Help

It consists of the following components.

• Several Perl-programs can be used for different search routines.
• Different algorithms concerning group actions are implemented in one executable program written in "SYMMETRICA".¹
• For some graphics the JavaScript VectorGraphics library "wz_jsgraphics.js" by Walter Zorn² is used. In order to print the graphics-output printing of the background must be enabled in the browser.
• Using pop-up windows further information can be derived, whence pop-up windows should also be enabled.
• The JavaScript library "SoundManager 2"³ is used to obtain a simple acoustic representation of the tone rows.

• How to input a tone row in numeric form
• How to input a tone row with note names
• The D₁₂ × D₁₂-orbit of a tone row
• D₁₂ × D₁₂-normal form of a tone row
• All information about a tone row
• Search the database of D₁₂ × D₁₂-orbits of tone rows
• How to input a tone row in normal form
• How to input a vector of tone rows
• How to input an interval-structure
• How to input the number of different intervals
• All interval rows
• Derived tone rows
• Combinatorial rows
• How to input the multiplicities of intervals
• How to input a trope structure
• How to input a list of trope numbers
• How to input the number of different tropes
• How to input the multiplicities of trope numbers
• Construction of trope structures
• The trope structure of a tone row
• Number of tropes in an n-scale
• List of all tropes in an n-scale
• The distance in Z₁₂
• How to input a diameter distance structure
• How to input the number of different diameter distances
• All-distances-twice rows
• How to input a distance structure
• How to input the type of a distance structure
• How to input the number of different distances
• Number of tone rows in an n-scale
• How to input the stabilizer type
• How to input the stabilizer type of D₁₂ × D₁₂-orbits
• How to input the stabilizer type of Aff₁(Z₁₂) × D₁₂-orbits
• How to input the stabilizer type of D₁₂ × Aff₁(Z₁₂)-orbits
• How to input the stabilizer type of Aff₁(Z₁₂) × Aff₁(Z₁₂)-orbits
• How to input the stabilizer type of 𝔇₁₂-orbits
• How to input the stabilizer type of 𝔄₁₂-orbits
• How to input the number of a tone row
• How to input the search area
• Orbits of quart circle invariant rows
• Orbits invariant under the 5-step
• Orbits invariant under the parameter exchange
• Help on chord diagrams
• How to input the number of a chord diagram
• How to input the order of a serial group
• How to input a permutation
• How to input a generator system of a permutation group
• Decomposition into D₁₂ × ⟨R⟩ -orbits (Schönberg-situation)
• The row matrix of a tone row
• Operation on a tone row
• Information on bigger orbits
• Simultaneous information on bigger orbits
• Help on finding a permuting element
• Help on orbits with high symmetry
• Number of k-chords in an n-scale
• List of all k-chords in an n-scale
• Normal form of a k-chord
• Search the database for musical information
• Input musical information into the database