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Quaternary codes, generated by GeoGnomo, are a series of numbers representing a location with an arbitrary accuracy. From these codes, GeoTono generates a musical score which can be reversed to retrieve the original Quaternary coordinates.


A Quaternary code is in the form of 30U,311311000011133012333. For GeoTono to generate a musical score, characters proceeding the comma are dropped, and the remaining characters are converted into binary. The binary representation is then divided into trits (groups of three bits).

Table 1.

Base-8 Note
000 C
001 D
010 E
011 F
100 G
101 A
110 B
111 c

The conversion from base-8 to musical notes.

Each trit permutation is a different note on the C major scale.

Table 2.

Number of Notes in Measure Length of Each Note(4/4 time)
4 2,3,1,2
3 2,4,2
2 4,4
1 8

The length of each note in a measure.

Lengths are determined by the number of notes in the measure.

The trits are read in base-8 to generate musical notes on the C major scale according to table 1. Then, a C note is prepended, and a G is appended to the musical score. Finally, lengths are assigned to the notes based on table 2.

Example Encoding

  1. The Quaternary code generated from GeoGnomo for Z/Yen’s office at level-21 is


  2. Characters before the comma, 6 in this case, are dropped. The remaining code is converted into binary,


  3. The binary is grouped into trits:

    110 111 010 111 010 101 100 001 011 101 110 101 100 101

    and then converted into musical notes on the C major scale using table 1


  4. Because the notes are played in the key of C major, a C is prepended, and a G is appended to the score.


  5. The notes are grouped into measures and lengths are assigned to them according to table 2.

    (4/4) | CBcE | cEAG | DFAB | AGAG ||

    (4/4) | 2312 | 2312 | 2312 | 2312 ||

The result can be displayed on a musical staff with abc.js.

Decoding can be achieved by reversing the process from step 4, since the lengths of the notes are independent of the Quaternary code. This is automated with the abc.js MIDI decoder package.


The music score can be played directly as MIDI audio.

Other Considerations

Abc.js has optional parameters for generating the musical score. The following parameters were used for generating the examples presented:

  • M: meter parameter value is 4/4 (default)

  • L: basic note length value is left blank

  • Bar lines are inserted after 4 notes group

  • R: is left blank


Currently, GeoTono prototype is built over the Quaternary Rectangular System (QRS). To view it live, please click here and go to LatLon to GeoGnomo Code (QRS) tab.

Further Examples

  1. Georgia State University:

    Quaternary code: 5,322123333333230030311

    Binary code: 111010011011111111111111101100001100110101

    Music Notation: "|C2c3E1F2|F2c3c1c2|c2A3G1D2|G2B3A1G2|"

    Figure 2: Georgia State University at level 21

  2. Tokyo:

    Quaternary code: 3,232103222211311000111

    Binary code: 101110010011101010100101110101000000010101

    Music Notation: “|C2A3B1E2|F2A3E1G2|A2B3A1C2|C2E3A1G2|”

    Figure 3: Tokyo at level 21

Further Development

  • The first level triangle/rectangle is not considered. However, this can be used for audio playback where a different instrument is used for each triangle/rectangle. See this documentation for further details. ( )

  • Note length is inserted based on the note grouping (see table 1). A table based on both the note grouping and the note pitches could be used to create more variations in the musical score.


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