RE: [tuning] Digest Number 3790

On Sun, 4 Dec 2005 "Mohajeri Shahin" wrote: RE: Bach invented equal
temperament
>
> Hi all
>
> Although name of bach is attached to invention of ET , but it was farabi
> who worked on pythagorean musical legacy and used 144-ET (may be
> impressed by Cleonides) and proposed and used theory of 12-ET . it is
> documented in his great book" moosighi-al-kabir" and works of
> Dr.barkeshli , great acoustician of iran . barkeshli named one degree of
> 144-EDO as farab : http://www.tonalsoft.com/enc/f/farab.aspx

On that page, monz writes -

[HTML source view]
<p>
The formula for calculating the farab-value of any ratio is: <var>farabs =
log₁₀(r) * [144 / log₁₀(2)]</var> or <var>farabs =
log₂(r) * 144</var>, where <var>r</var> is the ratio.
</p>

monz,
a small quibble. For ease of comprehension, why not
extract the 144 as the first factor? Thus:
<var>farabs = 144 * log₁₀(r)/ log₁₀(2)</var> or
<var>farabs = 144 * log₂(r)</var>,

It would make it easier to recognise this as having
the same general form as:
<var>semitones = 12 * log₁₀(r)/ log₁₀(2)</var> or
<var>semitones = 12 * log₂(r)</var>,

or as:
<var>cents = 1200 * log₁₀(r)/ log₁₀(2)</var> or
<var>cents = 1200 * log₂(r)</var>,

Regards,
Yahya

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