I know there are many books which describe why we have 12 pitches (for example this book: R.H.M Bosanquet - An elementary treatise on musical intervals and temperament, 1876 in the public domain).

These books focus on attempts to make mathematical formulas for pitches but few look at why we like to listen to the specific tones in the Western scales.

Reading articles by the inventors of microtonal music systems also addresses some things in this area.

But I am looking for more direct/clear reading about this.


3 Answers 3


I would recommend connecting with the Just Intonation Network. They have a bookstore of many worthwhile books on the topic. David Doty, who used to be with the network, has an excellent primer on just intonation that's available at his website.

The best work I've read on the topic from an intuitive rather than mathematical perspective is W. A. Mathieu's Harmonic Experience. It's truly an amazing work, breaking down the ideas of harmony into their parts before putting it all back together again. I highly recommend it.

Hope this helps!


Go looking for Howard Goodall's Big Bangs in Music. It is intended for a mainstream audience but it covers natural intervals and the various historical attempts at harmonising them until we arrived at the Westen even-tempered scale.


If you really want to get deep into the theory and the reasons that 12 tones "sound right", I can't recommend Harry Partch's Genesis of a New Music enough. He does have his hobbyhorse to ride on why equal temperment is bad and why we really need 43 tones to the octave, but the presentation of the bases for tuning and the twelve-note scale are detailed, clear, and very well done. It's a more mathematical treatment, but you don't have to understand much more than ratios to understand it.

His take is that we listen to many intervals that are not perfect, i.e., properly-tuned ratios of notes - exact ratios of frequencies sound purer and "sweeter" than the compromise intervals we use in equal temperment - and accept them because of the difficulty of constructing instruments which can play arbitrary intervals: the 12-note keyboard being a particular problem from his perspective.

He throws out other temperments (meantone, etc.) as making one scale perfect at the expense of all the others sounding less good, or even actively bad; his take is that we should be able to construct a full "circle-of-fifths" of scales, all of which sound as consonant as the scale based on the note we choose as the base note for our scales. Fascinating book, and well worth reading.


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