1ed97.5c: Difference between revisions

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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]]).
+'''97.5cET''' 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]]. 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 their complement, 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, 325/324, and 572/567, for example.
-{{harmonics in cet|97.5}}
 == Intervals ==
 {| class="wikitable center-1 right-2"
 ! Steps
 ! [[Cent]]s
+!Ratio approximated*
 |-
 | 1 || 97.5
+|16/15, 21/20, 35/33, 55/52
 |-
 | 2 || 195.0
+|28/25
 |-
 | 3 || 292.5
+|13/11
 |-
 | 4 || 390.0
+|5/4
 |-
 | 5 || 487.5
+|4/3
 |-
 | 6 || 585.0
+|7/5
 |-
 | 7 || 682.5
+|49/33
 |-
 | 8 || 780.0
+|11/7
 |-
 | 9 || 877.5
+|5/3
 |-
 | 10 || 975.0
+|16/9, 7/4
 |-
 | 11 || 1072.5
+|13/7
 |-
 | 12 || 1170.0
+|49/25
 |-
 | 13 || 1267.5
+|27/13
 |-
 | 14 || 1365.0
+|11/5
 |-
 | 15 || 1462.5
+|7/3
 |-
 | 16 || 1560.0
+|27/11, 49/20
 |-
 | 17 || 1657.5
+|13/5
 |-
 | 18 || 1755.0
+|11/4
 |-
 | 19 || 1852.5
+|35/12
 |-
 | 20 || 1950.0
+|49/16
+|-
+|21
+|2047.5
+|13/4
 |}
+<nowiki>*</nowiki>some simpler ratios, based on treating 97.5cET as a 4/3.5/3.7/3.11/3.13/3.9 subgroup temperament; other approaches are possible.
 == Music ==
-* [https://soundcloud.com/gareth-hearne/strange-waves-1 Strange Waves] by [[Gareth Hearne]]
+* [https://soundcloud.com/lillianhearne/strange-waves-1 Strange Waves] by [[Lillian Hearne]]
-* [https://soundcloud.com/gareth-hearne/blues-975 Blues 97.5] by Gareth Hearne
+* [https://soundcloud.com/lillianhearne/blues-975 Blues 97.5] by [[Lillian Hearne]]
 [[Category:Equal-step tuning]]