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. It is a strong 7-limit system, and distinctly consistent through the 17-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 [[Schismatic family #Sesquiquartififths|sesquiquartififths]] temperament.

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

~~301~~ is a ~~composite number~~, ~~since 301 = 7 * 43~~. ~~This is related to~~ the ~~proposal of~~ the ~~deaf French mathematician and acoustician~~ [~~https:~~//~~en.wikipedia.org~~/~~wiki~~/~~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~~.

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

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

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-'''301EDO''' is the [[EDO|equal division of the octave]] into 301 parts of 3.98671 [[cent]]s each. It is a strong 7-limit system, and distinctly consistent through the 17-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 [[Schismatic family #Sesquiquartififths|sesquiquartififths]] temperament.
+'''301edo''' is the [[EDO|equal division of the octave]] into 301 parts of 3.98671 [[cent]]s each.
-is a composite number, since 301 = 7 * 43. This is related to the proposal of the deaf French mathematician and acoustician [https://en.wikipedia.org/wiki/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.
+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 also tempers out {{monzo|168 -43 -43}} and 5250987/5242880, so it supports the [[Mitonismic temperaments #Meridic|meridic 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.
+edo also tempers out {{monzo| 168 -43 -43 }} and 5250987/5242880, so it supports the [[Mitonismic temperaments #Meridic|meridic temperament]].
 {{Primes in edo|edo=301|columns=11|prec=3}}