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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 A3z (123d) | Vol. 53z (63d) No. 1 | Year 1203z (2019d) ▶️



Click to view PDF

Editor: John Volan

Cover Title: Metrologies

Contents:

  • President’s Message | Donald Goodman III
  • Editorial: Taking the Measure of Measures | John Volan
  • New Members
  • In Memory of Gene Zirkel
  • Split-Promote-Discard | Treisaran
  • Up the Down Staircase | Prof. Jay L. Schiffman & Michale DeVlieger
  • Reprint: The Uncia⋅Metric System: A Dozenal System of Weights and Measures | Ralph E. Beard
  • Reprint: The Dozen, and Metrology | Tom Pendlebury
  • Systematic Dozenal Nomenclature Summary
  • The Primel Metrology | John Volan
    • A Coherent Dozenal-Metric “DGW” System
    • Diverging from Pendlebury
    • Quantitels
    • Branding
    • Scaling Prefixes and Colloquial Names
    • Colloquial Families
    • Accommodating TGM Units
    • English Binary Series
    • Primel Zoom
    • Reusing Unit Names
    • Warming Up to Temperature
    • The Angle on Angles
    • More to Come
    • Primel Online
    • In Conclusion
  • Dozenal Timekeeping | Paul Rapoport
    • The Diurnal and Semidiurnal Clock
    • The Holocene Calendar
    • The Experience
  • Use Perbiquas!
  • Dozens in the Media
    • Book Review: The Orthogonal Trilogy | Greg Egan
      • Orthogonal Disaster?
      • Orthogonal People?
      • Orthogonal Numbers?
      • Orthogonal Distance?
      • Orthoganal Time?
      • Orthogonal Angles?
      • Orthogonal Mass?
      • Orthogonal Conclusion?
    • 2016 — The start of a new (dozenal) century | Dr. James Grime
    • BBC Ideas: Is there a better way to count...? 12s anyone? | Stephen Wood
  • Application Form
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.