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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 24z (28d) | Vol. 12z (14d) No. 1 | Year 1172z (1958d) ▶️



Click to view PDF

Editor: Ralph Beard

Contents:

  • The Annual Meeting (page 1z)
  • The Annual Award (page 5z)
    • 1160z (1944d): F. Emerson Andrews
    • 1161z (1945d): George S. Terry
    • 1162z (1946d): F. Howard Seely
    • 1163z (1947d): Ralph H. Beard
    • 1164z (1948d): Harry C. Robert, Jr.
    • 1167z (1951d): J. Halcro Johnston
    • 1170z (1956d): Jean Essig
    • 1171z (1957d): Herbert Kay Humphrey
  • Doremic System of Angular Measurement | H. C. Churchman (page 8z)
    • Illustration: Doremique Map of the World (page 8z)
    • Properties of New Geophysical Mile (page Az)
      • Table of Angles (page 10z)
        • Angle (∠) Symbol for Doremic Theoretical Measurement of a Great Circle of the Earth
    • Paris Hemisphere (page 10z)
    • Time and Angle Comparison (page 12z)
      • Table (page 13z)
        • A Correlation of Time (d) and Angle (∠) Measurements in Doremic Nomenclature of Dozenal Base
    • Knaire Rate of Travel (page 14z)
    • Shooting a Star in Do-Re-Mi Language (page 15z)
    • Naire Meridians and Parallels (page 16z)
  • Redivivus Reckoning | Charles S. Bagley (page 19z)
  • New British Metric Committee (page 33z)
  • Counting in Dozens (page 4Bz)
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.