Module:Harmonics in equal: Difference between revisions
Default for prime harmonics; cut off at 21 for odd harmonics |
add consistency check |
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local p = {} | local p = {} | ||
-- direct mapping | |||
local function map(p, steps, num, denom) | |||
local s = math.log(p) / math.log(num/denom) | |||
return math.floor(s*steps + .5) | |||
end | |||
-- check consistency for 9, 15 and 21 | |||
local function check_consistency(steps, num, denom) | |||
local p3 = map(3, steps, num, denom) | |||
local p5 = map(5, steps, num, denom) | |||
local p7 = map(7, steps, num, denom) | |||
local p9 = map(9, steps, num, denom) | |||
local p15 = map(15, steps, num, denom) | |||
local p21 = map(21, steps, num, denom) | |||
return (p9 == 2*p3) and (p15 == p3*p5) and (p21 == p3*p7) | |||
end | |||
local function approx(steps, num, denom, intervals, title, prec) | local function approx(steps, num, denom, intervals, title, prec) | ||
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intervals.prime = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 } | intervals.prime = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 } | ||
intervals.prime_no2 = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 } | |||
intervals.odd = {3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53 } | intervals.odd = {3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53 } | ||
intervals.integer = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27} | intervals.integer = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27} | ||
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local start = eval_num_arg(frame.args['start'], 1) | local start = eval_num_arg(frame.args['start'], 1) | ||
-- option intervals | -- option intervals | ||
local select_intervals = " | local select_intervals = "integer" | ||
local name = steps .. 'ed' .. num .. '/' .. denom | local name = steps .. 'ed' .. num .. '/' .. denom | ||
| Line 83: | Line 99: | ||
if num == 2 then | if num == 2 then | ||
name = steps .. 'edo' | name = steps .. 'edo' | ||
select_intervals = "odd" | |||
if check_consistency(steps, num, denom) then | |||
select_intervals = "prime_no2" | |||
end | |||
elseif num == 3 then | elseif num == 3 then | ||
name = steps .. 'edt' | name = steps .. 'edt' | ||
| Line 91: | Line 111: | ||
if num == 3 and denom == 2 then | if num == 3 and denom == 2 then | ||
name = steps .. 'edf' | name = steps .. 'edf' | ||
end | |||
-- override default intervals | |||
if frame.args['intervals'] and string.len(frame.args['intervals']) > 0 then | |||
select_intervals = frame.args['intervals'] | |||
end | end | ||