301edo: Difference between revisions

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'''301edo''' is the [[EDO|equal division of the octave]] into 301 parts of 3.98671 [[cent]]s each.

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, [[~~847~~/~~845~~]], [[~~729~~/~~728~~]], [[1001/1000]], [[1716/1715]] in the 13-limit, and 561/560, [[833/832]], [[1089/1088]], [[1156/1155]], 1275/1274 and [[1701/1700]] in the 17-limit. Because it tempers out both 32805/32768 and 2401/2400, it supports the [[sesquiquartififths]] temperament.

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. Because it tempers out both 32805/32768 and 2401/2400, it supports the [[sesquiquartififths]] temperament.

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.

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

=== Prime harmonics ===

== Regular temperament properties ==

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

! rowspan="2" | Subgroup

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

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

! rowspan="2" | Optimal<br>8ve stretch (¢)

! colspan="2" | Tuning error

|-

! [[TE error|Absolute]] (¢)

! [[TE simple badness|Relative]] (%)

|-

| 2.3

| {{monzo| -477 301 }}

| [{{val| 301 477 }}]

| +0.0927

| 0.0927

| 2.33

|-

| 2.3.5

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

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

| +0.0048

| 0.1456

| 3.65

|-

| 2.3.5.7

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

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

| +0.0085

| 0.1262

| 3.17

|-

| 2.3.5.7.11

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

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

| +0.0734

| 0.1720

| 4.31

|-

| 2.3.5.7.11.13

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

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

| +0.0310

| 0.1834

| 4.60

|-

| 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 }}]

| +0.0721

| 0.1973

| 4.95

|}

[[Category:Equal divisions of the octave]]

[[Category:Meridic]]

@@ Line 1: / Line 1: @@
 '''301edo''' is the [[EDO|equal division of the octave]] into 301 parts of 3.98671 [[cent]]s each.
-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, [[847/845]], [[729/728]], [[1001/1000]], [[1716/1715]] in the 13-limit, and 561/560, [[833/832]], [[1089/1088]], [[1156/1155]], 1275/1274 and [[1701/1700]] in the 17-limit. Because it tempers out both 32805/32768 and 2401/2400, it supports the [[sesquiquartififths]] temperament.
+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. Because it tempers out both 32805/32768 and 2401/2400, it supports the [[sesquiquartififths]] temperament.
 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.
@@ Line 7: / Line 7: @@
 edo also tempers out {{monzo| 168 -43 -43 }} and 5250987/5242880, so it supports the [[Mitonismic temperaments #Meridic|meridic temperament]].
+=== Prime harmonics ===
 {{Primes in edo|edo=301|columns=11|prec=3}}
+== Regular temperament properties ==
+{| class="wikitable center-4 center-5 center-6"
+! rowspan="2" | Subgroup
+! rowspan="2" | [[Comma list]]
+! rowspan="2" | [[Mapping]]
+! rowspan="2" | Optimal<br>8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
+|-
+| 2.3
+| {{monzo| -477 301 }}
+| [{{val| 301 477 }}]
+| +0.0927
+| 0.0927
+| 2.33
+|-
+| 2.3.5
+| 32805/32768, {{monzo| 3 45 -32 }}
+| [{{val| 301 477 699 }}]
+| +0.0048
+| 0.1456
+| 3.65
+|-
+| 2.3.5.7
+| 2401/2400, 32805/32768, 1959552/1953125
+| [{{val| 301 477 699 845 }}]
+| +0.0085
+| 0.1262
+| 3.17
+|-
+| 2.3.5.7.11
+| 2401/2400, 3025/3024, 5632/5625, 8019/8000
+| [{{val| 301 477 699 845 1041 }}]
+| +0.0734
+| 0.1720
+| 4.31
+|-
+| 2.3.5.7.11.13
+| 729/728, 847/845, 1001/1000, 1716/1715, 3025/3024
+| [{{val| 301 477 699 845 1041 1114 }}]
+| +0.0310
+| 0.1834
+| 4.60
+|-
+| 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 }}]
+| +0.0721
+| 0.1973
+| 4.95
+|}
 [[Category:Equal divisions of the octave]]
 [[Category:Meridic]]