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<article xsi:noNamespaceSchemaLocation="http://jats.nlm.nih.gov/publishing/1.1/xsd/JATS-journalpublishing1-mathml3.xsd" dtd-version="1.1" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"><front><journal-meta><journal-id journal-id-type="publisher-id">EIR</journal-id><journal-title-group><journal-title>Educational Innovation Research</journal-title></journal-title-group><issn>3029-1844</issn><eissn>3029-1852</eissn><publisher><publisher-name>Bio-Byword Scientific Publishing Pty. Ltd.</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.26689/EIR.v4i6.15523</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title>The Influence of Linear Thinking on the Harmonic Language of Mahler’s Third Symphony—An Analytical Practice Based on the Theory of Linear Thinking</title><url>https://artdesignp.com/journal/EIR/4/6/10.26689/EIR.v4i6.15523</url><author>LiMeng</author><pub-date pub-type="publication-year"><year>2026</year></pub-date><volume>4</volume><issue>6</issue><history><date date-type="pub"><published-time>2026-06-26</published-time></date></history><abstract>As the nineteenth century gave way to the twentieth, the boundary between homophonic and polyphonic writing was increasingly dissolved, and linear progression emerged as a means of weakening tonal function. Drawing on linear thinking, Mahler cultivated idiosyncratic devices&amp;mdash;characteristic harmonic motives and composite harmony&amp;mdash;to propel tonal music toward the new idioms of the twentieth century. His Third Symphony employs linear progressions to grow from a core motive into an organism unified by tonal coherence. Combining R&amp;eacute;ti&amp;rsquo;s thematic-motivic analysis with Salzer&amp;rsquo;s post-Schenkerian approach, this article elucidates the constitutive features of Mahler&amp;rsquo;s harmonic language through multiple thematic layers and the linear prolongation of contrapuntal voices.</abstract><keywords>Mahler, Linear thinking, Thematic-motivic analysis, Structural prolongation</keywords></article-meta></front><body/><back><ref-list><ref id="B1" content-type="article"><label>1</label><element-citation publication-type="journal"><p>[1] Tian Q, 1986, Linear Thinking in Chinese Music. Musicology in China, 1986(4): 58&amp;ndash;67. &amp;nbsp;https://doi.org/10.14113/j.cnki.cn11-1316/j.1986.04.008
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