385edo: Difference between revisions

Line 3:

== Theory ==

385edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament [[tempering out|tempers out]] [[19683/19600]], [[589824/588245]], and [[703125/702464]] in the 7-limit; [[540/539]], [[8019/8000]], 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It [[support]]s [[hemipental]] and provides the [[optimal patent val]] for the 7-limit version thereof. Using the [[patent val]], it tempers out [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4096/4095]], [[6656/~~665~~]] and [[10648/10647]] in the 13-limit; and [[936/935]], [[1275/1274]], 1377/1375, and [[2601/2600]] in the 17-limit.

385edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament [[tempering out|tempers out]] [[19683/19600]], [[589824/588245]], and [[703125/702464]] in the 7-limit; [[540/539]], [[8019/8000]], 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It [[support]]s [[hemipental]] and provides the [[optimal patent val]] for the 7-limit version thereof. Using the [[patent val]], it tempers out [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4096/4095]], [[6656/6655]] and [[10648/10647]] in the 13-limit; and [[936/935]], [[1275/1274]], 1377/1375, and [[2601/2600]] in the 17-limit.

=== Prime harmonics ===

Line 76:

| 1

| 62\385

| 193.~~247~~

| 193.25

| ~~4096~~/~~3645~~

| 262144/234375

| [[Luna]]

|-

| 1

| 162/385

| 504.~~935~~

| 504.94

| 4/3

| [[Countermeantone]]

|-

| 5

| 80\385 (3\385)

| 249.35 (9.35)

| 81/70 (176/175)

| [[Hemipental]]

|-

| 5

| 160\385 (6\385)

| 498.~~701~~ (18.~~701~~)

| 498.70 (18.70)

| 4/3 (81/80)

| [[Pental]] (5-limit)

@@ Line 3: / Line 3: @@
 == Theory ==
-edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament [[tempering out|tempers out]] [[19683/19600]], [[589824/588245]], and [[703125/702464]] in the 7-limit; [[540/539]], [[8019/8000]], 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It [[support]]s [[hemipental]] and provides the [[optimal patent val]] for the 7-limit version thereof. Using the [[patent val]], it tempers out [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4096/4095]], [[6656/665]] and [[10648/10647]] in the 13-limit; and [[936/935]], [[1275/1274]], 1377/1375, and [[2601/2600]] in the 17-limit.
+edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament [[tempering out|tempers out]] [[19683/19600]], [[589824/588245]], and [[703125/702464]] in the 7-limit; [[540/539]], [[8019/8000]], 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It [[support]]s [[hemipental]] and provides the [[optimal patent val]] for the 7-limit version thereof. Using the [[patent val]], it tempers out [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4096/4095]], [[6656/6655]] and [[10648/10647]] in the 13-limit; and [[936/935]], [[1275/1274]], 1377/1375, and [[2601/2600]] in the 17-limit.
 === Prime harmonics ===
@@ Line 76: / Line 76: @@
 | 1
 | 62\385
-| 193.247
+| 193.25
-| 4096/3645
+| 262144/234375
 | [[Luna]]
 |-
 | 1
 | 162/385
-| 504.935
+| 504.94
 | 4/3
 | [[Countermeantone]]
+|-
+| 5
+| 80\385<br>(3\385)
+| 249.35<br>(9.35)
+| 81/70<br>(176/175)
+| [[Hemipental]]
 |-
 | 5
 | 160\385<br>(6\385)
-| 498.701<br>(18.701)
+| 498.70<br>(18.70)
 | 4/3<br>(81/80)
 | [[Pental]] (5-limit)