468edo: Difference between revisions

Line 3:

== Theory ==

468et tempers out [[78125000/78121827]], [[4375/4374]], [[250047/250000]], [[2401/2400]], 420175/419904, 200120949/200000000 and [[40353607/40310784]] in the 7-limit; 21437500/21434787, 151263/151250, 117649/117612, 514714375/514434888, 47265625/47258883, [[9801/9800]], [[3025/3024]], 1890625/1889568, 160083/160000, [[41503/41472]], 3294225/3294172, 43923/43904, 102487/102400 and [[1771561/1769472]] in the 11-limit. It provides the optimal patent val for [[unlit]].

468et tempers out [[78125000/78121827]], [[4375/4374]], [[250047/250000]], [[2401/2400]], 420175/419904, 200120949/200000000, and [[40353607/40310784]] in the 7-limit; 21437500/21434787, 151263/151250, 117649/117612, 514714375/514434888, 47265625/47258883, [[9801/9800]], [[3025/3024]], 1890625/1889568, 160083/160000, [[41503/41472]], 3294225/3294172, 43923/43904, 102487/102400, and [[1771561/1769472]] in the 11-limit. It provides the optimal patent val for [[unlit]].

=== Odd harmonics ===

Line 9:

=== Subsets and supersets ===

468 factors into ~~2<sup>2</sup> × 3<sup>2</sup> × 13~~, with subset edos {{EDOs|2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, and 234}}.

468 factors into {{factorisation|468}}, with subset edos {{EDOs|2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, and 234}}.

== Regular temperament properties ==

Line 26:

| {{monzo|371 -234}}

| {{mapping|468 742}}

| ~~−0~~.1922

| −0.1922

| 0.1921

| 7.49

Line 33:

| 2199023255552/2179240250625, 7629394531250/7625597484987

| {{mapping|468 742 1087}}

| ~~−0~~.2524

| −0.2524

| 0.1785

| 6.96

Line 40:

| 4375/4374, 2401/2400, 47141561040896/46708681640625

| {{mapping|468 742 1087 1314}}

| ~~−0~~.2253

| −0.2253

| 0.1615

| 6.30

Line 47:

| 3025/3024, 4375/4374, 2401/2400, 5767168/5740875

| {{mapping|468 742 1087 1314 1619}}

| ~~−0~~.1782

| −0.1782

| 0.1725

| 6.73

Line 54:

| 2080/2079, 1001/1000, 3025/3024, 1716/1715, 1982464/1974375

| {{mapping|468 742 1087 1314 1619 1732}}

| ~~−0~~.1709

| −0.1709

| 0.1583

| 6.17

Line 61:

| 2080/2079, 1001/1000, 3025/3024, 1716/1715, 17920/17901, 30464/30375

| {{mapping|468 742 1087 1314 1619 1732 1913}}

| ~~−0~~.1526

| −0.1526

| 0.1533

| 5.98

Line 100:

| [[Hemiennealimmal]]

|}

<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 ==
-et tempers out [[78125000/78121827]], [[4375/4374]], [[250047/250000]], [[2401/2400]], 420175/419904, 200120949/200000000 and [[40353607/40310784]] in the 7-limit; 21437500/21434787, 151263/151250, 117649/117612, 514714375/514434888, 47265625/47258883, [[9801/9800]], [[3025/3024]], 1890625/1889568, 160083/160000, [[41503/41472]], 3294225/3294172, 43923/43904, 102487/102400 and [[1771561/1769472]] in the 11-limit. It provides the optimal patent val for [[unlit]].
+et tempers out [[78125000/78121827]], [[4375/4374]], [[250047/250000]], [[2401/2400]], 420175/419904, 200120949/200000000, and [[40353607/40310784]] in the 7-limit; 21437500/21434787, 151263/151250, 117649/117612, 514714375/514434888, 47265625/47258883, [[9801/9800]], [[3025/3024]], 1890625/1889568, 160083/160000, [[41503/41472]], 3294225/3294172, 43923/43904, 102487/102400, and [[1771561/1769472]] in the 11-limit. It provides the optimal patent val for [[unlit]].
 === Odd harmonics ===
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-factors into 2<sup>2</sup> × 3<sup>2</sup> × 13, with subset edos {{EDOs|2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, and 234}}.
+factors into {{factorisation|468}}, with subset edos {{EDOs|2, 3, 4, 6, 9, 12, 13, 18, 26, 36, 39, 52, 78, 117, 156, and 234}}.
 == Regular temperament properties ==
@@ Line 26: / Line 26: @@
 | {{monzo|371 -234}}
 | {{mapping|468 742}}
-| &minus;0.1922
+| −0.1922
 | 0.1921
 | 7.49
@@ Line 33: / Line 33: @@
 | 2199023255552/2179240250625, 7629394531250/7625597484987
 | {{mapping|468 742 1087}}
-| &minus;0.2524
+| −0.2524
 | 0.1785
 | 6.96
@@ Line 40: / Line 40: @@
 | 4375/4374, 2401/2400, 47141561040896/46708681640625
 | {{mapping|468 742 1087 1314}}
-| &minus;0.2253
+| −0.2253
 | 0.1615
 | 6.30
@@ Line 47: / Line 47: @@
 | 3025/3024, 4375/4374, 2401/2400, 5767168/5740875
 | {{mapping|468 742 1087 1314 1619}}
-| &minus;0.1782
+| −0.1782
 | 0.1725
 | 6.73
@@ Line 54: / Line 54: @@
 | 2080/2079, 1001/1000, 3025/3024, 1716/1715, 1982464/1974375
 | {{mapping|468 742 1087 1314 1619 1732}}
-| &minus;0.1709
+| −0.1709
 | 0.1583
 | 6.17
@@ Line 61: / Line 61: @@
 | 2080/2079, 1001/1000, 3025/3024, 1716/1715, 17920/17901, 30464/30375
 | {{mapping|468 742 1087 1314 1619 1732 1913}}
-| &minus;0.1526
+| −0.1526
 | 0.1533
 | 5.98
@@ Line 100: / Line 100: @@
 | [[Hemiennealimmal]]
 |}
-<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