote-9-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-9-8049' title='The labeling of the PR cycle\u2019s generator as a single transformation is based on Hook\u2019s (2002, 89\u201392) description of the same. It offers the advantage of highlighting the cyclical nature of the transformations even if it sacrifices the uniqueness of the two neo-Riemannian transformations (P = &amp;lt;\u2013,0,0&amp;gt; and R = &amp;lt;\u2013,9,3&amp;gt;) involved in this cycle.'><sup>9<\/sup><\/a><\/span> Since the two sets of generators function independently from one another, this group of transformations is best modeled using the ordered-pair operations (&lt;\u2013,9,0&gt;<em><sup>a<\/sup><\/em>,&nbsp;&lt;+,7,7&gt;<em><sup>b<\/sup><\/em>), where $$a \\in \\mathbb{Z}_8 $$&nbsp; and $$b \\in \\mathbb{Z}_{12} $$&nbsp; represent the number of times each operation is applied. This group of transformations is isomorphic to the direct product group $$\\mathbb{Z}_8 \\times \\mathbb{Z}_{12}$$&nbsp; represented by (<em>a<\/em>,&nbsp;<em>b<\/em>) and can therefore be represented using the latter.<span id='easy-footnote-10-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-10-8049' title='Proof: We first prove that the transformations &amp;lt;\u2013,9,0&amp;gt; and &amp;lt;+,7,7&amp;gt; generate cyclic groups of order 8 and 12, respectively, thus demonstrating that these groups are respectively isomorphic to $$\\mathbb{Z}_8$$ and $$\\mathbb{Z}_{12}$$. The group (&amp;lt;\u2013,9,0&amp;gt;&lt;em&gt;&lt;sup&gt;a&lt;\/sup&gt;&lt;\/em&gt;,&amp;nbsp;&amp;lt;+,7,7&amp;gt;&lt;em&gt;&lt;sup&gt;b&lt;\/sup&gt;&lt;\/em&gt;), then, simply becomes a direct product of two cyclic groups.&lt;\/p&gt;\n&lt;p&gt;To find the order for &amp;lt;\u2013,9,0&amp;gt;, we must show that &amp;lt;\u2013,9,0&amp;gt;&lt;em&gt;&lt;sup&gt;a&lt;\/sup&gt;&lt;\/em&gt; = &amp;lt;+,0,0&amp;gt; when &lt;em&gt;a&lt;\/em&gt; = 8. Since the first component of the transformation is isomorphic to $$\\mathbb{Z}_2 $$&amp;nbsp; with \u201c+\u201d being the identity element (Hook 2002, 68), we see that &lt;em&gt;a&lt;\/em&gt; must be even. We can thus simplify the equation to &amp;lt;\u2013,9,0&amp;gt;&lt;em&gt;&lt;sup&gt;2m&lt;\/sup&gt;&lt;\/em&gt; = &amp;lt;+,9,9&amp;gt;&lt;em&gt;&lt;sup&gt;m&lt;\/sup&gt;&lt;\/em&gt; = &amp;lt;+,0,0&amp;gt;, where &lt;em&gt;m&lt;\/em&gt; = 2&lt;em&gt;a&lt;\/em&gt;. (On the product formula for transformations, see Hook 2002, 69). Since &amp;lt;+,9,9&amp;gt;&lt;em&gt;&lt;sup&gt;m&lt;\/sup&gt;&lt;\/em&gt; = &amp;lt;+,9&lt;em&gt;&lt;sup&gt;m&lt;\/sup&gt;&lt;\/em&gt;,9&lt;em&gt;&lt;sup&gt;m&lt;\/sup&gt;&lt;\/em&gt;&amp;gt;, we simply find the smallest &lt;em&gt;m&lt;\/em&gt; such that 9&lt;em&gt;&lt;sup&gt;m&lt;\/sup&gt;&lt;\/em&gt; = 0 mod 12. This gives us &lt;em&gt;m&lt;\/em&gt; = 4 and, subsequently, &lt;em&gt;a&lt;\/em&gt; = 8.&lt;\/p&gt;\n&lt;p&gt;The case is simpler for &amp;lt;+,7,7&amp;gt;. We must show that &amp;lt;+,7,7&amp;gt;&lt;em&gt;&lt;sup&gt;b&lt;\/sup&gt;&lt;\/em&gt; = &amp;lt;+,0,0&amp;gt; when &lt;em&gt;b&lt;\/em&gt; = 12. Since &amp;lt;+,7,7&amp;gt;&lt;em&gt;&lt;sup&gt;b&lt;\/sup&gt;&lt;\/em&gt; = &amp;lt;+,7&lt;em&gt;&lt;sup&gt;b&lt;\/sup&gt;&lt;\/em&gt;,7&lt;em&gt;&lt;sup&gt;b&lt;\/sup&gt;&lt;\/em&gt;&amp;gt;, we simply find the smallest &lt;em&gt;b&lt;\/em&gt; such that 7&lt;em&gt;&lt;sup&gt;b&lt;\/sup&gt;&lt;\/em&gt; = 0 mod 12. This gives us &lt;em&gt;b&lt;\/em&gt; = 12.'><sup>10<\/sup><\/a><\/span> In other words, using the form (<em>a<\/em>, <em>b<\/em>), <em>a<\/em> represents the number of nodes traveled along the octatonic PR cycle, whereas <em>b<\/em> indicates the number of fifths traversed.<\/p>\n<p>Example&nbsp;2 demonstrates the application of this nomenclature using the opening of the second duet. This group of operations contains two immediately relevant subgroups. The subgroup described by the transformations (<em>a<\/em>, 0) contains the set of all neo-Riemannian P and R transformations, while the subgroup described by (0, <em>b<\/em>) contains the set of all fifths-related transformations.<span id='easy-footnote-11-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-11-8049' title='Proof: This proof follows from the previous. See also Proposition 2 in Dummit and Foote (2003, 154).'><sup>11<\/sup><\/a><\/span>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-02-jablko-group-demonstration\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-02-Jablko-Group-Demonstration.jpg\" alt=\"\" class=\"wp-image-8076\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-02-Jablko-Group-Demonstration.jpg 2293w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-02-Jablko-Group-Demonstration-300x274.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-02-Jablko-Group-Demonstration-1024x936.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-02-Jablko-Group-Demonstration-768x702.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-02-Jablko-Group-Demonstration-1536x1403.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-02-Jablko-Group-Demonstration-2048x1871.jpg 2048w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>Example 2: \u201cJablko,\u201d mm.&nbsp;11\u201326, demonstrating group operations of the neo-Riemannian transformations and fifths operations.<\/figcaption><\/figure><\/div>\n\n\n<p>Using this system, we can proceed to analyze the harmonic contents of the duet. This essay will include harmonic areas in the analysis if they receive cadential confirmation, are emphasized through motivic salience or prolonged exposure, and\/or are significant passing or neighboring harmonies with a PR or fifths cycle. The first condition confirms the arrival of a key area through cadential progressions. Since Dvo\u0159\u00e1k\u2019s musical style relies on locally diatonic harmonic gestures, these cadences continue to serve as points of arrival in Dvo\u0159\u00e1k\u2019s music.<span id='easy-footnote-12-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-12-8049' title='Dvo\u0159\u00e1k\u2019s relative conservatism, especially in formal-harmonic syntax, has been noted by scholars such as David Beveridge (1980), Miroslav \u010cern\u00fd (2007), and Peter Smith (2020).'><sup>12<\/sup><\/a><\/span> The second condition includes harmonies that might not function locally as tonic but are given a level of prominence by carrying an important motivic idea or simply sounding for a significant amount of time (at least two measures). This condition often applies near the beginning of musical phrases. The final condition, a significant passing motion within a PR or fifths cycle, accounts for various harmonies that, while brief and not cadentially confirmed, perform a crucial role in the harmonic profile of each duet by facilitating a link between two adjacent nodes on their respective harmonic cycles. Given the passing nature of this last category, however, they will frequently be shown in parentheses.<\/p>\n<p>All duets follow a similar harmonic-formal layout in which each song travels away from its home key to some climactic turning point\u2014the point farthest removed from the home key\u2014before turning back. Like the home key of each song, these turning points contribute substantially to the narratives depicted in each song. The following analyses trace the songs through these key areas and interpret the narrative suggested by these paths.<\/p>\n\n\n<h2 class=\"wp-block-heading\"><strong>3. I: Mo\u017enost (Possibility)<\/strong><\/h2>\n\n\n<p>As the title suggests, the duets open with hope, as the text likens the cuckoo with the narrator\u2019s hope of being reunited with her beloved.<span id='easy-footnote-13-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-13-8049' title='This analysis will refer to the protagonist through she\/her pronouns, given that these duets are written for soprano and alto voices. Neff, the commissioner of these works, explicitly requested that they be written for female voices. Given that these are folk-song texts, the object of the conversation is not always consistent. In the first two songs, the text uses words like \u201cpanenka\u201d and \u201cmil\u00e1,\u201d both of which refer to a feminine-gendered beloved. The third and fourth songs, on the other hand, refer to the object as \u201csynek\u201d and \u201csyne\u010dku,\u201d both of which refer to a son. In nearly all cases, however, there seems to be some indication that the object is a younger person that the protagonist loves, though not necessarily romantically. For this analysis, I will use terms like the \u201cobject\u201d and \u201cbeloved\u201d as general descriptors of this person.'><sup>13<\/sup><\/a><\/span> This hope is mirrored by both the harmonic and metric features of the duet, in which hope of resolution is always present but never entirely realized. Example&nbsp;3 provides the score, along with the harmonic transformations that operate across most of the opening song. Example&nbsp;4 summarizes these relationships both temporally and spatially. Example&nbsp;4a provides harmonic relationships through time. Each step upward along the vertical axis correlates to a (1, 0) transformation within the PR<sub>1, 2<\/sub> cycle, and each step downward conversely correlates to a (\u20131, 0) transformation. Example&nbsp;4b, on the other hand, provides a spatial representation of this progression along a visualized PR<sub>1,2<\/sub> cycle, where a (1,&nbsp;0) transformation correlates to a counterclockwise move along the diagram.<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-large is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-03-moznost-group-operations\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-03-Moznost-Group-Operations-1024x835.jpg\" alt=\"\" class=\"wp-image-8078\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-03-Moznost-Group-Operations-1024x835.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-03-Moznost-Group-Operations-300x245.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-03-Moznost-Group-Operations-768x626.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-03-Moznost-Group-Operations-1536x1252.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-03-Moznost-Group-Operations-2048x1669.jpg 2048w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>Example 3: \u201cMo\u017enost,\u201d mm.&nbsp;3\u201317, demonstrating the group operations and key areas at play.<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-04a-table-of-keys_page_2\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-04a-Table-of-Keys_Page_2.png\" alt=\"\" class=\"wp-image-8080\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-04a-Table-of-Keys_Page_2.png 2719w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-04a-Table-of-Keys_Page_2-300x203.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-04a-Table-of-Keys_Page_2-1024x693.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-04a-Table-of-Keys_Page_2-768x520.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-04a-Table-of-Keys_Page_2-1536x1040.png 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-04a-Table-of-Keys_Page_2-2048x1387.png 2048w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>(a)<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-04b-pr-cycles_page_2\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-04b-PR-Cycles_Page_2.png\" alt=\"\" class=\"wp-image-8081\" width=\"256\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-04b-PR-Cycles_Page_2.png 1225w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-04b-PR-Cycles_Page_2-296x300.png 296w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-04b-PR-Cycles_Page_2-1011x1024.png 1011w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-04b-PR-Cycles_Page_2-768x778.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-04b-PR-Cycles_Page_2-100x100.png 100w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>Example 4: Transformational operations and key areas in \u201cMo\u017enost,\u201d illustrated by (a) a timeline progression and (b) a progression around the PR cycles.<\/figcaption><\/figure><\/div>\n\n\n\n<p>The song can be parsed into two sections that mirror one another. The first section arrives at its climactic turning point, G major, via a PR transformation, while the second moves back to E major using the same transformation in reverse. In this song, the smoothness of the PR transformations are foregrounded through the piano\u2019s voice leading. As Example&nbsp;5 illustrates, these harmonies maintain close voice leading not only in the abstract sense but also in their explicit voicing on the piano.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-05-moznost-parsimonious-voice-leading-final\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-05-Moznost-Parsimonious-Voice-Leading-Final-scaled.jpg\" alt=\"\" class=\"wp-image-8083\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-05-Moznost-Parsimonious-Voice-Leading-Final-scaled.jpg 2560w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-05-Moznost-Parsimonious-Voice-Leading-Final-300x118.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-05-Moznost-Parsimonious-Voice-Leading-Final-1024x401.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-05-Moznost-Parsimonious-Voice-Leading-Final-768x301.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-05-Moznost-Parsimonious-Voice-Leading-Final-1536x602.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-05-Moznost-Parsimonious-Voice-Leading-Final-2048x803.jpg 2048w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>Example 5: \u201cMo\u017enost,\u201d mm.&nbsp;3\u20134, 9, and 10\u201313, demonstrating the parsimonious surface-level voice leading in the piano part.<\/figcaption><\/figure><\/div>\n\n\n\n<p>Narratively speaking, these PR transformations depict the presence of hope, although the protagonist must fend off moments of doubt. A two-measure accompaniment opens in E major. The vocalists enter in m.&nbsp;3 by describing the cuckoo and soon thereafter conclude with what could be understood as a somewhat early PAC in m.&nbsp;5 (Example&nbsp;6). The metric placement of this potential PAC is particularly intriguing, as it takes place within the only notated time signature change in the entire collection of duets.<span id='easy-footnote-14-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-14-8049' title='The prosody of the text does not offer much by way of suggesting one meter or the other and, if anything, possibly strengthens the final beat of mm. 5 and 8. The first strophe\u2019s \u201cbo\u0159e\u201d and \u201cdvo\u0159e\u201d contain two neutral syllables each, whereas \u201cnebudu tv\u00e1\u201d and \u201cnekuk\u00e1\u201d of the second strophe both accent the beat weakened through the change to quadruple time. The time change here is, if anything, made in spite of the natural text stress, not to accommodate the latter.'><sup>14<\/sup><\/a><\/span> This sudden change into quadruple time makes it possible to understand this resolution as taking place effectively on a triple-meter downbeat. However, the intentional time change could suggest that care is taken to evade the downbeat resolution. As the title suggests, hope is present, but depending on the interpretation taken, it might be either attained or lost.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-06-moznost-opening\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-06-Moznost-Opening.png\" alt=\"\" class=\"wp-image-8085\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-06-Moznost-Opening.png 3013w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-06-Moznost-Opening-300x118.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-06-Moznost-Opening-1024x402.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-06-Moznost-Opening-768x301.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-06-Moznost-Opening-1536x603.png 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-06-Moznost-Opening-2048x803.png 2048w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>Example 6: \u201cMo\u017enost,\u201d mm. 3\u20138, illustrating the possible cadences in the opening phrases.<\/figcaption><\/figure><\/div>\n\n\n<p>The phrase repeats in mm.&nbsp;6\u20138, at which point the text establishes a connection between the cuckoo and the object of the narrator\u2019s description. This time, however, a PAC candidate does not materialize; instead, the soprano turns away from $$\\hat{1}$$ to conclude the phrase with an IAC. Here, we see a level of doubt settle in the narrator\u2019s mind: she is sure of the cuckoo\u2019s calling, but she is less certain that she will see her love again. The switch to quadruple time at the cadences in mm.&nbsp;5 and 8 also results in the only two incomplete hypermeasures in a collection replete with four-measure regularity, yet again emphasizing the strangeness of this passage.<\/p>\n<p>Following this opening, the music progresses through E&nbsp;minor in m.&nbsp;9 to G major in m.&nbsp;11 (Example&nbsp;7). At the same moment that the music moves away from E major, the narrator turns from the cuckoo to herself and raises the possibility that her love might not be reunited to her. With this reference to the self, the song associates E major with an idealistic hope and G major, its turning point, with reality.<span id='easy-footnote-15-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-15-8049' title='On forms of address and how they impact narratives in other songs, see BaileyShea (2021, 126\u2013145).'><sup>15<\/sup><\/a><\/span> Metrically speaking, this cadence is equally suggestive. In m.&nbsp;12, the soprano and alto lines diverge from one another for the first time, with the soprano concluding on the V of m.&nbsp;12 and the alto continuing into the I of m.&nbsp;13. As such, this moment could be heard as either a half cadence or an IAC. For the soprano, authentic cadential arrival on G major never materializes, but is cut off at V. The alto, however, does arrive on I on the unequivocal downbeat that eluded the opening cadences, albeit somewhat beneath the surface. As such, this instance possibly represents a moment in which the narrator rejects G major on the surface by denying its resolution onto I, but the resolution onto tonic underneath reveals that reality has taken hold more than the narrator wants to admit.<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-07-moznost-closing\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-07-Moznost-Closing.png\" alt=\"\" class=\"wp-image-8086\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-07-Moznost-Closing.png 3013w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-07-Moznost-Closing-300x120.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-07-Moznost-Closing-1024x409.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-07-Moznost-Closing-768x307.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-07-Moznost-Closing-1536x613.png 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-07-Moznost-Closing-2048x818.png 2048w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>Example 7: \u201cMo\u017enost,\u201d mm. 11\u201317, illustrating possible cadences in the second half of the song.<\/figcaption><\/figure><\/div>\n\n\n<p>Following this ambiguous cadence, the music turns back, through E minor, to the opening key of E major, just as the text returns its focus to the cuckoo. This time, the meter does not change, and the final tonic falls on the downbeat, providing a metrical resolution that has been sought after since the start of the song. This metrical stability, however, is shadowed by an inconclusive harmonic-melodic resolution. Not only does the soprano close with $$\\hat{3}$$, but the root-position V is abandoned in m.&nbsp;15 as the bass steps up to $$\\hat{7}$$, producing a weakened IAC. While E major arrives here on a decisive downbeat, the lack of a conclusive cadence signifies that, while hope is remains present, it is not fully secured.<\/p>\n<p>In the end, the hope presented in the text remains only potential. Even though the song concludes on a downbeat in E major at a point where the narrator is talking about the possibility of meeting with her beloved, the weakening of the final cadence denies any clear confirmation of this outcome. If anything, the progressive inconclusiveness of each phrase ending\u2014from the potential PAC of m.&nbsp;5 to the attenuated IAC of m.&nbsp;16\u2014foreshadows the unstable nature of this hopeful union.<\/p>\n\n\n<h2 class=\"wp-block-heading\"><strong>4. II: Jablko (Apple)<\/strong><\/h2>\n\n\n<p>The second song begins in G major, the key that referred to possible separation between the narrator and her love in the previous song. The text now describes the same separation: as much as the apple rolls away, it can never reach her beloved, indicating that this separation involves more than physical distance. The final line of the text reveals the potentially tragic direction to which the text now turns. The narrator\u2019s object is now \u201cwith the Lord God,\u201d and no longer alive in the narrator\u2019s world.<\/p>\n<p>This gradual loss of hope is depicted through harmonic means, as this song contains the first of many instances in which the descending fifths (0,&nbsp;\u20131) progression is used. PR transformations, though prominently featured, are somewhat less foregrounded on the surface. Whereas the opening duet contained parsimonious voice leading in the piano, the voice leading in this duet is limited to an abstract level. Although the voices preserve some semblance of voice-leading parsimony, the piano\u2019s right hand moves relatively strictly by preserving the shape of root-position triads. Example&nbsp;8 depicts some of these transformations in the opening sections of the score.<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-08-jablko-group-operations\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-08-Jablko-Group-Operations.jpg\" alt=\"\" class=\"wp-image-8089\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-08-Jablko-Group-Operations.jpg 2290w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-08-Jablko-Group-Operations-300x259.jpg 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-08-Jablko-Group-Operations-1024x884.jpg 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-08-Jablko-Group-Operations-768x663.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-08-Jablko-Group-Operations-1536x1325.jpg 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-08-Jablko-Group-Operations-2048x1767.jpg 2048w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>Example 8: \u201cJablko,\u201d mm.&nbsp;1\u201326, demonstrating the group operations and key areas at play.<\/figcaption><\/figure><\/div>\n\n\n<p>Example&nbsp;9 shows the same two illustrations of the song\u2019s tonal path as before.<span id='easy-footnote-16-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-16-8049' title='Given that this duet uses motions by fifth to cross into other octatonic collections, examples going forward use color coding to indicate octatonic collections outside of the opening one. Black denotes operations in the OCT&lt;sub&gt;1,2&lt;\/sub&gt; region, green depicts the OCT&lt;sub&gt;0,1&lt;\/sub&gt; region, and red depicts the OCT&lt;sub&gt;0,2&lt;\/sub&gt; region.'><sup>16<\/sup><\/a><\/span> Like the first song, this one can be divided into two sections (mm.&nbsp;1\u201326 and mm.&nbsp;27\u201351). The duet moves out of PR<sub>1,2<\/sub> and into PR<sub>0,1<\/sub> for most of the song\u2019s second half. The song opens with a piano introduction consisting of descending sixteenth notes, possibly a musical portrayal of a rolling apple. As the vocalists enter, the song attempts to return to E major, the key of \u201cMo\u017enost,\u201d just as the text\u2019s apple tries to roll back to the narrator\u2019s beloved. This attempt prompts a series of (1,&nbsp;0) transformations, initially into an E-minor HC of m.&nbsp;22, then to E major in the following measure.<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-09a-table-of-keys_page_3\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-09a-Table-of-Keys_Page_3.png\" alt=\"\" class=\"wp-image-8091\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-09a-Table-of-Keys_Page_3.png 4446w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-09a-Table-of-Keys_Page_3-300x159.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-09a-Table-of-Keys_Page_3-1024x544.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-09a-Table-of-Keys_Page_3-768x408.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-09a-Table-of-Keys_Page_3-1536x816.png 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-09a-Table-of-Keys_Page_3-2048x1088.png 2048w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>(a)<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-09b-pr-cycles_page_3\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-09b-PR-Cycles_Page_3.png\" alt=\"\" class=\"wp-image-8092\" width=\"256\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-09b-PR-Cycles_Page_3.png 1248w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-09b-PR-Cycles_Page_3-124x300.png 124w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-09b-PR-Cycles_Page_3-424x1024.png 424w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-09b-PR-Cycles_Page_3-768x1856.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-09b-PR-Cycles_Page_3-636x1536.png 636w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-09b-PR-Cycles_Page_3-847x2048.png 847w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>(b)<br><br>Example 9: Transformational operations and key areas in \u201cJablko,\u201d illustrating (a) a timeline progression and (b) a progression around the PR cycles.<\/figcaption><\/figure><\/div>\n\n\n<p>The arrival onto E major in m.&nbsp;23 suggests that the goal has just been reached. However, this harmony proves to be only fleeting. As soon as it is reached, the music transforms E major from a tonic to an extremely brief dominant. This functional shift initiates a motion by fifths, or (0,&nbsp;\u20131), to A major. That the first manifestation of the descending fifth motion in the set is also the first gesture to deny the realization of E major foreshadows later manifestations of harmonic motions along the (0, <em>b<\/em>) axis. This new harmony moves by (1, 0) to F$$\\sharp$$ minor, the song\u2019s point of furthest remove, in m.&nbsp;26, cueing the onset of the song\u2019s second part. These transformations in the PR<sub>0,1<\/sub> cycle use different harmonies than the outset of this duet, signaling that this new space is somehow otherworldly relative to the narrator\u2019s initial state.<\/p>\n<p>This sense of otherworldliness is reflected by the two worlds of the text. The narrator\u2019s hope is in PR<sub>1,2<\/sub>, which contains E&nbsp;major; the object, on the other hand, is \u201cwith the Lord God\u201d (in PR<sub>0,1<\/sub>) and therefore remains out of reach. The non-overlapping nature of the two cycles indicates the degree of separation between these two characters and supports the text\u2019s descriptions that, no matter how the apple rolls, it is unable to reach the beloved. The song ends in G major by means of a brief but clear descending fifths progression from A minor, highlighting further the (0,&nbsp;\u20131) gesture that initially thwarted the return to E major.<\/p>\n<p>These harmonic associations are further enhanced by textural changes in this song. The consistent texture of the duet singing with piano doubling fades across the song, indicating the increasing degree of separation between the protagonist and her object. Beginning in m.&nbsp;15, the piano\u2019s doubling of the melody moves up the octave. By m.&nbsp;19, the piano doubling ceases entirely. The doubling returns in m.&nbsp;23, but it is offset by one eighth note. At the same time, the alto drops out completely and, when it reappears in m.&nbsp;27, the two voices are contrapuntal, rather than homophonic. This increasing tension between the performing forces\u2014the most significant one in the entire cycle\u2014illustrates texturally that the protagonist\u2019s beloved is increasingly out of reach.<\/p>\n\n\n<h2 class=\"wp-block-heading\"><strong>5. III: V\u011bne\u010dek (Garland)<\/strong><\/h2>\n\n\n<p>The third song is in B$$\\flat$$ major and continues the same trajectory traversed by the first two songs. The PR motion from the E major of \u201cMo\u017enost\u201d to the G major of \u201cJablko\u201d is replicated to arrive at the current key. Additionally, B$$\\flat$$ major and E major occupy polar opposite ends of PR<sub>1,2<\/sub>. As such, the third song heightens the narrative to a climax. In much the same way that each duet contains a small-scale turning point, this duet can itself be understood as a large-scale turning point to the entire cycle, both harmonically and narratively: as the key proceeds to the point furthest removed from E major in PR<sub>1,2<\/sub>, the narrator moves to the point furthest removed from her initial state.<\/p>\n<p>Example&nbsp;10 provides the tonal layout of the song. Unlike \u201cMo\u017enost\u201d and \u201cJablko,\u201d both of which track a single path away from and back to the home key, \u201cV\u011bne\u010dek\u201d contains two stanzas, each tracing a different path away from and back to B$$\\flat$$&nbsp;major. Example&nbsp;11 shows the transformations operating within the opening measures. The first stanza (mm.&nbsp;1\u201318) stays fairly close to the home key, as all three transformations move by no more than one step along either dimension. The second stanza (mm.&nbsp;19\u201340) takes a more drastic turn: B$$\\flat$$ major immediately undergoes a (\u20132, 1) transformation\u2014the largest single move in the entire set thus far\u2014into the song\u2019s climactic turning point, A$$\\flat$$ major. Following this, an R transformation produces F&nbsp;minor. A descending fifths sequence modulates back to the home key, yet again highlighting the growing prominence of the (0,&nbsp;<em>b<\/em>) progressions.<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-10a-table-of-keys_page_4\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-10a-Table-of-Keys_Page_4.png\" alt=\"\" class=\"wp-image-8094\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-10a-Table-of-Keys_Page_4.png 4230w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-10a-Table-of-Keys_Page_4-300x185.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-10a-Table-of-Keys_Page_4-1024x631.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-10a-Table-of-Keys_Page_4-768x473.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-10a-Table-of-Keys_Page_4-1536x946.png 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-10a-Table-of-Keys_Page_4-2048x1262.png 2048w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>(a)<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-10b-pr-cycles_page_4\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-10b-PR-Cycles_Page_4.png\" alt=\"\" class=\"wp-image-8095\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-10b-PR-Cycles_Page_4.png 2258w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-10b-PR-Cycles_Page_4-300x286.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-10b-PR-Cycles_Page_4-1024x977.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-10b-PR-Cycles_Page_4-768x733.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-10b-PR-Cycles_Page_4-1536x1466.png 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-10b-PR-Cycles_Page_4-2048x1955.png 2048w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>(b)<br><br>Example 10: Transformational operations and key areas in \u201cV\u011bne\u010dek,\u201d illustrating (a) a timeline progression and (b) a progression around the PR cycles.<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-11-venecek-group-operations\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-11-Venecek-Group-Operations-scaled.jpg\" alt=\"\" class=\"wp-image-8098\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-11-Venecek-Group-Operations-scaled.jpg 2131w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-11-Venecek-Group-Operations-250x300.jpg 250w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-11-Venecek-Group-Operations-852x1024.jpg 852w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-11-Venecek-Group-Operations-768x923.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-11-Venecek-Group-Operations-1278x1536.jpg 1278w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-11-Venecek-Group-Operations-1705x2048.jpg 1705w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>Example 11: \u201cV\u011bne\u010dek,\u201d mm.&nbsp;3\u201330, demonstrating the group operations and key areas at play.<\/figcaption><\/figure><\/div>\n\n\n<p>The text of this song sets up a metaphor between reapers harvesting in the field and death. Although at first the main image centers around harvesting, its context within the song cycle points toward the latter. The narrator reflects on someone named Martinek, the narrator\u2019s son and the \u201cbeloved\u201d that has been referred to, who goes to greet the reapers. In the second stanza, the narrator shifts from a reflexive address to a direct one, marked by the introduction of second-person pronouns. However, the recipient of the address is not Martinek, but rather, a garland that she has promised to him, which she describes as being plucked prematurely. Martinek\u2019s name does not appear once in this section. Addressing the garland simultaneously generates intimacy and distance: the narrator is directly speaking to another, but that other is only a substitute for a person the listener was just introduced to. This, along with the use of past tense throughout and the context established by the previous songs, indicates the premature death of the protagonist\u2019s beloved. The protagonist, unable to address the deceased Martinek, and possibly unwilling to confront the reality of Martinek\u2019s death, speaks only to a garland, both as a makeshift object of address, and also to mollify the pain from having to accept his passing.<\/p>\n<p>Martinek\u2019s passing is hinted at musically in several ways. The first and most telling is that, in mm.&nbsp;11\u201318, when the protagonist speaks of her love returning, the texture is reduced to solo voices and, much like in the previous song, the melody is not doubled in the piano, once again implying distance between the narrator and her beloved.<span id='easy-footnote-17-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-17-8049' title='The call-and-response nature of this section is particularly striking, given that there is no dialogue in the text. Both soprano and alto sing from the same narrative perspective of the protagonist\u2019s reflexive address.'><sup>17<\/sup><\/a><\/span> Additionally, the location of B$$\\flat$$ major as the polar opposite key from E major in PR<sub>1,2<\/sub> corroborates this narrative. In the second strophe, the turn to A$$\\flat$$ major and F minor in mm.&nbsp;23ff. casts the tonal trajectory of the song even further afield, now into PR<sub>0,2<\/sub>. Much like in \u201cJablko,\u201d the song is thrown into foreign space.<\/p>\n<p>The tension between PR and fifth-related transformations is further heightened in this duet. As Example&nbsp;10 demonstrates, aside from the two R transformations in mm.&nbsp;11 and 30, practically all remaining motions are by fifth or by step, with an emphasis on the former.<span id='easy-footnote-18-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-18-8049' title='Even in cases where chords move by step, it can be argued that an elided double fifths motion is the operative underlying gesture. The move from G minor to F major in m.&amp;nbsp;18, for example, is interceded by a brief dominant seventh harmony on C the measure before.'><sup>18<\/sup><\/a><\/span> The most prominent instances of these progressions by fifth are shown in Example&nbsp;12. The change from neo-Riemannian transformations to fifth-related chains highlights the latter\u2019s distinct harmonic profile, thereby sonically embodying Martinek\u2019s otherworldly position. Alternatively, the fifths represent a transcendence into another world, since descending fifths are a primary way of transcending the closed octatonic regions created by the PR cycles.<span id='easy-footnote-19-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-19-8049' title='Richard Cohn (2012, 155\u2013158) demonstrates the generation of the octatonic collection using chords of Jack Douthett and Peter Steinbach\u2019s (1998, 256) 4-Cube Trio and likens it to the hexatonic collections of the cube dances. The present analysis demonstrates that the same octatonic collection may be generated by triads using P and R transformations and utilizes these in a manner akin to Cohn\u2019s (1999, 216) \u201cstar cluster\u201d regions.'><sup>19<\/sup><\/a><\/span> The switch to descending fifths chains illustrates the new path required to exit the narrator\u2019s PR<sub>1,2<\/sub> world and reach the beloved (in PR<sub>0,2<\/sub>).<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-12-venecek-desc-fifths\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-12-Venecek-desc.-fifths.png\" alt=\"\" class=\"wp-image-8099\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-12-Venecek-desc.-fifths.png 3013w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-12-Venecek-desc.-fifths-300x114.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-12-Venecek-desc.-fifths-1024x389.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-12-Venecek-desc.-fifths-768x292.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-12-Venecek-desc.-fifths-1536x584.png 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-12-Venecek-desc.-fifths-2048x779.png 2048w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>Example 12: Progressions by fifth in \u201cV\u011bne\u010dek,\u201d mm.&nbsp;27\u201337<\/figcaption><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>6. IV: Ho\u0159e (Grief)<\/strong><\/h2>\n\n\n<p>The final song provides the tragic ending to the duet cycle. Given that the previous song already occupied B$$\\flat$$ major, the key furthest removed from E major within the PR<sub>1,2<\/sub> cycle, this song does not continue along the same PR trajectory to D$$\\flat$$ major, as any path along PR<sub>1,2<\/sub> would only bring the key closer to E major. Instead, this final song is set in B major, a member of PR<sub>0,2<\/sub>\u2014the region occupied by much of the third song. In a sense, this key change reflects the grief that the title describes. The narrator now realizes that she is unable to reach her beloved, much like the opening E major is unreachable by PR transformations from the current key.<\/p>\n<p>Despite this foreignness, this new key is closer to the opening than either of the previous ones. Although no (<em>a<\/em>, 0) transformation can return to E major, B major is only a fifth away from E major and, as such, one only needs (0, \u20131) to return to the home key. However, the protagonist either does not sense this close connection or she refuses to concede by succumbing to fifths motions to return. Even though the latter half of each strophe concludes with a prominent descending fifths progression, it cuts off one step short, landing only on B.<\/p>\n<p>Example&nbsp;13 provides the progression of keys visited in the song, and Example&nbsp;14 gives the opening two strophes of its three-strophic form. Each strophe contains two sections, demonstrating remarkable formal and harmonic similarities to the opening song. The first section traces the same PR transformation heard in \u201cMo\u017enost\u201d into the climactic moment, while the second returns to the home key to close the cycle. This time, however, the return replaces the parsimonious voice leading with descending fifths.<\/p>\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-13a-table-of-keys_page_5\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-13a-Table-of-Keys_Page_5.png\" alt=\"\" class=\"wp-image-8392\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-13a-Table-of-Keys_Page_5.png 1592w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-13a-Table-of-Keys_Page_5-300x176.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-13a-Table-of-Keys_Page_5-1024x599.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-13a-Table-of-Keys_Page_5-768x450.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-13a-Table-of-Keys_Page_5-1536x899.png 1536w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>(a)<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-13b-pr-cycles_page_5\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-13b-PR-Cycles_Page_5.png\" alt=\"\" class=\"wp-image-8104\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-13b-PR-Cycles_Page_5.png 2256w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-13b-PR-Cycles_Page_5-300x286.png 300w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-13b-PR-Cycles_Page_5-1024x978.png 1024w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-13b-PR-Cycles_Page_5-768x733.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-13b-PR-Cycles_Page_5-1536x1467.png 1536w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-13b-PR-Cycles_Page_5-2048x1955.png 2048w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>(b)<br><br>Example 13: Transformational operations and key areas in \u201cHo\u0159e,\u201d illustrating (a) a timeline progression and (b) a progression around the PR cycles.<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-14-hore-group-operations\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-14-Hore-Group-Operations-scaled.jpg\" alt=\"\" class=\"wp-image-8105\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-14-Hore-Group-Operations-scaled.jpg 1973w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-14-Hore-Group-Operations-231x300.jpg 231w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-14-Hore-Group-Operations-789x1024.jpg 789w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-14-Hore-Group-Operations-768x996.jpg 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-14-Hore-Group-Operations-1184x1536.jpg 1184w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-14-Hore-Group-Operations-1578x2048.jpg 1578w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>Example 14: \u201cHo\u0159e,\u201d mm.&nbsp;1\u201313, demonstrating the transformations and key areas at play.<\/figcaption><\/figure><\/div>\n\n\n<p>The duet moves relatively quickly to G major by m.&nbsp;4. Although this is a typical PL transformation, its sole appearance in the duet cycles thus far nevertheless makes it a striking gesture. This transformation temporarily moves us back to the turning point of \u201cMo\u017enost\u201d and the home key of \u201cJablko,\u201d likely mimicking the text\u2019s references to the apple. Shortly thereafter, it proceeds to the key of B&nbsp;minor in m.&nbsp;16 and then D major in m.&nbsp;17, also the turning point of the song. This song traces the same motions as \u201cMo\u017enost,\u201d recalling the initial descent out of hope. Unlike in \u201cMo\u017enost,\u201d however, the reality in which the protagonist finds herself is now far starker, just as the surface-level voice leading is no longer parsimonious as it was in the opening duet. Even though the motion from B&nbsp;major in m.&nbsp;1 to D&nbsp;major in m.&nbsp;17 is a neo-Riemannian PR, the chords now move in parallel motion with their roots rather than surface-level parsimony.<\/p>\n<p>Whereas the second part of \u201cMo\u017enost\u201d returns to the original key by reversing its initial PR transformation, \u201cHo\u0159e\u201d launches into a descending fifths sequence to complete the return to B major. The gesture that initially thwarted a return to E major in \u201cJablko\u201d now dominates the final song. Furthermore, this motion by chromatic fifths supports a nearly complete lament tetrachord in the melody, musically depicting the protagonist\u2019s mourning. In the end, the narrator stops in B major by m.&nbsp;8\u2014just one step short of E major\u2014on a melodically incomplete IAC.<span id='easy-footnote-20-8049' class='easy-footnote-margin-adjust'><\/span><span class='easy-footnote'><a href='https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/#easy-footnote-bottom-20-8049' title='On the melodically incomplete IAC, see my own work in Zhang (2022, 194\u2013196).'><sup>20<\/sup><\/a><\/span> Unlike the first song, in which the vocal melody stopped on $$\\hat{3}$$, the sequence is reattempted in the following two measures, this time arriving on a PAC in B major, closing out the song cycle remarkably close to, but ultimately separated from, the key of the opening song.<\/p>\n\n\n<h2 class=\"wp-block-heading\"><strong>7. Concluding Thoughts: Cyclical Elements of Hope and Grief<\/strong><\/h2>\n\n\n\n<p>Examples&nbsp;15 and 16 provide two illustrations of the paths through all four songs. While Example&nbsp;15 illustrates more effectively the motions to and from each movement\u2019s respective home keys as each song unfolds, Example&nbsp;16 emphasizes each song\u2019s octatonic-spatial location through the three PR cycles and demonstrates the separation between each of the songs in the song cycle.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-15-table-of-keys_page_1-3\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-15-Table-of-Keys_Page_1-3.png\" alt=\"\" width=\"1024\"\/><\/a><figcaption>Example 15: Timeline of key areas throughout the Moravian Duets, Op. 38.<\/figcaption><\/figure><\/div>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-16-pr-cycles_page_1\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-16-PR-Cycles_Page_1.png\" alt=\"\" class=\"wp-image-8108\" width=\"512\" srcset=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-16-PR-Cycles_Page_1.png 2550w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-16-PR-Cycles_Page_1-232x300.png 232w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-16-PR-Cycles_Page_1-791x1024.png 791w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-16-PR-Cycles_Page_1-768x994.png 768w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-16-PR-Cycles_Page_1-1187x1536.png 1187w, https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-16-PR-Cycles_Page_1-1583x2048.png 1583w\" sizes=\"(max-width: 706px) 89vw, (max-width: 767px) 82vw, 740px\" \/><\/a><figcaption>Example 16: Spatial representation of key areas throughout the Moravian Duets, Op. 38.<\/figcaption><\/figure><\/div>\n\n\n\n<p>To be sure, the work undertaken in the present study by no means exhausts the many possible avenues for investigation in these duets, such as rhythm and meter. While the hypermetrical profile of the duets remains quadruple, with the exception of the evaded downbeats in \u201cMo\u017enost,\u201d piano interludes almost invariably contain only two measures\u2014or half a hypermeasure\u2014of content. This subtle disruption of the work\u2019s otherwise consistent hypermetrical profile indicates some level of subsurface tension in an otherwise unobtrusive hypermetrical grid. Second, the work appears to feature a level of narrative communicated by the surface-level rhythm as demonstrated in Example&nbsp;17. This involvement of the rhythmic domain further illustrates the potential for rhythm to play a bigger role in advancing this narrative than what was addressed in this essay.<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/zhang36-ex-17-moravian-duets-meter\/\"><img decoding=\"async\" src=\"https:\/\/theory.esm.rochester.edu\/integral\/wp-content\/uploads\/2023\/04\/zhang36-Ex.-17-Moravian-Duets-Meter.jpg\" alt=\"\" class=\"wp-image-8112\" width=\"1024\"\/><\/a><figcaption>Example 17: Metrical features and transformations in the Moravian Duets, Op. 38.<\/figcaption><\/figure><\/div>\n\n\n\n<p>Although the narrative appears to indicate a linear path from the start of \u201cMo\u017enost\u201d to its conclusion in \u201cHo\u0159e,\u201d the duets nevertheless offer several cyclical elements. The most prominent of these cyclical features is that \u201cHo\u0159e\u201d concludes the cycle remarkably close to the opening key. This distance of (0, 1) from the opening key hints that, despite all of the modulations both within and between songs, the final key is not so far off from where the duet cycle began, and that perhaps the end is not quite as hopeless as the narrator believes. While the protagonist appears convinced that hope is irredeemably lost, the closeness of the final key to where we began suggests that we may be closer to the opening than we dared imagine.<\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>References<\/strong><\/h2>\n\n\n<p>Adams, David. 2003. <em>The Song and Duet Texts of Anton\u00edn Dvo\u0159\u00e1k<\/em>. Geneseo, NY: Leyerle Publications.<\/p>\n<p>BaileyShea, Matthew. 2021. <em>Lines and Lyrics: An Introduction to Poetry and Song<\/em>. New Haven: Yale University Press.<\/p>\n<p>Bazayev, Inessa. 2018. \u201cAn Octatonic History of Prokoviev\u2019s Compositional Oeuvre.\u201d <em>Music Theory Online<\/em>, 24 (2). Accessed 27 Feb. 2023. <a href=\"https:\/\/mtosmt.org\/issues\/mto.18.24.2\/mto.18.24.2.bazayev.html\">https:\/\/mtosmt.org\/issues\/mto.18.24.2\/mto.18.24.2.bazayev.html<\/a>.<\/p>\n<p>Beckerman, Michael. 2003. <em>New Worlds of Dvo\u0159\u00e1k: Searching in America for the Composer\u2019s Inner Life<\/em>. New York: W.W. Norton &amp; Company.<\/p>\n<p>Beveridge, David. 1980. \u201cRomantic Ideas in a Classical Frame: The Sonata Forms of&nbsp; Dvo\u0159\u00e1k.\u201d PhD diss., University of California, Berkeley.<\/p>\n<p>Bl\u00e4ttler, Damian. 2022. \u201cRavel\u2019s Octatonic Scripts.\u201d <em>Music Theory Spectrum<\/em>, 44 (2): 276\u2013303.<\/p>\n<p>Bul\u00ed\u0159, Michal. 1990. \u201cDvo\u0159\u00e1kovy prvn\u00ed kontakty s Moravou. [Dvo\u0159\u00e1k\u2019s first contacts with Moravia.]\u201d <em>Opus Musicum<\/em>, 22 (9): 278\u2013283.<\/p>\n<p>Burger, Arthur. 1968. \u201cProblems of Pitch Organization in Stravinsky.\u201d In <em>Perspectives on Schoenberg and Stravinsky<\/em>. Edited by Benjamin Boretz and Edward T. Cone. 123\u2013154. Princeton: Princeton University Press. Originally published 1963 in <em>Perspectives of New Music<\/em>, 2 (1): 11\u201342.<\/p>\n<p>\u010cern\u00fd, Miroslav. 2007. \u201cAnton\u00edn Dvo\u0159\u00e1k und die Sonatenform. [Anton\u00edn Dvo\u0159\u00e1k and the Sonata Form.]\u201d In <em>The Work of Anton\u00edn Dvo\u0159\u00e1k (1841\u20131904): Aspects of Composition, Problems of Editing, Reception: Proceedings of the International Musicological Conference, Prague, September 8\u201311, 2004<\/em>. Edited by Jarmila Gabrielov\u00e1 and Jan Kachl\u00edk, 41\u201351. Prague: Institute of Ethnology, Academy of Sciences of the Czech Republic.<\/p>\n<p>Chandler, Oliver. 2020. \u201c\u2018Octatonic\u2019 Voice Leading and Diatonic Function in the <em>Allegro molto <\/em>from Elgar\u2019s String Quartet in E minor, op. 83.\u201d <em>Music Theory Online<\/em>, 26 (1). Accessed 27 Feb. 2023. <a href=\"https:\/\/mtosmt.org\/issues\/mto.20.26.1\/mto.20.26.1.chandler.html\">https:\/\/mtosmt.org\/issues\/mto.20.26.1\/mto.20.26.1.chandler.html<\/a>.<\/p>\n<p>Cohn, Richard. 1991. \u201cBart\u00f3k\u2019s Octatonic Strategies: A Motivic Approach.\u201d <em>Journal of the American Musicological Society<\/em>, 44 (2): 279\u2013297.<\/p>\n<p>\u2014\u2014\u2014. 1999. \u201cAs Wonderful as Star Clusters: Instruments for Gazing at Tonality in Schubert.\u201d <em>19<sup>th<\/sup>-Century Music<\/em>, 22 (3): 213\u2013232.<\/p>\n<p>\u2014\u2014\u2014. 2012. <em>Audacious Euphony: Chromatic Harmony and the Triad\u2019s Second Nature<\/em>. New York: Oxford University Press.<\/p>\n<p>D\u00f6ge, Klaus. 2001. \u201cDvo\u0159\u00e1k, Anton\u00edn (Leopold).\u201d <em>Oxford Music Online<\/em>. Accessed 15 Feb. 2022. <a href=\"https:\/\/www.oxfordmusiconline.com\/grovemusic\/view\/10.1093\/gmo\/9781561592630.001.0001\/omo-9781561592630-e-0000051222\">https:\/\/www.oxfordmusiconline.com\/grovemusic\/view\/10.1093\/gmo\/9781561592630.001.0001\/omo-9781561592630-e-0000051222<\/a>.<\/p>\n<p>Douthett, Jack, and Peter Steinbach. 1998. \u201cParsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition.\u201d <em>Journal of Music Theory<\/em>, 42 (2): 241\u2013264.<\/p>\n<p>Dummit, David, and Richard Foote. 2003. <em>Abstract Algebra<\/em>, 3 ed. Hoboken: John Wiley and Sons, Inc.<\/p>\n<p>Forte, Allen. 1991. \u201cDebussy and the Octatonic.\u201d <em>Music Analysis<\/em>, 10 (1\/2): 125\u2013169.<\/p>\n<p>Hook, Julian. 2002. \u201cUniform Triadic Transformations.\u201d <em>Journal of Music Theory<\/em>, 46 (1): 57\u2013126.<\/p>\n<p>Kahan, Sylvia. 2005. \u201c\u2018Rien de la tonalite usuelle\u2019: Edmond de Polignac and the Octatonic Scale in Nineteenth-Century France.\u201d <em>19<sup>th<\/sup>-Century Music<\/em>, 29 (2): 97\u2013120.<\/p>\n<p>Plotkin, Richard. 2019. \u201cChord Proximity, Parsimony, and Analysis with Filtered Point-Symmetry.\u201d <em>Music Theory Online<\/em>, 25 (2). Accessed 27 Feb. 2023. <a href=\"https:\/\/mtosmt.org\/issues\/mto.19.25.2\/mto.19.25.2.plotkin.html\">https:\/\/mtosmt.org\/issues\/mto.19.25.2\/mto.19.25.2.plotkin.html<\/a>.<\/p>\n<p>Smith, Peter H. 2020. \u201cDvo\u0159\u00e1k and Subordinate Theme Closure: \u2018Positive\u2019 Analytic Results for a \u2018Negative\u2019 Approach to Romantic Form.\u201d <em>Journal of Music Theory<\/em>, 64 (2): 203\u2013240.<\/p>\n<p>\u0160ourek, Otakar. 2004. \u201cMoravian Duets.\u201d In <em>Anton\u00edn Dvo\u0159\u00e1k, Moravian Duets, Op. 20, 32, 38: Critical edition based on the composer\u2019s manuscript<\/em>. Edited by Otakar \u0160ourek et al, X\u2013XII. B\u00e4renreiter Praha.<\/p>\n<p>Taruskin, Richard. 2011. \u201cCatching Up with Rimsky-Korsakov.\u201d <em>Music Theory Spectrum<\/em>, 33 (2): 169\u2013185.<\/p>\n<p>Taylor, Benedict. 2010. \u201cModal Four-Note Pitch Collections in the Music of Dvo\u0159\u00e1k\u2019s American Period.\u201d <em>Music Theory Spectrum<\/em>, 32 (1): 44\u201359.<\/p>\n<p>Volek, Jaroslav. 1984. \u201cTektonick\u00e9 ambivalence v symphoni\u00edch Anton\u00edna Dvo\u0159\u00e1ka. [Tectonic ambivalence in the symphonies of Anton\u00edn Dvo\u0159\u00e1k.]\u201d <em>Hudebn\u00ed V\u011bda 1<\/em>, 21: 3\u201331.<\/p>\n<p>Zhang, Xieyi (Abby). 2022. \u201cApparently Imperfect: On the Analytical Issues of the IAC.\u201d <em>Music Theory Spectrum<\/em>, 44 (2): 191\u2013212.ta<\/p>","protected":false},"excerpt":{"rendered":"<p>Xieyi (Abby) Zhang Abstract Despite being considered some of his most pivotal compositions, Dvo\u0159\u00e1k\u2019s Moravian Duets, op. 38, have long been analytically overlooked. The present essay uses neo-Riemannian methods to understand the final set of Dvo\u0159\u00e1k\u2019s Moravian Duets and demonstrates that these parsimonious voice-leading techniques\u2014ones that came to dominate Dvo\u0159\u00e1k\u2019s compositional style\u2014play against descending fifths &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/theory.esm.rochester.edu\/integral\/36-2023\/zhang\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Hope to Grief: An Analysis of Dvo\u0159\u00e1k\u2019s <i>Moravian Duets<\/i>, op. 38&#8243;<\/span><\/a><\/p>\n","protected":false},"author":18,"featured_media":0,"parent":7648,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_oasis_is_in_workflow":0,"_oasis_original":0,"_exactmetrics_skip_tracking":false,"_exactmetrics_sitenote_active":false,"_exactmetrics_sitenote_note":"","_exactmetrics_sitenote_category":0,"footnotes":""},"class_list":["post-8049","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/pages\/8049","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/users\/18"}],"replies":[{"embeddable":true,"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/comments?post=8049"}],"version-history":[{"count":53,"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/pages\/8049\/revisions"}],"predecessor-version":[{"id":8994,"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/pages\/8049\/revisions\/8994"}],"up":[{"embeddable":true,"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/pages\/7648"}],"wp:attachment":[{"href":"https:\/\/theory.esm.rochester.edu\/integral\/wp-json\/wp\/v2\/media?parent=8049"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}