What are Tonal Bitcoins? In what application is this system of notation superior to the decimal notation? Are there any clients or other services supporting the tonal system?
Programmers will immediately recognise this as hexadecimal. For non-programmers hexadecimal uses the following representations: 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F. Note that decimal 10 to 15 are represented by the single letters A to F, such that FF is decimal 255 or (16 * 15)+(1 * 15). To differentiate a decimal number from a hexadecimal number the conventions 0x10 (decimal 16) or 10h are widely recognised.
The Tonal bitcoin representation attempts to offer an alternative representation of BTC known as TBC (Tonal Bitcoin) and uses the various Tonal letters to represent them. The Tonal alphabet is more complex than the hexadecimal system and requires special fonts to be available on the systems using it.
It is unlikely that this archaic approach to base 16 is ever likely to gain traction when much more widespread approaches are available.
Units covering powers of 2 in computing
It should be noted that in 1998 the International Electrotechnical Commission (IEC), Institute of Electrical and Electronics Engineers (IEEE) and the International Committee for Weights and Measures (CIPM) adopted a purely "powers of 2" approach for some use cases. Notably the representation of computer storage and data transmission rates.
This gives rise to 2 unit systems - one base 10, the other base 2:
The primary power of 10 notation we're all familiar with:
Thus there is even less reason to use the Tonal system since a widespread alternative with well-defined prefixes has already been ratified for some time.
Tonal Bitcoins (TBC) are an interpretation of the low-level Bitcoin system with Tonal units (similar to how BTC is a SI interpretation).
The Tonal number system is superior to decimal for virtually every human use, but is (similar to Dvorak keyboards, or your first second language) difficult to learn for people who were raised only with decimal. It is superior because humans naturally work in powers of 2, and this can be easily demonstrated in many areas: despite the common decimal system forced (literally) on societies today, people still find ways to use binary (for example, USD "quarters" or slicing pizza - ever try to slice 5 pieces?).
The Python Bitcoin client Spesmilo supports both BTC and TBC (and mixed) interpretations by configuration, provided a Tonal-compatible font is detected on your system. While the tonal system has not been officially adopted in any nation, it is a natural "next step" from some US customary units. The Tonal system, unlike the newer hexadecimal system, is complete and provides not only digits (rather than ambiguously hijacking letters) but also pronunciations, weights, measures, time, and a calendar, necessary to use it in daily life.