{"id":567,"date":"2015-02-10T21:22:04","date_gmt":"2015-02-10T21:22:04","guid":{"rendered":"http:\/\/casfaculty.case.edu\/ross-duffin\/?page_id=567"},"modified":"2017-02-02T19:53:00","modified_gmt":"2017-02-02T19:53:00","slug":"just-intonation-in-renaissance-theory-practice","status":"publish","type":"page","link":"https:\/\/casfaculty.case.edu\/ross-duffin\/just-intonation-in-renaissance-theory-practice\/","title":{"rendered":"Just Intonation in Renaissance Theory & Practice"},"content":{"rendered":"
\n

By Ross W. Duffin<\/h3>\n

 <\/p>\n

Abstract<\/span><\/h3>\n<\/div>\n

Just intonation has a reputation as a chimerical, theoretical system that simply cannot work in practice. This is based on the assessment of most modern authorities and supported by misgivings expressed during the Renaissance when the practice was supposedly at its height. Looming large among such misgivings are the tuning puzzles printed by the 16th-century mathematician, Giovanni Battista Benedetti. However, Renaissance music theorists are so unanimous in advocating the simple acoustical ratios of Just intonation that it seems clear that some reconciliation must have occurred between the theory and practice of it. This article explores the basic theory of Just intonation as well as problematic passages used to deny its practicability, and proposes solutions that attempt to satisfy both the theory and the ear. Ultimately, a resource is offered to help modern performers approach this valuable art.Fn01.1<\/a><\/h4>\n

\u00a0<\/h3>\n

Table of Contents<\/strong><\/h3>\n

Introduction<\/b><\/span><\/a><\/p>\n

Theoretical Background<\/b><\/span><\/a><\/p>\n

Benedetti’s Puzzles<\/b><\/span><\/a><\/p>\n

Problematic Passages<\/b><\/span><\/a><\/p>\n

Is Just Tuning Possible?<\/b><\/span><\/a><\/p>\n

A New Approach<\/b><\/span><\/a><\/p>\n

The Exercises<\/b><\/span><\/a><\/p>\n

\u00a0\u00a0\u00a0\u00a0Problem Spots<\/a><\/b><\/span><\/p>\n

\u00a0\u00a0\u00a0\u00a0Rehearsal Usage<\/a><\/b><\/span><\/p>\n

Conclusion<\/b><\/span><\/a><\/p>\n

Footnotes<\/h3>\n","protected":false},"excerpt":{"rendered":"

By Ross W. Duffin<\/p>\n

 <\/p>\n

AbstractJust intonation has a reputation as a chimerical, theoretical system that simply cannot work in practice. This is based on the assessment of most modern authorities and supported by misgivings expressed during the Renaissance when the practice was supposedly at its height. Looming large among such misgivings are the tuning puzzles printed by the 16th-century mathematician, Giovanni Battista Benedetti. However, Renaissance music theorists are so unanimous in advocating the simple acoustical ratios of Just intonation that it seems clear that some reconciliation must have occurred between the theory and practice of it.<\/p>\n

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