3395edo: Difference between revisions

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== Theory ==

3395edo is an extremely strong 17- and 19-limit system, and a [[The Riemann ~~Zeta~~ function and tuning #Zeta EDO lists|zeta peak, integral and gap edo]]. It has a lower 17-limit [[TE relative error]] than any edo until [[7033edo|7033]], and a lower 19-limit relative error than any edo until [[8269edo|8269]]. Besides, it provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out [[6656/6655]], the jacobin comma, and for [[quartismic]], which also tempers out [[123201/123200]]. A basis for the 17-limit commas is {6656/6655, 12376/12375, 28561/28560, 31213/31212, 37180/37179, 937125/937024}, and for the 19-limit, {6656/6655, 12376/12375, 12636/12635, 13377/13376, 14365/14364, 23409/23408, 28561/28560}.

3395edo is an extremely strong 17- and 19-limit system, and a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral, and gap edo]]. It has a lower 17-limit [[TE relative error]] than any edo until [[7033edo|7033]], and a lower 19-limit relative error than any edo until [[8269edo|8269]]. Besides, it provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out [[6656/6655]], the jacobin comma, and for [[quartismic]], which also tempers out [[123201/123200]]. A basis for the 17-limit commas is {6656/6655, 12376/12375, 28561/28560, 31213/31212, 37180/37179, 937125/937024}, and for the 19-limit, {6656/6655, 12376/12375, 12636/12635, 13377/13376, 14365/14364, 23409/23408, 28561/28560}.

=== Prime harmonics ===

=== ~~Divisors~~ ===

=== Subsets and supersets ===

3395 ~~= 5 × 7 × 97~~, ~~with~~ subset edos 5, 7, 35, 97, 485, and 679.

Since 3395 factors into {{factorization|3395}}, 3395edo has subset edos 5, 7, 35, 97, 485, and 679.

== Regular temperament properties ==

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=== Rank-2 temperaments ===

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

! Periods per 8ve

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

! Generator~~ (Reduced)~~

|-

! Cents~~ (Reduced)~~

! Periods per 8ve

! Associated ~~Ratio~~

! Generator*

! ~~Temperament~~

! Cents*

! Associated ratio*

! Temperaments

|-

| 1

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| 819.676

| 55115776/34328125

| [[~~Gene's jacobin~~]]

| [[Genojacobin]]

|-

| 35

| 1409\3395 (51\3395)

| 498.027 (18.026)

| 4/3 (?)

| [[Bromine]]

|-

| 97

| 1409\3395 (9\3395)

| 498.027 (3.181)

| 4/3 (?)

| [[Berkelium]]

|}

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

[[Category:Jacobin]]

[[Category:Quartismic]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|3395}}
+{{ED intro}}
 == Theory ==
-edo is an extremely strong 17- and 19-limit system, and a [[The Riemann Zeta function and tuning #Zeta EDO lists|zeta peak, integral and gap edo]]. It has a lower 17-limit [[TE relative error]] than any edo until [[7033edo|7033]], and a lower 19-limit relative error than any edo until [[8269edo|8269]]. Besides, it provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out [[6656/6655]], the jacobin comma, and for [[quartismic]], which also tempers out [[123201/123200]]. A basis for the 17-limit commas is {6656/6655, 12376/12375, 28561/28560, 31213/31212, 37180/37179, 937125/937024}, and for the 19-limit, {6656/6655, 12376/12375, 12636/12635, 13377/13376, 14365/14364, 23409/23408, 28561/28560}.
+edo is an extremely strong 17- and 19-limit system, and a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral, and gap edo]]. It has a lower 17-limit [[TE relative error]] than any edo until [[7033edo|7033]], and a lower 19-limit relative error than any edo until [[8269edo|8269]]. Besides, it provides the [[optimal patent val]] for the 13-limit rank-5 temperament tempering out [[6656/6655]], the jacobin comma, and for [[quartismic]], which also tempers out [[123201/123200]]. A basis for the 17-limit commas is {6656/6655, 12376/12375, 28561/28560, 31213/31212, 37180/37179, 937125/937024}, and for the 19-limit, {6656/6655, 12376/12375, 12636/12635, 13377/13376, 14365/14364, 23409/23408, 28561/28560}.
 === Prime harmonics ===
 {{Harmonics in equal|3395|columns=11}}
-=== Divisors ===
+=== Subsets and supersets ===
-= 5 × 7 × 97, with subset edos 5, 7, 35, 97, 485, and 679.
+Since 3395 factors into {{factorization|3395}}, 3395edo has subset edos 5, 7, 35, 97, 485, and 679.
 == Regular temperament properties ==
@@ Line 16: / Line 16: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-! Periods<br>per 8ve
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Generator<br>(Reduced)
+|-
-! Cents<br>(Reduced)
+! Periods<br />per 8ve
-! Associated<br>Ratio
+! Generator*
-! Temperament
+! Cents*
+! Associated<br />ratio*
+! Temperaments
 |-
 | 1
@@ Line 26: / Line 28: @@
 | 819.676
 | 55115776/34328125
-| [[Gene's jacobin]]
+| [[Genojacobin]]
+|-
+| 35
+| 1409\3395<br />(51\3395)
+| 498.027<br />(18.026)
+| 4/3<br />(?)
+| [[Bromine]]
+|-
+| 97
+| 1409\3395<br />(9\3395)
+| 498.027<br />(3.181)
+| 4/3<br />(?)
+| [[Berkelium]]
 |}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 [[Category:Jacobin]]
 [[Category:Quartismic]]