Numerical System of Raqqos

The Numerical System of Raqqos, also known as *Shir'is Horaba* "Horaba Counting" is the traditional counting system or Raqqos. It was the historical counting system of the Ankhosian Empire.

## The *Horaba* and its denominations

The Raqqosian numerical system is a mixed-radix numerical system used for describing a unit named the "Horaba", which is equivalent to the number 373,248,000. The Horaba is broken down into six denominations, which form the basis of the Raqqosian numerical system.

The radix of these denominations alternates between base 12 and base 60. Each numerical representation is expressed using a sequence of units that are each a multiple of the next smaller one, but not by the same factor.

 Place Value

For example, the number 31,103,280 would be written as 59518,4001143,20059720116059*1* . This can otherwise be expressed as 59Sindar11Malin59Qidir11Bejel59Alin.

## Written Notation

The Raqqosian numerical system comprises of two notation systems, the Mina'shiri and the Ba'Shiri notations.

### Mina'shiri notation system

The *Mina'shiri* ("wage count") notation denotes the denominations of the Horaba. It is written using the characters H, D, S, M, Q, B and A. It is common in modern notation to underline these characters, for ease of legibility. It is also fairly common to separate them by an empty space in non-formal contexts.

*The character L is sometimes used to represent the Alin, due to the visual similarities between the mina'shiri character A and the ba'shiri character ~~Ʌ.~~*

### Ba'shiri notation system

Each radix in the *mina'shiri* notation is recorded through the *ba'shiri'* ("number count") notation system, a set of characters which are combined in order to represent each of the numbers 1 through 60.

 3
 6
 30
 60

For example, the number 59 would be represented as U~~M̈M̈Ʌ~~ɅI (or 130124161311.)

### Combining the notation systems

When combining the *Ba'shiri* counting number system with the *Mina'shiri* notation characters HDSMQBL, one can write numbers in full Raqqosian (*Shir'is Horaba*) notation.

For example, the number 31,103,280 (used as an example in the above section) would be written as U~~M̈M̈Ʌ~~ɅIS~~Ʌ~~ɅIMU~~M̈M̈Ʌ~~ɅQ~~Ʌ~~ɅIBU~~M̈M̈Ʌ~~ɅA. This can also be written with spaces and the underlining of the Mina'shiri notation for ease of legibility: U~~M̈M̈Ʌ~~ɅIS ~~Ʌ~~ɅIM U~~M̈M̈Ʌ~~ɅQ ~~Ʌ~~ɅIB U~~M̈M̈Ʌ~~ɅA.

(Using Pemblish numerals this would be written as 59Sindar11Malin59Qidir11Bejel59Alin. As above, this can otherwise be expressed as 59518,4001143,20059720116059*1*.)

## Modern adaptations

Due to the common numerical understanding of the Occidental numerical system among merchants and beauraucrats, it is common for Occidental numerals to be used instead of *Ba'shiri* notation. For example, 719 would be represented as 11B 59A, rather than ~~Ʌ~~ɅIB U~~M̈M̈Ʌ~~ɅA.

## Historical Written Forms ***(WIP)***

The Raqqosian numerical system has undergone various revisions to improve its usability and speed of writing.

Ancient Form: Full Bases, Denominations are written from smallest to largest, Unreformed names and denominations

 3
 6

'Legacy' Traditional: Full Bases, Smallest > Largest, Reformed names, Unreformed denominations

'Revised' Traditional: Contracted Bases, Largest > Smallest, Common names and denominations

Modernised: Contracted Notation, Contracted 'maximum minus' 1 bases(1H minus 1, represented as D<->B59A [instead of 11D,59S,11M,59Q,11B,59A), Contracted Bases, Largest > Smallest, Common names and annotations

Revised Modern: Simplified Bases, Largest > Smallest, Common names and annotations

Hybrid: Use of Pemblish numbers, Simplified Bases, Simplified Notation, Largest > Smallest, Common names and annotations

U~~MM~~ɅIIM