An online lecture on Pythagorean tuning as used in medieval polyphony. This lecture is organized into six outlined sections titled Introduction, Basic concepts, Pythagorean tuning and Gothic polyphony, Pythagorean tuning in more detail, Pythagorean tuning: a just appraisal in context and Bibliography. This site is entirely text based with some charts used to illustrate or summarize specific points or concepts. It includes detailed mathematical explanations of the various tuning methods, as well as numerous references to the use of these tuning systems at various points in the history of western music.
Type of Material:
Online lecture.
Recommended Uses:
This learning object could be used as a introductory text/lecture on Medieval tuning and polyphony. It could also be used to supplement research into performance practice in the Medieval period, a music history course on the Middle Ages or a theory course or section on tuning systems. This material would also be excellent for anyone keenly interested in the relationships between mathematics and music.
Technical Requirements:
A standard browser is needed to view this material.
Identify Major Learning Goals:
The major learning goals of this site is to introduce students to the fundamental concepts of Pythagorean tuning as developed in the Medieval period. This material explains how the exact frequencies of various pitches are derived based on the pure intervals of Pythagorean tuning. It goes on to explain how these intervals are modified to make certain accomodations in other tuning systems.
Target Student Population:
Upper class undergraduate and graduate students. This material requires an understanding of theory and music history.
Prerequisite Knowledge or Skills:
A basic knowledge and understanding of music theory, an overview understanding of the music of the Medieval period and basic understanding of tuning systems and the physics of sound. Advanced references to both mathematics and music history are included. One could still digest much of the material having proficiency in only one of these areas, but proficiency in both mathematics and music history is necessary to grasp all of it.
Content Quality
Rating:
Strengths:
The content of this site is accurate and the quality is very high. This site provides a step-by-step explanation of Pythagorean tuning. It is a complex topic and one in which there is little content available that introduces this topic to students.
Concerns:
This site offers only a few charts to help explain concepts in a visual format. It offers no audio examples. The material would also be too dense for someone wanting a concise definition of Pythagorean Tuning.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
The site reads in a very logical progression moving from an Introduction to Basic Concepts to the relationship of Pythagorean tuning to Gothic polyphony to the ratios and scales and closing with a through appraisal of Pythagorean tuning and it's relationship to Medieval music as well as later tuning systems and periods of Western music.
It is organized through an extensive outline which allows the reader to follow the logic of topics as well as navigate the site. Sections 1-4 are organized into smaller step-by-step topics allowing the first-time student a well organized path to understanding the fundamental concepts. Topics 1-4 has the most potential effectiveness as a teaching tool due to it's easy to understand explanations and organization. Topic 5 Pythagorean tuning: a just appraisal in context is more complex and better utilized in an advanced course on Medieval music and/or tuning systems.
Concerns:
The effectiveness of this site could be improved my more visual tools to illustrate topics as well as audio examples so student may listen to the practical application of the concepts presented.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
This site is easy to use. The organization of the material is quite good. No special technological requirements.
Concerns:
No concerns.
Other Issues and Comments:
No other issues.
Creative Commons:
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