157edo: Difference between revisions

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=== Prime harmonics ===
=== Prime harmonics ===
{{Primes in edo|157}}
{{Primes in edo|157}}
== 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| 249 -157 }}
| [{{val| 157 249 }}]
| -0.388
| 0.388
| 5.08
|-
| 2.3.5
| 78732/78125, {{val| 37 -16 -5 }}
| [{{val| 157 249 365 }}]
| -0.760
| 0.614
| 8.04
|-
| 2.3.5.7
| 2401/2400, 5120/5103, 78732/78125
| [{{val| 157 249 365 441 }}]
| -0.737
| 0.533
| 6.98
|-
| 2.3.5.7.11
| 176/175, 1331/1323, 2401/2400, 5120/5103
| [{{val| 157 249 365 441 543 }}]
| -0.532
| 0.629
| 8.24
|-
| 2.3.5.7.11.13
| 176/175, 351/350, 847/845, 1331/1323, 2197/2187
| [{{val| 157 249 365 441 543 581 }}]
| -0.454
| 0.600
| 7.86
|-
| 2.3.5.7.11.13.17
| 176/175, 256/255, 351/350, 442/441, 715/714, 2197/2187
| [{{val| 157 249 365 441 543 581 642 }}]
| -0.461
| 0.556
| 7.28
|-
| 2.3.5.7.11.13.17.19
| 176/175, 256/255, 286/285, 351/350, 361/360, 442/441, 476/475
| [{{val| 157 249 365 441 543 581 642 667 }}]
| -0.420
| 0.531
| 6.95
|}
=== Rank-2 temperaments ===
{| class="wikitable center-all right-3 left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per octave
! Generator<br>(reduced)
! Cents<br>(reduced)
! Associated<br>ratio
! Temperament
|-
| 1
| 46\157
| 351.59
| 49/40
| [[Hemififths]]
|-
| 1
| 56\157
| 428.03
| 2800/2187
| [[Osiris]]
|-
| 1
| 58\157
| 443.31
| 49/40
| [[Sensipent]]
|-
| 1
| 64\157
| 489.17
| 250/189
| [[Catafourth]]
|}


[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
[[Category:Prime EDO]]
[[Category:Prime EDO]]

Revision as of 08:35, 16 July 2021

The 157 equal divisions of the octave (157edo), or the 157(-tone) equal temperament (157tet, 157et) when viewed from a regular temperament perspective, is the equal division of the octave into 157 parts of 7.6433 cents each.

Theory

157et tempers out 78732/78125 (sensipent comma) and 137438953472/134521003125 in the 5-limit; 2401/2400, 5120/5103, and 110592/109375 in the 7-limit (supporting the hemififths and the catafourth). Using the patent val, it tempers out 176/175, 1331/1323, 3773/3750 and 8019/8000 in the 11-limit; 351/350, 352/351, 847/845, 1573/1568, and 2197/2187 in the 13-limit.

157edo is the 37th prime EDO.

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 [249 -157⟩ [⟨157 249]] -0.388 0.388 5.08
2.3.5 78732/78125, ⟨37 -16 -5] [⟨157 249 365]] -0.760 0.614 8.04
2.3.5.7 2401/2400, 5120/5103, 78732/78125 [⟨157 249 365 441]] -0.737 0.533 6.98
2.3.5.7.11 176/175, 1331/1323, 2401/2400, 5120/5103 [⟨157 249 365 441 543]] -0.532 0.629 8.24
2.3.5.7.11.13 176/175, 351/350, 847/845, 1331/1323, 2197/2187 [⟨157 249 365 441 543 581]] -0.454 0.600 7.86
2.3.5.7.11.13.17 176/175, 256/255, 351/350, 442/441, 715/714, 2197/2187 [⟨157 249 365 441 543 581 642]] -0.461 0.556 7.28
2.3.5.7.11.13.17.19 176/175, 256/255, 286/285, 351/350, 361/360, 442/441, 476/475 [⟨157 249 365 441 543 581 642 667]] -0.420 0.531 6.95

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per octave 		Generator
(reduced) 		Cents
(reduced) 		Associated
ratio 		Temperament
1 46\157 351.59 49/40 Hemififths
1 56\157 428.03 2800/2187 Osiris
1 58\157 443.31 49/40 Sensipent
1 64\157 489.17 250/189 Catafourth
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