171edo: Difference between revisions

Line 54:

| style="border-top: double;" | 243/242, 441/440, 4375/4356, 16384/16335

| style="border-top: double;" | [{{val| 171 271 397 480 592 }}] (171)

| style="border-top: double;" | -0.093

| style="border-top: double;" | −0.093

| style="border-top: double;" | 0.401

| style="border-top: double;" | 5.71

Line 64:

| style="border-top: double;" | 0.418

| style="border-top: double;" | 5.96

|-

| style="border-top: double;" | 2.3.5.7.13

| style="border-top: double;" | 625/624, 729/728, 2205/2197, 2401/2400

| style="border-top: double;" | [{{val| 171 271 397 480 633 }}]

| style="border-top: double;" | −0.001

| style="border-top: double;" | 0.220

| style="border-top: double;" | 3.13

|-

| 2.3.5.7.13.17

| 625/624, 729/728, 833/832, 1225/1224, 2205/2197

| [{{val| 171 271 397 480 633 699 }}]

| −0.013

| 0.202

| 2.88

|}

* 171et is lower in relative error than any previous equal temperaments in the 7-limit. Not until [[441edo|441]] do we find a better equal temperaments in terms of absolute error, and not until [[3125edo|3125]] do we find one in terms of relative error.

Line 70:

Line 84:

{| class="wikitable center-all left-5"

|+Table of rank-2 temperaments by generator

! Periods per 8ve

! Periods per 8ve

! Generator (Reduced)

! Generator (Reduced)

! Cents (Reduced)

! Cents (Reduced)

! Associated Ratio

! Temperaments

@@ Line 54: / Line 54: @@
 | style="border-top: double;" | 243/242, 441/440, 4375/4356, 16384/16335
 | style="border-top: double;" | [{{val| 171 271 397 480 592 }}] (171)
-| style="border-top: double;" | -0.093
+| style="border-top: double;" | &minus;0.093
 | style="border-top: double;" | 0.401
 | style="border-top: double;" | 5.71
@@ Line 64: / Line 64: @@
 | style="border-top: double;" | 0.418
 | style="border-top: double;" | 5.96
+|-
+| style="border-top: double;" | 2.3.5.7.13
+| style="border-top: double;" | 625/624, 729/728, 2205/2197, 2401/2400
+| style="border-top: double;" | [{{val| 171 271 397 480 633 }}]
+| style="border-top: double;" | &minus;0.001
+| style="border-top: double;" | 0.220
+| style="border-top: double;" | 3.13
+|-
+| 2.3.5.7.13.17
+| 625/624, 729/728, 833/832, 1225/1224, 2205/2197
+| [{{val| 171 271 397 480 633 699 }}]
+| &minus;0.013
+| 0.202
+| 2.88
 |}
 * 171et is lower in relative error than any previous equal temperaments in the 7-limit. Not until [[441edo|441]] do we find a better equal temperaments in terms of absolute error, and not until [[3125edo|3125]] do we find one in terms of relative error.
@@ Line 70: / Line 84: @@
 {| class="wikitable center-all left-5"
 |+Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+! Periods <br>per 8ve
-! Generator<br>(Reduced)
+! Generator <br>(Reduced)
-! Cents<br>(Reduced)
+! Cents <br>(Reduced)
 ! Associated<br>Ratio
 ! Temperaments