373edo: Difference between revisions

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~~The '''373 equal divisions of the octave''' ('''373edo'''), or the '''373(-tone) equal temperament''' ('''373tet''', '''373et''') when viewed from a [[regular temperament]] perspective, is the [[~~EDO|~~equal division of the octave]] into~~ 373 ~~parts of about 3.22 [[cent]]s each.~~

== Theory ==

373edo is [[consistent]] to the [[15-odd-limit]], with ~~harmonics~~ 3 through 13 all tuned flat. It tempers out {{monzo| 8 14 -13 }} ([[parakleisma]]) and {{monzo| -51 19 9 }} (untriton comma) in the 5-limit; 2401/2400 ([[breedsma]]), 65625/65536 (horwell), and 43046721/42875000 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, and 496125/495616 in the 11-limit; [[729/728]], [[1001/1000]], [[1716/1715]], [[4225/4224]], and [[10648/10647]] in the 13-limit, enabling [[squbemic chords]] and [[sinbadmic chords]]. It [[support]]s the [[Breedsmic temperaments #Hemitert|hemitert temperament]].

373edo is [[consistency|distinctly consistent]] to the [[15-odd-limit]]. It has a flat tendency, with [[harmonic]]s 3 through 13 all tuned flat. The equal temperament [[tempering out|tempers out]] {{monzo| 8 14 -13 }} ([[parakleisma]]) and {{monzo| -51 19 9 }} (untriton comma) in the 5-limit; 2401/2400 ([[breedsma]]), 65625/65536 ([[horwell comma]]), and 43046721/42875000 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, and 496125/495616 in the 11-limit; [[729/728]], [[1001/1000]], [[1716/1715]], [[4225/4224]], and [[10648/10647]] in the 13-limit, enabling [[squbemic chords]] and [[sinbadmic chords]]. It [[support]]s the [[Breedsmic temperaments #Hemitert|hemitert temperament]].

=== Prime harmonics ===

=== Subsets and supersets ===

373edo is the 74th [[prime edo]].

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

~~{{Primes in edo|373}}~~

== Regular temperament properties ==

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

! rowspan="2" | Subgroup

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

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

! rowspan="2" | [[Comma list|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| -591 373 }}

| [{{~~val~~| 373 591 }}]

| {{mapping| 373 591 }}

| +0.1939

| 0.1939

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| 2.3.5

| {{monzo| 8 14 -13 }}, {{monzo| -51 19 9 }}

| [{{~~val~~| 373 591 866 }}]

| {{mapping| 373 591 866 }}

| +0.1658

| 0.1632

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| 2.3.5.7

| 2401/2400, 65625/65536, 43046721/42875000

| [{{~~val~~| 373 591 866 1047 }}]

| {{mapping| 373 591 866 1047 }}

| +0.1654

| 0.1413

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| 2.3.5.7.11

| 2401/2400, 3025/3024, 8019/8000, 65625/65536

| [{{~~val~~| 373 591 866 1047 1290 }}]

| {{mapping| 373 591 866 1047 1290 }}

| +0.2008

| 0.1449

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| 2.3.5.7.11.13

| 729/728, 1001/1000, 1716/1715, 3025/3024, 4225/4224

| [{{~~val~~| 373 591 866 1047 1290 1380 }}]

| {{mapping| 373 591 866 1047 1290 1380 }}

| +0.2056

| 0.1327

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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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| [[Untriton]] (5-limit)

|}

<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~~]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-The '''373 equal divisions of the octave''' ('''373edo'''), or the '''373(-tone) equal temperament''' ('''373tet''', '''373et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 373 parts of about 3.22 [[cent]]s each.
+{{EDO intro|373}}
 == Theory ==
-edo is [[consistent]] to the [[15-odd-limit]], with harmonics 3 through 13 all tuned flat. It tempers out {{monzo| 8 14 -13 }} ([[parakleisma]]) and {{monzo| -51 19 9 }} (untriton comma) in the 5-limit; 2401/2400 ([[breedsma]]), 65625/65536 (horwell), and 43046721/42875000 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, and 496125/495616 in the 11-limit; [[729/728]], [[1001/1000]], [[1716/1715]], [[4225/4224]], and [[10648/10647]] in the 13-limit, enabling [[squbemic chords]] and [[sinbadmic chords]]. It [[support]]s the [[Breedsmic temperaments #Hemitert|hemitert temperament]].
+edo is [[consistency|distinctly consistent]] to the [[15-odd-limit]]. It has a flat tendency, with [[harmonic]]s 3 through 13 all tuned flat. The equal temperament [[tempering out|tempers out]] {{monzo| 8 14 -13 }} ([[parakleisma]]) and {{monzo| -51 19 9 }} (untriton comma) in the 5-limit; 2401/2400 ([[breedsma]]), 65625/65536 ([[horwell comma]]), and 43046721/42875000 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, and 496125/495616 in the 11-limit; [[729/728]], [[1001/1000]], [[1716/1715]], [[4225/4224]], and [[10648/10647]] in the 13-limit, enabling [[squbemic chords]] and [[sinbadmic chords]]. It [[support]]s the [[Breedsmic temperaments #Hemitert|hemitert temperament]].
+=== Prime harmonics ===
+{{Harmonics in equal|373}}
+=== Subsets and supersets ===
 edo is the 74th [[prime edo]].
-=== Prime harmonics ===
-{{Primes in edo|373}}
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
-! rowspan="2" | Subgroup
+! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Comma list|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 23: / Line 24: @@
 | 2.3
 | {{monzo| -591 373 }}
-| [{{val| 373 591 }}]
+| {{mapping| 373 591 }}
 | +0.1939
 | 0.1939
@@ Line 30: / Line 31: @@
 | 2.3.5
 | {{monzo| 8 14 -13 }}, {{monzo| -51 19 9 }}
-| [{{val| 373 591 866 }}]
+| {{mapping| 373 591 866 }}
 | +0.1658
 | 0.1632
@@ Line 37: / Line 38: @@
 | 2.3.5.7
 | 2401/2400, 65625/65536, 43046721/42875000
-| [{{val| 373 591 866 1047 }}]
+| {{mapping| 373 591 866 1047 }}
 | +0.1654
 | 0.1413
@@ Line 44: / Line 45: @@
 | 2.3.5.7.11
 | 2401/2400, 3025/3024, 8019/8000, 65625/65536
-| [{{val| 373 591 866 1047 1290 }}]
+| {{mapping| 373 591 866 1047 1290 }}
 | +0.2008
 | 0.1449
@@ Line 51: / Line 52: @@
 | 2.3.5.7.11.13
 | 729/728, 1001/1000, 1716/1715, 3025/3024, 4225/4224
-| [{{val| 373 591 866 1047 1290 1380 }}]
+| {{mapping| 373 591 866 1047 1290 1380 }}
 | +0.2056
 | 0.1327
@@ 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 102: / Line 103: @@
 | [[Untriton]] (5-limit)
 |}
+<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]]