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=<span style="color: #003838; font-family: 'Times New Roman',Times,serif; font-size: 113%;">193 tone equal temperament</span>=
{{Infobox ET
| Prime factorization = 193 (prime)
| Step size = 6.21762¢
| Fifth = 113\193 (702.59¢)
| Semitones = 19:14 (118.13¢ : 87.05¢)
| Consistency = 11
}}
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 6.21762 [[cent]]s each.


The '''193EDO''' divides the octave into 193 equal parts of 6.21762 cents each. It provides the [[Optimal_patent_val|optimal patent val]] for [[Kleismic_family#Sqrtphi|sqrtphi temperament]] in the 13-, 17- and 19- limits, and for 13-limit [[Swetismic_temperaments#Minos|minos]] and [[Mirkwai_family#Indra|vish]] temperaments.
== Theory ==
193edo provides the [[optimal patent val]] for [[Kleismic_family #Sqrtphi|sqrtphi temperament]] in the 13-, 17- and 19- limits, and for 13-limit [[Swetismic_temperaments #Minos|minos]] and [[Mirkwai_family #Indra|vish]] temperaments. It is the 44th [[prime_numbers|prime]] EDO.


=== Prime harmonics ===
{{Primes in edo|193}}
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal 8ve <br>stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
| 2.3
| {{monzo| 306 -193 }}
| [{{val| 193 306 }}]
| -0.2005
| 0.2005
| 3.225
|-
| 2.3.5
| 15625/15552, {{monzo|50 -33 1}}
| [{{val| 193 306 448 }}]
| -0.0158
| 0.3084
| 4.960
|-
| 2.3.5.7
| 5120/5103, 15625/15552, 16875/16807
| [{{val| 193 306 448 542 }}]
| -0.1118
| 0.3146
| 5.059
|-
| 2.3.5.7.11
| 540/539, 1375/1372, 4375/4356, 5120/5103
| [{{val| 193 306 448 542 668 }}]
| -0.2080
| 0.3408
| 5.481
|-
| 2.3.5.7.11.13
| 325/324, 364/363, 540/539, 625/624, 4096/4095
| [{{val| 193 306 448 542 668 714 }}]
| -0.1216
| 0.3662
| 5.890
|-
| 2.3.5.7.11.13.17
| 325/324, 364/363, 375/374, 442/441, 595/594, 4096/4095
| [{{val| 193 306 448 542 668 714 789 }}]
| -0.1302
| 0.3397
| 5.464
|-
| 2.3.5.7.11.13.17.19
| 325/324, 364/363, 375/374, 400/399, 442/441, 595/594, 1216/1215
| [{{val| 193 306 448 542 668 714 789 820 }}]
| -0.1414
| 0.3191
| 5.133
|}
== Sqrtphi scale in 193edo ==
Approximation of the intervals:
Approximation of the intervals:


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Phi: '''134\193''' (833.16062 cents), both inside in the [[7L_2s|superdiatonic]] scale: 25 25 25 9 25 25 25 25 9
Phi: '''134\193''' (833.16062 cents), both inside in the [[7L_2s|superdiatonic]] scale: 25 25 25 9 25 25 25 25 9


193edo is the 44th [[prime_numbers|prime]] EDO.
[[Category:Sqrtphi]]
 
[[Category:sqrtphi]]
[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
[[Category:Prime EDO]]
[[Category:Prime EDO]]
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