547edo: Difference between revisions
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{{EDO intro|547}} | {{EDO intro|547}} | ||
== Theory == | |||
547edo is a strong [[5-limit]] system, tuning [[fortune]], [[gammic]], and [[vavoom]] temperaments. Past the 5-limit, good subgroups of choice include 2.3.5.13.17.31, or 2.3.5.77.29/23. | 547edo is a strong [[5-limit]] system, tuning [[fortune]], [[gammic]], and [[vavoom]] temperaments. Past the 5-limit, good subgroups of choice include 2.3.5.13.17.31, or 2.3.5.77.29/23. | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
547edo is the 101st [[prime edo]]. 1641edo, which divides edostep in 3, corrects the mapping for the 11-limit. | 547edo is the 101st [[prime edo]]. 1641edo, which divides edostep in 3, corrects the mapping for the 11-limit. | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |[[Subgroup]] | |||
! rowspan="2" |[[Comma list|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|867 -547}} | |||
|{{mapping|547 867}} | |||
| -0.0177 | |||
| 0.0177 | |||
| 0.81 | |||
|- | |||
|2.3.5 | |||
|{{monzo|39 -29 3}}, {{monzo|-29 -11 20}} | |||
|{{mapping|547 867 1270}} | |||
| +0.0180 | |||
| 0.0525 | |||
| 2.39 | |||
|- | |||
|2.3.5.7 | |||
|4375/4374, 4096000/4084101, 23066015625/23018340352 | |||
|{{mapping|547 867 1270 1536}} | |||
| -0.0601 | |||
| 0.1428 | |||
| 6.51 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br>Ratio* | |||
! Temperaments | |||
|- | |||
|1 | |||
|16\547 | |||
|35.10 | |||
|1990656/1953125 | |||
|[[Gammic]] | |||
|- | |||
|1 | |||
|51\547 | |||
|111.88 | |||
|16/15 | |||
|[[Vavoom]] | |||
|- | |||
|1 | |||
|101\547 | |||
|221.57 | |||
|8388608/7381125 | |||
|[[Fortune]] | |||
|- | |||
|1 | |||
|105\547 | |||
|230.35 | |||
|8/7 | |||
|[[Gamera]] | |||
|- | |||
|1 | |||
|258\547 | |||
|566.00 | |||
|104/75 | |||
|[[Tricot]] | |||
|} | |||
Revision as of 06:42, 12 December 2023
| ← 546edo | 547edo | 548edo → |
Theory
547edo is a strong 5-limit system, tuning fortune, gammic, and vavoom temperaments. Past the 5-limit, good subgroups of choice include 2.3.5.13.17.31, or 2.3.5.77.29/23.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | +0.056 | -0.208 | +0.827 | -0.678 | -0.308 | +0.346 | +0.842 | -0.852 | -0.692 | +0.120 |
| Relative (%) | +0.0 | +2.6 | -9.5 | +37.7 | -30.9 | -14.1 | +15.8 | +38.4 | -38.8 | -31.6 | +5.5 | |
| Steps (reduced) |
547 (0) |
867 (320) |
1270 (176) |
1536 (442) |
1892 (251) |
2024 (383) |
2236 (48) |
2324 (136) |
2474 (286) |
2657 (469) |
2710 (522) | |
Subsets and supersets
547edo is the 101st prime edo. 1641edo, which divides edostep in 3, corrects the mapping for the 11-limit.
Regular temperament properties
| Subgroup | Comma List | Mapping | Optimal 8ve Stretch (¢) |
Tuning Error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [867 -547⟩ | [⟨547 867]] | -0.0177 | 0.0177 | 0.81 |
| 2.3.5 | [39 -29 3⟩, [-29 -11 20⟩ | [⟨547 867 1270]] | +0.0180 | 0.0525 | 2.39 |
| 2.3.5.7 | 4375/4374, 4096000/4084101, 23066015625/23018340352 | [⟨547 867 1270 1536]] | -0.0601 | 0.1428 | 6.51 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 16\547 | 35.10 | 1990656/1953125 | Gammic |
| 1 | 51\547 | 111.88 | 16/15 | Vavoom |
| 1 | 101\547 | 221.57 | 8388608/7381125 | Fortune |
| 1 | 105\547 | 230.35 | 8/7 | Gamera |
| 1 | 258\547 | 566.00 | 104/75 | Tricot |