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Temperament Evaluator

This Python 3 script can be used to compute various regular temperament data.

Requirements

  • SciPy
    • various tasks including optimization, temperament measures, wedgie, etc.
  • SymPy
    • various tasks including symbolic solution, mapping normalization, comma basis, etc.
  • tqdm
    • to render the progress bar for et_sequence
pip install scipy sympy tqdm

te_common.py

Common functions. Required by virtually all subsequent modules.

Use the Subgroup class to create a just intonation subgroup. Parameters:

  • ratios: list of ratios, fractional notation supported.
  • monzos: matrix of monzos, alternative way to initialize it.

Use the Norm class to create a norm profile for the tuning space. Parameters:

  • wtype: Weight method. Has "tenney" (default), "equilateral", and "wilson"/"benedetti".
  • wamount: Weight scaling factor. Default is 1.
  • skew: Skew. This is Mike Battaglia's k. Default is 0, meaning no skew. For Weil, use 1.
  • order: Order. Default is 2, meaning Euclidean. For XOP tuning, use np.inf.

te_optimizer.py

Optimizes tunings. Custom norm profile, constraints and destretch are supported. It is recommended to use te_temperament_measures instead since it calls this module and it has a more accessible interface.

Requires te_common.

Use wrapper_main to optimize a temperament. Parameters:

  • breeds: first positional, required. The map of the temperament.
  • subgroup: optional. Custom subgroup for the map. Default is prime harmonics.
  • norm: optional. Norm profile for the tuning space. See above.
  • inharmonic: optional. For subgroup temperaments, treats the basis as if they were primes. Default is False.
  • constraint: optional. Constrains this subgroup to pure. Default is empty.
  • destretch: optional. Destretches this ratio to pure. Default is empty.
  • show: optional. Displays the result. Default is True.

Important: a single monzo should be entered as a vector. A monzo list should be entered as an array of column vectors.

te_optimizer_legacy.py

Legacy single-file edition (doesn't require te_common.py). Support for subgroup tuning is limited.

te_symbolic.py

Solves Euclidean tunings symbolically. It is recommended to use te_temperament_measures instead since it calls this module and it has a more accessible interface.

Requires te_common.

Use wrapper_symbolic to solve for a Euclidean tuning of a temperament. Parameters:

  • breeds: first positional, required. The map of the temperament.
  • subgroup: optional. Custom subgroup for the map. Default is prime harmonics.
  • norm: optional. Norm profile for the tuning space. See above.
  • inharmonic: optional. For subgroup temperaments, treats the basis as if they were primes. Default is False.
  • constraint: optional. Constrains this subgroup to pure. Default is empty.
  • destretch: optional. Destretches this ratio to pure. Default is empty.
  • show: optional. Displays the result. Default is True.

te_temperament_measures.py

Analyses tunings and computes temperament measures from the temperament mapping matrix.

Requires te_common, te_optimizer, and optionally te_symbolic.

Use Temperament to construct a temperament object. Methods:

  • tune: calls wrapper_main/wrapper_symbolic and shows the generator, tuning map, error map, tuning error, and tuning bias. Parameters:
    • optimizer: optional. Optimizer. "main": calls wrapper_main. "sym": calls wrapper_symbolic. Default is "main".
    • norm: optional. Norm profile for the tuning space. See above.
    • inharmonic: optional. For subgroup temperaments, treats the basis as if they were primes. Default is False.
    • constraint: optional. Constrains this subgroup to pure. Default is empty.
    • destretch: optional. Destretches this ratio to pure. Default is empty.
  • temperament_measures: shows the complexity, error, and badness (simple and logflat). Parameters:
    • ntype: optional. Averaging normalizer. Has "breed" (default), "smith", "dirichlet" and "none".
    • norm: optional. Norm profile for the tuning space. See above.
    • inharmonic: optional. For subgroup temperaments, treats the basis as if they were primes. Default is False.
    • error_scale: optional. Scales the error. Default is 1200 (cents).
    • badness_scale: optional. Scales the badness. Default is 1 (octaves).
  • wedgie: returns and shows the wedgie of the temperament.
  • comma_basis: returns and shows the comma basis of the temperament.

Important: a single monzo should be entered as a vector. A monzo list should be entered as an array of column vectors.

te_equal.py

Tools related to equal temperaments.

  • Constructs higher-rank temperaments using equal temperaments.
  • Finds the GPVs from the comma list.

Requires te_common, te_optimizer, and te_temperament_measures.

Use et_construct to quickly construct temperaments from equal temperaments. Parameters:

  • et_list: first positional, required. The equal temperament list.
  • subgroup: second positional, required. The subgroup for the equal temperament list.

Use et_sequence to iterate through all GPVs. Parameters:

  • monzos: optional*. Specifies the commas to be tempered out. Default is empty, implying JI.
  • subgroup: optional*. Custom subgroup for the map. Default is prime harmonics.
    • * At least one of the above must be specified, for the script to know the dimension.
  • ntype: optional. Averaging normalizer. See above.
  • norm: optional. Norm profile for the tuning space. See above.
  • inharmonic: optional. For subgroup temperaments, treats the basis as if they were primes. Default is False.
  • cond: optional. Supports "error", "badness", or "logflat badness". Default is "error".
  • pv: optional. If True, only patent vals will be considered. Default is False.
  • prog: optional. If True, threshold will be updated. Default is True.
  • threshold: optional. Temperaments failing this will not be shown. Default is 20.
  • search_range: optional. Specifies the upper bound where to stop searching. Default is 1200.

Important: a single monzo should be entered as a vector. A monzo list should be entered as an array of column vectors.

te_lattice.py

Not fully functional yet. Currently able to find the complexity spectrum from the temperament map.

Support for subgroup temperaments is limited.

Requires te_common and te_temperament_measures.

Use TemperamentLattice to construct a temperament object. Methods:

  • find_temperamental_norm: shows the temperamental complexity of an interval.
  • find_complexity_spectrum: shows the complexity spectrum of a temperament