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Re: Finding Optimal Integer Ratio for Any Decimal Fraction

To: mathgroup@smc.vnet.net
Subject: [mg12293] Re: [mg12270] Finding Optimal Integer Ratio for Any Decimal Fraction
From: Daniel Lichtblau <danl@wolfram.com>
Date: Thu, 7 May 1998 18:51:29 -0400
References: <199805050730.DAA17192@smc.vnet.net.>

Benjamin Tubb wrote:
> 
> I'm trying to find an optimal integer ratio for any given decimal value
> within two constraints: 1) a maximum denominator and 2) a specified
> decimal precision of match accuracy. For example: given a maximum
> denominator of 2048, what is the smallest lowest common denominator
> (LCD) ratio equaling close to 1.00057779 with a precision to the fifth
> decimal place (i.e. the first '7' in this case)? The intent is to
> generate a table of LCD integer ratios for each of the 1200 cents in 12
> tone equal temperament.
> 
> ----------------
> Benjamin Tubb
> AIM: brtubb
> brtubb@cybertron.com
> http://home.cybertron.com/~brtubb


No guarantees, but Rationalize with a tolerance specified may often be
of assistance. For example,

In[21]:= Rationalize[1.00057779, 10^-6]
         1732
Out[21]= ----
         1731

In[23]:= N[%%]//InputForm
Out[23]//InputForm= 1.000577700751011

Daniel Lichtblau
Wolfram Research

References:
- Finding Optimal Integer Ratio for Any Decimal Fraction
  - From: "Benjamin Tubb" <brtubb@cybertron.com>

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