389edo: Difference between revisions

389edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps, which makes it a [[dual-fifth system]]. Otherwise, it has a reasonable approximation to harmonics [[7/1|7]], [[9/1|9]], and [[17/1|17]], with optional additions of either [[5/1|5]] or [[11/1|11]] and [[15/1|15]], making it suitable for a 2.9.5.7.17 or 2.9.15.7.11.17 [[subgroup]] interpretation.

=== Odd harmonics ===

{{Harmonics in equal|389}}

389edo is the 77th [[prime edo]].  

389edo represents the ''north solstice'' (summer in the northern hemisphere) ''leap year cycle 69/389'' as devised by Sym454 inventor Irvin Bromberg. The outcome scale uses 327\389, or 62\389 as its generator. The solstice leap day scale with 94 notes uses 269\389 as a generator. Since this is a [[maximal evenness]] scale, temperament can be generated by simply merging the numerator and the denominator.

 

 

 

 

! [[TE error|Absolute]] (¢)

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

| 2.3.5

| {{monzo| 20 -17 3 }}, {{monzo| -39 -12 25 }}

| {{mapping| 389 617 903 }}

| −0.19

| 0.500

| 16.2

| 2.3.5

| 2109375/2097152, {{monzo|-7 44 -27 }}

| {{mapping| 389 616 903 }} (389b)

| +0.46

| 0.451

| 14.6

| 2.5.7

| 2100875/2097152, {{monzo| 0 52 -43 }}

| {{mapping| 389 903 1092 }}

| +0.12

| 0.131

| 4.2

| 2.5.7.11.17

| 6664/6655, 156250/155771, 180625/180224, 184960/184877

| {{mapping| 389 903 1092 1346 1590 }}

| +0.03

| 0.177

| 5.7