Xenharmonic Wiki

Module:MOS: Difference between revisions

← Older editNewer edit →
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
Added functions for basic 1-step sizes
Ganaram inukshuk (talk | contribs)
autopatrolled, emailconfirmed
6,211 edits
Bugfixes, added size-offset param to chroma-count function; added normalize function that turns negative intervals back into positive intervals (since intervals here are meant to be interpreted as distances between two scale degrees)
Line 257: Line 257:


-- Compute the vector for a single small step.
-- Compute the vector for a single small step.
function p.large_step()
function p.small_step()
local result = {
local result = {
['L'] = 0,
['L'] = 0,
Line 266: Line 266:


-- Compute the vector for a single chroma. It's a large step minus a small step.
-- Compute the vector for a single chroma. It's a large step minus a small step.
-- Adding or subtracting any interval by this interval changes its "size".
function p.chroma()
function p.chroma()
local result = {
local result = {
Line 279: Line 280:
end
end


-- Compute the vector for a diminished step. It's a small stuep minus a chroma.
-- Compute the vector for a diminished step. It's a small step minus a chroma.
function p.diminished_step()
function p.diminished_step()
return p.interval_sub(p.small_step(), p.chroma())
return p.interval_sub(p.small_step(), p.chroma())
Line 293: Line 294:
-- Mossteps larger than the equave (eg, the minor 9th in non-xen music theory)
-- Mossteps larger than the equave (eg, the minor 9th in non-xen music theory)
-- are allowed.
-- are allowed.
-- The size param is a value that denotes whether the interval is the large size
-- The size_offset denotes whether the interval is the large size (0) or the
-- (0) or the small size (-1). This can exceed the range of [-1, 0] to represent
-- small size (-1). This can exceed the range of [-1, 0] to represent intervals
-- intervals raised/lowered by multiple chromas (augmented, diminished, etc).
-- raised/lowered by multiple chromas (augmented, diminished, etc).
-- Note that for period intervals (eg, the root and equave), there is only one
-- Note that for period intervals (eg, the root and equave), there is only one
-- size (0 = perfect), so -1 is diminished and 1 is augmented.
-- size (0 = perfect), so -1 is diminished and 1 is augmented.
function p.interval(mos, step_count, size)
function p.interval(mos, step_count, size_offset)
local size = size or 0 -- Optional param; defaults to large size
local size_offset = size_offset or 0 -- Optional param; defaults to large size
local step_sequence = p.brightest_mode(mos)
local step_sequence = p.brightest_mode(mos)
step_sequence = string.rep(step_sequence, math.ceil(step_count/(mos.nL + mos.ns)))
step_sequence = string.rep(step_sequence, math.ceil(step_count/(mos.nL + mos.ns)))
Line 305: Line 306:
local interval_vector = p.interval_from_step_sequence(step_sequence)
local interval_vector = p.interval_from_step_sequence(step_sequence)
interval_vector['L'] = interval_vector['L'] + size
interval_vector['L'] = interval_vector['L'] + size_offset
interval_vector['s'] = interval_vector['s'] - size
interval_vector['s'] = interval_vector['s'] - size_offset
return interval_vector
return interval_vector
end
end
Line 344: Line 345:
return interval_vector
return interval_vector
end
-- Intervals always denote positive values as they are distances between two
-- scale degrees, even if in the interval vector, one value is negative.
-- In cases where a negative interval is encountered or was previously needed,
-- such as if negative intervals denote direction (downwards stacking instead of
-- upwards stacking), normalize_interavl() makes those intervals positive again.
-- EG, a perfect 4-diastep (perfect 5th) is the vector { 3, 1 }, but so is
-- { -3, -1 }.
function p.normalize_interval(interval)
return p.interval_step_count(interval) < 0 and p.interval_mul(interval, -1) or interval
end
end


Line 386: Line 398:
-- perfect size (for period/root/equave intervals). This requires the mos as
-- perfect size (for period/root/equave intervals). This requires the mos as
-- input.
-- input.
function p.interval_chroma_count(interval, mos)
-- The offset param is used to denote whether the interval is the large size (0)
-- or the small size (-1). This way, the small size of an interval is shown as
-- having zero chromas IF the interval is to be viewed as its small size rather
-- than the large size. This can exceed the range [-1, 0] if needed.
function p.interval_chroma_count(interval, mos, size_offset)
local size_offset = size_offset or 0
local step_count = p.interval_step_count(interval)
local step_count = p.interval_step_count(interval)
local base_interval = p.interval(mos, step_count, 0)
local base_interval = p.interval(mos, step_count, 0)
return interval['L'] - base_interval['L']
return interval['L'] - base_interval['L'] - size_offset
end
end


Line 446: Line 463:
local periods = p.interval_mul(p.period(mos), reduce_amt)
local periods = p.interval_mul(p.period(mos), reduce_amt)
return p.interval_sub(interval)
return p.interval_sub(interval, periods)
end
end


Line 510: Line 527:
-- Tester function
-- Tester function
function p.tester()
function p.tester()
--return p.add_intervals({ ['L'] = 3, ['s'] = 1}, { ['L'] = 3, ['s'] = 1})
 
--return p.interval(p.new(5, 2), 11, 0)
local interval = p.dark_gen(p.new(5,2))
--return p.dark_gen(p.new(5, 2))
return p.interval_chroma_count(interval, p.new(5,2), -1)
--local interval = p.period_reduce({ ['L'] = 5, ['s'] = 11}, p.new(3,6))
--return p.dark_gen_step_count(p.new(5,2))
return p.interval_chroma_count({ ['L'] = 3, ['s'] = 1}, p.new(5,2))
end
end


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