1289edo: Difference between revisions

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== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{{comma basis begin}}
! 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
| 2.3
Line 32: Line 24:
| {{monzo|-16 35 -17}}, {{monzo|91 -12 -31}}
| {{monzo|-16 35 -17}}, {{monzo|91 -12 -31}}
| {{mapping|1289 2043 2993}}
| {{mapping|1289 2043 2993}}
| -0.0014
| &minus;0.0014
| 0.0097
| 0.0097
| 1.04
| 1.04
Line 39: Line 31:
| 2460375/2458624, 78125000/78121827, 12884901888/12867859375
| 2460375/2458624, 78125000/78121827, 12884901888/12867859375
| {{mapping|1289 2043 2993 3619}}
| {{mapping|1289 2043 2993 3619}}
| -0.0275
| &minus;0.0275
| 0.0461
| 0.0461
| 4.95
| 4.95
Line 46: Line 38:
| 3025/3024, 180224/180075, 2460375/2458624, 50014503/50000000
| 3025/3024, 180224/180075, 2460375/2458624, 50014503/50000000
| {{mapping|1289 2043 2993 3619 4459}}
| {{mapping|1289 2043 2993 3619 4459}}
| -0.0109
| &minus;0.0109
| 0.0530
| 0.0530
| 5.69
| 5.69
Line 53: Line 45:
| 3025/3024, 1716/1715, 4096/4095, 91125/91091, 5282739/5281250
| 3025/3024, 1716/1715, 4096/4095, 91125/91091, 5282739/5281250
| {{mapping|1289 2043 2993 3619 4459 4770}}
| {{mapping|1289 2043 2993 3619 4459 4770}}
| -0.0146
| &minus;0.0146
| 0.0491
| 0.0491
| 5.27
| 5.27
Line 60: Line 52:
| 3025/3024, 1716/1715, 4096/4095, 2500/2499, 37180/37179, 3536379/3536000
| 3025/3024, 1716/1715, 4096/4095, 2500/2499, 37180/37179, 3536379/3536000
| {{mapping|1289 2043 2993 3619 4459 4770 5269}}
| {{mapping|1289 2043 2993 3619 4459 4770 5269}}
| -0.0210
| &minus;0.0210
| 0.0481
| 0.0481
| 5.17
| 5.17
Line 67: Line 59:
| 3025/3024, 1716/1715, 2376/2375, 4096/4095, 2500/2499, 270864/270725, 75735/75712
| 3025/3024, 1716/1715, 2376/2375, 4096/4095, 2500/2499, 270864/270725, 75735/75712
| {{mapping|1289 2043 2993 3619 4459 4770 5269 5476}}
| {{mapping|1289 2043 2993 3619 4459 4770 5269 5476}}
| -0.0299
| &minus;0.0299
| 0.0508
| 0.0508
| 5.46
| 5.46
Line 73: Line 65:


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
| 1
| 1
Line 98: Line 84:
| 8388608/7381125
| 8388608/7381125
| [[Fortune]]
| [[Fortune]]
|}
{{rank-2 end}}
 
{{orf}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct

Revision as of 03:20, 16 November 2024

← 1288edo 1289edo 1290edo →
Prime factorization 1289 (prime)
Step size 0.930954 ¢ 
Fifth 754\1289 (701.939 ¢)
Semitones (A1:m2) 122:97 (113.6 ¢ : 90.3 ¢)
Consistency limit 9
Distinct consistency limit 9

Template:EDO intro

Theory

1289edo is consistent to the 9-odd-limit. As an equal temperament, it tempers out [-16 35 -17⟩ (minortone comma) in the 5-limit. Using the patent val, it tempers out 3025/3024, 180224/180075, 2460375/2458624 and 50014503/50000000 in the 11-limit; 1716/1715, 4096/4095, 91125/91091 and 5282739/5281250 in the 13-limit. In the 2.3.13.23.29.31 subgroup it tempers out 19344/19343, in the 2.3.5.7.11.23.31 subgroup 19251/19250.

Prime harmonics

Approximation of prime harmonics in 1289edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.016 +0.032 +0.297 -0.193 +0.124 +0.242 +0.392 +0.120 +0.058 +0.038
Relative (%) +0.0 -1.7 +3.5 +32.0 -20.7 +13.3 +26.0 +42.1 +12.9 +6.2 +4.1
Steps
(reduced) 		1289
(0) 		2043
(754) 		2993
(415) 		3619
(1041) 		4459
(592) 		4770
(903) 		5269
(113) 		5476
(320) 		5831
(675) 		6262
(1106) 		6386
(1230)

Subsets and supersets

1289edo is the 209th prime edo.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [-2043 1289⟩ | [⟨1289 2043]] | +0.0049 | 0.0049 | 0.53 |- | 2.3.5 | [-16 35 -17⟩, [91 -12 -31⟩ | [⟨1289 2043 2993]] | −0.0014 | 0.0097 | 1.04 |- | 2.3.5.7 | 2460375/2458624, 78125000/78121827, 12884901888/12867859375 | [⟨1289 2043 2993 3619]] | −0.0275 | 0.0461 | 4.95 |- | 2.3.5.7.11 | 3025/3024, 180224/180075, 2460375/2458624, 50014503/50000000 | [⟨1289 2043 2993 3619 4459]] | −0.0109 | 0.0530 | 5.69 |- | 2.3.5.7.11.13 | 3025/3024, 1716/1715, 4096/4095, 91125/91091, 5282739/5281250 | [⟨1289 2043 2993 3619 4459 4770]] | −0.0146 | 0.0491 | 5.27 |- | 2.3.5.7.11.13.17 | 3025/3024, 1716/1715, 4096/4095, 2500/2499, 37180/37179, 3536379/3536000 | [⟨1289 2043 2993 3619 4459 4770 5269]] | −0.0210 | 0.0481 | 5.17 |- | 2.3.5.7.11.13.17.19 | 3025/3024, 1716/1715, 2376/2375, 4096/4095, 2500/2499, 270864/270725, 75735/75712 | [⟨1289 2043 2993 3619 4459 4770 5269 5476]] | −0.0299 | 0.0508 | 5.46 |}

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 142\1289 | 132.196 | [-38 5 13⟩ | Astro |- | 1 | 196\1289 | 182.467 | 10/9 | Minortone |- | 1 | 238\1289 | 221.567 | 8388608/7381125 | Fortune Template:Rank-2 end Template:Orf

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