Search the database of D₁₂ × D₁₂-orbits of tone rows

• tone rows with given normal form, (see Section 3.2 of [1])
• tone rows with given interval structure, (see Section 3.4 of [1])
• tone rows with prescribed number of different intervals in their interval structure,
• tone rows with given trope structure, (see Section 3.5.5 of [1])
• tone rows with trope numbers from a prescribed subset of {1,…,35},
• tone rows with prescribed number of different trope numbers in their trope structure,
• tone rows with prescribed diameter distance, (see Section 3.6 of [1])
• tone rows with prescribed number of different distances in their diameter distance,
• tone rows with prescribed stabilizer type, (see Section 3.3 of [1])
• tone rows with given number in the list of all 836 017 orbits,
• all-interval rows, (see Section 3.4.1 of [1])
• orbits of tone rows invariant under the quart-circle, (see Sections 1.3 and 3.1 of [1])
• orbits of tone rows invariant under the 5-step, (see Section 3.1 of [1])
• orbits of tone rows invariant under the parameter exchange, (see Section 4.1 of [1])
• orbits of derived tone rows, (see Section 3.7.3 of [1])
• tone rows with given chord diagram, (see Sections 3.8 of [1]).

By using radio-buttons the alphabet is chosen for representing the tone rows. There are some additional display options: If "Graphical" is chosen, then for each D₁₂ × D₁₂-orbit of tone rows the chromatic circular representation is shown. In this situation at most 100 search results are displayed on a single page. If "Normal" is chosen, then the chromatic circular representation is not shown, but up to 6000 search results can be displayed. If "Simple" is chosen, then the information on a single tone row is contained in a single line. This is the fastest display option. Again it is possible to display at most 6000 search entries. Each line in the output is separated by | in 14 columns. The first column contains the number of the orbit from {1,…,836 017}, the second column the normal form of the tone row represented over the alphabet A₃, the third column the trope structure, the fourth column the number of different trope numbers, the fifth column the stabilizer type given by a number from {1,…,17}, the sixth column the interval structure represented over the alphabet A₃, the seventh column the number of different intervals, the eighth column the diameter distance structure, the ninth column the number of different diameter distances, the next three columns indicate whether the orbit is invariant under the quart circle, the five step, or the parameter exchange (where 0 means "no" and 1 means "yes" in the corresponding column). Finally, the last but one column indicates whether the row is a derived row or not. If it is derived, then it indicates the lengths of the subsequences from which it can be derived, otherwise it shows 0. The last column contains the number of the chord diagram from the set {1,…, 554}.

Using the "Normal" or "Graphical" display option for each search result it will be possible to open pop-up windows showing

• the chord diagram,
• the decomposition of the orbit into D₁₂ × ⟨R⟩ -orbits,
• musical information on the D₁₂ × D₁₂-orbit and on the 𝔄₁₂-orbit containing this orbit,
• all elements of the orbit,
• the stabilizer of the normal form of the orbit,
• the trope structure of the normal form of the orbit,
• the chromatic circular representation of the orbit.

If there are more search results than could be displayed (more than 100 or 6000 respectively), then it is possible to continue the search pressing a button at the end of the page with the search results. .

It is also possible to pass all the search results to other parts of the database:

• Get further information on bigger orbits
• Add further search criteria
• Search for musical information
• Simultaneous information on bigger orbits
• Chord diagrams and Gauss numbers
• Decomposition into D₁₂ × ⟨R⟩ -orbits