1547edo: Difference between revisions

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==Theory==
==Theory==
{{harmonics in equal|1547}}
{{harmonics in equal|1547}}
1547edo is excellent in the 7-limit.
1547edo is excellent in the 7-limit. It tempers out [[4375/4374]] and it is a member of the [[optimal GPV sequence]] for the rank-3 temperament associated with this comma.


In the 5-limit, it supports [[gross]].  
In the 5-limit, it supports [[gross]].  
Line 13: Line 13:
1547's divisors are {{EDOs|1, 7, 13, 17, 91, 119, 221}}.
1547's divisors are {{EDOs|1, 7, 13, 17, 91, 119, 221}}.
==Regular temperament properties==
==Regular temperament properties==
===Rank-2 temperaments by generator===
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal 8ve
Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|2452 -1547}}
|[{{val|1547 2542}}]
|<nowiki>-0.015</nowiki>
|0.015
|
|-
|2.3.5
|<nowiki>-52 -17 34, 40 -56 21</nowiki>
|[{{val|1547 2542 3592}}]
|<nowiki>-0.008</nowiki>
|
|
|-
|2.3.5.7
|4375/4374, -1   4 11 -11, 46 -14 -3  -6
|[{{val|1547 2542 3592 4343}}]
| -0.007
|0.014
|
|-
|2.3.5.7.11
|4375/4374, 151263/151250, 820125/819896, 2097152/2096325
|[{{val|1547 2542 3592 4343 5352}}]
|<nowiki>-0.017</nowiki>
|0.024
|
|-
|2.3.5.7.11.13
|4375/4374, 4096/4095, 10648/10647, 91125/91091, 105644/105625
|[{{val|1547 2542 3592 4343 5352 5725}}]
|<nowiki>-0.029</nowiki>
|0.034
|
|}
===Rank-2 temperaments===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+Table of rank-2 temperaments by generator

Revision as of 13:04, 5 January 2023

← 1546edo 1547edo 1548edo →
Prime factorization 7 × 13 × 17
Step size 0.775695 ¢ 
Fifth 905\1547 (702.004 ¢)
Semitones (A1:m2) 147:116 (114 ¢ : 89.98 ¢)
Consistency limit 15
Distinct consistency limit 15

Template:EDO intro

Theory

Approximation of prime harmonics in 1547edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.049 -0.018 +0.017 +0.201 +0.326 -0.237 +0.354 +0.039 -0.230 -0.110
Relative (%) +0.0 +6.3 -2.3 +2.2 +25.9 +42.0 -30.5 +45.6 +5.0 -29.7 -14.2
Steps
(reduced) 		1547
(0) 		2452
(905) 		3592
(498) 		4343
(1249) 		5352
(711) 		5725
(1084) 		6323
(135) 		6572
(384) 		6998
(810) 		7515
(1327) 		7664
(1476)

1547edo is excellent in the 7-limit. It tempers out 4375/4374 and it is a member of the optimal GPV sequence for the rank-3 temperament associated with this comma.

In the 5-limit, it supports gross.

In the 7-limit, it supports semidimi and brahmagupta.

In the 17-limit, it supports 91th-octave temperament protactinium.

1547's divisors are 1, 7, 13, 17, 91, 119, 221.

Regular temperament properties

Subgroup Comma List Mapping Optimal 8ve

Stretch (¢)

Tuning Error
Absolute (¢) Relative (%)
2.3 [2452 -1547⟩ [⟨1547 2542]] -0.015 0.015
2.3.5 -52 -17 34, 40 -56 21 [⟨1547 2542 3592]] -0.008
2.3.5.7 4375/4374, -1   4 11 -11, 46 -14 -3  -6 [⟨1547 2542 3592 4343]] -0.007 0.014
2.3.5.7.11 4375/4374, 151263/151250, 820125/819896, 2097152/2096325 [⟨1547 2542 3592 4343 5352]] -0.017 0.024
2.3.5.7.11.13 4375/4374, 4096/4095, 10648/10647, 91125/91091, 105644/105625 [⟨1547 2542 3592 4343 5352 5725]] -0.029 0.034

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator
(reduced) 		Cents
(reduced) 		Associated
ratio 		Temperaments
1 118\1547 91.532 [9 -32 18> Gross
1 579\1547 449.127 35/27 Semidimi
7 670\1547
(7\1547) 		519.715
(5.429) 		27/20
(325/324) 		Brahmagupta
91 905\1547
(4\1547) 		702.003
(3.103) 		3/2
(?) 		Protactinium
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