Dozenal Roman Numerals

In the topic on graduation divisions for measurement scales at Base Dozen Forum, Metrology, Graduation Subdivisions, the proposal today in the third post there almost suggests specification of marks on the scale by additive and subtractive denominational numerals like Roman numerals but in base twelve, as follows:

Code:


|   |   |   |   |   |   |   |   |   |   |   |   |
|       |   |   |       |       |   |   |       |
|           |           |           |           |
|                                               |
    I  II  III IIↅ Iↅ  ↅ  ↅI ↅII ↅIII IIO IO  O
0   1   2   3   4   5   6   7   8   9   10  11  12


The symbol for the number six is related to the Greek alphanumeric character digamma or final sigma for the number six. It looks like the Gothic letter Jer 𐌾 unicode U+1033E.

For the number twelve, I have chosen the letter O, which in Roman numerals was used for the number eleven from the word onze. This word is similar to ounce related to twelve. Eleven is close to twelve, and the circle can be thought of as representing completion when twelve is reached.

To make an extensive system of denominational numerals for base twelve, more symbols are required, preferably enough to reach at least the third power of the base. There were Roman symbols for certain fractions which were dozenal divisions. Some of these symbols are as illustrated below:

Code:


|  |  |  |  |  |  |  |  |  |  |  |  |
|     |  |  |     |     |  |  |     |
|        |        |        |        |
|                                   |
   "              ℈                 Ƶ
   Ƶ  Z  Ↄ  ZZ    Є                 -
   -  :  ∴  ∷  ⁙  S                 I
   I  II          ↅ


The rows of symbols underneath the graduation marks represent the fractions at the successive orders of magnitude or powers of the base twelve. These fractions have names in the Latin language as follows:

Symbol	Fraction Decimally	Name
))	1/1728	siliqua
℈	1/288	scrupulum
S	1/144	dimidia sextula
S	1/72	sextula
Ↄ	1/48	sicilicus
SS	1/36	binae sextula
Є	1/24	semuncia
-	1/12	uncia
S	1/2	semis
I	1	as

Since I do not have characters for the dimidia sextula and sextula appearing from their proper Unicodes, I will use Ƶ and Z for them. For the siliqua, I will use the double quotation mark ".

References:

• https://dozenal.forumotion.com/t47-graduation-subdivisions#173
  
• https://en.wikipedia.org/wiki/Roman_numerals
  
• https://en.wikipedia.org/wiki/Gothic_alphabet
  

(To be continued …)

The uncia means a twelfth of any unit. Thus,

for length: 1 pes = twelve uncia,
for area: 1 jugerum = twelve uncia,
for volume: 1 litra which as a pound or pint of liquid = twelve ounces, but later sixteen fluid ounces, and
for weight: 1 libra = twelve uncia

Weight
Where the unit of weight was the pound or Roman libra, the uncia was an ounce. An Apothecaries' system of weight was based on the troy pound. The symbol for an ounce as used in medical prescriptions was ℥, which we could use for the uncia instead of a horizontal line or dot. The Apothecaries' pound symbol was ℔, a type of abbreviation from the Latin word libra. In the Apothecaries' notation, a dram or drachm symbolised by ʒ was an eighth of an ounce, and would be halfway between the dimidia sextula and sextula. It is more of a binary type of division than a dozenal one, and can be omitted from the dozenal scheme in a proposal for dozenal Roman style numerals. The scruple represented by the symbol ℈ was also part of the Apothecaries' notation, and represented half of a twelfth of an ounce. There were twenty grains to a scruple, but this is not a dozenal number and can be avoided. Instead, the siliqua or carat as a square dozenth of the uncia can be retained. The caret symbol ^ might be used for it as a pun. Another possibility for being easily accessible from a keyboard is ¦. There is a Unicode number 10192 for a Roman semuncia sign.

Currency
Denominations of currency as coins were based on weight and fineness of the metal. As they were more subject to devaluation through decreasing fineness, their ratios were not as stable as those of the weights. Instead of the symbol I for the unit, a sign for the pound, such as the currency symbols £ or ₤ Unicode U+20A4, could be used. From the division of the pound lira into the solidus and denarius, the pound, shilling and penny system of currency evolved. There were twenty shillings to the pound, and twelve pence to the shilling. If the multiple of the solidus in the pound were a dozenal number, we could employ the solidus sign / as a pun for that fraction. Alternatively, the long-S symbol ſ of the shilling might be used. There were two dozen of the siliqua to the solidus, according to the "Late Empire coin values (337–476)" in the Roman Currency article on Wikipedia. Other words for the solidus coin might be nomisma in Greek, which has Unicode 1018E, or bezant. As for Greek currency, there were six obol to a drachma. The Roman obolus was worth three of the siliqua, or a quarter of a twelfth of an uncia. As a pun, the obolus can be symbolised by the obelus, as a dagger mark †.

Denominational Numerals Proposal
The scheme aligned to the ruler from the previous post yesterday can be extended and decluttered as follows:

Code:


|   |   |   |   |   |   |   |   |   |   |   |   |
|       |   |   |       |       |   |   |       |
|           |           |           |           |
|                                               |
    "       †           ℈                       Ƶ
    Ƶ ʒ ſ   Ↄ           Є                       ℥
    ℥       ∴           S                       £
    £                   ↅ


If the siliqua or carat is treated as the unit, then the denominations maintaining the same ratios are enough for the first three powers of the base twelve, as well as the half and quarter powers.

References:

• https://en.wikipedia.org/wiki/Ancient_Roman_units_of_measurement
  
• https://en.wikipedia.org/wiki/Pound_(mass)
  "The unit is descended from the Roman libra (hence the abbreviation "lb"). "
  
• https://en.wikipedia.org/wiki/Apothecaries%27_system
  
• https://dozenal.forumotion.com/t42-troy
  
• https://en.wikipedia.org/wiki/Dram_(unit)
  
• https://www.unicode.org/charts/PDF/U10190.pdf
  
• https://en.wikipedia.org/wiki/Lira
  
• https://en.wikipedia.org/wiki/Shilling
  "In origin, the word schilling designated the solidus of Late Antiquity, the gold coin that replaced the aureus in the 4th century. The Anglo-Saxon scillingas of the 7th century were still small gold coins."
  
• https://en.wikipedia.org/wiki/Slash_(punctuation)#shilling
  
• https://en.wikipedia.org/wiki/Roman_currency
  
• https://en.wikipedia.org/wiki/Solidus_(coin)
  
• https://en.wikipedia.org/wiki/Bezant
  
• https://www.unicode.org/charts/PDF/U10140.pdf
  
• https://en.wikipedia.org/wiki/Obol_(coin)
  "six obols make a drachma or a handful, since that was as many as the hand could grasp.[2] Heraklides of Pontus (died ca. 310 BC) is cited as having mentioned the obols of Heraion and also gives the etymology of obolos (the name of the coin) from obelos (the word for "spit, spike, nail")."
  
• https://en.wikipedia.org/wiki/Obelus