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Dozenal Society of America
Promoting base twelve and alternative base mathematics
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The Dozenal Society of America
The DSA is a voluntary, nonprofit education corporation, organized for the conduct of research and education of the public in the use of dozenal (also called duodecimal or base-twelve) in calculations, mathematics, weights and measures, and other branches of pure and applied science.

The Duodecimal Bulletin

◀️ Issue: Whole Number 64z (76d) | Vol. 33z (39d) No. 1 | Year 119Az (1990d) ▶️



Click to view PDF

Editor: Dr. Patricia Zirkel

Cover Title: Alice Berridge, Gene Zirkel, Tony Scordato named DSA Fellows

Contents:

  • Minutes of Annual Meeting 1989d (1199z)
    • Board of Directors Metting
    • Annual Membership Meeting
      • Reports of Officers and Individuals
        • President’s Report | Fred Newhall
        • Treasurer’s Report | Anthony Catania (presented by Alice Berridge)
        • Editor’s Report | Dr. Patricia Zirkel (presented by Gene Zirkel)
      • Reports of Committees
        • Annual Meeting Committee | Barbran Smith, Anthony Catania, Larry Aufiero, Alice Berridge
        • Finance Committee
        • Nominating Committee
    • Afternoon Presentations
      • Jay Schiffman | A Survey of Duodecimal Number Theory
  • Dozens in Australia
    • Peter D. Thomas | The Modular System: A Preview of the Counting and Measurement System of the 21st Century
    • Modular Convention Bureau
  • Square Root of Two — Revisted | Brian Dean
  • Nu-Age World Calendar | Fred Newhall
  • Music, Scales and Dozens, Part I | Dr. John Impagliazzo
    • Introduction
    • Mathematical Considerations
    • Pythagorean Scales
  • Dozenal Jottings | From Members and Friends
    • Gene Zirkel
    • Arthur Whillock | response to David Fairchild | Pendlebury did indeed design a slide rule
    • Donald Hammond
    • Modular Convention Bureau (Australia) | MCB Newsletter; Australian Metric Record
    • Charles F. Marschner
    • Jamison Handy, Arthur Whillock, Charles Marschner, Charles Ashbacher | responding about hexadecimal A–F
    • New members: John Stewart, Ian B. Patten, Peter D. Thomas
  • In Memoriam — Bob Boase
  • Dozenal Calculators | Paul Rapoport
  • Why Change?
  • Counting in Dozens
Copyright © 11B9–120Az (2013–2026d). The Dozenal Society of America. Contact Us.
Creative Commons License
This site and the documents on it are licensed under a Creative Commons Attribution 4.0 International License.

This site expresses numbers in alternative bases, particularly dozenal (also called duodecimal, or base twelve).
The DSA does not endorse any particular notation or pronunciation scheme for alternative bases.
However this site defaults to the following to ensure online readability across all platforms:
“Computerese” uppercase letters represent transdecimal digits: A = ten, B = eleven, C = twelve, etc.
Single-character subscripts annotate bases: d = decimal, z = dozenal, x = hexadecimal, etc., e.g., 2014d = 11BAz = 7DEx.

(0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 ...)d
(0 1 2 3 4 5 6 7 8 9  A  B 10 11 12 13 14 15 16 17 18 19 1A 1B 20 21 22 23 24 25 26 27 28 29 2A 2B 30 ...)z
(0 1 2 3 4 5 6 7 8 9  A  B  C  D  E  F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 20 21 22 23 24 ...)x

PDF documents on this site reflect changing practices among dozenalists over the years:
Various symbols have been used to represent digits ten and eleven:
Dwiggins 𝒳 and Ɛ (often rendered X and E); Bell Telephone * and #; Pitman turned 2 and 3 (↊ and ↋); etc.
Italics were once used to distinguish dozenal numbers from decimal: e.g. 0.5 = 0.6.
Later, semicolon became a separate‑identity “dozenal point”, versus period as “decimal point”: e.g., 0.5 = 0;6.
However, subscript base annotations provide a more versatile solution that is least‑change: e.g., 0.5d = 0.6z = 0.8x

Dozenal offers superior divisibility over decimal, which can make everyday arithmetic easier to learn:
⅙ = 0.2z | ¼ = 0.3z | ⅓ = 0.4z | ½ = 0.6z | ⅔ = 0.8z | ¾ = 0.9z | ⅚ = 0.Az
⅙ = 0.1666…d | ¼ = 0.25d | ⅓ = 0.333…d | ½ = 0.5d | ⅔ = 0.666…d | ¾ = 0.75d | ⅚ = 0.8333…d

EACH ONE, TEACH ONE.