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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 38z (44d) | Vol. 20z (24d) No. 1 | Year 1181z (1968d) ▶️



Click to view PDF

Editor: Jamison “Jux” Handy, Jr.

Associate Editor: Henry Churchman

Contents:

  • Meeting of the Board and Annual Meeting of 1181z (1969d) (page 1z, page 24z)
    • Proceedings of 1181-03-26.460z (1969-03-30 09:00d) (page 1z)
    • Election of Board Members (page 2z)
    • Proceedings of 1181-03-27.460z (1969-03-31 09:00d) (page 2z)
    • Report of the Secretary (page 3z)
    • Editor’s Report (page 3z)
    • Election of Officers (page 4z)
    • New Business (page 4z)
    • Further Session of the Society, 1181-04-01.460z (1969-04-01 09:00d) (page 5z)
  • Metric Timepieces and the Moon | Henry C. Churchman (page 6z)
  • Comments on Standard | Tom B. Linton (page 7z)
  • Metric Time: How a Modern Scientist Tells Time Today | Henry C. Churchman (page 8z)
    • Figure 1: Clock (page 8z)
    • Figure 2: Scientists’ Metric vs Base Ten Method (page 9z)
  • English E-Z Locator Exposition | Brian R. Bishop (page Az, page 24z)
  • Study of a Modern Meter and the Obsolete 18thd Century Meter | Henry C. Churchman (page Bz)
  • The Great Gross Candy Bar, A Filler (page 10z)
  • Chromatic Musical Scales and Notations | Eric Kothe (page 11z)
    • Part Two: Musical Scales (page 11z)
      • Figure 13d: Degree of Consonance (page 11z)
      • Figure 14d: Frequency Ratios of Conventional Musical Notes (page 12z)
      • Figure 15d: Diatonic C-Scale (page 12z)
      • Figure 16d: Church Modes (page 13z)
      • Figure 17d: Greater Perfect System (page 13z)
      • Figure 18d: Diatonic Clavichord Keyboard (Guido’s Scale) (page 14z)
      • Figure 19d: Enharmonic C-Scale (page 14z)
      • Figure 20d: Diagram of the action of a Double-action Pedal Harp (page 14z)
      • Figure 21d: Frequencies of Musical Notes (page 15z)
      • Figure 22d: Pythagorean C-Scale (page 15z)
      • Figure 23d: Succession of Fifths, and Wolf Fifth (page 16z)
      • Figure 24d: Solmization Mnemonic (page 18z)
      • Figure 25d: Pitch Extent of Musical Intervals (page 19z)
    • Part Three: Chromatic Notations (page 1Az)
      • Figure 26d: Musica Enchiriadis Notation (page 1Bz)
      • Figure 27d: Boethius Musical Notation (page 1Bz)
      • Figure 28d: Notations for Sharps, Flats, and Naturals (page 20z)
      • Figure 29d: Evolutions of Clef Symbols (page 21z)
  • A Tribute to George S. Terry, 1113-1181z (1887-1969d)| F. Emerson Andrews (page 22z)
  • Cartoon: Soft-Sell Sam (page 24z)
  • Excerpts from Letters and Comments (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.