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'''16ED5/2''' is the equal division of the [[5/2]] interval into 16 parts of 99.1446 [[cent]]s each. This is the scale which occurs as the dominant reformed Mixolydian mode tuned as an equal division of a just interval.
{{Infobox ET}}
'''16ED5/2''' is the equal division of the [[5/2]] interval into 16 parts of 99.1446 [[cent]]s each. 16 equal divisions of the just major tenth is not a "real" xenharmonic tuning; it is a slightly compressed version of the normal [[12edo|12-tone scale]].
== Intervals ==
{| class="wikitable"
|+
! Degrees
! colspan="3" | Enneatonic
! Cents
|-
| 1
| 1#/2b
| colspan="2" | F#/Gb
| 99.145
|-
| 2
| 2
| colspan="2" | G
| 198.289
|-
| 3
| 2#/3b
| G#/Jb
| ''G#/Ab''
| 297.433
|-
| 4
| 3
| J
| ''A''
| 396.578
|-
| 5
| 3#/4b
| J#/Ab
| ''A#/Bb''
| 495.723
|-
| 6
| 4
| A
| ''B''
| 594.868
|-
| 7
| 5
| B
| ''H''
| 694.012
|-
| 8
| 5#/6b
| B#/Hb
| ''H#/Cb''
| 793.157
|-
| 9
| 6
| H
| ''C''
| 892.3015
|-
| 10
| 6#/7b
| H#/Cb
| ''C#/Db''
| 991.446
|-
| 11
| 7
| C
| ''D''
| 1090.591
|-
| 12
| 7#/8b
| C#/Db
| ''D#/Sb''
| 1189.735
|-
| 13
| 8
| D
| ''S''
| 1288.88
|-
| 14
| 8#/9b
| D#/Eb
| ''S#/Eb''
| 1388.0245
|-
| 15
| 9
| colspan="2" | E
| 1487.169
|-
| 16
| 1
| colspan="2" | F
| 1586.314
|}
 
== Harmonics ==
{{Harmonics in equal
| steps = 16
| num = 5
| denom = 2
}}
{{Harmonics in equal
| steps = 16
| num = 5
| denom = 2
| start = 12
| collapsed = 1
}}
 
== Regular temperaments ==
{{Main| Quintaleap family }}
 
16ed5/2 can also be thought of as a [[generator]] of the 2.3.5.17.19 [[subgroup temperament]] which tempers out 256/255, 361/360, and 4624/4617, which is a [[cluster temperament]] with 12 clusters of notes in an octave (''quintaleap'' temperament). This temperament is supported by {{Optimal ET sequence| 12-, 109-, 121-, 133-, 145- }}, and [[157edo]].
 
Tempering out 400/399 (equating 20/19 and 21/20) leads to ''[[quintupole]]'' (12&121), and tempering out 476/475 (equating 19/17 with 28/25) leads to ''[[quinticosiennic]]'' (12&145).
 
Another temperament related to 16ed5/2 is ''[[quintapole]]'' (12&85). It is practically identical to the [[18/17s equal temperament #Related temperament|Galilei tuning]], which is generated by the ratios 2/1 and 18/17.
 
== Scale tree ==
Ed5/2 scales can be approximated in [[EDO]]s by subdividing their approximations of 5/2.


== Intervals ==
{| class="wikitable"
{| class="wikitable"
|+
|+
!Degrees
! colspan="4" |Major tenth
! colspan="3" |Enneatonic
! Period
!ed38\29
!Notes
!Golden
|-
!ed5/2
|9\7
!ed(7φ+6)\5(φ+1)
|
!ed4\3=''r¢''
|
|
|96.429
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|-
|-
|1
|
|1#/2b
|31\24
| colspan="2" |F#/Gb
|
|98.276
|
|98.3795
|96.875
|99.145
|
|99.2705
|''100''
|-
|-
|2
|22\17
|2
|
| colspan="2" |G
|
|196.552
|
|196.759
|97.059
|198.289
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|198.541
|''200''
|-
|-
|3
|
|2#/3b
|35\27
|G#/Jb
|
|''G#/Ab''
|
|294.828
|97.{{Overline|2}}
|295.138
|
|297.433
|297.8115
|''300''
|-
|-
|4
| 13\10
|3
|
|J
|
|''A''
|
|393.103
|97.5
|393.518
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|396.578
|397.082
|''400''
|-
|-
|5
|17\13
|3#/4b
|
|J#/Ab
|
|''A#/Bb''
|
|491.379
|98.077
|491.897
|
|495.723
|496.3525
|''500''
|-
|-
|6
|21\16
|4
|
|A
|
|''B''
|
|589.655
|98.4375
|590.277
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|594.868
|595.623
|''600''
|-
|-
|7
|
|5
|25\19
|B
|
|''H''
|
|687.931
|98.684
|688.656
|
|694.012
|694.894
|''700''
|-
|-
|8
|
|5#/6b
|
|B#/Hb
|29\22
|''H#/Cb''
|
|786.207
|98.8{{Overline|63}}
|787.036
|
|793.157
|794.164
|''800''
|-
|-
|9
|
|6
|
|H
|
|''C''
|33\25
|884.483
|99
|885.415
|
|892.3015
|893.435
|''900''
|-
|-
|10
|4\3
|6#/7b
|
|H#/Cb
|
|''C#/Db''
|
|982.759
|100
|983.795
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|991.446
|992.705
|''1000''
|-
|-
|11
|
|7
| 19\14
|C
|
|''D''
|
|1081.0345
|101.786
|1082.174
|
|1090.591
|1091.976
|''1100''
|-
|-
|12
|15\11
|7#/8b
|
|C#/Db
|
|''D#/Sb''
|
|1179.31
|102.{{Overline|27}}
|1180.554
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|1189.735
|1191.246
|''1200''
|-
|-
|13
|
|8
|26\19
|D
|
|''S''
|
|1277.586
|102.632
|1278.933
|
|1288.88
|1290.517
|''1300''
|-
|-
|14
|11\8
|8#/9b
|
|D#/Eb
|
|''S#/Eb''
|
|1375.862
|103.125
|1377.313
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|1388.0245
|1389.787
|''1400''
|-
|-
|15
|
|9
|18\13
| colspan="2" |E
|
|1474.138
|
|1475.692
|103.846
|1487.169
|
|1489.058
|''1500''
|-
|-
|16
|
|1
|
| colspan="2" |F
|25\18
|1572.414
|
|1574.0715
|104.1{{Overline|6}}
|1586.314
|
|1588.328
|''1600''
|}
|}
Coincidentally, 133 steps of the pyrite edX of this size exceed 11 octaves by only 2.978¢.


== 16ed5/2 as a generator ==
== See also ==
'''<font style="font-size: 1.35em">Trisa-quingu (12&amp;121)</font>'''<br>
* [[12edo|12EDO]] - relative EDO
'''<font style="font-size: 1.2em">5-limit</font>'''<br>
* [[28ed5|28ED5]] - relative ED5
Comma: {{monzo|37 -16 -5}}<br>
* [[34ed7|34ED7]] - relative ED7
Mapping: [{{val|1 2 1}}, {{val|0 -5 16}}]<br>
* [[40ed10|40ED10]] - relative ED10
POTE generator: ~135/128 = 99.267<br>
* [[42ed11|42ED11]] - relative ED11
Vals: 12, 85, 97, 109, 121, 133, 278c, 411bc, 544bc<br>
* [[18/17 equal-step tuning|AS18/17]] - relative [[AS|ambitonal sequence]]
Badness: 0.444506<br><br>
'''<font style="font-size: 1.35em">[[Octagar temperaments #Quintupole|Quintupole]] (12&amp;121)</font>'''<br>
{{See also|34ed7 #34ed7 as a generator}}
'''<font style="font-size: 1.2em">7-limit</font>'''<br>
Comma list: 4000/3969, 458752/455625<br>
Mapping: [{{val|1 2 1 0}}, {{val|0 -5 16 34}}]<br>
POTE generator: ~135/128 = 99.175<br>
Vals: 12, 97, 109, 121<br>
Badness: 0.111620<br><br>
'''<font style="font-size: 1.2em">11-limit</font>'''<br>
Comma list: 896/891, 1375/1372, 4375/4356<br>
Mapping: [{{val|1 2 1 0 -1}}, {{val|0 -5 16 34 54}}]<br>
POTE generator: ~132/125 = 99.156<br>
Vals: 12, 109, 121, 351bde, 472bdee<br>
Badness: 0.056501<br><br>
'''<font style="font-size: 1.35em">[[Marvel temperaments|12&amp;85 temperament]]</font>'''<br>
'''<font style="font-size: 1.2em">7-limit</font>'''<br>
Comma list: 225/224, 7812500/7411887<br>
Mapping: [{{val|1 2 1 1}}, {{val|0 -5 16 22}}]<br>
POTE generator: ~21/20 = 98.994<br>
Vals: 12, 73c, 85, 97d<br>
Badness: 0.192498<br><br>
'''<font style="font-size: 1.2em">11-limit</font>'''<br>
Comma list: 100/99, 225/224, 85184/84035<br>
Mapping: [{{val|1 2 1 1 0}}, {{val|0 -5 16 22 42}}]<br>
POTE generator: ~21/20 = 98.954<br>
Vals: 12, 73ce, 85, 97d<br>
Badness: 0.104353<br><br>


[[Category:EdX]]
[[Category:Nonoctave]]
[[Category:Nonoctave]]
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