193edo: Difference between revisions
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The '''193 equal divisions of the octave''' ('''193edo'''), or the '''193(-tone) equal temperament''' ('''193tet''', '''193et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 193 parts of about 6. | The '''193 equal divisions of the octave''' ('''193edo'''), or the '''193(-tone) equal temperament''' ('''193tet''', '''193et''') when viewed from a [[regular temperament]] perspective, is the [[EDO|equal division of the octave]] into 193 parts of about 6.22 [[cent]]s each. | ||
== Theory == | == Theory == | ||
193edo provides the [[optimal patent val]] for [[ | 193edo provides the [[optimal patent val]] for the [[sqrtphi]] temperament in the 13-, 17- and 19-limits, and for the 13-limit [[Swetismic temperaments #Minos|minos]] and [[Mirkwai family #Indra|vish]] temperaments. It is the 44th [[prime edo]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{ | {{Harmonics in equal|193}} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
| Line 30: | Line 30: | ||
| -0.2005 | | -0.2005 | ||
| 0.2005 | | 0.2005 | ||
| 3. | | 3.23 | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| Line 37: | Line 37: | ||
| -0.0158 | | -0.0158 | ||
| 0.3084 | | 0.3084 | ||
| 4. | | 4.96 | ||
|- | |- | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| Line 44: | Line 44: | ||
| -0.1118 | | -0.1118 | ||
| 0.3146 | | 0.3146 | ||
| 5. | | 5.06 | ||
|- | |- | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| Line 51: | Line 51: | ||
| -0.2080 | | -0.2080 | ||
| 0.3408 | | 0.3408 | ||
| 5. | | 5.48 | ||
|- | |- | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| Line 58: | Line 58: | ||
| -0.1216 | | -0.1216 | ||
| 0.3662 | | 0.3662 | ||
| 5. | | 5.89 | ||
|- | |- | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| Line 65: | Line 65: | ||
| -0.1302 | | -0.1302 | ||
| 0.3397 | | 0.3397 | ||
| 5. | | 5.46 | ||
|- | |- | ||
| 2.3.5.7.11.13.17.19 | | 2.3.5.7.11.13.17.19 | ||
| Line 72: | Line 72: | ||
| -0.1414 | | -0.1414 | ||
| 0.3191 | | 0.3191 | ||
| 5. | | 5.13 | ||
|} | |} | ||
== | == Scales == | ||
Approximation of | * Approximation of sqrt (π): '''159\193''' (988.60104 cents), and of φ: '''134\193''' (833.16062 cents), both inside in the [[7L 2s|superdiatonic]] scale: 25 25 25 9 25 25 25 25 9 | ||
[[Category:Sqrtphi]] | [[Category:Sqrtphi]] | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||