  # farab

[Joe Monzo, from Mohajeri Shahin, Yahoo tuning group message 57773 (Mon Mar 28, 2005 6:08 am)]

A term from Mehdi Barkeshli to designate the interval measurement unit used by al-Farabi.

A farab is ~8.3333 cents, or exactly 8 1/3 cents.

A farab is calculated as the 144th root of 2 -- 144√2 or 2(1/144) -- with a ratio of approximately 1:1.004825126, which is an irrational number. This interval therefore divides the octave, which is assumed to have the ratio 2:1, into 144 equal parts. Thus a farab represents one degree in 144-edo tuning.

The familiar 12-edo semitone is equal to exactly 12 farabs, since 144 divides evenly by 12 exactly 12 times.

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

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###### References

Barkeshli, Mehdi. [date]

[work on al-Farabi]

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### farabs calculator

Ratio may be entered as fraction or floating-point decimal number.
(value must be greater than 1)

For EDOs (equal-temperaments), type: "a/b" (without quotes)
where "a" = EDO degree and "b" = EDO cardinality.
(value must be less than 1)

Enter ratio: = farabs

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