The Dozenal Society of America

The Society is a voluntary nonprofit educational corporation, organized for the conduct of research and education of the public in the use of base twelve in calculations, mathematics, weights and measures, and other branches of pure and applied science.

Duodecimal Bulletin:

About the Bulletin
Archive Index
Pictorial Synopses
About the Archive

Dozenal Resources

Welcome to the Dozenal Society of America’s electronic brochure database. How do we do base twelve (duodecimal) math? Visit The Basics, which offers a few articles which help you get started using base twelve. Over the coming months in 2011, the DSA will be remastering articles from its Duodecimal Bulletin which cover basic operations so that beginners and students studying number bases might have access to our authorities on duodecimal arithmetic. We’ve got plenty of other articles as well, from how to design your own base twelve numerals, who started the DSA, what do DSA Members think about the SI-Metric System, and advanced articles about dozenal number theory. Click here for the most commonly downloaded files or check out a list of link categories. Note that this part of the site, along with the Duodecimal Bulletin Digital Archive, grow continuously, so visit often! Click What’s New for the latest posts.

Common Downloads

This quick-access section of the Resources page features popular basic and a selection of the most interesting remastered articles in our database! Can’t find something you need? Check out the Category List, the Duodecimal Bulletin Digital Archive, or join us and help make it happen!


“Fundamental Operations in the Duodecimal System”
by Prof. Jay Schiffman, 1982, db31315 & db32204.
The most popular DSA download! A highly recommended, thorough explanation of the four basic operations (addition, multiplication, division, and subtraction) in base twelve. Prof. Schiffman rigorously walks us through how one computes in dozenal, using decimal as an analogy to the dozenal processes. Download the British version.


“A Brief Introduction to Dozenal Counting”
Prof. Gene Zirkel, 1995, db38206.
Prof. Zirkel describes the origins of our base ten system, why dozenal is superior to decimal as a number base, and some dozenal basics. Download the British version.


“Decimal-Dozenal Conversion Rules”
Prof. Gene Zirkel and others, 2005.
This document offers rules and examples for converting decimal numbers to dozenal and vice versa. The material is partially drawn from pages 19;-20; of the Manual of the Dozen System.
Download the British version.


“Why Change?” by Ralph Beard, 1948, db043r2.
The first Editor of the Duodecimal Bulletin parallels the duodecimal number base with the adoption of Hindu-Arabic numerals and positional notation in medieval Europe. Dozenal must replace decimal, because the latter has “not enough factors” in comparison to dozenal.


“An Excursion in Numbers” by F. Emerson Andrews.
the landmark article in the Atlantic Monthly, which eventually led to the founding of the Duodecimal Society of America


“My Love Affair with Dozens” by F. Emerson Andrews.
One of the DSA’s Founders describes how he, a writer, fell in love with the number twelve through reason, and how the Duodecimal Society of America came to be established.


“Eggsactly a Dozen”
Prof. James Malone, 1981, db2610b.
A Nassau Community College professor shares a simple way to look at dozenal conversion of decimal whole numbers.


“Symbology Overview”
Editorial, 2010, db4X211.
The Duodecimal Bulletin examines all dozenal numeral proposals known at the time in this two-part editorial. Part I looks into “Least Change” proposals (as classified by R. Beard.) See db4E111 above for Part II.


“A Numeral Toolbox”
Michael Thomas De Vlieger, 2010, db4E111.
This article, part II of a two-issue exploration of all dozenal symbologies, suggests a few simple methods of designing numerals for transdecimal number bases. Studies of “Separate Identity’ symbologies reveals relationships among their numeral symbols. The symbologies of large number bases are also examined.

symbology synopsis

“The DSA Symbology Synopsis”
Continually updated, last update January 2011.
This 11" × 17" landscape-format poster summarizes numerals devised for dozenal, hexadecimal, and other bases. The DSA Symbology Synopsis brings together all symbols surveyed by Duodecimal Bulletin Vol. 4X; No. 2 and Vol. 4E; No. 1, as well as those submitted by readers and gleaned subsequently on the internet.


“Music, Scales, and Dozens”
by Dr. John Impagliazzo, 1990, db33116 & db33208.
Dr. Impagliazzo methodically examines the Pythagorean, Just Intonation, and Well-Tempered (dozenal) music scales and illustrates their differences.


“Manual of the Dozen System”by the DSA, 1960.
This is a classic manual which was distributed to Members and interested corresponders, which contains descriptions of various basic dozenal concepts. Tables of logarithms, exponents, and fractions are included. Also includes part of Henry Churchman’s dozenal system of measure and a section offering dozenal references.


“A History of the DSA”
by Prof. Gene Zirkel, 2008, db49209.
Originally appearing on this website as “A Brief History of the Society”, this is a full color account of the DSA as seen through Prof. Gene Zirkel’s eyes. Includes a list of Annual (Beard) Award Recipients, officers, Editors of the Duodecimal Bulletin and more. Part I of two.


“Reflections on the DSGB”
by Prof. Gene Zirkel, 2009, db4X113.
Prof. Zirkel compiled some thoughts from key DSGB Members including Brian Bishop, Shaun Ferguson, and Robert Carnaghan on the history of the Dozenal Society of Great Britain. Part II of two.


“Multiplication Tables of Various Bases”
Michael T. De Vlieger, 2011. Revised 7 February 2011.
A continually-expanding set of multiplication tables for positive, integral number bases greater than 2. Bases covered (decimal notation) include 2-30, 32, 36, 40, and 60. (Next revisions plan to cover 42, 45, 48, 50, 54, 56, 64, 66, 72, 80, 81, 90, 96, 100, 108, 120, 125, 128).

Article Categories and Links

The Dozenal Society offers other articles, currently mostly originating from remastered articles that appeared on this website, as well as the most current issues of the Duodecimal Bulletin. More categories and articles will appear from time to time, so check back often!

The Basics. Here are a few articles which help you get started using base twelve.

Numerals. One of the foremost considerations among dozenalists is how to symbolize the digits of base twelve, and how to pronounce dozenal numbers.

General and Dozenal Mathematics. Here you’ll find various articles exploring general mathematics as it relates to duodecimal notation, as well as dozenal mathematical articles.

Music and the Dozen. Musicians and mathematicians alike will tell you that twelve and harmony have a lot to do with one another.

Dozenal Advocacy / “Dozenalism”. A set of articles by those who feel strongly that dozenal is the optimum number base for general use by civilization.

History and People of the Dozenal Societies. Read about the Dozenal Societies and their Members.

“Best Base” articles. Which is the best number base? Is it hexadecimal, octal, base 6, or decimal?

Duodecimal Bulletin’s “Featured Figures” Department. Take a look at these figures.

Other Number Bases. Some examinations of other bases may help you decide for yourself which number base is the best tool for general human computation.

British (Pitman) Versions. If you prefer the Issac Pitman notation to the DSA’ standard Dwiggins numerals, we provide several popular downloads here.

“What’s New?”. Check in here to take a look at the latest DSA resources.

Future categories: dozenal applications (such as music, above), full dozenal system articles, measurement systems, our take on the SI/metric system, recreation (such as the levity section), reference and tools. Got a category you’re interested in? Write the Editor an email at Editor(at)Dozenal(dot)org!

Visit the Duodecimal Bulletin Digital Archive

This page revised Wednesday 30 November 2011.