190edo: Difference between revisions

{{EDO intro|190}}

The equal temperament is interesting because of the utility of its approximations; it [[tempering out|tempers out]] [[1029/1024]], [[4375/4374]], [[385/384]], [[441/440]], [[3025/3024]] and [[9801/9800]]. It provides the [[optimal patent val]] for both the 7- and 11-limit versions of [[unidec]], the 72 & 118 temperament, which tempers out 1029/1024, 4375/4374, and in the 11-limit, 385/384 and 441/440. It also provides the optimal patent val for the rank-3 11-limit temperament [[portent]], which tempers out 385/384 and 441/440, and [[gamelan]], the rank-3 7-limit temperament which tempers out 1029/1024, as well as [[slendric]], the 2.3.7 subgroup temperament featured in the [[#Music]] section. In the 13-limit, 190et tempers out [[625/624]], [[729/728]], [[847/845]], [[1001/1000]] and [[1575/1573]], and provides the optimal patent val for the [[ekadash]] temperament and the rank-3 [[portentous]] temperament.

! rowspan="2" | [[Comma list|Comma List]]

| {{monzo| -301 190 }}

| {{mapping| 190 301 }}

| {{mapping| 190 301 441 }}

| {{mapping| 190 301 441 533 }}

| {{mapping| 190 301 441 533 657 }}

| {{mapping| 190 301 441 533 657 703 }}

| {{mapping| 190 301 441 533 657 703 776 }} (190g)

| {{mapping| 190 301 441 533 657 703 776 807 }} (190g)

| {{mapping| 190 301 441 533 657 703 776 807 859 }} (190g)

|+Table of rank-2 temperaments by generator

! Associated<br>Ratio*

! Temperaments

| [[Pental (temperament)|Pental]]

| [[Decal]]

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

[[Category:Listen]]