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Module:ED intro: Difference between revisions

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Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
Work-in-progress
 
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
Still work-in-progress; includes todo on what to bugfix
Line 1: Line 1:
local ord = require('Module:Ordinal')
local ord = require('Module:Ordinal')
local utils = require('Module:Utils')
local utils = require('Module:Utils')
local rat = require('Module:Rational')
local p = {}
local p = {}
-- TODO:
-- - Enforce ED types: edo, edt, edf, edh, edr, edc for octave, tritave/twelfth,
--  fifth, arbitrary harmonic h, arbitrary ratio r, and arbitrary cent value c.
--  Note that EDs of named constants, like pi, are currently not included, as
--  they probably need their own typing (ednc) separate from edc.
-- - Bugfix edr not reporting the correct equave


function p.parse_ed(unparsed)
function p.parse_ed(unparsed)
local unparsed = unparsed or "12edpi"
local unparsed = unparsed or "12edo"
-- If the unparsed ed is only a numeric value, default to edo
-- If the unparsed ed is only a numeric value, default to edo
Line 12: Line 20:
-- Parse
-- Parse
local steps, suffix, equave = unparsed:match('^(%d+)([Ee][Dd](.+))$')
local steps, equave = unparsed:match('^(%d+)[Ee][Dd](.+)$')
steps = tonumber(steps)
-- If the equave is text, then the equave is:
-- If the equave is text, then the equave is:
Line 18: Line 27:
-- t: tritave or twelfth, 3/1 (3rd harmonic)
-- t: tritave or twelfth, 3/1 (3rd harmonic)
-- f: fifth, 3/2
-- f: fifth, 3/2
-- For irrational/transcendental constants:
local ed_type = ""
-- pi or π: 3.141593
local ratio = "n/a"
-- phi or φ: 1.618034
local cents = 0
-- n (typically used for e): 2.718282
if equave == "o" or equave == "O" or equave == "2" then
if equave == "o" or equave == "O" then
equave = "2"
equave = "2"
elseif equave == "t" or equave == "T" then
ratio = "2/1"
cents = 1200
ed_type = "edo"
elseif equave == "t" or equave == "T" or equave == "3" then
equave = "3"
equave = "3"
elseif equave == "f" or equave == "F" then
ratio = "3/1"
cents = math.log(3) * 1200 / math.log(2)
ed_type = "edt"
elseif equave == "f" or equave == "F" or equave == "3/2" then
equave = "3/2"
equave = "3/2"
elseif equave == "pi" or equave == "π" then
ratio = "3/2"
equave = "" .. math.pi
cents = math.log(3/2) * 1200 / math.log(2)
elseif equave == "phi" or equave == "φ" then
ed_type = "edf"
equave = "1.6180339887499"
end
elseif equave == "n" or equave == "N" then
equave = "" .. math.exp(1)
-- For equaves not 2/1, 3/1, or 3/2
if ed_type == "" then
-- If the equave is a number or ratio, convert it to cents
-- If the equave is already a cent value, extract it
local is_cents = string.match(equave, '^(.+)c') ~= nil
local is_numeric = tonumber(equave) ~= nil
local is_ratio = string.match(equave, '^%d+/%d+$') ~= nil
if is_cents then
cents = tonumber(equave:match('^(.+)c'))
ed_type = "edc"
elseif is_numeric then
cents = math.log(tonumber(equave)) * 1200 / math.log(2)
-- Classify ed type as either ed of a constant (if not a whole number)
-- or ed of a harmonic (if it's a whole number); if it is a harmonic,
-- write it as a ratio (h/1)
if math.floor(tonumber(equave)) ~= tonumber(equave) then
ed_type = "edc"
else
ed_type = "edh"
ratio = equave .. "/1"
end
elseif is_ratio then
local ratio = rat.parse(equave)
cents = rat.cents(ratio)
equave = rat.as_ratio(ratio) -- Ensures ratio is simplified
ratio = equave
ed_type = "edr"
end
end
end


return { ['steps'] = steps, ['suffix'] = suffix, ['equave'] = equave }
return { ['cents'] = cents, ['equave'] = equave, ['steps'] = steps, ['ratio'] = ratio, ['type'] = ed_type }
end
end


function p.ed_intro(ed)
function p.ed_intro(ed)
 
local ed = ed or "12ed19/13"
local parsed_ed = p.parse_ed(ed)
local ed_type = parsed_ed['type']
-- Intro formats for each possible case
-- Intro formats for each possible case
-- - Common abbrevs: edo, edt, edf
-- - Common abbrevs: edo, edt, edf; these have specially written intros
-- - General harmonic: edh (h-th harmonic)
-- - General harmonic: edh (h-th harmonic)
-- - Arbitrary JI ratio: edp/q
-- - Arbitrary JI ratio: edr (ratio of p/q)
-- - Arbitrary constant: edc
-- - Arbitrary constant: edc
-- - Equal-step tunings: 1edo, 1edt, 1edf, 1edh, 1edp/q, 1edc
-- - Equal-step tunings: 1edo, 1edt, 1edf, 1edh, 1edp/q, 1edc
local intro_text = ""
local intro_text = ""
if is_est then
if is_est then
if is_edo then
if ed_type == "edo" then
intro_text = "'''1 equal division of the octave''' (abbreviated '''1edo''' or '''1ed2'''), also called '''1-tone equal temperament''' ('''1tet'''), or '''1 equal temperament''' ('''1et''') when viewed under a [[regular temperament]] perspective, is the [[tuning system]] where adjacent pitches are one [[octave]], or exactly/about s [[¢]], from each other.\n"
intro_text = "'''1 equal division of the octave''' (abbreviated '''1edo''' or '''1ed2'''), also called '''1-tone equal temperament''' ('''1tet'''), or '''1 equal temperament''' ('''1et''') when viewed under a [[regular temperament]] perspective, is the [[tuning system]] where adjacent pitches are one [[octave]], or exactly/about ''s'' [[¢]], from each other."
elseif is_edt then
elseif ed_type == "edt" then
intro_text = "'''1 equal division of the tritave''' (abbreviated '''1edt''' or '''1ed3''') is the [[non-octave]] [[tuning system]] where adjacent pitches are one tritave ([[3/1]]), or exactly/about s [[¢]], apart from each other.\n"
intro_text = "'''1 equal division of the tritave''' (abbreviated '''1edt''' or '''1ed3''') is the [[non-octave]] [[tuning system]] where adjacent pitches are one tritave ([[3/1]]), or exactly/about ''s'' [[¢]], apart from each other."
elseif is_edf then
elseif ed_type == "edf" then
intro_text = "'''1 equal division of the fifth''' (abbreviated '''1edf''' or '''1ed3/2''') is the [[non-octave]] [[tuning system]] where adjacent pitches are one perfect fifth ([[3/2]]), or exactly/about s [[¢]], apart from each other.\n"
intro_text = "'''1 equal division of the fifth''' (abbreviated '''1edf''' or '''1ed3/2''') is the [[non-octave]] [[tuning system]] where adjacent pitches are one perfect fifth ([[3/2]]), or exactly/about ''s'' [[¢]], apart from each other."
elseif is_harmonic then
elseif ed_type == "edh" then
intro_text = "'''1 equal division of the ''h''th harmonic''' (abbreviated '''1ed''h''''') is the [[non-octave]] [[tuning system]] where adjacent pitches are one interval of [[''h''/1]], or exactly/about s [[¢]], apart from each other.\n"
intro_text = "'''1 equal division of the ''hth'' harmonic''' (abbreviated '''1ed''h''''') is the [[non-octave]] [[tuning system]] where adjacent pitches are one interval of [[''h''/1]], or exactly/about ''s'' [[¢]], apart from each other."
elseif is_edpq then
elseif ed_type == "edr" then
intro_text = "'''1 equal division of ''p''/''q''''' (abbreviated '''1ed''p''/''q''''') is the [[non-octave]] [[tuning system]] where adjacent pitches are one interval of [[''p''/''q'']], or exactly/about s [[¢]], apart from each other.\n"
intro_text = "'''1 equal division of ''p''/''q''''' (abbreviated '''1ed''p''/''q''''') is the [[non-octave]] [[tuning system]] where adjacent pitches are one interval of [[''p''/''q'']], or exactly/about ''s'' [[¢]], apart from each other."
elseif is_edc then
elseif ed_type == "edc" then
intro_text = "'''1 equal division of ''c''¢''' (abbreviated '''1ed''c''''') is the [[non-octave]] [[tuning system]] where adjacent pitches are s [[¢]], apart from each other.\n"
intro_text = "'''1 equal division of ''c''¢''' (abbreviated '''1ed''c''''') is the [[non-octave]] [[tuning system]] where adjacent pitches are ''s'' [[¢]], apart from each other."
end
end
else
else
if is_edo then
if ed_type == "edo" then
intro_text = "'''''k'' equal divisions of the octave''' (abbreviated '''''k''edo''' or '''''k''ed2'''), also called '''''k''-tone equal temperament''' ('''''k''tet'''), or '''''k'' equal temperament''' ('''''k''et''') when viewed under a [[regular temperament]] perspective, is the [[tuning system]] that divides the [[octave]] into ''k'' [[equal]] parts of exactly/about s [[¢]] each. Each step of ''k''edo represents a [[frequency ratio]] of 2<sup>1/''k''</sup>, or the ''k''th root of 2.\n"
intro_text = "'''''k'' equal divisions of the octave''' (abbreviated '''''k''edo''' or '''''k''ed2'''), also called '''''k''-tone equal temperament''' ('''''k''tet'''), or '''''k'' equal temperament''' ('''''k''et''') when viewed under a [[regular temperament]] perspective, is the [[tuning system]] that divides the [[octave]] into ''k'' [[equal]] parts of exactly/about ''s'' [[¢]] each. Each step of ''k''edo represents a [[frequency ratio]] of 2<sup>1/''k''</sup>, or the ''kth'' root of 2."
elseif is_edt then
elseif ed_type == "edt" then
intro_text = "'''''k'' equal divisions of the tritave''' (abbreviated '''''k''edt''' or '''''k''ed3''') is the [[non-octave]] [[tuning system]] that divides the interval [[3/1]] – also called the [[tritave]] or perfect twelfth – into ''k'' equal parts of exactly/about s [[¢]] each. Each step of ''k''edt represents a [[frequency ratio]] of 3<sup>1/''k''</sup>, or the ''k''th root of 3.\n"
intro_text = "'''''k'' equal divisions of the tritave''' (abbreviated '''''k''edt''' or '''''k''ed3''') is the [[non-octave]] [[tuning system]] that divides the interval [[3/1]] – also called the [[tritave]] or perfect twelfth – into ''k'' equal parts of exactly/about ''s'' [[¢]] each. Each step of ''k''edt represents a [[frequency ratio]] of 3<sup>1/''k''</sup>, or the ''kth'' root of 3."
elseif is_edf then
elseif ed_type == "edf" then
intro_text = "'''''k'' equal divisions of the fifth''' (abbreviated '''''k''edf''' or '''''k''ed3/2''') is the [[non-octave]] [[tuning system]] that divides the interval [[3/2]], or perfect fifth, into ''k'' equal parts of exactly/about s [[¢]] each. Each step of ''k''edf represents a [[frequency ratio]] of (3/2)<sup>1/''k''</sup>, or the ''k''th root of 3/2.\n"
intro_text = "'''''k'' equal divisions of the fifth''' (abbreviated '''''k''edf''' or '''''k''ed3/2''') is the [[non-octave]] [[tuning system]] that divides the interval [[3/2]], or perfect fifth, into ''k'' equal parts of exactly/about ''s'' [[¢]] each. Each step of ''k''edf represents a [[frequency ratio]] of (3/2)<sup>1/''k''</sup>, or the ''kth'' root of 3/2."
elseif is_harmonic then
elseif ed_type == "edh" then
intro_text = "'''''k'' equal divisions of the ''h''th harmonic''' (abbreviated '''''k''ed''h''''') is the [[non-octave]] [[tuning system]] that divides the interval [[''h''/1]], or the ''h''th harmonic, into ''k'' equal parts of exactly/about s [[¢]] each. Each step of ''k''ed''h'' represents a [[frequency ratio]] of ''h''<sup>1/''k''</sup>, or the ''k''th root of ''h''.\n"
intro_text = "'''''k'' equal divisions of the ''hth'' harmonic''' (abbreviated '''''k''ed''h''''') is the [[non-octave]] [[tuning system]] that divides the interval [[''h''/1]], or the ''hth'' harmonic, into ''k'' equal parts of exactly/about ''s'' [[¢]] each. Each step of ''k''ed''h'' represents a [[frequency ratio]] of ''h''<sup>1/''k''</sup>, or the ''kth'' root of ''h''."
elseif is_edpq then
elseif ed_type == "edr" then
intro_text = "'''''k'' equal divisions of ''p''/''q''''' (abbreviated '''''k''ed''p''/''q''''') is the [[non-octave]] [[tuning system]] that divides the interval [[''p''/''q'']] into ''k'' [[equal]] pieces of exactly/about s [[¢]] each. Each step of ''k''ed''p''/''q'' represents the [[frequency ratio]] of (''p''/''q'')<sup>1/''k''</sup>, or the ''k''th root of ''p''/''q''.\n"
intro_text = "'''''k'' equal divisions of ''p''/''q''''' (abbreviated '''''k''ed''p''/''q''''') is the [[non-octave]] [[tuning system]] that divides the interval [[''p''/''q'']] into ''k'' [[equal]] pieces of exactly/about ''s'' [[¢]] each. Each step of ''k''ed''p''/''q'' represents the [[frequency ratio]] of (''p''/''q'')<sup>1/''k''</sup>, or the ''kth'' root of ''p''/''q''."
elseif is_edc then
elseif ed_type == "edc" then
intro_text = "'''''k'' equal divisions of ''c''¢''' (abbreviated '''''k''ed''c''c''' or '''''k''ed''c''¢''') is the [[non-octave]] [[tuning system]] that divides interval of r¢ is divided into ''k'' [[equal]] pieces of exactly/about s [[¢]] each. Each step of ''k''ed''c'' represents the [[frequency ratio]] of ''c''<sup>1/''k''</sup>, or the ''k''th root of ''c''.\n"
intro_text = "'''''k'' equal divisions of ''c''¢''' (abbreviated '''''k''ed''c''c''' or '''''k''ed''c''¢''') is the [[non-octave]] [[tuning system]] that divides interval of ''c''¢ is divided into ''k'' [[equal]] pieces of exactly/about ''s'' [[¢]] each."
end
end
end
end
-- Produce a map of text to replace
-- - ''k'': number of steps in ed
-- - ''s'': size of a step
-- - ''p''/''q'': equave as a ratio
-- - ''h'': equave as a harmonic
-- - ''c'': equave as a cent value
-- - ''hth'': harmonic as an ordinal
-- - ''kth'': step count as an ordinal
local step_size = parsed_ed['cents'] / parsed_ed['steps']
local text_replace_map = {
["''k''"] = parsed_ed['steps'],
["''s''"] = utils._round(step_size, 3),
["''c''"] = utils._round(parsed_ed['cents'], 3),
["''p''/''q''"] = parsed_ed['ratio'],
["''h''"] = parsed_ed['equave'],
["''hth''"] = ord._ordinal(parsed_ed['equave']),
["''kth''"] = ord._ordinal(parsed_ed['steps']),
["exactly/about"] = (utils._round(step_size, 3) == step_size and "exactly" or "about")
}
for key, value in pairs(text_replace_map) do
intro_text = string.gsub(intro_text, key, value)
end
return intro_text
end
end


return p
return p
Retrieved from "https://en.xen.wiki/w/Module:ED_intro"