383edo: Difference between revisions

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{{Infobox ET

~~| Prime factorization = 383 (prime)~~

~~| Step size = 3.13316¢~~

~~| Fifth = 224\383 (701.83¢)~~

~~| Semitones = 36:29 (112.79¢ : 90.86¢)~~

~~| Consistency = 15~~

}}

The '''383 equal divisions of the octave''' ('''383edo'''), or the '''383(-tone) equal temperament''' ('''383tet''', '''383et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 383 parts of about 3.13 [[cent]]s each.

== Theory ==

383edo is ~~distinctly~~ [[consistent]] through the [[15-odd-limit]] with a flat tendency. It tempers out 32805/32768 ([[schisma]]) in the 5-limit; [[2401/2400]] in the 7-limit; [[~~6250~~/~~6237~~]], [[4000/3993]] and [[~~3025~~/~~3024~~]] in the 11-limit; and [[625/624]], [[1575/1573]] and [[2080/2079]] in the 13-limit. It provides the [[optimal patent val]] for the [[countertertiaschis]] temperament, and a good tuning for [[sesquiquartififths]] in the higher ~~limit~~.

383edo is [[consistency|distinctly consistent]] through the [[15-odd-limit]] with a flat tendency. As an equal temperament, it [[tempering out|tempers out]] 32805/32768 ([[schisma]]) in the [[5-limit]]; [[2401/2400]] in the [[7-limit]]; [[3025/3024]], [[4000/3993]] and [[6250/6237]] in the [[11-limit]]; and [[625/624]], [[1575/1573]] and [[2080/2079]] in the [[13-limit]]. It provides the [[optimal patent val]] for the [[countertertiaschis]] temperament, and a good tuning for [[sesquiquartififths]] in the higher limits.

=== Prime harmonics ===

=== Subsets and supersets ===

383edo is the 76th [[prime edo]].

~~=== Prime harmonics ===~~

~~{{Harmonics in equal|383|columns=11}}~~

== Regular temperament properties ==

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

|-

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

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

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

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

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

! rowspan="2" | Optimal 8ve stretch (¢)

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

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

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| 2.3

| {{monzo| -607 383 }}

| [{{~~val~~| 383 607 }}]

| {{mapping| 383 607 }}

| +0.0402

| 0.0402

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| 2.3.5

| 32805/32768, {{monzo| -8 -55 41}}

| [{{~~val~~| 383 607 889 }}]

| {{mapping| 383 607 889 }}

| +0.1610

| 0.1741

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| 2.3.5.7

| 2401/2400, 32805/32768, 68359375/68024448

| [{{~~val~~| 383 607 889 1075 }}]

| {{mapping| 383 607 889 1075 }}

| +0.1813

| 0.1548

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| 2.3.5.7.11

| 2401/2400, 3025/3024, 4000/3993, 32805/32768

| [{{~~val~~| 383 607 889 1075 1325 }}]

| {{mapping| 383 607 889 1075 1325 }}

| +0.1382

| 0.1631

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| 2.3.5.7.11.13

| 625/624, 1575/1573, 2080/2079, 2401/2400, 10985/10976

| [{{~~val~~| 383 607 889 1075 1325 1417 }}]

| {{mapping| 383 607 889 1075 1325 1417 }}

| +0.1531

| 0.1525

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=== Rank-2 temperaments ===

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

|+Table of rank-2 temperaments by generator

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

! Periods per ~~Octave~~

|-

! Generator~~ (Reduced)~~

! Periods per 8ve

! Cents~~ (Reduced)~~

! Generator*

! Associated ~~Ratio~~

! Cents*

! Associated ratio*

! Temperaments

|-

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| 498.17

| 4/3

| [[Helmholtz]]

| [[Helmholtz (temperament)|Helmholtz]]

|}

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

== Music ==

; [[Francium]]

* "Mark A Player" from ''I Want To'' (2025) – [https://open.spotify.com/track/1M3LmqPfXRjpxuuTRgEufN Spotify] | [https://francium223.bandcamp.com/track/mark-a-player Bandcamp] | [https://www.youtube.com/watch?v=ePR_S5cNZvI YouTube] – in Marconic, 383edo tuning

~~[[Category:Equal divisions of the octave|###]] ~~

~~[[Category:Prime EDO]]~~

[[Category:Countertertiaschis]]

@@ Line 1: / Line 1: @@
-{{Infobox ET
+{{Infobox ET}}
-| Prime factorization = 383 (prime)
+{{ED intro}}
-| Step size = 3.13316¢
-| Fifth = 224\383 (701.83¢)
-| Semitones = 36:29 (112.79¢ : 90.86¢)
-| Consistency = 15
-}}
-The '''383 equal divisions of the octave''' ('''383edo'''), or the '''383(-tone) equal temperament''' ('''383tet''', '''383et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 383 parts of about 3.13 [[cent]]s each.
 == Theory ==
-edo is distinctly [[consistent]] through the [[15-odd-limit]] with a flat tendency. It tempers out 32805/32768 ([[schisma]]) in the 5-limit; [[2401/2400]] in the 7-limit; [[6250/6237]], [[4000/3993]] and [[3025/3024]] in the 11-limit; and [[625/624]], [[1575/1573]] and [[2080/2079]] in the 13-limit. It provides the [[optimal patent val]] for the [[countertertiaschis]] temperament, and a good tuning for [[sesquiquartififths]] in the higher limit.
+edo is [[consistency|distinctly consistent]] through the [[15-odd-limit]] with a flat tendency. As an equal temperament, it [[tempering out|tempers out]] 32805/32768 ([[schisma]]) in the [[5-limit]]; [[2401/2400]] in the [[7-limit]]; [[3025/3024]], [[4000/3993]] and [[6250/6237]] in the [[11-limit]]; and [[625/624]], [[1575/1573]] and [[2080/2079]] in the [[13-limit]]. It provides the [[optimal patent val]] for the [[countertertiaschis]] temperament, and a good tuning for [[sesquiquartififths]] in the higher limits.
+=== Prime harmonics ===
+{{Harmonics in equal|383}}
+=== Subsets and supersets ===
 edo is the 76th [[prime edo]].
-=== Prime harmonics ===
-{{Harmonics in equal|383|columns=11}}
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[Comma list]]
 ! rowspan="2" | [[Mapping]]
-! rowspan="2" | Optimal<br>8ve Stretch (¢)
+! rowspan="2" | Optimal<br />8ve stretch (¢)
-! colspan="2" | Tuning Error
+! colspan="2" | Tuning error
 |-
 ! [[TE error|Absolute]] (¢)
@@ Line 29: / Line 25: @@
 | 2.3
 | {{monzo| -607 383 }}
-| [{{val| 383 607 }}]
+| {{mapping| 383 607 }}
 | +0.0402
 | 0.0402
@@ Line 36: / Line 32: @@
 | 2.3.5
 | 32805/32768, {{monzo| -8 -55 41}}
-| [{{val| 383 607 889 }}]
+| {{mapping| 383 607 889 }}
 | +0.1610
 | 0.1741
@@ Line 43: / Line 39: @@
 | 2.3.5.7
 | 2401/2400, 32805/32768, 68359375/68024448
-| [{{val| 383 607 889 1075 }}]
+| {{mapping| 383 607 889 1075 }}
 | +0.1813
 | 0.1548
@@ Line 50: / Line 46: @@
 | 2.3.5.7.11
 | 2401/2400, 3025/3024, 4000/3993, 32805/32768
-| [{{val| 383 607 889 1075 1325 }}]
+| {{mapping| 383 607 889 1075 1325 }}
 | +0.1382
 | 0.1631
@@ Line 57: / Line 53: @@
 | 2.3.5.7.11.13
 | 625/624, 1575/1573, 2080/2079, 2401/2400, 10985/10976
-| [{{val| 383 607 889 1075 1325 1417 }}]
+| {{mapping| 383 607 889 1075 1325 1417 }}
 | +0.1531
 | 0.1525
@@ Line 65: / Line 61: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per Octave
+|-
-! Generator<br>(Reduced)
+! Periods<br />per 8ve
-! Cents<br>(Reduced)
+! Generator*
-! Associated<br>Ratio
+! Cents*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 94: / Line 91: @@
 | 498.17
 | 4/3
-| [[Helmholtz]]
+| [[Helmholtz (temperament)|Helmholtz]]
 |}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+== Music ==
+; [[Francium]]
+* "Mark A Player" from ''I Want To'' (2025) – [https://open.spotify.com/track/1M3LmqPfXRjpxuuTRgEufN Spotify] | [https://francium223.bandcamp.com/track/mark-a-player Bandcamp] | [https://www.youtube.com/watch?v=ePR_S5cNZvI YouTube] – in Marconic, 383edo tuning
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
-[[Category:Prime EDO]]
 [[Category:Countertertiaschis]]