397edo: Difference between revisions

397edo is only [[consistent]] to the [[5-odd-limit]], with three mappings possible for the 7-limit:

* {{val| 397 629 922 1115 }} ([[patent val]])

* {{val| 397 629 922 '''1114''' }} (397d val)

* {{val| 397 629 '''921''' '''1114''' }} (397cd val)

Using the patent val, it tempers out [[129140163/128000000]] and {{monzo| 55 -1 -23 }} in the 5-limit; [[6144/6125]], [[16875/16807]] and 129140163/128000000 in the 7-limit; [[support]]ing [[grendel]].

Using the 397d val, it tempers out 129140163/128000000 and {{monzo| 55 -1 -23 }} in the 5-limit; [[3136/3125]], [[420175/419904]] and 33756345/33554432 in the 7-limit; supporting [[sengagen]].

Using the 397cd val, it tempers out 390625000/387420489 and {{monzo| -55 23 8 }} in the 5-limit; [[2401/2400]], 390625/387072 and [[14348907/14336000]] in the 7-limit; supporting [[cotritone]].

397edo is the 78th [[prime edo]]. [[1588edo]], which quadruples it, gives a good correction to the harmonic 7.

! 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| -629 397 }}

| {{mapping| 397 629 }}

| 2.3.5

| 129140163/128000000, {{monzo| 55 -1 -23 }}

| {{mapping| 397 629 922 }}

| 1

| 8\397

| 24.18

| 686/675

| [[Sengagen]] (397d)

| 1

| 37\397

| 111.84

| 16/15

| [[Vavoom]]

| 1

| 128\397

| 386.90

| 5/4

| [[Grendel]] (397)

| 1

| 171\397

| 516.88

| 27/20

| [[Gravity]]

| 1

| 193\397

| 583.38

| 7/5

| [[Cotritone]] (397cd)