241edo: Difference between revisions

Line 3:

== Theory ==

241edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. It has a sharp tendency, with [[prime harmonic]]s 3 through 13 all tuned sharp. ~~The equal temperament~~ [[~~tempering out|~~tempers out]] [[78732/78125]] in the 5-limit, [[19683/19600]] and [[3136/3125]] in the 7-limit, [[540/539]], 43923/43904, [[65536/65219]], and 151263/151250 in the 11-limit, and [[351/350]], [[676/675]], [[729/728]], [[1001/1000]] and [[2080/2079]] in the 13-limit. It provides the [[optimal patent val]] for [[subpental]].

241edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. It has a sharp tendency, with [[prime harmonic]]s 3 through 13 all tuned sharp. It [[tempers out]] [[78732/78125]] in the 5-limit, [[19683/19600]] and [[3136/3125]] in the 7-limit, [[540/539]], 43923/43904, [[65536/65219]], and 151263/151250 in the 11-limit, and [[351/350]], [[676/675]], [[729/728]], [[1001/1000]] and [[2080/2079]] in the 13-limit. It provides the [[optimal patent val]] for [[subpental]].

=== Prime harmonics ===

Line 26:

| {{monzo| 382 -241 }}

| {{mapping| 241 382 }}

| ~~−0~~.038

| −0.038

| 0.038

| 0.76

Line 33:

| 78732/78125, {{monzo| 56 -28 -5 }}

| {{mapping| 241 382 560 }}

| ~~−0~~.322

| −0.322

| 0.403

| 8.10

Line 40:

| 3136/3125, 19683/19600, 829940/823543

| {{mapping| 241 382 560 677 }}

| ~~−0~~.431

| −0.431

| 0.397

| 7.97

Line 47:

| 540/539, 3136/3125, 8019/8000, 15488/15435

| {{mapping| 241 382 560 677 834 }}

| ~~−0~~.425

| −0.425

| 0.355

| 7.14

Line 54:

| 351/350, 540/539, 676/675, 3136/3125, 10648/10647

| {{mapping| 241 382 560 677 834 892 }}

| ~~−0~~.397

| −0.397

| 0.330

| 6.63

Line 99:

| [[Gary]]

|}

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if ~~it is~~ distinct

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

[[Category:Subpental]]

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. It has a sharp tendency, with [[prime harmonic]]s 3 through 13 all tuned sharp. The equal temperament [[tempering out|tempers out]] [[78732/78125]] in the 5-limit, [[19683/19600]] and [[3136/3125]] in the 7-limit, [[540/539]], 43923/43904, [[65536/65219]], and 151263/151250 in the 11-limit, and [[351/350]], [[676/675]], [[729/728]], [[1001/1000]] and [[2080/2079]] in the 13-limit. It provides the [[optimal patent val]] for [[subpental]].
+edo is [[consistency|distinctly consistent]] in the [[15-odd-limit]]. It has a sharp tendency, with [[prime harmonic]]s 3 through 13 all tuned sharp. It [[tempers out]] [[78732/78125]] in the 5-limit, [[19683/19600]] and [[3136/3125]] in the 7-limit, [[540/539]], 43923/43904, [[65536/65219]], and 151263/151250 in the 11-limit, and [[351/350]], [[676/675]], [[729/728]], [[1001/1000]] and [[2080/2079]] in the 13-limit. It provides the [[optimal patent val]] for [[subpental]].
 === Prime harmonics ===
@@ Line 26: / Line 26: @@
 | {{monzo| 382 -241 }}
 | {{mapping| 241 382 }}
-| &minus;0.038
+| −0.038
 | 0.038
 | 0.76
@@ Line 33: / Line 33: @@
 | 78732/78125, {{monzo| 56 -28 -5 }}
 | {{mapping| 241 382 560 }}
-| &minus;0.322
+| −0.322
 | 0.403
 | 8.10
@@ Line 40: / Line 40: @@
 | 3136/3125, 19683/19600, 829940/823543
 | {{mapping| 241 382 560 677 }}
-| &minus;0.431
+| −0.431
 | 0.397
 | 7.97
@@ Line 47: / Line 47: @@
 | 540/539, 3136/3125, 8019/8000, 15488/15435
 | {{mapping| 241 382 560 677 834 }}
-| &minus;0.425
+| −0.425
 | 0.355
 | 7.14
@@ Line 54: / Line 54: @@
 | 351/350, 540/539, 676/675, 3136/3125, 10648/10647
 | {{mapping| 241 382 560 677 834 892 }}
-| &minus;0.397
+| −0.397
 | 0.330
 | 6.63
@@ Line 99: / Line 99: @@
 | [[Gary]]
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 [[Category:Subpental]]