742edo: Difference between revisions

== Regular temperament properties ==

|-

| 2.3.5

| {{monzo| 23 6 -14 }}, {{monzo| -84 53 }}

| {{mapping| 742 1176 1723 }}

| 0.0555

| 3.43

| 2401/2400, 14348907/14336000, {{monzo| 23 6 -14 }}

| {{mapping| 742 1176 1723 2083 }}

| 0.0525

| 3.24

| 2401/2400, 9801/9800, 172032/171875, 1240029/1239040

| {{mapping| 742 1176 1723 2083 2567 }}

| 0.0501

| 3.10

| 2401/2400, 4096/4095, 6656/6655, 9801/9800, 39366/39325

| {{mapping| 742 1176 1723 2083 2567 2746 }}

| 0.0608

| 3.76

| 1701/1700, 2058/2057, 2401/2400, 2601/2600, 4096/4095, 6656/6655

| {{mapping| 742 1176 1723 2083 2567 2746 3033 }}

| 0.0564

| 3.49

| 1701/1700, 2058/2057, 2376/2375, 2401/2400, 2432/2431, 2601/2600, 3213/3211

| {{mapping| 742 1176 1723 2083 2567 2746 3033 3152 }}

| 0.0531

| 3.28

| 1197/1196, 1496/1495, 1701/1700, 2025/2024, 2058/2057, 2401/2400, 2601/2600, 3213/3211

| {{mapping| 742 1176 1723 2083 2567 2746 3033 3152 3357 }} (742i)

| 0.0699

| 4.32

* 742et has a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any previous equal temperaments. It is only bettered by [[935edo|935]] in terms of absolute error, and by [[1178edo|1178]] in terms of relative error.  

* 742et (742i val) is also notable in the 17- and 23-limit, where it has lower absolute errors than any previous equal temperaments. In the 17-limit it beats [[581edo|581]] and is bettered by [[764edo|764]]; in the 23-limit it beats [[718edo|718]] and is bettered by [[814edo|814]].  

=== Rank-2 temperaments ===

|-

| 1

|-

| 14

| [[Silicon]]

|-

| 53

| [[Mercator]]

|-

| 53

| [[Iodine]]