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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 6Bz (83d) | Vol. 35z (41d) No. 2 | Year 11A0z (1992d) ▶️



Click to view PDF

Editor: Dr. Patricia Zirkel

Cover Title: Dozenal Music Revisited

Contents:

  • Board of Directors Meeting
  • Conversion of Numbers to Base Dek | Jean Kelly
  • Dyhexal Numbers: How They Facilitate Arithmetic | Gerard Robert Brost
    • Introduction
    • Some advantages of base twelve mathematics
    • Dyhexal notation
  • Math Forum | Betsy Colwell
  • Available from the Society
  • Dozenal Music Revisited | John D. Hansen, Jr.
  • Dozenal Jottings | From Members and Friends
    • Ken Stilwell
    • Underwood Dudley | A Budget of Trisections
    • Bill Crosby called! (Pvt William S. Crosby)
    • Jay Schiffman
    • Alice Berridge
    • John Churchman, regarding Henry Churchman
    • John D. Hansen | entered DSA into contest at Radio Electronics
    • Arthur Whillock (DSGB)
    • Charles Ashbacher
    • Don Hammond (DSGB) | Rational Fahrenheit Scale
    • Sizable donations: Richard Trelfa, Henry Churchman, Dr. Robert Lovell, “Skip” Scifres
    • New member: Robert High
  • Think About It!!!
  • DSA Seal Puzzle Solutions | Charles Ashbacher
  • In Memoriam — Isaac Asimov
  • Another Solution to a Base Twelve Crossnumber Puzzle | Jay L. Schiffman
  • 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.
d