499edo: Difference between revisions

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== Theory ==

499et tempers out [[33554432/33480783]], 359661568/358722675 and [[2401/2400]] in the 7-limit; 100663296/100656875, 2097152/2096325, [[536870912/535869675]], 151263/151250, 104857600/104825259, [[131072/130977]], [[200704/200475]], 17537553/17500000, [[19712/19683]], 1479016/1476225, [[3025/3024]], [[41503/41472]], [[532400/531441]] and 67110351/67108864 in the 11-limit.

499et tempers out [[33554432/33480783]], 359661568/358722675 and [[2401/2400]] in the 7-limit; 100663296/100656875, 2097152/2096325, [[536870912/535869675]], 151263/151250, 104857600/104825259, [[131072/130977]], [[200704/200475]], 17537553/17500000, [[19712/19683]], 1479016/1476225, [[3025/3024]], [[41503/41472]], [[532400/531441]], and 67110351/67108864 in the 11-limit.

=== Prime harmonics ===

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== Regular temperament properties ==

{~~{comma basis begin}}~~

{| class="wikitable center-4 center-5 center-6"

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list]]

! rowspan="2" | [[Mapping]]

! rowspan="2" | Optimal<br />8ve stretch (¢)

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

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

|-

| 2.3

| {{monzo|791 -499}}

| {{val|499 791}}

| -0.0787

| −0.0787

| 0.0787

| 3.27

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| {{monzo|32 -7 -9}}, {{monzo|1 36 -25}}

| {{val|499 791 1159}}

| -0.1760

| −0.1760

| 0.1519

| 6.32

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| 2401/2400, 1959552/1953125, 26873856/26796875

| {{val|499 791 1159 1401}}

| -0.1598

| −0.1598

| 0.1345

| 5.59

~~{{comma basis end}~~}

|}

=== Rank-2 temperaments ===

{{rank-2 ~~begin}}~~

{| class="wikitable center-all left-5"

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Periods<br />per 8ve

! Generator*

! Cents*

! Associated<br />ratio*

! Temperaments

|-

| 1

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| 2800/2187

| [[Osiris]]

~~{{rank-2 end}~~}

|}

~~{{orf}}~~

<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct

== Music ==

; [[Francium]]

* "~~Still~~ not desperate enough" from ''hope in dark times'' (2024) ~~–~~ [https://open.spotify.com/track/4BkTyDG9JO2vRKrtta3iwz Spotify] | [https://francium223.bandcamp.com/track/still-not-desperate-enough Bandcamp] | [https://www.youtube.com/watch?v=nTYClZbsH4k YouTube]

* "still not desperate enough" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/4BkTyDG9JO2vRKrtta3iwz Spotify] | [https://francium223.bandcamp.com/track/still-not-desperate-enough Bandcamp] | [https://www.youtube.com/watch?v=nTYClZbsH4k YouTube]

* "Dumping Thickness" from ''Check Us Out'' (2026) – [https://open.spotify.com/track/5ytxIITz1HVR81FPaxZF78 Spotify] | [https://francium223.bandcamp.com/track/dumping-thickness Bandcamp] | [https://www.youtube.com/watch?v=saRSyUZwEZ0 YouTube]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|499}}
+{{ED intro}}
 == Theory ==
-et tempers out [[33554432/33480783]], 359661568/358722675 and [[2401/2400]] in the 7-limit; 100663296/100656875, 2097152/2096325, [[536870912/535869675]], 151263/151250, 104857600/104825259, [[131072/130977]], [[200704/200475]], 17537553/17500000, [[19712/19683]], 1479016/1476225, [[3025/3024]], [[41503/41472]], [[532400/531441]] and 67110351/67108864 in the 11-limit.
+et tempers out [[33554432/33480783]], 359661568/358722675 and [[2401/2400]] in the 7-limit; 100663296/100656875, 2097152/2096325, [[536870912/535869675]], 151263/151250, 104857600/104825259, [[131072/130977]], [[200704/200475]], 17537553/17500000, [[19712/19683]], 1479016/1476225, [[3025/3024]], [[41503/41472]], [[532400/531441]], and 67110351/67108864 in the 11-limit.
 === Prime harmonics ===
@@ Line 12: / Line 12: @@
 == Regular temperament properties ==
-{{comma basis begin}}
+{| class="wikitable center-4 center-5 center-6"
+|-
+! rowspan="2" | [[Subgroup]]
+! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br />8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
 |-
 | 2.3
 | {{monzo|791 -499}}
 | {{val|499 791}}
-| -0.0787
+| −0.0787
 | 0.0787
 | 3.27
@@ Line 24: / Line 33: @@
 | {{monzo|32 -7 -9}}, {{monzo|1 36 -25}}
 | {{val|499 791 1159}}
-| -0.1760
+| −0.1760
 | 0.1519
 | 6.32
@@ Line 31: / Line 40: @@
 | 2401/2400, 1959552/1953125, 26873856/26796875
 | {{val|499 791 1159 1401}}
-| -0.1598
+| −0.1598
 | 0.1345
 | 5.59
-{{comma basis end}}
+|}
 === Rank-2 temperaments ===
-{{rank-2 begin}}
+{| class="wikitable center-all left-5"
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
+! Generator*
+! Cents*
+! Associated<br />ratio*
+! Temperaments
 |-
 | 1
@@ Line 62: / Line 78: @@
 | 2800/2187
 | [[Osiris]]
-{{rank-2 end}}
+|}
-{{orf}}
+<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
 == Music ==
 ; [[Francium]]
-* "Still not desperate enough" from ''hope in dark times'' (2024) &ndash; [https://open.spotify.com/track/4BkTyDG9JO2vRKrtta3iwz Spotify] | [https://francium223.bandcamp.com/track/still-not-desperate-enough Bandcamp] | [https://www.youtube.com/watch?v=nTYClZbsH4k YouTube]
+* "still not desperate enough" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/4BkTyDG9JO2vRKrtta3iwz Spotify] | [https://francium223.bandcamp.com/track/still-not-desperate-enough Bandcamp] | [https://www.youtube.com/watch?v=nTYClZbsH4k YouTube]
+* "Dumping Thickness" from ''Check Us Out'' (2026) – [https://open.spotify.com/track/5ytxIITz1HVR81FPaxZF78 Spotify] | [https://francium223.bandcamp.com/track/dumping-thickness Bandcamp] | [https://www.youtube.com/watch?v=saRSyUZwEZ0 YouTube]
 [[Category:Listen]]