1759edo: Difference between revisions

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== Theory ==

1759edo is [[consistent]] to the [[23-odd-limit]], [[~~temper out|~~tempering out]] [[3025/3024]], [[2500/2499]], [[5985/5984]], [[4225/4224]], [[6175/6174]], 3520/3519, 14875/14872 and [[256000/255879]]. It [[support]]s [[etampesic]]. [[Essentially tempered ~~chords~~]] in 1759et include [[vicetertismic chords]].

1759edo is [[consistent]] to the [[23-odd-limit]], [[tempering out]] [[3025/3024]], [[2500/2499]], [[5985/5984]], [[4225/4224]], [[6175/6174]], 3520/3519, 14875/14872 and [[256000/255879]]. It [[support]]s [[etampesic]]. [[Essentially tempered chord]]s in 1759et include [[vicetertismic chords]].

=== 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|2788 -1759}}

| {{mapping|1759 2788}}

| ~~−0~~.0110

| −0.0110

| 0.0110

| 1.61

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| 0.0315

| 4.62

~~{{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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| 16/15

| [[Vavoom]]

~~{{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]]

* "Regret" from ''Naughty Girl Era'' (2024) – [https://open.spotify.com/track/2pDNJUQzjQaPJcl1cwLJco Spotify] | [https://francium223.bandcamp.com/track/regret Bandcamp] | [https://www.youtube.com/watch?v=mB-qWsSfn3g YouTube]

* ''1759'' (2025) – [https://open.spotify.com/album/3zA7ZVP09WlBw4WRjpjAZZ Spotify] | [https://francium223.bandcamp.com/album/1759 Bandcamp] | [https://www.youtube.com/playlist?list=PLLZE7hMjEXRYDHsUEkhpthaxFB4xoK9Tc YouTube] – 4-piece EP in 1759edo

* "Chupacara Smith" from ''Don't Give Your Kids These Names!'' (2025) − [https://open.spotify.com/track/4Wr1wq3jAAuUdlEqCtrXI1 Spotify] | [https://francium223.bandcamp.com/track/chupacara-smith Bandcamp] | [https://www.youtube.com/watch?v=diKcFA0m21A YouTube]

* "good enough" from ''with our kindness.'' (2026) – [https://francium223.bandcamp.com/track/good-enough Bandcamp] | [https://www.youtube.com/watch?v=tG7Xm8i4uVs YouTube]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|1759}}
+{{ED intro}}
 == Theory ==
-edo is [[consistent]] to the [[23-odd-limit]], [[temper out|tempering out]] [[3025/3024]], [[2500/2499]], [[5985/5984]], [[4225/4224]], [[6175/6174]], 3520/3519, 14875/14872 and [[256000/255879]]. It [[support]]s [[etampesic]]. [[Essentially tempered chords]] in 1759et include [[vicetertismic chords]].
+edo is [[consistent]] to the [[23-odd-limit]], [[tempering out]] [[3025/3024]], [[2500/2499]], [[5985/5984]], [[4225/4224]], [[6175/6174]], 3520/3519, 14875/14872 and [[256000/255879]]. It [[support]]s [[etampesic]]. [[Essentially tempered chord]]s in 1759et include [[vicetertismic chords]].
 === 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|2788 -1759}}
 | {{mapping|1759 2788}}
-| &minus;0.0110
+| −0.0110
 | 0.0110
 | 1.61
@@ Line 62: / Line 71: @@
 | 0.0315
 | 4.62
-{{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 72: / Line 88: @@
 | 16/15
 | [[Vavoom]]
-{{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]]
+* "Regret" from ''Naughty Girl Era'' (2024) – [https://open.spotify.com/track/2pDNJUQzjQaPJcl1cwLJco Spotify] | [https://francium223.bandcamp.com/track/regret Bandcamp] | [https://www.youtube.com/watch?v=mB-qWsSfn3g YouTube]
+* ''1759'' (2025) – [https://open.spotify.com/album/3zA7ZVP09WlBw4WRjpjAZZ Spotify] | [https://francium223.bandcamp.com/album/1759 Bandcamp] | [https://www.youtube.com/playlist?list=PLLZE7hMjEXRYDHsUEkhpthaxFB4xoK9Tc YouTube] – 4-piece EP in 1759edo
+* "Chupacara Smith" from ''Don't Give Your Kids These Names!'' (2025) − [https://open.spotify.com/track/4Wr1wq3jAAuUdlEqCtrXI1 Spotify] | [https://francium223.bandcamp.com/track/chupacara-smith Bandcamp] | [https://www.youtube.com/watch?v=diKcFA0m21A YouTube]
+* "good enough" from ''with our kindness.'' (2026) – [https://francium223.bandcamp.com/track/good-enough Bandcamp] | [https://www.youtube.com/watch?v=tG7Xm8i4uVs YouTube]