This nonfiction treatise surveys how the structure of tones links physics and harmony, presenting methods to measure and compare intervals, millioctaves, and temperaments. It blends historical insight with concrete calculations, making complex ideas accessible to readers curious about how scales are built and why tuning matters.

Starting from foundational concepts like the fifth and fourth, it guides you through the idea of normal tones, comma-intervals, and the role of temperaments in real-world music practice. You’ll see how ancient and later theories evolved into a measurable system for understanding scales and harmony, including discussions of Pythagoras, tonal circles, and the practical limits of pure intervals.

How intervals are defined and calculated, including millioctaves and log-based measures
Differences between normal tones and comma-intervals in scale construction
The concept of temperaments and how they shape practical tuning choices
Historical context that connects physics, physiology, and harmony

Ideal for readers of music theory, acoustics, and anyone curious about how tuning theory informs performance and composition.

"About this title" may belong to another edition of this title.

Store Description

We first started out as ?The Paperback Exchange,? a chain of physical bookstores where we would part exchange your beloved books for new stories to transport you to faraway places. However, as shopping started to evolve to online shops and marketplaces, we bid our stores goodbye to become ?PBShop.? This transition has only allowed us to blossom as we now ship thousands of titles to book lovers across the globe. We pride ourselves in being a community of local book lovers which allows our passion and devotion to shine in everything we do. In 2020 we not only celebrated our 20th birthday but our 1st birthday as being completely employee owned after becoming an E.O.T in September 2019. We are proud to be different and embrace standing apart on a book mountain by working from a virtual inventory which allows us to provide thousands of books that may be difficult to get for your bookshelf or your studies. Working with a number of different suppliers allows us to explore other avenues such as puzzles, sheet music and even stationery so we really do have something for everyone. Life is about being versatile in all realms of existence. If this is your first visit or you are a returning customer, we would like to welcome you to the PBShop family, for there is no friend as loyal as a book. We are a company who put our customers at the centre of everything we do as we understand the importance of reading because once you learn to read, you will forever be free. There are a whole lot of things in this world of ours that we are yet to explore, which is why we will forever inspire curious minds.

Visit Seller's Storefront

Seller's business information

Pbshop.co.uk Ltd
Unit 22 Horcott Industrial Estate, Horcott Road, Fairford, GL7 4BX, United Kingdom

Sale & Shipping Terms

Terms of Sale

Returns Policy
We ask all customers to contact us for authorisation should they wish to return their order. Orders returned without authorisation may not be credited.
If you wish to return, please contact us within 14 days of receiving your order to obtain authorisation.

Returns requested beyond this time will not be authorised.

Our team will provide full instructions on how to return your order and once received our returns department will process your refund.
Please note the cost to return any...

More Information

Shipping Terms

Books are shipped from UK warehouse. Delivery thereafter is between 4 and 14 business days dependant upon your location - please do contact us with any queries you may have.

Shipping rates within U.S.A.

Shipping rates within U.S.A.
Order quantity	7 to 14 business days	7 to 14 business days
First item	US$ 0.00	US$ 0.00

Delivery times are set by sellers and vary by carrier and location. Orders passing through Customs may face delays and buyers are responsible for any associated duties or fees. Sellers may contact you regarding additional charges to cover any increased costs to ship your items.