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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 39z (45d) | Vol. 21z (25d) No. 1 | Year 1182z (1970d) ▶️



Click to view PDF

Editor: Jamison “Jux” Handy, Jr.

Associate Editor: Henry Churchman

Contents:

  • Towards a Base Twelve Computer | B. A. M. Moon | Director, Computer Centre, Univ. of Canterbury (page 1z)
    • Table 1: Relative Costs and Information per Digit, for Various Bases (page 2z)
    • Appendix: A modification of a result of Bucholz (page 3z)
    • References (page 4z)
  • The Nufut or “Nubbin”: A Transitional Dimension for the Jet Age? by Henry Churchman (page 4z)
  • Chromatic Musical Scales and Notations | Erich Kothe (page 5z)
    • Part Three (cont’d): Chromatic Notations (page 5z)
      • Figure 30d: Gothic Choral Notation (page 5z)
      • Figure 31d (page 5z)
      • Figure 32d: 8 Above or Below Clef (page 6z)
      • Figure 33d: Great Eleven-Line Staff (page 6z)
      • Figure 34d: Patent Notes (page 6z)
      • Figure 35d: Natural, Sharp, Double-Sharp, Flat, Double-Flat (page 7z)
      • Figure 36d: C Major Mode (page 7z)
      • Figure 37d: C Minor Modes (page 8z)
      • Figure 38d: All Keys (page 8z)
      • Figure 39d: Conventional Keyboard (page Az)
      • Figure 40d: Janko Keyboard (page Az)
      • Figure 41d: Angel Menchaca System (page Bz)
      • Figure 42d: Roualle de Boisgelou System (page 10z)
      • Figure 43d: Riemann, Sacher, Engelke, and Viennese Notations (page 10z)
      • Figure 44d: Rohleder and Bäßler Notations (page 11z)
      • Figure 45d (page 12z)
      • Figure 46d: Godjevatz Notation (page 13z)
      • Figure 47d: Kothe Notations (page 14z)
      • Figure 48d: Comparison between Conventional, Godjevatz, and Kothe Notations (page 15z)
  • The Dometric System | Allan C. Boschen (page 16z)
    • Advantages of Dozenal Counting and of Dometric (page 16z)
    • Educational Values from Dozenals and Dometric (page 16z)
    • Fractions and Duodecimal Equivalents (page 17z)
    • Future Possibilities (page 17z)
    • Computer Applications (page 17z)
    • Projected Duodecimal Metric Usage in the World (page 18z)
  • Quo Vadis | Henry C. Churchman (page 19z)
  • Melodrama at “The Old Homestead”: A Happening (page 1Az)
  • Number-Base Oddments | Shaun Ferguson (page 1Bz)
  • Elusive Peace and Base Twelve | Henry Churchman (page 20z)
  • A Tribute To Jean Essig | Brian Bishop (page 21z)
  • Accolade to the National Education Association | Henry C. Churchman (page 22z)
  • Excerpts from Letters and Communications (page 22z)
  • Editorial: We Could Go Metric Pleasantly | Henry C. Churchman (page 23z)
  • 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.