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Module:ED intro: Difference between revisions

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Changes to function names; added new functions
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local p = {}
local p = {}


-- TODO: rewrite to support the following in separate functions
-- TODO: Add support for the following
-- - edh - equal divisions of a harmonic
-- - edr - equal divisions of an arbitrary ratio
-- - edc - equal divisions of a non-integer constant or cent value
-- - edc - equal divisions of a non-integer constant or cent value
-- - edo - a special case of edh, where the harmonic is 2/1
-- - edt - a special case of edh, where the harmonic is 3/1
-- - edf - a special case of edr, where the ratio is 3/2


-- Notes:
-- Notes:
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--  were formerly called equal-step tunings but were reclassified as 1ed.
--  were formerly called equal-step tunings but were reclassified as 1ed.
-- - Equal divisions of irrational constants (such as pi and e) are not very
-- - Equal divisions of irrational constants (such as pi and e) are not very
--  common, but can be denoted as equal divisions of arbitrary cent values if
--  common, but count as equal divisions of arbitrary cent values.
--  needed.


-- Parse ed function
-- Parse ed function
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return { ['cents'] = cents, ['equave'] = equave, ['ratio'] = ratio, ['steps'] = steps, ['suffix'] = suffix, ['type'] = ed_type }
return { ['cents'] = cents, ['equave'] = equave, ['ratio'] = ratio, ['steps'] = steps, ['suffix'] = suffix, ['type'] = ed_type }
end
-- Separate function for edo intro
function p.edo_intro(ed)
local ed = ed or 12
-- Exactly or about? Round to 3 DPs
local edstep_size = 1200 / ed
local edstep_size_rounded = utils._round(edstep_size, 3)
local is_exact = edstep_size - edstep_size_rounded == 0
local ordinal = ord._ordinal(ed)
local intro_text = ""
if ed == 1 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]] where adjacent pitches are one interval of 2/1 (one [[octave]]) apart, or exactly/about ''s'' [[¢]]."
else
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 represents a [[frequency ratio]] of 2<sup>1/''k''</sup>, or the ''kth'' root of 2."
end
-- Replace certain strings with the intended final versions
intro_text = string.gsub(intro_text, "''k''", ed)
intro_text = string.gsub(intro_text, "exactly/about", (is_exact and "exactly" or "about"))
intro_text = string.gsub(intro_text, "''s''", string.format("%.3f", edstep_size))
intro_text = string.gsub(intro_text, "''kth''", ord._ordinal(ed))
return intro_text
end
-- Separate function for edt intro
function p.edt_intro(ed)
local ed = ed or 13
-- Exactly or about? Round to 3 DPs
local edstep_size = math.log(3) * 1200 / math.log(2) / ed
local edstep_size_rounded = utils._round(edstep_size, 3)
local is_exact = edstep_size - edstep_size_rounded == 0
local ordinal = ord._ordinal(ed)
local intro_text = ""
if ed == 1 then
intro_text = "'''''k'' equal divisions of the tritave''', '''perfect twelfth''', or '''3rd harmonic''' (abbreviated '''''k''edt''' or '''''k''ed3'''), is the [[nonoctave]] [[tuning system]] where adjacent pitches are one interval of 3/1 (one [[tritave]]) apart, or exactly/about ''s'' [[¢]]."
else
intro_text = "'''''k'' equal divisions of the tritave''', '''perfect twelfth''', or '''3rd harmonic''' (abbreviated '''''k''edt''' or '''''k''ed3'''), is the [[nonoctave]] [[tuning system]] that divides the interval of [[3/1]] into ''k'' [[equal]] parts of exactly/about ''s'' [[¢]] each. Each step represents a [[frequency ratio]] of 3<sup>1/''k''</sup>, or the ''kth'' root of 3."
end
-- Replace certain strings with the intended final versions
intro_text = string.gsub(intro_text, "''k''", ed)
intro_text = string.gsub(intro_text, "exactly/about", (is_exact and "exactly" or "about"))
intro_text = string.gsub(intro_text, "''s''", string.format("%.3f", edstep_size))
intro_text = string.gsub(intro_text, "''kth''", ord._ordinal(ed))
return intro_text
end
-- Separate function for edf intro
function p.edf_intro(ed)
local ed = ed or 7
-- Exactly or about? Round to 3 DPs
local edstep_size = math.log(3/2) * 1200 / math.log(2) / ed
local edstep_size_rounded = utils._round(edstep_size, 3)
local is_exact = edstep_size - edstep_size_rounded == 0
local ordinal = ord._ordinal(ed)
local intro_text = ""
if ed == 1 then
intro_text = "'''''k'' equal divisions of the perfect fifth''' (abbreviated '''''k''edf''' or '''''k''ed3/2'''), is the [[nonoctave]] [[tuning system]] where adjacent pitches are one interval of 3/2 (one [[tritave]]) apart, or exactly/about ''s'' [[¢]]."
else
intro_text = "'''''k'' equal divisions of the perfect fifth''' (abbreviated '''''k''edf''' or '''''k''ed3/2'''), is the [[nonoctave]] [[tuning system]] that divides the interval of [[3/2]] into ''k'' [[equal]] parts of exactly/about ''s'' [[¢]] each. Each step represents a [[frequency ratio]] of (3/2)<sup>1/''k''</sup>, or the ''kth'' root of 3/2."
end
-- Replace certain strings with the intended final versions
intro_text = string.gsub(intro_text, "''k''", ed)
intro_text = string.gsub(intro_text, "exactly/about", (is_exact and "exactly" or "about"))
intro_text = string.gsub(intro_text, "''s''", string.format("%.3f", edstep_size))
intro_text = string.gsub(intro_text, "''kth''", ord._ordinal(ed))
return intro_text
end
-- Separate function for edh intro (arbitrary harmonic)
function p.edh_intro(ed, harmonic)
local ed = ed or 12
local harmonic = harmonic or 4
-- Exactly or about? Round to 3 DPs
local edstep_size = math.log(harmonic) * 1200 / math.log(2) / ed
local edstep_size_rounded = utils._round(edstep_size, 3)
local is_exact = edstep_size - edstep_size_rounded == 0
local ordinal = ord._ordinal(ed)
local intro_text = ""
if ed == 1 then
intro_text = "'''''k'' equal divisions of the hth harmonic''' (abbreviated '''''k''ed''h'''''), is the [[nonoctave]] [[tuning system]] where adjacent pitches are one interval of [[''h''/1]] apart, or exactly/about ''s'' [[¢]]."
else
intro_text = "'''''k'' equal divisions of the hth harmonic''' (abbreviated '''''k''ed''h'''''), is the [[nonoctave]] [[tuning system]] that divides the interval of [[''h''/1]] into ''k'' [[equal]] parts of exactly/about ''s'' [[¢]] each. Each step represents a [[frequency ratio]] of ''h''<sup>1/''k''</sup>, or the ''kth'' root of ''h''."
end
-- Replace certain strings with the intended final versions
intro_text = string.gsub(intro_text, "''k''", ed)
intro_text = string.gsub(intro_text, "exactly/about", (is_exact and "exactly" or "about"))
intro_text = string.gsub(intro_text, "''s''", string.format("%.3f", edstep_size))
intro_text = string.gsub(intro_text, "''kth''", ord._ordinal(ed))
intro_text = string.gsub(intro_text, "hth", ord._ordinal(harmonic))
intro_text = string.gsub(intro_text, "''h''", harmonic)
return intro_text
end
-- Separate function for edr intro (arbitrary ratio)
function p.edr_intro(ed, ratio)
local ed = ed or 12
local ratio = ratio or rat.new(9,4)
-- Exactly or about? Round to 3 DPs
local edstep_size = rat.cents(ratio) / ed
local edstep_size_rounded = utils._round(edstep_size, 3)
local is_exact = edstep_size - edstep_size_rounded == 0
local ordinal = ord._ordinal(ed)
local intro_text = ""
if ed == 1 then
intro_text = "'''''k'' equal divisions of ''p/q''''' (abbreviated '''''k''ed''p/q''''') is the [[nonoctave]] [[tuning system]] where adjacent pitches are one interval of [[p/q]] apart, or exactly/about ''s'' [[¢]]."
else
intro_text = "'''''k'' equal divisions of ''p/q''''' (abbreviated '''''k''ed''p/q''''') is the [[nonoctave]] [[tuning system]] that divides the interval of [[''p/q'']] into ''k'' [[equal]] parts of exactly/about ''s'' [[¢]] each. Each step represents a [[frequency ratio]] of ''p/q''<sup>1/''k''</sup>, or the ''kth'' root of ''p/q''."
end
-- Replace certain strings with the intended final versions
intro_text = string.gsub(intro_text, "''k''", ed)
intro_text = string.gsub(intro_text, "exactly/about", (is_exact and "exactly" or "about"))
intro_text = string.gsub(intro_text, "''s''", string.format("%.3f", edstep_size))
intro_text = string.gsub(intro_text, "''kth''", ord._ordinal(ed))
intro_text = string.gsub(intro_text, "''p/q''", rat.as_ratio(ratio))
return intro_text
end
function p.edc_intro(ed, cents, constant_symbol)
return "Equal divisions of an arbitrary cent value currently not supported."
end
end


-- Primary function
-- Primary function
function p.ed_intro(ed)
function p._ed_intro(ed)
local ed = ed or "12edo"
local ed = ed or "12edo"
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-- Wrapper function; for use with a template
-- Wrapper function; for use with a template
function p.ed_intro_frame(frame)
function p.ed_intro(frame)
local ed = frame.args['ED']
local ed = frame.args['ED']


return p.ed_intro(ed)
return p._ed_intro(ed)
end
end


return p
return p
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