May 1, 2024
Updated May 9, 2025
34 minute read
Intervals, in a broad sense, represent the space or difference between two points or values. While this concept appears in various fields, this article will primarily focus on two significant interpretations: mathematical intervals and musical intervals. In mathematics, an interval refers to a set of real numbers lying between two specific numbers, called endpoints. This seemingly simple idea is fundamental to many areas of mathematics, enabling us to define ranges, express uncertainty in measurements, and form the basis for more advanced concepts like calculus. In music, an interval describes the difference in pitch between two notes. Understanding musical intervals is crucial for comprehending melody, harmony, and the construction of chords, forming the very building blocks of music.
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Reading list
We've selected 27 books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
Intervals.
A widely used and highly reputable textbook for undergraduate music theory programs. It provides a comprehensive treatment of tonal harmony, with intervals serving as foundational building blocks. is essential for gaining a deep understanding of how intervals function within tonal music and is commonly used as a primary textbook at academic institutions. The latest edition includes updated content and online resources.
Comprehensive reference work on music theory. It includes a section on intervals, as well as other topics such as harmony, counterpoint, and form.
This textbook integrates music theory, analysis, and aural skills, making it highly relevant to understanding intervals in a practical context. It covers intervals from foundational concepts to their role in complex musical structures. Widely adopted in undergraduate programs, it valuable resource for solidifying understanding and developing aural recognition of intervals. The 5th edition features diverse musical examples and enhanced online resources.
Considered a classic in the field of tonal harmony, this book offers a rigorous approach to voice leading and harmonic analysis, both of which rely heavily on a thorough understanding of intervals. While it can be challenging, it provides a deep and nuanced perspective on how intervals create musical structure. It is often used in undergraduate and graduate programs and is highly valued by professionals. The 5th edition updates examples and presentation.
Another prominent integrated music theory textbook used in undergraduate curricula. It provides a solid foundation in music theory, including comprehensive coverage of intervals and their application in harmony and analysis. is known for its clear explanations and extensive musical examples, making it a reliable resource for students to deepen their understanding. The 4th edition includes updated content and online materials.
This comprehensive treatise covers all aspects of music theory, including a detailed discussion of intervals and their use in various musical contexts.
Classic work on intervallic harmony. It provides a thorough discussion of the use of intervals in music, as well as other topics such as dissonance, consonance, and tonality.
Comprehensive history of Western music theory. It includes a section on the history of intervals, as well as other topics such as harmony, counterpoint, and form.
Is specifically designed to develop aural skills, which is crucial for internalizing the sound of intervals. It offers a systematic approach to ear training exercises, focusing heavily on interval recognition and sight singing. This must-read for anyone serious about developing their musical ear and is widely used in academic ear training courses. The 2nd edition provides a research-based curriculum.
Designed for students entering graduate programs, this book provides a comprehensive review of undergraduate tonal theory, including a thorough re-examination of intervals and their roles in harmony and voice leading. It is an excellent resource for solidifying existing knowledge and preparing for advanced study. Often used in graduate review courses.
An essential resource for musicians interested in jazz. explores intervals and their function within jazz harmony, scales, and improvisation. It provides a different perspective on intervals compared to classical theory texts and is considered a must-read for jazz musicians and students. It serves as a valuable reference tool for understanding contemporary applications of intervals in jazz contexts.
A more streamlined alternative to larger tonal harmony textbooks, this book still provides a solid introduction to the fundamentals, including intervals. It is suitable for undergraduate courses or for individuals seeking a concise yet thorough overview of tonal harmony. It helps solidify understanding of basic intervallic relationships and their harmonic implications. The 4th edition recent update.
Explores the role of intervals in musical aesthetics, discussing their expressive and structural potential.
Delves into music theory beyond traditional tonality, introducing concepts like pitch-class sets and serialism. Understanding intervals in this context is crucial, as they are analyzed based on the number of semitones rather than diatonic relationships. This book is highly relevant for graduate students and professionals studying 20th and 21st-century music and offers a contemporary perspective on intervals. The 4th edition reflects current scholarship.
A foundational text in the theory of atonal music, introducing set theory as a method for analyzing pitch-class relationships. focuses heavily on intervals (specifically interval classes) in a non-tonal context, providing a rigorous framework for understanding intervallic structures in 20th-century music. It crucial resource for graduate students and scholars in contemporary music theory.
A seminal work by one of the most influential composers of the 20th century. Schoenberg explores harmony from a historical and theoretical perspective, offering deep insights into the nature of intervals and their evolution. While challenging, it is considered a classic text for advanced students and professionals seeking a profound understanding of harmonic principles. It provides a historical context for contemporary theoretical thought.
A widely used textbook on species counterpoint, offering a clear and practical approach to combining melodic lines. This directly reinforces the understanding and application of intervals in a linear context. It valuable resource for undergraduate and graduate students studying counterpoint and composition, providing a solid foundation in this essential skill.
This translation of Fux's 18th-century treatise foundational text for understanding species counterpoint, which is based on the careful control of intervals between melodic lines. While historical, the principles taught are crucial for developing strong voice leading skills and a deep understanding of intervallic relationships. It classic and valuable for advanced students and those interested in historical theory.
A comprehensive reference book covering all aspects of jazz theory, including detailed explanations of intervals, scales, chords, and their applications in jazz. While not a step-by-step textbook, it is an invaluable resource for students and professionals needing to reference specific concepts related to intervals and harmony in jazz. It offers broad coverage of contemporary jazz practices.
Provides a comprehensive overview of music theory, including a section on intervals. It is written in a clear and concise style, making it accessible to beginners.
Rameau's foundational work cornerstone of tonal harmony theory, introducing concepts like the fundamental bass and chord inversion, which are directly related to intervals. Reading this classic text provides invaluable historical context for understanding how our modern concepts of harmony and intervals developed. It is best suited for advanced students and researchers interested in the history of music theory.
Is similar to Music Theory for Dummies in that it provides a comprehensive overview of music theory. However, it is written in a more conversational style, making it a good choice for those who want a more informal approach.
This anthology serves as a companion to Karpinski's ear training manual, providing a wealth of musical examples specifically chosen for sight singing practice. Working through these examples helps students apply their knowledge of intervals in a musical setting and reinforces aural recognition. It is an excellent supplementary resource for ear training courses. The 2nd edition provides a wide range of melodies.
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