301edo: Difference between revisions

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== Theory ==

301edo is a strong 7-limit system, and distinctly [[consistent]] through the [[17-odd-limit]]. It tempers out [[32805/32768]] in the 5-limit, [[2401/2400]] in the 7-limit, [[3025/3024]], [[5632/5625]], [[8019/8000]] in the 11-limit, [[729/728]], [[847/845]], [[1001/1000]], [[1716/1715]], [[2200/2197]] in the 13-limit, and 561/560, [[833/832]], [[1089/1088]], [[1156/1155]], 1275/1274 and [[1701/1700]] in the 17-limit. Since it tempers out both 32805/32768 and 2401/2400, it [[support]]s the [[sesquiquartififths]] temperament.

301edo is a strong 7-limit system, and distinctly [[consistent]] through the [[17-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[32805/32768]] in the 5-limit, [[2401/2400]] in the 7-limit, [[3025/3024]], [[5632/5625]], [[8019/8000]] in the 11-limit, [[729/728]], [[847/845]], [[1001/1000]], [[1716/1715]], [[2200/2197]] in the 13-limit, and 561/560, [[833/832]], [[1089/1088]], [[1156/1155]], 1275/1274 and [[1701/1700]] in the 17-limit. Since it tempers out both 32805/32768 and 2401/2400, it [[support]]s the [[sesquiquartififths]] temperament.

=== Prime harmonics ===

=== ~~Divisors~~ ===

=== Subsets and supersets ===

301 ~~is a composite number, since 301 =~~ 7 × 43. This is related to the proposal of the deaf French mathematician and acoustician ~~[[Wikipedia: Joseph Sauveur~~|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 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.

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

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| 2.3

| {{monzo| -477 301 }}

| [{{~~val~~| 301 477 }}]

| {{mapping| 301 477 }}

| +0.0927

| 0.0927

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| 2.3.5

| 32805/32768, {{monzo| 3 45 -32 }}

| [{{~~val~~| 301 477 699 }}]

| {{mapping| 301 477 699 }}

| +0.0048

| 0.1456

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| 2.3.5.7

| 2401/2400, 32805/32768, 1959552/1953125

| [{{~~val~~| 301 477 699 845 }}]

| {{mapping| 301 477 699 845 }}

| +0.0085

| 0.1262

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| 2.3.5.7.11

| 2401/2400, 3025/3024, 5632/5625, 8019/8000

| [{{~~val~~| 301 477 699 845 1041 }}]

| {{mapping| 301 477 699 845 1041 }}

| +0.0734

| 0.1720

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| 2.3.5.7.11.13

| 729/728, 847/845, 1001/1000, 1716/1715, 3025/3024

| [{{~~val~~| 301 477 699 845 1041 1114 }}]

| {{mapping| 301 477 699 845 1041 1114 }}

| +0.0310

| 0.1834

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| 2.3.5.7.11.13.17

| 561/560, 729/728, 833/832, 847/845, 1001/1000, 1089/1088

| [{{~~val~~| 301 477 699 845 1041 1114 1230 }}]

| {{mapping| 301 477 699 845 1041 1114 1230 }}

| +0.0721

| 0.1973

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|+Table of rank-2 temperaments by generator

! Periods per 8ve

! Generator~~ (Reduced)~~

! Generator*

! Cents~~ (Reduced)~~

! Cents*

! Associated Ratio

! Associated Ratio*

! Temperaments

|-

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| [[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|###]] ~~

[[Category:Meridic]]

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is a strong 7-limit system, and distinctly [[consistent]] through the [[17-odd-limit]]. It tempers out [[32805/32768]] in the 5-limit, [[2401/2400]] in the 7-limit, [[3025/3024]], [[5632/5625]], [[8019/8000]] in the 11-limit, [[729/728]], [[847/845]], [[1001/1000]], [[1716/1715]], [[2200/2197]] in the 13-limit, and 561/560, [[833/832]], [[1089/1088]], [[1156/1155]], 1275/1274 and [[1701/1700]] in the 17-limit. Since it tempers out both 32805/32768 and 2401/2400, it [[support]]s the [[sesquiquartififths]] temperament.
+edo is a strong 7-limit system, and distinctly [[consistent]] through the [[17-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[32805/32768]] in the 5-limit, [[2401/2400]] in the 7-limit, [[3025/3024]], [[5632/5625]], [[8019/8000]] in the 11-limit, [[729/728]], [[847/845]], [[1001/1000]], [[1716/1715]], [[2200/2197]] in the 13-limit, and 561/560, [[833/832]], [[1089/1088]], [[1156/1155]], 1275/1274 and [[1701/1700]] in the 17-limit. Since it tempers out both 32805/32768 and 2401/2400, it [[support]]s the [[sesquiquartififths]] temperament.
 === Prime harmonics ===
 {{Harmonics in equal|301}}
-=== Divisors ===
+=== Subsets and supersets ===
-is a composite number, since 301 = 7 × 43. This is related to the proposal of the deaf French mathematician and acoustician [[Wikipedia: Joseph Sauveur|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 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.
 edo also tempers out {{monzo| 168 -43 -43 }} and 5250987/5242880, so it supports the [[Mitonismic temperaments #Meridic|meridic temperament]].
@@ Line 26: / Line 26: @@
 | 2.3
 | {{monzo| -477 301 }}
-| [{{val| 301 477 }}]
+| {{mapping| 301 477 }}
 | +0.0927
 | 0.0927
@@ Line 33: / Line 33: @@
 | 2.3.5
 | 32805/32768, {{monzo| 3 45 -32 }}
-| [{{val| 301 477 699 }}]
+| {{mapping| 301 477 699 }}
 | +0.0048
 | 0.1456
@@ Line 40: / Line 40: @@
 | 2.3.5.7
 | 2401/2400, 32805/32768, 1959552/1953125
-| [{{val| 301 477 699 845 }}]
+| {{mapping| 301 477 699 845 }}
 | +0.0085
 | 0.1262
@@ Line 47: / Line 47: @@
 | 2.3.5.7.11
 | 2401/2400, 3025/3024, 5632/5625, 8019/8000
-| [{{val| 301 477 699 845 1041 }}]
+| {{mapping| 301 477 699 845 1041 }}
 | +0.0734
 | 0.1720
@@ Line 54: / Line 54: @@
 | 2.3.5.7.11.13
 | 729/728, 847/845, 1001/1000, 1716/1715, 3025/3024
-| [{{val| 301 477 699 845 1041 1114 }}]
+| {{mapping| 301 477 699 845 1041 1114 }}
 | +0.0310
 | 0.1834
@@ Line 61: / Line 61: @@
 | 2.3.5.7.11.13.17
 | 561/560, 729/728, 833/832, 847/845, 1001/1000, 1089/1088
-| [{{val| 301 477 699 845 1041 1114 1230 }}]
+| {{mapping| 301 477 699 845 1041 1114 1230 }}
 | +0.0721
 | 0.1973
@@ Line 71: / Line 71: @@
 |+Table of rank-2 temperaments by generator
 ! Periods<br>per 8ve
-! Generator<br>(Reduced)
+! Generator*
-! Cents<br>(Reduced)
+! Cents*
-! Associated<br>Ratio
+! Associated<br>Ratio*
 ! Temperaments
 |-
@@ Line 118: / Line 118: @@
 | [[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 -->
 [[Category:Meridic]]