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'''97.5cET''' is an [[equal-step tuning]] with steps of 97.5 [[cent]]s (or each 13th step of [[160edo]]). This system doesn't contain good approximations of fourth ([[4/3]]), fifths [[3/2]], octave [[2/1]], major ninth (nonet) [[9/4]], eleventh [[8/3]], and tritave [[3/1]] which makes it quite "atonal" and xenharmonic (but nevertheless harmonic in its way, see [[#Music]]).
{{Infobox ET|160ed8192}}
{{harmonics in cet|97.5}}
'''1 equal division of 97.5¢''' ('''1ed97.5c'''), also known as '''arithmetic pitch sequence of 97.5¢''' ('''APS97.5¢'''), is an [[equal-step tuning]] with steps of 97.5 [[cent]]s (or each 13th step of [[160edo]]). It approximates the 9th harmonic to within 2c, and may alternatively be tuned or conceived of as [[39ed9]]. It can also be conceived slightly less accurately as [[25ed4]]. In contrast to [[12edo]], which is very similar in step size, it is not considered to approximate the octave ([[2/1]]) or perfect fifth ([[3/2]]), and has a workable, but rather (~10.5c) flat approximation of the perfect fourth ([[4/3]]). It excels however in the 4/3.5/3.7/3.11/3.13/3.9 [[Just intonation subgroup|subgroup]], in which it tempers out [[64/63]], [[100/99]], [[275/273]], and [[325/324]], for example.
 
[[:File:97.5cET scale.mp4|File:97.5cET scale]]
== Intervals ==
== Intervals ==
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
! Steps
! Steps
! [[Cent]]s
! [[Cent]]s
!Ratio approximated*
|-
|-
| 1 || 97.5
| 1 || 97.5
|16/15, 21/20, 35/33, 55/52
|-
|-
| 2 || 195.0
| 2 || 195.0
|28/25, 44/39
|-
|-
| 3 || 292.5
| 3 || 292.5
|13/11
|-
|-
| 4 || 390.0
| 4 || 390.0
|5/4
|-
|-
| 5 || 487.5
| 5 || 487.5
|4/3, 33/25
|-
|-
| 6 || 585.0
| 6 || 585.0
|7/5
|-
|-
| 7 || 682.5
| 7 || 682.5
|49/33
|-
|-
| 8 || 780.0
| 8 || 780.0
|11/7, 39/25
|-
|-
| 9 || 877.5
| 9 || 877.5
|5/3
|-
|-
| 10 || 975.0
| 10 || 975.0
|16/9, 7/4, 44/25
|-
|-
| 11 || 1072.5
| 11 || 1072.5
|13/7
|-
|-
| 12 || 1170.0
| 12 || 1170.0
|49/25
|-
|-
| 13 || 1267.5
| 13 || 1267.5
|27/13
|-
|-
| 14 || 1365.0
| 14 || 1365.0
|11/5
|-
|-
| 15 || 1462.5
| 15 || 1462.5
|7/3
|-
|-
| 16 || 1560.0
| 16 || 1560.0
|27/11, 49/20
|-
|-
| 17 || 1657.5
| 17 || 1657.5
|13/5
|-
|-
| 18 || 1755.0
| 18 || 1755.0
|11/4, 36/13
|-
|-
| 19 || 1852.5
| 19 || 1852.5
|35/12
|-
|-
| 20 || 1950.0
| 20 || 1950.0
|49/16
|-
|21
|2047.5
|13/4, 36/11
|-
|22
|2145.0
|45/13
|-
|23
|2242.5
|48/13
|-
|24
|2340.0
|27/7
|-
|25
|2437.5
|45/11
|-
|26
|2533.0
|48/11
|-
|27
|2632.5
|60/13
|-
|28
|2730.0
|63/13
|-
|29
|2827.5
|36/7, 81/16
|-
|30
|2925.0
|27/5, 60/11
|-
|31
|3022.5
|63/11
|-
|32
|3120.0
|
|-
|33
|3215.5
|45/7
|-
|34
|3315.0
|27/4
|-
|35
|3412.5
|36/5
|-
|36
|3510.0
|99/13
|-
|37
|3607.5
|
|-
|38
|3705.0
|60/7
|-
|39
|3802.5
|9/1
|}
|}
<nowiki>*</nowiki>some simpler ratios, based on treating 1ed97.5c as a 4/3.5/3.7/3.11/3.13/3.9 subgroup temperament; other approaches are possible.
== Music ==
== Music ==
 
'''[[Lillian Hearne]]'''
* [https://soundcloud.com/gareth-hearne/strange-waves-1 Strange Waves] by [[Gareth Hearne]]
* [https://soundcloud.com/lillianhearne/strange-waves-1 Strange Waves]
* [https://soundcloud.com/gareth-hearne/blues-975 Blues 97.5] by Gareth Hearne
* [https://soundcloud.com/lillianhearne/blues-975 Blues 97.5]


[[Category:Equal-step tuning]]
[[Category:Equal-step tuning]]
[[Category:Nonoctave]]
[[Category:Nonoctave]]
[[Category:Edonoi]]
[[Category:Listen]]
[[Category:Listen]]
Retrieved from "https://en.xen.wiki/w/1ed97.5c"