Arsenii A. arseniiv

This is a simple search tool to find commas between intervals (maybe even irrational ones, though it would try to show them as fractions). You just specify a list of basis intervals to measure against each other, an upper bound in cents to filter interval combinations through, and the desired count. The code then iterates over suitable combinations from smaller to larger taxicab distances in the lattice spanned by the basis, ensuring simpler commas show first. (But which is simpler depends on your basis! 3/2 and 4/3 is one thing, 3 and 2 is another, 9/8 and 32/27 is yet another still.)

The output of

show_commas(['4/3', '5/4', '6/5', '7/6'], under_cents=25, count=15)

here in main is:

  7.712c = 225/224 = (4/3)^-1 (5/4)^2 (6/5)^0 (7/6)^-1 
 21.902c = 875/864 = (4/3)^0 (5/4)^1 (6/5)^-2 (7/6)^1

Finally I understand how to define PGA invariantly

When using framerowks stemming from linear algebra to do calculation, we have to use coordinates (and so, bases). But this is often extraneous for mathematical analysis of what and why we are doing. So when we construct an object that’s independent of any basis chosen, it’s usually desirable to do so without introducing any choice of basis beforehand.

For a long time, an invariant construction of projective geometric algebra, a Clifford algebra approach to calculate with points, lines, segments and so on, and translations of the point space as opposed to just rotations and reflections which an unflavored geometric algebra does, eluded me.

Doing stuff with tuneBfree

tuneBfree is naren’s fork of a setBfree tonewheel organ emulation that allows custom tuning using MTS-ESP. It being one of the first microtunable tonewheel organ synths, I thought it might be useful to write a quick post of what one might wish to consider or have in mind tuning it.

MTS-ESP connection basics

An MTS-ESP master plugin like MTS-ESP Mini should be present in your project somewhere. It can be in passthru mode to conserve resources; the only thing you need to be sure of is that it says that a client is connected. If tuneBfree is the sole MTS-ESP-aware plugin in there, that’s it! Load a tuning and it will apply immediately.

Note that hosts like Carla or Element, as far I was able to work them, don’t allow MTS-ESP connection. Either I didn’t do something crucial or you need another more diversely functional DAW.

	from __future__ import annotations
	from collections import deque
	from itertools import count, cycle, islice
	from typing import Final, Iterator
	from time import perf_counter

	def sieve() -> Iterator[int]:
	"""
	A slightly improved Eratosthenes prime sieve, implemented using iterators.
	Cycles start on squares of primes because adding them earlier is unnecessary.

	"""
	Reference implementation of continued fraction routines
	by 0.5°.
	"""

	from __future__ import annotations
	from dataclasses import InitVar, dataclass
	from itertools import pairwise
	from math import floor, inf, isinf, isnan, isqrt, lcm, sqrt
	from typing import Iterable, Iterator, Literal, Sequence, overload

	from __future__ import annotations
	from collections import defaultdict
	from dataclasses import dataclass
	from fractions import Fraction
	from typing import Callable, Final, Iterable, Iterator


	@dataclass(frozen=True, slots=True)
	class Prob[TDom, TProb: (float, Fraction)]:
	"""Probability monad."""

	from __future__ import annotations
	from collections import defaultdict
	from typing import Final, Iterable, Iterator, Mapping, Sequence
	import operator
	from dataclasses import dataclass
	from itertools import accumulate, permutations, product
	from math import prod
	from fractions import Fraction as F

	def avg_variety(scale_steps: Sequence[F]) -> float:

	from collections import defaultdict
	from dataclasses import dataclass
	from fractions import Fraction
	from itertools import pairwise
	from typing import Final, Sequence

	@dataclass
	class EdIntervals:
	ed_fractions: list[Fraction]
	sources: dict[Fraction, list[int]]

	"""
	Fitting a scale to have a given pattern of steps between notes.

	Install `sympy` and `more_itertools`.
	"""

	from typing import Sequence
	from collections import defaultdict
	from dataclasses import dataclass
	from fractions import Fraction

	'''
	Replaces notes with flats with enharmonic sharps in SFZ and DSPRESET files.
	'''

	from pathlib import Path
	from typing import Final
	import re

	DS_EXTS: Final = frozenset(['.dspreset'])
	SFZ_EXTS: Final = frozenset(['.sfz'])