383edo: Difference between revisions

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~~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. The equal temperament [[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 limit.

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

=== Prime harmonics ===

=== Subsets and supersets ===

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

== Regular temperament properties ==

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

|+Table of rank-2 temperaments by generator

! Periods per ~~Octave~~

! Periods per 8ve

! Generator~~ (Reduced)~~

! Generator*

! Cents~~ (Reduced)~~

! Cents*

! Associated Ratio

! Associated Ratio*

! Temperaments

|-

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| [[Helmholtz]]

|}

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

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

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

[[Category:Countertertiaschis]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-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.
+{{EDO intro|383}}
 == 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. The equal temperament [[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 limit.
-edo is the 76th [[prime edo]].
 === Prime harmonics ===
 {{Harmonics in equal|383|columns=11}}
+=== Subsets and supersets ===
+edo is the 76th [[prime edo]].
 == Regular temperament properties ==
@@ Line 23: / Line 24: @@
 | 2.3
 | {{monzo| -607 383 }}
-| [{{val| 383 607 }}]
+| {{mapping| 383 607 }}
 | +0.0402
 | 0.0402
@@ Line 30: / Line 31: @@
 | 2.3.5
 | 32805/32768, {{monzo| -8 -55 41}}
-| [{{val| 383 607 889 }}]
+| {{mapping| 383 607 889 }}
 | +0.1610
 | 0.1741
@@ Line 37: / Line 38: @@
 | 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 44: / Line 45: @@
 | 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 51: / Line 52: @@
 | 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 60: / Line 61: @@
 {| class="wikitable center-all left-5"
 |+Table of rank-2 temperaments by generator
-! Periods<br>per Octave
+! Periods<br>per 8ve
-! Generator<br>(Reduced)
+! Generator*
-! Cents<br>(Reduced)
+! Cents*
-! Associated<br>Ratio
+! Associated<br>Ratio*
 ! Temperaments
 |-
@@ Line 90: / Line 91: @@
 | [[Helmholtz]]
 |}
+<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
-[[Category:Prime EDO]]
 [[Category:Countertertiaschis]]