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'''32EDT''' is the [[Edt|equal division of the third harmonic]] into 32 parts of 59.4361 [[cent|cents]] each, corresponding to 20.1898 [[edo]]. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17, and 19 are all sharp. It tempers out 3125/3087 in the 7-limit; 891/875, 1331/1323 and 2475/2401 in the 11-limit; 275/273, 351/343, 729/714, 847/845 and 1575/1573 in the 13-limit; 121/119, 189/197 and 225/221 in the 17-limit (no-twos subgroup). It is the eighth [[The_Riemann_Zeta_Function_and_Tuning#Removing primes|zeta peak tritave division]].
{{Infobox ET}}
'''32EDT''' is the [[Edt|equal division of the third harmonic]] into 32 parts of 59.4361 [[cent]]s each, corresponding to 20.1898 [[edo]]. It has a distinct sharp tendency, in the sense that if 3 is pure, 5, 7, 11, 13, 17, and 19 are all sharp. It tempers out 3125/3087 and 885735/823543 in the 7-limit; 891/875, 1331/1323, and 2475/2401 in the 11-limit; 275/273, 351/343, 729/715, and 847/845 in the 13-limit; 121/119, 189/187, 225/221, 459/455, and 845/833 in the 17-limit; 135/133, 171/169, 247/245, 325/323, and 363/361 in the 19-limit (no-twos subgroup). It is the eighth [[the Riemann zeta function and tuning#Removing primes|zeta peak tritave division]].


=Intervals=
== Harmonics ==
{{Harmonics in equal
| steps = 32
| num = 3
| denom = 1
| columns = 9
| intervals = prime
}}
{{Harmonics in equal
| steps = 32
| num = 3
| denom = 1
| start = 12
| collapsed = 1
| intervals = odd
}}


== Intervals ==
{| class="wikitable"
{| class="wikitable"
|-
|-
! step
! Step
! cents
! [[Cent]]s
! [[Hekt]]s
|-
|-
| | 1
| 1
| | 59.436
| 59.436
| 40.625
|-
|-
| | 2
| 2
| | 118.872
| 118.872
| 81.25
|-
|-
| | 3
| 3
| | 178.308
| 178.308
| 121.875
|-
|-
| | 4
| 4
| | 237.744
| 237.744
| 162.5
|-
|-
| | 5
| 5
| | 297.180
| 297.180
| 203.125
|-
|-
| | 6
| 6
| | 356.617
| 356.617
| 243.75
|-
|-
| | 7
| 7
| | 416.053
| 416.053
| 284.375
|-
|-
| | 8
| 8
| | 475.489
| 475.489
| 325
|-
|-
| | 9
| 9
| | 534.925
| 534.925
| 365.625
|-
|-
| | 10
| 10
| | 594.361
| 594.361
| 406.25
|-
|-
| | 11
| 11
| | 653.797
| 653.797
| 446.875
|-
|-
| | 12
| 12
| | 713.233
| 713.233
| 487.5
|-
|-
| | 13
| 13
| | 772.669
| 772.669
| 528.125
|-
|-
| | 14
| 14
| | 832.105
| 832.105
| 568.75
|-
|-
| | 15
| 15
| | 891.541
| 891.541
| 609.375
|-
|-
| | 16
| 16
| | 950.978
| 950.978
| 650
|-
|-
| | 17
| 17
| | 1010.414
| 1010.414
| 690.625
|-
|-
| | 18
| 18
| | 1069.850
| 1069.85
| 731.25
|-
|-
| | 19
| 19
| | 1129.286
| 1129.286
| 774.875
|-
|-
| | 20
| 20
| | 1188.722
| 1188.722
| 812.5
|-
|-
| | 21
| 21
| | 1248.158
| 1248.158
| 853.125.
|-
|-
| | 22
| 22
| | 1307.594
| 1307.594
| 893.75
|-
|-
| | 23
| 23
| | 1367.030
| 1367.03
| 934.375
|-
|-
| | 24
| 24
| | 1426.466
| 1426.466
| 975
|-
|-
| | 25
| 25
| | 1485.902
| 1485.902
| 1015.625
|-
|-
| | 26
| 26
| | 1545.338
| 1545.338
| 1056.25
|-
|-
| | 27
| 27
| | 1604.775
| 1604.775
| 1096.875
|-
|-
| | 28
| 28
| | 1664.211
| 1664.211
| 1137.5
|-
|-
| | 29
| 29
| | 1723.647
| 1723.647
| 1178.125
|-
|-
| | 30
| 30
| | 1783.083
| 1783.083
| 1218.75
|-
|-
| | 31
| 31
| | 1842.519
| 1842.519
| 1259.375
|-
|-
| | 32
| 32
| | 1901.955
| 1901.955
| 1300
|}
|}


[[Category:Edt]]
{{todo|expand}}
[[Category:Edonoi]]
Retrieved from "https://en.xen.wiki/w/32edt"