Database on tone rows and tropes

Harald Fripertinger, Peter Lackner ✝

Last update: November 29, 2022

Manual in pdf-format

• D₁₂ × D₁₂-orbits of tone rows
  • The D₁₂ × D₁₂-orbit of a tone row
  • The D₁₂ × D₁₂-normal form of a tone row
  • All information about a tone row
  • Search the database of D₁₂ × D₁₂-orbits of tone rows
  • Chord diagrams and Gauss words
  • Distance structures
  • Multiplicities of intervals
• The trope structure
  • Multiplicities of trope numbers
  • Construction of trope structures
  • The trope structure of a tone row
  • Number of tropes in an n-scale
  • List all tropes in an n-scale
• General orbits of tone rows
  • Orbits of a tone row in the 12-scale
  • Normal forms of a tone row in the 12-scale
  • The stabilizer of a tone row
  • Decomposition into D₁₂ × ⟨R⟩ -orbits
  • The row matrix of a tone row
  • Operation on a tone row
  • Number of tone rows in an n-scale
• Bigger orbits
  • Information on bigger orbits
  • Simultaneous Information on bigger orbits
  • Find a permuting element
  • Bigger orbits with high symmetry
• Chords
  • Number of k-chords in an n-scale
  • List all k-chords
  • Normal form of a k-chord
• Musical Information
  • Search the database for musical information
  • Input musical information into the database
• Help
  • 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
• List of all D₁₂-tropes
• List of all chord diagrams
  • Chord diagrams 1-50
  • Chord diagrams 51-100
  • Chord diagrams 101-150
  • Chord diagrams 151-200
  • Chord diagrams 201-250
  • Chord diagrams 251-300
  • Chord diagrams 301-350
  • Chord diagrams 351-400
  • Chord diagrams 401-450
  • Chord diagrams 451-500
  • Chord diagrams 501-554
• List of all diameter distance structures
• List of all distance structure types
• List of distance structures
• References
• Footnotes