Seal of the DSA
Join Us!
Dozenal Society of America
Promoting base twelve and alternative base mathematics
Support the DSA
Donate
Follow Us
Icon for DSA's X Icon for DSA's Facebook Icon for DSA's RSS
Share This Page
Icon for sharing via X Icon for sharing via Facebook Icon for sharing via email
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 1Az (22d) | Vol. Bz (11d) No. 1 | Year 116Bz (1955d) ▶️



Click to view PDF

Editor: Ralph Beard

Contents:

  • The Do-Re-Mi System of Dozenal Nomenclature: A Trip into the Land of Ever-Ever | Henry Clarence Churchman (page 1z)
    • A Simple Approach to Doremial Nomenclature (page 2z)
    • The Three Digit Column (Hundreds) (page 3z)
    • The Four Digit Column (Thousands) (page 3z)
    • The Five, Six, and Seven Digit Columns and Over (page 4z)
  • Another Arithmocrypt | Mary Lloyd (page 5z)
  • The Annual Meeting (page 6z)
  • A Message from President Camp | Kingsland Camp (page 8z)
  • Interlingua and the Duodecimal Nomenclature | Alexander Gode (page 9z)
    • Cardinal Duodecimal Numerals in Interlingua (page 11z)
    • Ordinal Duodecimal Numerals in Interlingua (page 13z)
    • Fractions in Interlingua (page 13z)
  • Are We Ready? (page 14z)
  • The Twelve Winds and Their Portals: An Excerpt from the Book of Enoch | Kenneth C. McCulloch (page 15z)
  • An Old Unique Issue of U.S. Postage Stamps | Lewis Carl Seelbach (page 16z)
  • Student Membership (page 17z)
  • Mathematical Recreations | Donald M. Brown, Editor (page 18z)
  • Your Invitation (page 21z)
  • Time and Angle Conversion Tables | Jay M. Anderson (page 22z)
    • Conversion of Time to Duodecimals (page 23z)
    • Conversion of Angle to Duodecimals (page 23z)
    • Conversion of Duodecimals to Time and Angle (page 24z)
  • Incentives and Objectives (page 25z)
  • Counting in Dozens (page 26z)
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.