1106edo: Difference between revisions

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== Theory ==

1106edo is a [[~~The Riemann zeta function and tuning #Zeta EDO lists|~~zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] being {{EDOs| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs| 270, 342 and 612 }}. It is less strong in the 13- and 17-limit, but even so is ~~distinctly~~ [[consistent]] through the [[17-odd-limit]].

1106edo is a [[zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] being {{EDOs| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs| 270, 342 and 612 }}. It is less strong in the 13- and 17-limit, but even so is [[consistency|distinctly consistent]] through the [[17-odd-limit]].

It notably supports [[supermajor]], [[brahmagupta]], and [[orga]] in the 7-limit, and notably [[semisupermajor]] in the 11-limit. In the higher limits, it supports the 79th-octave temperament [[gold]].

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=== Subsets and supersets ===

Since 1106 factors into ~~2 × 7 × 79~~, it has subset edos {{EDOs| 2, 7, 14, 79, 158, and 553 }}.

Since 1106 factors into {{factorization|1106}}, it has subset edos {{EDOs| 2, 7, 14, 79, 158, and 553 }}.

== Regular temperament properties ==

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| 2.3

| {{monzo| 1753 -1106 }}

| {{~~val~~| 1106 1753 }}

| {{mapping| 1106 1753 }}

| -0.010

| 0.010

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| 2.3.5

| {{monzo| -53 10 16 }}, {{monzo| 40 -56 21 }}

| {{~~val~~| 1106 1753 2568 }}

| {{mapping| 1106 1753 2568 }}

| +0.001

| 0.019

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| 2.3.5.7

| 4375/4374, 52734375/52706752, {{monzo| 46 -14 -3 -6 }}

| {{~~val~~| 1106 1753 2568 3105 }}

| {{mapping| 1106 1753 2568 3105 }}

| -0.006

| 0.020

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| 2.3.5.7.11

| 3025/3024, 4375/4374, 5767168/5764801, 35156250/35153041

| {{~~val~~| 1106 1753 2568 3105 3826 }}

| {{mapping| 1106 1753 2568 3105 3826 }}

| +0.004

| 0.026

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| 2.3.5.7.11.13

| 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625

| {{~~val~~| 1106 1753 2568 3105 3826 4093 }}

| {{mapping| 1106 1753 2568 3105 3826 4093 }}

| -0.012

| 0.043

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| 2.3.5.7.11.13.17

| 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619

| {{~~val~~| 1106 1753 2568 3105 3826 4093 4521 }}

| {{mapping| 1106 1753 2568 3105 3826 4093 4521 }}

| -0.021

| 0.045

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=== Rank-2 temperaments ===

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

|+Table of rank-2 temperaments by generator

|-

! Periods<br>per 8ve

! Generator*

! Cents*

! Associated<br>Ratio

! Associated<br>Ratio*

! Temperaments

|-

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] being {{EDOs| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs| 270, 342 and 612 }}. It is less strong in the 13- and 17-limit, but even so is distinctly [[consistent]] through the [[17-odd-limit]].
+edo is a [[zeta peak edo]]. It is strong as a 7-limit system; the only edos lower than it with a lower 7-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] being {{EDOs| 171, 270, 342, 441 and 612 }}. It is even stronger in the 11-limit; the only ones beating it out now being {{EDOs| 270, 342 and 612 }}. It is less strong in the 13- and 17-limit, but even so is [[consistency|distinctly consistent]] through the [[17-odd-limit]].
 It notably supports [[supermajor]], [[brahmagupta]], and [[orga]] in the 7-limit, and notably [[semisupermajor]] in the 11-limit. In the higher limits, it supports the 79th-octave temperament [[gold]].
@@ Line 11: / Line 11: @@
 === Subsets and supersets ===
-Since 1106 factors into 2 × 7 × 79, it has subset edos {{EDOs| 2, 7, 14, 79, 158, and 553 }}.
+Since 1106 factors into {{factorization|1106}}, it has subset edos {{EDOs| 2, 7, 14, 79, 158, and 553 }}.
 == Regular temperament properties ==
@@ Line 26: / Line 26: @@
 | 2.3
 | {{monzo| 1753 -1106 }}
-| {{val| 1106 1753 }}
+| {{mapping| 1106 1753 }}
 | -0.010
 | 0.010
@@ Line 33: / Line 33: @@
 | 2.3.5
 | {{monzo| -53 10 16 }}, {{monzo| 40 -56 21 }}
-| {{val| 1106 1753 2568 }}
+| {{mapping| 1106 1753 2568 }}
 | +0.001
 | 0.019
@@ Line 40: / Line 40: @@
 | 2.3.5.7
 | 4375/4374, 52734375/52706752, {{monzo| 46 -14 -3 -6 }}
-| {{val| 1106 1753 2568 3105 }}
+| {{mapping| 1106 1753 2568 3105 }}
 | -0.006
 | 0.020
@@ Line 47: / Line 47: @@
 | 2.3.5.7.11
 | 3025/3024, 4375/4374, 5767168/5764801, 35156250/35153041
-| {{val| 1106 1753 2568 3105 3826 }}
+| {{mapping| 1106 1753 2568 3105 3826 }}
 | +0.004
 | 0.026
@@ Line 54: / Line 54: @@
 | 2.3.5.7.11.13
 | 3025/3024, 4096/4095, 4375/4374, 78125/78078, 105644/105625
-| {{val| 1106 1753 2568 3105 3826 4093 }}
+| {{mapping| 1106 1753 2568 3105 3826 4093 }}
 | -0.012
 | 0.043
@@ Line 61: / Line 61: @@
 | 2.3.5.7.11.13.17
 | 2500/2499, 3025/3024, 4096/4095, 4375/4374, 4914/4913, 8624/8619
-| {{val| 1106 1753 2568 3105 3826 4093 4521 }}
+| {{mapping| 1106 1753 2568 3105 3826 4093 4521 }}
 | -0.021
 | 0.045
@@ Line 69: / Line 69: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
+|+Table of rank-2 temperaments by generator
+|-
 ! Periods<br>per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio
+! Associated<br>Ratio*
 ! Temperaments
 |-