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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|275}}
{{ED intro}}


== Theory ==
== Theory ==
If harmonic 5 is used, 275et tends very sharp. It tempers out {{monzo| 24 -21 4 }} ([[vulture comma]]) and {{monzo| 19 10 -15 }} ([[trisedodge comma]]) in the 5-limit; [[6144/6125]] and [[10976/10935]] in the 7-limit.  
If [[harmonic]] [[5/1|5]] is used, 275et tends very sharp. It [[tempering out|tempers out]] {{monzo| 24 -21 4 }} ([[vulture comma]]) and {{monzo| 19 10 -15 }} (trisedodge comma) in the 5-limit; [[6144/6125]] and [[10976/10935]] in the 7-limit.  


The 275e val {{val| 275 436 639 772 '''952''' }} being the best, tempers out [[441/440]], [[4000/3993]], [[14700/14641]], and [[19712/19683]]. This can be extended to the 13-limit through [[364/363]], [[676/675]], [[1001/1000]], and [[2080/2079]].  
The 275e val {{val| 275 436 639 772 '''952''' }} being the best, tempers out [[441/440]], [[4000/3993]], [[14700/14641]], and [[19712/19683]]. This can be extended to the 13-limit through [[364/363]], [[676/675]], [[1001/1000]], [[1575/1573]] and [[2080/2079]].  


The 275 val {{val| 275 436 639 772 '''951''' }} tempers out [[3025/3024]], [[3773/3750]], [[8019/8000]]. This can be extended to the 13-limit through [[352/351]], 676/675, [[1716/1715]], [[2200/2197]], and [[3584/3575]].  
The 275 val {{val| 275 436 639 772 '''951''' }} tempers out [[3025/3024]], 3773/3750, [[8019/8000]]. This can be extended to the 13-limit through [[352/351]], 676/675, [[1716/1715]], [[2200/2197]], and 3584/3575.  


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|275|intervals=prime|columns=11}}
{{Harmonics in equal|275|intervals=prime}}


[[Category:Equal divisions of the octave]]
=== Subsets and supersets ===
Since 275 factors into {{factorisation|275}}, 275edo has subset edos {{EDOs| 5, 11, 25 and 55 }}.
 
== 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| 436 -275 }}
| {{mapping| 275 436 }}
| −0.1863
| 0.1862
| 4.27
|-
| 2.3.5
| {{monzo| 24 -21 4 }}, {{monzo| 19 10 -15 }}
| {{mapping| 275 436 639 }}
| −0.4184
| 0.3618
| 8.29
|-
| 2.3.5.7
| 6144/6125, 10976/10935, 9882516/9765625
| {{mapping| 275 436 639 772 }}
| −0.3051
| 0.3698
| 8.48
|-
| 2.3.5.7.11
| 441/440, 4000/3993, 6144/6125, 10976/10935
| {{mapping| 275 436 639 772 952 }} (275e)
| −0.4096
| 0.3912
| 8.97
|-
| 2.3.5.7.11.13
| 364/363, 441/440, 676/675, 6144/6125, 10976/10935
| {{mapping| 275 436 639 772 952 1018 }} (275e)
| −0.4158
| 0.3574
| 8.19
|}
 
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br />per 8ve
! Generator*
! Cents*
! Associated<br />ratio*
! Temperaments
|-
| 1
| 6\275
| 26.18
| 1594323/1562500
| [[Sfourth]] (5-limit)
|-
| 1
| 109\275
| 485.64
| 320/243
| [[Vulture]] (5-limit)
|-
| 1
| 128\275
| 558.55
| 112/81
| [[Condor]] (275e)
|-
| 5
| 17\275
| 74.18
| 25/24
| [[Countdown]] (275e)
|-
| 11
| 114\275<br />(11\275)
| 497.45<br />(48.00)
| 4/3<br />(36/35)
| [[Hendecatonic]]
|}
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
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