118edo: Difference between revisions

118edo represents the intersection of the [[5-limit]] [[schismatic]] and [[parakleismic]] temperaments, [[tempering out]] both the [[schisma]], {{monzo| -15 8 1 }} and the [[parakleisma]], {{monzo| 8 14 -13 }}, as well as the [[vishnuzma]], {{monzo| 23 6 -14 }}, the [[hemithirds comma]], {{monzo| 38 -2 -15 }}, and the [[kwazy comma]], {{monzo| -53 10 16 }}. It is the first 5-limit equal division which clearly gives microtempering, with errors well under half a cent. As a result, 118edo also excellently approximates the 22 Shruti scale.

118edo is the 17th [[The Riemann zeta function and tuning|zeta peak edo]], and it has decent approximations to harmonics [[7/1|7]], [[11/1|11]], [[17/1|17]], and [[19/1|19]]. In the 7-limit, it is particularly notable for tempering out the [[gamelisma]], 1029/1024, and is an excellent tuning for the rank-3 [[Gamelismic family|gamelismic]] temperament, and for [[guiron]], the rank-2 temperament also tempering out the schisma, 32805/32768. It also tempers out 3136/3125, the [[hemimean comma]], but [[99edo]] does better with that.

| [[27/22]], 16/13 I**

| Minor tridecimal neurtral third, "major-neutral" third

| {{monzo| -187 118 }}

| {{mapping| 118 187 }}

| −0.119

| {{mapping| 118 187 274 }}

| {{mapping| 118 187 274 331 }}

| {{mapping| 118 187 274 331 408 }}

| {{mapping| 118 187 274 331 408 437 }} (118)

| {{mapping| 118 187 274 331 408 436 }} (118f)

| {{mapping| 118 187 274 331 408 482 }}

| {{mapping| 118 187 274 331 408 482 501 }}

| [[Luna]] / [[hemithirds]] / [[lunatic]]

| [[Slendric]] / [[guiron]]

| [[Parakleismic]] / paralytic

| [[Helmholtz]] / [[pontiac]] / helenoid / pontic

| [[Vishnu]] / ananta (118) / acyuta (118f)

| [[Kwazy]] / [[bisupermajor]]

| 31\118<br>(28\118)

| 315.25<br>(284.75)

| 6/5<br>(33/28)

<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct