559edo: Difference between revisions

Line 3:

== Theory ==

559edo [[tempering out|tempers out]] the luna comma, {{monzo| 38 -2 -15 }} and the minortone comma, {{monzo| -16 35 -17 }} in the [[5-limit]], as well as the [[monzisma]], {{monzo| 54 -37 2 }}; [[4375/4374]], [[2100875/2097152]], and 282475249/281250000 in the [[7-limit]]; 12005/11979, [[41503/41472]], 160083/160000, and 172032/171875 in the [[11-limit]]. Rank-2 temperaments it [[support]]s include [[mitonic]], [[lunatic]], [[acrokleismic]], [[monzism]], and [[meridic]].

559edo is a strong 5-limit system. The equal temperament [[tempering out|tempers out]] the luna comma, {{monzo| 38 -2 -15 }} and the minortone comma, {{monzo| -16 35 -17 }} in the [[5-limit]], as well as the [[monzisma]], {{monzo| 54 -37 2 }}; [[4375/4374]], [[2100875/2097152]], and 282475249/281250000 in the [[7-limit]]; 12005/11979, [[41503/41472]], 160083/160000, and 172032/171875 in the [[11-limit]]. Rank-2 temperaments it [[support]]s include [[mitonic]], [[lunatic]], [[acrokleismic]], [[monzism]], and [[meridic]].

=== Prime harmonics ===

Line 21:

| 2.3

| {{monzo| 886 -559 }}

| [{{~~val~~| 559 886 }}]

| {{mapping| 559 886 }}

| -0.0040

| 0.0040

Line 28:

| 2.3.5

| {{monzo| 38 -2 -15 }}, {{monzo| -16 35 -17 }}

| [{{~~val~~| 559 886 1298 }}]

| {{mapping| 559 886 1298 }}

| -0.0157

| 0.0168

Line 35:

| 2.3.5.7

| 4375/4374, 2100875/2097152, {{monzo| -4 -2 -9 10 }}

| [{{~~val~~| 559 886 1298 1569 }}]

| {{mapping| 559 886 1298 1569 }}

| +0.0478

| 0.1109

Line 42:

| 2.3.5.7.11

| 4375/4374, 12005/11979, 41503/41472, 172032/171875

| [{{~~val~~| 559 886 1298 1569 1934 }}]

| {{mapping| 559 886 1298 1569 1934 }}

| 0.0161

| 0.1175

Line 51:

{| 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

|-

Line 87:

| [[Meridic]]

|}

<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|~~###~~]] ~~~~

@@ Line 3: / Line 3: @@
 == Theory ==
-edo [[tempering out|tempers out]] the luna comma, {{monzo| 38 -2 -15 }} and the minortone comma, {{monzo| -16 35 -17 }} in the [[5-limit]], as well as the [[monzisma]], {{monzo| 54 -37 2 }}; [[4375/4374]], [[2100875/2097152]], and 282475249/281250000 in the [[7-limit]]; 12005/11979, [[41503/41472]], 160083/160000, and 172032/171875 in the [[11-limit]]. Rank-2 temperaments it [[support]]s include [[mitonic]], [[lunatic]], [[acrokleismic]], [[monzism]], and [[meridic]].
+edo is a strong 5-limit system. The equal temperament [[tempering out|tempers out]] the luna comma, {{monzo| 38 -2 -15 }} and the minortone comma, {{monzo| -16 35 -17 }} in the [[5-limit]], as well as the [[monzisma]], {{monzo| 54 -37 2 }}; [[4375/4374]], [[2100875/2097152]], and 282475249/281250000 in the [[7-limit]]; 12005/11979, [[41503/41472]], 160083/160000, and 172032/171875 in the [[11-limit]]. Rank-2 temperaments it [[support]]s include [[mitonic]], [[lunatic]], [[acrokleismic]], [[monzism]], and [[meridic]].
 === Prime harmonics ===
@@ Line 21: / Line 21: @@
 | 2.3
 | {{monzo| 886 -559 }}
-| [{{val| 559 886 }}]
+| {{mapping| 559 886 }}
 | -0.0040
 | 0.0040
@@ Line 28: / Line 28: @@
 | 2.3.5
 | {{monzo| 38 -2 -15 }}, {{monzo| -16 35 -17 }}
-| [{{val| 559 886 1298 }}]
+| {{mapping| 559 886 1298 }}
 | -0.0157
 | 0.0168
@@ Line 35: / Line 35: @@
 | 2.3.5.7
 | 4375/4374, 2100875/2097152, {{monzo| -4 -2 -9 10 }}
-| [{{val| 559 886 1298 1569 }}]
+| {{mapping| 559 886 1298 1569 }}
 | +0.0478
 | 0.1109
@@ Line 42: / Line 42: @@
 | 2.3.5.7.11
 | 4375/4374, 12005/11979, 41503/41472, 172032/171875
-| [{{val| 559 886 1298 1569 1934 }}]
+| {{mapping| 559 886 1298 1569 1934 }}
 | 0.0161
 | 0.1175
@@ Line 51: / Line 51: @@
 {| 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 87: / Line 87: @@
 | [[Meridic]]
 |}
+<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 -->