574edo: Difference between revisions

Line 3:

== Theory ==

~~574 = 14 × 41, and~~ 574edo shares the [[harmonic]] [[3/1|3]] with [[41edo]]. Unfortunately, it is only [[consistent]] to the [[5-odd-limit]], and the [[patent val]] and the 574d [[val]] are about equally viable.

574edo shares the [[harmonic]] [[3/1|3]] with [[41edo]]. Unfortunately, it is only [[consistent]] to the [[5-odd-limit]], and the [[patent val]] and the 574d [[val]] are about equally viable.

The 574d val [[~~tempering out|~~tempers out]] 4375/4374 ([[ragisma]]), 29360128/29296875 (quasiorwellisma), and 40500000/40353607 in the 7-limit; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the 11-limit; [[676/675]], [[4225/4224]], and [[10648/10647]] in the 13-limit.

The 574d val [[tempers out]] 4375/4374 ([[ragisma]]), 29360128/29296875 (quasiorwellisma), and 40500000/40353607 in the 7-limit; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the 11-limit; [[676/675]], [[4225/4224]], and [[10648/10647]] in the 13-limit.

The patent val tempers out 2100875/2097152 ([[rainy comma]]), 6115295232/6103515625 ([[vishnuzma]]), 49009212/48828125, and 78125000/78121827 ([[euzenius comma]]) in the 7-limit; 5632/5625, 42875/42768, 117649/117128, [[131072/130977]], 160083/160000, 161280/161051, 166698/166375, 391314/390625, and [[532400/531441]] in the 11-limit; 676/675, [[1001/1000]], [[2080/2079]], [[4096/4095]], and 4225/4224 in the 13-limit.

Line 30:

| {{monzo| 23 6 -14 }}, {{monzo| 42 -47 14 }}

| {{mapping| 574 910 1333 }}

| ~~−0~~.1658

| −0.1658

| 0.1260

| 6.03

Line 37:

| 4375/4374, 29360128/29296875, 40500000/40353607

| {{mapping| 574 910 1333 1612 }} (574d)

| ~~−0~~.2320

| −0.2320

| 0.1583

| 7.57

Line 44:

| 3025/3024, 4375/4374, 5632/5625, 40500000/40353607

| {{mapping| 574 910 1333 1612 1986 }} (574d)

| ~~−0~~.2202

| −0.2202

| 0.1435

| 6.87

Line 51:

| 676/675, 3025/3024, 4225/4224, 4375/4374, 41600/41503

| {{mapping| 574 910 1333 1612 1986 2124 }} (574d)

| ~~−0~~.1786

| −0.1786

| 0.1607

| 7.69

Line 58:

| 10976/10935, 2100875/2097152, 49009212/48828125

| {{mapping| 574 910 1333 1611 }} (574)

| ~~−0~~.0459

| −0.0459

| 0.2347

| 11.23

Line 65:

| 5632/5625, 10976/10935, 131072/130977, 166698/166375

| {{mapping| 574 910 1333 1611 1986 }} (574)

| ~~−0~~.0713

| −0.0713

| 0.2160

| 10.33

Line 72:

| 676/675, 1001/1000, 4096/4095, 10976/10935, 166698/166375

| {{mapping| 574 910 1333 1611 1986 2124 }} (574)

| ~~−0~~.0544

| −0.0544

| 0.2007

| 9.60

Line 93:

| [[Vishnu]] (574d)

|}

<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

@@ Line 3: / Line 3: @@
 == Theory ==
-= 14 × 41, and 574edo shares the [[harmonic]] [[3/1|3]] with [[41edo]]. Unfortunately, it is only [[consistent]] to the [[5-odd-limit]], and the [[patent val]] and the 574d [[val]] are about equally viable.
+edo shares the [[harmonic]] [[3/1|3]] with [[41edo]]. Unfortunately, it is only [[consistent]] to the [[5-odd-limit]], and the [[patent val]] and the 574d [[val]] are about equally viable.
-The 574d val [[tempering out|tempers out]] 4375/4374 ([[ragisma]]), 29360128/29296875 (quasiorwellisma), and 40500000/40353607 in the 7-limit; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the 11-limit; [[676/675]], [[4225/4224]], and [[10648/10647]] in the 13-limit.
+The 574d val [[tempers out]] 4375/4374 ([[ragisma]]), 29360128/29296875 (quasiorwellisma), and 40500000/40353607 in the 7-limit; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the 11-limit; [[676/675]], [[4225/4224]], and [[10648/10647]] in the 13-limit.
 The patent val tempers out 2100875/2097152 ([[rainy comma]]), 6115295232/6103515625 ([[vishnuzma]]), 49009212/48828125, and 78125000/78121827 ([[euzenius comma]]) in the 7-limit; 5632/5625, 42875/42768, 117649/117128, [[131072/130977]], 160083/160000, 161280/161051, 166698/166375, 391314/390625, and [[532400/531441]] in the 11-limit; 676/675, [[1001/1000]], [[2080/2079]], [[4096/4095]], and 4225/4224 in the 13-limit.
@@ Line 30: / Line 30: @@
 | {{monzo| 23 6 -14 }}, {{monzo| 42 -47 14 }}
 | {{mapping| 574 910 1333 }}
-| &minus;0.1658
+| −0.1658
 | 0.1260
 | 6.03
@@ Line 37: / Line 37: @@
 | 4375/4374, 29360128/29296875, 40500000/40353607
 | {{mapping| 574 910 1333 1612 }} (574d)
-| &minus;0.2320
+| −0.2320
 | 0.1583
 | 7.57
@@ Line 44: / Line 44: @@
 | 3025/3024, 4375/4374, 5632/5625, 40500000/40353607
 | {{mapping| 574 910 1333 1612 1986 }} (574d)
-| &minus;0.2202
+| −0.2202
 | 0.1435
 | 6.87
@@ Line 51: / Line 51: @@
 | 676/675, 3025/3024, 4225/4224, 4375/4374, 41600/41503
 | {{mapping| 574 910 1333 1612 1986 2124 }} (574d)
-| &minus;0.1786
+| −0.1786
 | 0.1607
 | 7.69
@@ Line 58: / Line 58: @@
 | 10976/10935, 2100875/2097152, 49009212/48828125
 | {{mapping| 574 910 1333 1611 }} (574)
-| &minus;0.0459
+| −0.0459
 | 0.2347
 | 11.23
@@ Line 65: / Line 65: @@
 | 5632/5625, 10976/10935, 131072/130977, 166698/166375
 | {{mapping| 574 910 1333 1611 1986 }} (574)
-| &minus;0.0713
+| −0.0713
 | 0.2160
 | 10.33
@@ Line 72: / Line 72: @@
 | 676/675, 1001/1000, 4096/4095, 10976/10935, 166698/166375
 | {{mapping| 574 910 1333 1611 1986 2124 }} (574)
-| &minus;0.0544
+| −0.0544
 | 0.2007
 | 9.60
@@ Line 93: / Line 93: @@
 | [[Vishnu]] (574d)
 |}
-<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