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## Theory

The famous53 equal divisiondivides the octave into 53 equal comma-sized parts of 22.642 cents each. It is notable as a 5-limit system, a fact apparently first noted by Isaac Newton, tempering out the schisma, 32805/32768, the kleisma, 15625/15552, the amity comma, 1600000/1594323 and the semicomma, 2109375/2097152. In the 7-limit it tempers out 225/224, 1728/1715 and 3125/3087, the marvel comma, the gariboh, and the orwell comma. In the 11-limit, it tempers out 99/98 and 121/120, and is the optimal patent val for Big Brother temperament, which tempers out both, as well as 11-limit orwell temperament, which also tempers out the 11-limit comma 176/175. In the 13-limit, it tempers out 169/168 and 245/243, and gives the optimal patent val for athene temperament. It is the eighth zeta integral edo and the 16th prime edo, following 47edo and coming before 59edo.53EDO has also found a certain dissemination as an EDO tuning for Arabic/Turkish/Persian music.

It can also be treated as a no-elevens, no-seventeens tuning, on which it is consistent all the way up to the 21-limit.

Wikipeda article about 53edo

## Linear temperaments

List of edo-distinct 53et rank two temperaments## Just Approximation

53edo provides excellent approximations for the classic 5-limit just chords and scales, such as the Ptolemy-Zarlino "just major" scale.One notable property of 53EDO is that it offers good approximations for both pure and pythagorean major thirds.

The perfect fifth is almost perfectly equal to the just interval 3/2, with only a 0.07 cent difference! 53EDO is practically equal to an extended Pythagorean. The 14- and 17- degree intervals are also very close to 6/5 and 5/4 respectively, and so 5-limit tuning can also be closely approximated. In addition, the 43-degree interval is only 4.8 cents away from the just ratio 7/4, so 53EDO can also be used for 7-limit harmony, tempering out the septimal kleisma, 225/224.

## Intervals

vvm2

double-down minor 2nd

Ebvv

vvm3

double-down minor 3rd

Fvv

vv4

double-down 4th

Gvv

vd5

downdim 5th

Abv

d5

dim 5th

Ab

^d5

updim 5th

Ab^

^^d5

double-up dim 5th

Ab^^

vvm6

double-down minor 6th

Bbvv

vvm7

double-down minor 7th

Cvv

vv8

double-down 8ve

Dvv

## Compositions

Bach WTC1 Prelude 1 in 53 by Bach and Mykhaylo KhramovBach WTC1 Fugue 1 in 53 by Bach and Mykhaylo Khramov

Whisper Song in 53EDO play by Prent Rodgers

Trio in Orwell play by Gene Ward Smith

Desert Prayer by Aaron Krister Johnson

Whisper Song in 53 EDO by Prent Rodgers

Elf Dine on Ho Ho play and Spun play by Andrew Heathwaite

The Fallen of Kleismic15play by Chris Vaisvil

mothers by Cam Taylor