The Dozenal Society of America

“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.

“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).