Fluid just intonation: Difference between revisions

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 The sheet music for ''Microtonal Composition in "Fluid Just Intonation"''  includes a table of allowed ratios, and how much they differ from their [[12edo]] tempered version (in [[cents]]).
-However, the JI ratios and the cents values do not all agree with one another.
+However, the JI ratios and the cent values do not all agree with one another.
 So, this page will include two tables, one based on the JI ratios provided in the sheet music, and one based on the cent values.
@@ Line 22: / Line 22: @@
 {| class="wikitable"
-! Scale degree!! Ratio
+! Scale degree
-!Tuning adjustment in [[cents]]
+! Ratio
+! Tuning adjustment (cents)
 |-
-|1||1/1
+|  1
-|0
+| [[1/1]]
+|  0
 |-
-|b2||16/15
+|  b2
+| [[16/15]]
 |  +12
 |-
-|2||9/8
+|  2
+| [[9/8]]
 |  +4
 |-
-|b3||6/5
+|  b3
+| [[6/5]]
 |  +16
 |-
-|3||5/4
+|  3
+| [[5/4]]
 |  -14
 |-
-|4||4/3
+|  4
+| [[4/3]]
 |  -2
 |-
-|#4/b5||11/8
+|  #4/b5
+| [[11/8]]
 |  -49
 |-
-|5||3/2
+|  5
+| [[3/2]]
 |  +2
 |-
-|b6||8/5
+|  b6
+| [[8/5]]
 |  +14
 |-
-|6||5/3
+|  6
+| [[5/3]]
 |  -16
 |-
-| rowspan="2" |b7||7/4 (dom7)
+| rowspan="2" |b7
-|  -31 (dom7)
+| [[7/4]] (''dom7'')
+|  -31 (''dom7'')
 |-
-|9/5 (m7)
+| [[9/5]] (''m7'')
-|  +18 (m7)
+|  +18 (''m7'')
 |-
-|7||15/8
+|  7
+| [[15/8]]
 |  -12
 |-
-|8ve||2/1
+|  8ve
-|0
+| [[2/1]]
+|  0
 |}
@@ Line 72: / Line 86: @@
 {| class="wikitable"
-! Scale degree!! Ratio!!Tuning adjustment in [[cents]]
+! Scale degree!! Ratio!!Tuning adjustment (cents)
 |-
-|1||1/1||0
+|1||[[1/1]]||0
 |-
-|b2||17/16||+5
+|b2||[[17/16]]||+5
 |-
-|2||9/8||+4
+|2||[[9/8]]||+4
 |-
-|b3||6/5||+16
+|b3||[[6/5]]||+16
 |-
-|3||5/4||-14
+|3||[[5/4]]||-14
 |-
-|4||4/3||-2
+|4||[[4/3]]||-2
 |-
-|#4/b5||11/8||-49
+|#4/b5||[[11/8]]||-49
 |-
-|5||3/2||+2
+|5||[[3/2]]||+2
 |-
-|b6||13/8||+41
+|b6||[[13/8]]||+41
 |-
-|6||27/16||+6
+|6||[[27/16]]||+6
 |-
-| rowspan="2" |b7||7/4 (dom7)||-31 (dom7)
+| rowspan="2" |b7||[[7/4]] (''dom7'')||-31 (''dom7'')
 |-
-|9/5 (m7)||+18 (m7)
+|[[9/5]] (''m7'')||+18 (''m7'')
 |-
-|7||15/8||-12
+|7||[[15/8]]||-12
 |-
-|8ve||2/1||0
+|8ve||[[2/1]]||0
 |}
-== Subsets and supersets ==
+=== Relationship to other tunings ===
-Fluid just intonation is a subset of [[13-limit]] just intonation (going by the sheet music's cent values), and possibly also [[11-limit]] just intonation (going by the sheet music's JI ratios).
-It is also a subset of the [[polymicrotonal]] tuning of ([[15afdo]] and [[16afdo]]).
+'''According to the sheet music's stated JI ratios:'''
+Fluid just intonation is a subset of [[11-limit]] just intonation.
+[[30afdo]] is the smallest [[Overtone scale|mode of the harmonic series]] that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.
+[[EDOs]] with progressively better approximations of fluid just intonation's allowed ratios include: {{EDOs|'''19''', 22, 28, '''31''', '''41''', 72, '''87''', '''118'''...}}
+'''According to the sheet music's stated cent values:'''
+Fluid just intonation is a subset of [[17-limit]] just intonation.
+[[32afdo]] is the smallest mode of the harmonic series that can approximate all of fluid just intonation's allowed ratios with a median error of 0 cents and a maximum error less than 20 cents.
+[[EDOs]] with progressively better approximations of fluid just intonation's allowed ratios include: {{EDOs|'''19''', 24, 30, '''31''', 33, '''41''', 46, 66, 77, '''87''', 90, 94, '''118'''...}}
 == Influences ==