296edo: Difference between revisions
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The '''296 equal temperament''' | {{Infobox ET | ||
| Prime factorization = 2<sup>3</sup> × 37 | |||
| Step size = 4.05405¢ | |||
| Fifth = 173\296 (702.35¢) | |||
| Semitones = 27:23 (109.46¢ : 93.24¢) | |||
| Consistency = 15 | |||
}} | |||
The '''296 equal divisions of the octave''' ('''296edo'''), or the '''296(-tone) equal temperament''' ('''296tet''', '''296et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 296 parts of about 4.05 [[cent]]s each. | |||
== Theory == | |||
In the 5-limit, 296et not only tempers out the [[semicomma]] of 5-limit orwell (orson) temperament, 2109375/2097152, it also provides its [[optimal patent val]], and tempers out the minortone comma, {{monzo| -16 35 -17 }}. It is also an interesting temperament in higher limits, being distinctly consistent through to the 15-odd-limit. In the 7-limit it tempers out [[4375/4374]] and 16875/16807, supporting 7-limit [[octoid]] temperament. In the 11-limit, it tempers out 1375/1372, [[6250/6237]], [[540/539]], [[4000/3993]] and [[3025/3024]], and in the 13-limit [[625/624]], [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], so that it also supports the 11- and 13-limit versions of octoid. | In the 5-limit, 296et not only tempers out the [[semicomma]] of 5-limit orwell (orson) temperament, 2109375/2097152, it also provides its [[optimal patent val]], and tempers out the minortone comma, {{monzo| -16 35 -17 }}. It is also an interesting temperament in higher limits, being distinctly consistent through to the 15-odd-limit. In the 7-limit it tempers out [[4375/4374]] and 16875/16807, supporting 7-limit [[octoid]] temperament. In the 11-limit, it tempers out 1375/1372, [[6250/6237]], [[540/539]], [[4000/3993]] and [[3025/3024]], and in the 13-limit [[625/624]], [[729/728]], [[1575/1573]], [[1716/1715]], [[2080/2079]], so that it also supports the 11- and 13-limit versions of octoid. | ||
Revision as of 13:47, 27 December 2021
| ← 295edo | 296edo | 297edo → |
The 296 equal divisions of the octave (296edo), or the 296(-tone) equal temperament (296tet, 296et) when viewed from a regular temperament perspective, is the equal division of the octave into 296 parts of about 4.05 cents each.
Theory
In the 5-limit, 296et not only tempers out the semicomma of 5-limit orwell (orson) temperament, 2109375/2097152, it also provides its optimal patent val, and tempers out the minortone comma, [-16 35 -17⟩. It is also an interesting temperament in higher limits, being distinctly consistent through to the 15-odd-limit. In the 7-limit it tempers out 4375/4374 and 16875/16807, supporting 7-limit octoid temperament. In the 11-limit, it tempers out 1375/1372, 6250/6237, 540/539, 4000/3993 and 3025/3024, and in the 13-limit 625/624, 729/728, 1575/1573, 1716/1715, 2080/2079, so that it also supports the 11- and 13-limit versions of octoid.
296 is divisible by 2, 4, 8, 37, 74 and 148.
Prime harmonics
Script error: No such module "primes_in_edo".
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-469 296⟩ | [⟨296 469]] | +0.1904 | 0.1905 | 4.70 |
| 2.3.5 | 2109375/2097152, [-16 35 -17⟩ | [⟨296 469 687]] | +0.2962 | 0.2158 | 5.32 |
| 2.3.5.7 | 4375/4374, 16875/16807, 2100875/2097152 | [⟨296 469 687 831]] | +0.2138 | 0.2350 | 5.80 |
| 2.3.5.7.11 | 540/539, 1375/1372, 4000/3993, 2100875/2097152 | [⟨296 469 687 831 1024]] | +0.1691 | 0.2284 | 5.63 |
| 2.3.5.7.11.13 | 540/539, 625/624, 729/728, 1375/1372, 15379/15360 | [⟨296 469 687 831 1024 1095]] | +0.2012 | 0.2206 | 5.44 |