89edo: Difference between revisions

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'''89edo''' divides the octave into 89 steps of size 13.48 [[cent]]s each, and [[tempering out|tempers out]] the commas [[126/125]], [[1728/1715]], [[32805/32768]], [[2401/2400]], [[176/175]], [[243/242]], [[441/440]] and [[540/539]]. It is an especially good tuning for [[Starling temperaments|myna temperament]], both in the [[7-limit]], tempering out 126/125 and 1728/1715, and in the [[11-limit]], where 176/175 is tempered out also. It is likewise a good tuning for the rank three temperament thrush, tempering out 126/125 and 176/175.

89 has a fifth less than a cent flat and a major third less than five cents sharp, with a 7 two cents sharp and an 11 1.5 cents sharp. It thus delivers reasonably good 11-limit harmony and very good no-fives harmony along with the very useful approximations represented by its commas. On a related note, a notable characteristic of this EDO is that it is the lowest in a series of four consecutive EDOs to temper out [[~~Quartismic temperaments~~|117440512/117406179]].

89 has a fifth less than a cent flat and a major third less than five cents sharp, with a 7 two cents sharp and an 11 1.5 cents sharp. It thus delivers reasonably good 11-limit harmony and very good no-fives harmony along with the very useful approximations represented by its commas. On a related note, a notable characteristic of this EDO is that it is the lowest in a series of four consecutive EDOs to temper out [[Quartisma|117440512/117406179]].

89edo is the 24th [[prime_numbers|prime]] edo, and the 11th in the Fibonacci sequence, which means its 55th step approximates logarithmic phi (i.e. (phi-1)*1200 cents) within a fraction of a cent.

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 '''89edo''' divides the octave into 89 steps of size 13.48 [[cent]]s each, and [[tempering out|tempers out]] the commas [[126/125]], [[1728/1715]], [[32805/32768]], [[2401/2400]], [[176/175]], [[243/242]], [[441/440]] and [[540/539]]. It is an especially good tuning for [[Starling temperaments|myna temperament]], both in the [[7-limit]], tempering out 126/125 and 1728/1715, and in the [[11-limit]], where 176/175 is tempered out also. It is likewise a good tuning for the rank three temperament thrush, tempering out 126/125 and 176/175.
-has a fifth less than a cent flat and a major third less than five cents sharp, with a 7 two cents sharp and an 11 1.5 cents sharp. It thus delivers reasonably good 11-limit harmony and very good no-fives harmony along with the very useful approximations represented by its commas.  On a related note, a notable characteristic of this EDO is that it is the lowest in a series of four consecutive EDOs to temper out [[Quartismic temperaments|117440512/117406179]].
+has a fifth less than a cent flat and a major third less than five cents sharp, with a 7 two cents sharp and an 11 1.5 cents sharp. It thus delivers reasonably good 11-limit harmony and very good no-fives harmony along with the very useful approximations represented by its commas.  On a related note, a notable characteristic of this EDO is that it is the lowest in a series of four consecutive EDOs to temper out [[Quartisma|117440512/117406179]].
 edo is the 24th [[prime_numbers|prime]] edo, and the 11th in the Fibonacci sequence, which means its 55th step approximates logarithmic phi (i.e. (phi-1)*1200 cents) within a fraction of a cent.