307edo: Difference between revisions

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== Theory ==

~~307et tempers out 1220703125~~/~~1219784832~~, ~~48828125/48771072~~, ~~95703125/95551488 and~~ [[2401/2400]] in the 7-limit~~; 100663296/100656875~~, ~~939524096/935859375~~, [[~~16384~~/~~16335~~]]~~, 226492416/226474325, 2359296/2358125~~, [[6250/6237]]~~, 172032/171875, 42875/42768, 4302592/4296875~~, 15488/15435, ~~3388~~/~~3375, 766656/765625, 166375/165888, 391314/390625, 3294225/3294172~~, 43923/43904 ~~and 102487/102400 in the 11-limit~~.

307edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1|3]] is about halfway between its steps. It can be considered in either the 2.9.5.7 [[subgroup]] or the 2.9.15.21 subgroup, but the former is more flexible as it lends itself to an [[extension]] to the 2.9.5.7.11.13.17.19.23.

===Odd harmonics===

Using the full 7-limit [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[2401/2400]] in the 7-limit, and in the 11-limit extension, [[3388/3375]], [[6250/6237]], 15488/15435, [[16384/16335]], and 43923/43904.

=== Odd harmonics ===

===Subsets and supersets===

=== Subsets and supersets ===

307edo is the 63rd [[prime edo]]. [[614edo]], which doubles it, gives a good correction to the harmonic 3.

==Regular temperament properties==

== Regular temperament properties ==

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

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

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

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

~~! rowspan="2" |Optimal<br>8ve Stretch (¢)~~

~~! colspan="2" |Tuning Error~~

|-

~~![[TE error|Absolute]] (¢)~~

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

|-

|2.9

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

|{{monzo|-973 307}}

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

|{{~~val~~|307 973}}

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

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

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

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

|-

| 2.9

| {{monzo| -973 307 }}

| {{mapping| 307 973 }}

| +0.1029

| 0.1030

| 2.64

|-

|2.9.5

| 2.9.5

|32805/32768, {{monzo|2 47 -65}}

| 32805/32768, {{monzo| 2 47 -65 }}

|{{~~val~~|307 973 713}}

| {{mapping|307 973 713 }}

| -0.0257

| −0.0257

| 0.2004

| 5.13

|-

|2.9.5.7

| 2.9.5.7

|32805/32768, 118098/117649, 589824/588245

| 32805/32768, 118098/117649, 589824/588245

|{{~~val~~|307 973 713 862}}

| {{mapping| 307 973 713 862 }}

| -0.0687

| −0.0687

| 0.1889

| 4.87

|-

|2.9.5.7.11

| 2.9.5.7.11

|5632/5625, 8019/8000, 32805/32768, 46656/46585

| 5632/5625, 8019/8000, 32805/32768, 46656/46585

|{{~~val~~|307 973 713 862 1062}}

| {{mapping| 307 973 713 862 1062 }}

| -0.0447

| −0.0447

| 0.1756

| 4.49

|-

|2.9.5.7.11.13

| 2.9.5.7.11.13

|729/728, 1001/1000, 4096/4095, 6656/6655, 10648/10647

| 729/728, 1001/1000, 4096/4095, 6656/6655, 10648/10647

|{{~~val~~|307 973 713 862 1062 1136}}

| {{mapping| 307 973 713 862 1062 1136 }}

| -0.0311

| −0.0311

| 0.1632

| 4.18

|-

|2.9.5.7.11.13.17

| 2.9.5.7.11.13.17

|729/728, 936/935, 1001/1000, 1377/1375, 2025/2023, 7744/7735

| 729/728, 936/935, 1001/1000, 1377/1375, 2025/2023, 7744/7735

|{{~~val~~|307 973 713 862 1062 1136 1255}}

| {{mapping| 307 973 713 862 1062 1136 1255 }}

| -0.0470

| −0.0470

| 0.1560

| 3.99

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== Music ==

; [[Francium]]

* "Broken Music From A Broken Mind" from ''Melancholie'' (2023) [https://open.spotify.com/track/3FBm2hcuQwuH5rNjQ9IOZ9 Spotify] | [https://francium223.bandcamp.com/track/broken-music-from-a-broken-mind Bandcamp] | [https://www.youtube.com/watch?v=CKq9y6qk10g YouTube]

* "Broken Music From A Broken Mind" from ''Melancholie'' (2023) – [https://open.spotify.com/track/3FBm2hcuQwuH5rNjQ9IOZ9 Spotify] | [https://francium223.bandcamp.com/track/broken-music-from-a-broken-mind Bandcamp] | [https://www.youtube.com/watch?v=CKq9y6qk10g YouTube]

* "Naughty Unicorn" from ''You Are A...'' (2024) – [https://open.spotify.com/track/0c4QHJKHWYb7ErWHRXs0BA Spotify] | [https://francium223.bandcamp.com/track/naughty-unicorn Bandcamp] | [https://www.youtube.com/watch?v=wGfydgfwreQ YouTube]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|307}}
+{{ED intro}}
 == Theory ==
-et tempers out 1220703125/1219784832, 48828125/48771072, 95703125/95551488 and [[2401/2400]] in the 7-limit; 100663296/100656875, 939524096/935859375, [[16384/16335]], 226492416/226474325, 2359296/2358125, [[6250/6237]], 172032/171875, 42875/42768, 4302592/4296875, 15488/15435, 3388/3375, 766656/765625, 166375/165888, 391314/390625, 3294225/3294172, 43923/43904 and 102487/102400 in the 11-limit.
+edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1|3]] is about halfway between its steps. It can be considered in either the 2.9.5.7 [[subgroup]] or the 2.9.15.21 subgroup, but the former is more flexible as it lends itself to an [[extension]] to the 2.9.5.7.11.13.17.19.23.
-===Odd harmonics===
+Using the full 7-limit [[patent val]] nonetheless, the equal temperament [[tempering out|tempers out]] [[2401/2400]] in the 7-limit, and in the 11-limit extension, [[3388/3375]], [[6250/6237]], 15488/15435, [[16384/16335]], and 43923/43904.
+=== Odd harmonics ===
 {{Harmonics in equal|307}}
-===Subsets and supersets===
+=== Subsets and supersets ===
 edo is the 63rd [[prime edo]]. [[614edo]], which doubles it, gives a good correction to the harmonic 3.
-==Regular temperament properties==
+== Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" |[[Subgroup]]
-! rowspan="2" |[[Comma list|Comma List]]
-! rowspan="2" |[[Mapping]]
-! rowspan="2" |Optimal<br>8ve Stretch (¢)
-! colspan="2" |Tuning Error
-|-
-![[TE error|Absolute]] (¢)
-![[TE simple badness|Relative]] (%)
 |-
-|2.9
+! rowspan="2" | [[Subgroup]]
-|{{monzo|-973 307}}
+! rowspan="2" | [[Comma list]]
-|{{val|307 973}}
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br />8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
+|-
+| 2.9
+| {{monzo| -973 307 }}
+| {{mapping| 307 973 }}
 | +0.1029
 | 0.1030
 | 2.64
 |-
-|2.9.5
+| 2.9.5
-|32805/32768, {{monzo|2 47 -65}}
+| 32805/32768, {{monzo| 2 47 -65 }}
-|{{val|307 973 713}}
+| {{mapping|307 973 713 }}
-| -0.0257
+| −0.0257
 | 0.2004
 | 5.13
 |-
-|2.9.5.7
+| 2.9.5.7
-|32805/32768, 118098/117649, 589824/588245
+| 32805/32768, 118098/117649, 589824/588245
-|{{val|307 973 713 862}}
+| {{mapping| 307 973 713 862 }}
-| -0.0687
+| −0.0687
 | 0.1889
 | 4.87
 |-
-|2.9.5.7.11
+| 2.9.5.7.11
-|5632/5625, 8019/8000, 32805/32768, 46656/46585
+| 5632/5625, 8019/8000, 32805/32768, 46656/46585
-|{{val|307 973 713 862 1062}}
+| {{mapping| 307 973 713 862 1062 }}
-| -0.0447
+| −0.0447
 | 0.1756
 | 4.49
 |-
-|2.9.5.7.11.13
+| 2.9.5.7.11.13
-|729/728, 1001/1000, 4096/4095, 6656/6655, 10648/10647
+| 729/728, 1001/1000, 4096/4095, 6656/6655, 10648/10647
-|{{val|307 973 713 862 1062 1136}}
+| {{mapping| 307 973 713 862 1062 1136 }}
-| -0.0311
+| −0.0311
 | 0.1632
 | 4.18
 |-
-|2.9.5.7.11.13.17
+| 2.9.5.7.11.13.17
-|729/728, 936/935, 1001/1000, 1377/1375, 2025/2023, 7744/7735
+| 729/728, 936/935, 1001/1000, 1377/1375, 2025/2023, 7744/7735
-|{{val|307 973 713 862 1062 1136 1255}}
+| {{mapping| 307 973 713 862 1062 1136 1255 }}
-| -0.0470
+| −0.0470
 | 0.1560
 | 3.99
@@ Line 63: / Line 70: @@
 == Music ==
 ; [[Francium]]
-* "Broken Music From A Broken Mind" from ''Melancholie'' (2023) [https://open.spotify.com/track/3FBm2hcuQwuH5rNjQ9IOZ9 Spotify] | [https://francium223.bandcamp.com/track/broken-music-from-a-broken-mind Bandcamp] | [https://www.youtube.com/watch?v=CKq9y6qk10g YouTube]
+* "Broken Music From A Broken Mind" from ''Melancholie'' (2023) – [https://open.spotify.com/track/3FBm2hcuQwuH5rNjQ9IOZ9 Spotify] | [https://francium223.bandcamp.com/track/broken-music-from-a-broken-mind Bandcamp] | [https://www.youtube.com/watch?v=CKq9y6qk10g YouTube]
+* "Naughty Unicorn" from ''You Are A...'' (2024) – [https://open.spotify.com/track/0c4QHJKHWYb7ErWHRXs0BA Spotify] | [https://francium223.bandcamp.com/track/naughty-unicorn Bandcamp] | [https://www.youtube.com/watch?v=wGfydgfwreQ YouTube]
 [[Category:Listen]]