227edo: Difference between revisions

The equal temperament tempers out 15625/15552 ([[15625/15552|kleisma]]) and {{monzo| 61 -37 -1 }} in the 5-limit; [[5120/5103]], [[65625/65536]], and 117649/116640 in the 7-limit, so that it [[support]]s [[countercata]]. In the 11-limit, it tempers out [[385/384]], 2200/2187, 3388/3375, and 12005/11979, so that it provides the [[optimal patent val]] for 11-limit countercata. In the 13-limit, it tempers out [[325/324]], [[352/351]], [[625/624]], [[676/675]], and [[847/845]], and again supplies a good tuning for 13-limit countercata, although [[140edo]] tunes it better in this case.  

227edo is accurate for the 13th harmonic, as the denominator of a convergent to log₂13, after [[10edo|10]] and before [[5231edo|5231]].

==Regular temperament properties==

! rowspan="2" |[[Subgroup]]

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

! rowspan="2" |[[Mapping]]

! rowspan="2" |Optimal<br>8ve Stretch (¢)

! colspan="2" |Tuning Error

![[TE error|Absolute]] (¢)

![[TE simple badness|Relative]] (%)

|2.3

|{{monzo|360 -227}}

|{{val|227 360}}

|2.3.5

|15625/15552, {{monzo|61 -37 -1}}

|{{val|227 360 527}}

|2.3.5.7

|5120/5103, 15625/15552, 65625/65536

|{{val|227 360 527 637}}

|2.3.5.7.11

|385/384, 2200/2187, 3388/3375, 5120/5103

|{{val|227 360 527 637 785}}

|2.3.5.7.11.13

|325/324, 352/351, 385/384, 625/624, 847/845

|{{val|227 360 527 637 785 840}}

|2.3.5.7.11.13.17

|352/351, 595/594, 715/714, 847/845, 1001/1000, 3185/3179

|{{val|227 360 527 637 785 840 928}}

! Generator<br>(reduced)

! Cents<br>(reduced)

! Associated<br>ratio

|1

|25\227

|132.16

|{{monzo|-38 5 13}}

|[[Astro]] / [[kastro]]

|1

|60\227

|317.18

|6/5

|[[Hanson]] / [[countercata]]

|1

|94\227

|496.92

|4/3

|[[Undecental]]