301edo: Difference between revisions

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== Theory ==

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=== Subsets and supersets ===

Since 301 factors into ~~7 × 43~~, 301edo has [[7edo]] and [[43edo]] as its subsets. This is related to the proposal of the deaf French mathematician and acoustician {{w|Joseph Sauveur}} to divide the octave in 43 parts called ''merides'', and those into seven more parts called ''heptamerides''. Back in the days of slide rules and log tables, this made sense since by multiplying the log base ten of the interval in question by 1000, one came close to how many heptamerides it constituted.

Since 301 factors into {{factorisation|301}}, 301edo has [[7edo]] and [[43edo]] as its subsets. This is related to the proposal of the deaf French mathematician and acoustician {{w|Joseph Sauveur}} to divide the octave in 43 parts called ''merides'', and those into seven more parts called ''heptamerides''. Back in the days of slide rules and log tables, this made sense since by multiplying the log base ten of the interval in question by 1000, one came close to how many heptamerides it constituted.

301edo also tempers out {{monzo| 168 -43 -43 }} and 5250987/5242880, so it supports the [[Mitonismic temperaments #Meridic|meridic temperament]].

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== Regular temperament properties ==

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

|-

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

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

! rowspan="2" | [[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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=== Rank-2 temperaments ===

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

|+Table of rank-2 temperaments by generator

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

! Periods per 8ve

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ~~Ratio~~*

! Associated ratio*

! Temperaments

|-

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| 498.34

| 4/3

| [[Helmholtz]]

| [[Helmholtz (temperament)|Helmholtz]]

|-

| 7

| 125\301 (4\301)

| 125\301 (4\301)

| 498.34 (15.95)

| 498.34 (15.95)

| 4/3 (245/243)

| 4/3 (245/243)

| [[Septant]]

|-

| 43

| 125\301 (1\301)

| 125\301 (1\301)

| 498.34 (3.99)

| 498.34 (3.99)

| 4/3 (540/539)

| 4/3 (540/539)

| [[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

<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct

[[Category:Meridic]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|301}}
+{{ED intro}}
 == Theory ==
@@ Line 9: / Line 9: @@
 === Subsets and supersets ===
-Since 301 factors into 7 × 43, 301edo has [[7edo]] and [[43edo]] as its subsets. This is related to the proposal of the deaf French mathematician and acoustician {{w|Joseph Sauveur}} to divide the octave in 43 parts called ''merides'', and those into seven more parts called ''heptamerides''. Back in the days of slide rules and log tables, this made sense since by multiplying the log base ten of the interval in question by 1000, one came close to how many heptamerides it constituted.
+Since 301 factors into {{factorisation|301}}, 301edo has [[7edo]] and [[43edo]] as its subsets. This is related to the proposal of the deaf French mathematician and acoustician {{w|Joseph Sauveur}} to divide the octave in 43 parts called ''merides'', and those into seven more parts called ''heptamerides''. Back in the days of slide rules and log tables, this made sense since by multiplying the log base ten of the interval in question by 1000, one came close to how many heptamerides it constituted.
 edo also tempers out {{monzo| 168 -43 -43 }} and 5250987/5242880, so it supports the [[Mitonismic temperaments #Meridic|meridic temperament]].
@@ Line 15: / Line 15: @@
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
-! rowspan="2" | [[Comma list|Comma List]]
+! rowspan="2" | [[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 69: / Line 70: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-|+Table of rank-2 temperaments by generator
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
-! Periods<br>per 8ve
+|-
+! Periods<br />per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio*
+! Associated<br />ratio*
 ! Temperaments
 |-
@@ Line 104: / Line 106: @@
 | 498.34
 | 4/3
-| [[Helmholtz]]
+| [[Helmholtz (temperament)|Helmholtz]]
 |-
 | 7
-| 125\301<br>(4\301)
+| 125\301<br />(4\301)
-| 498.34<br>(15.95)
+| 498.34<br />(15.95)
-| 4/3<br>(245/243)
+| 4/3<br />(245/243)
 | [[Septant]]
 |-
 | 43
-| 125\301<br>(1\301)
+| 125\301<br />(1\301)
-| 498.34<br>(3.99)
+| 498.34<br />(3.99)
-| 4/3<br>(540/539)
+| 4/3<br />(540/539)
 | [[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
+<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct
 [[Category:Meridic]]