Fluid just intonation: Difference between revisions

← Older edit

VisualWikitext

@@ Line 11: / Line 11: @@
 Each chord contains a ''common note'' shared with the previous chord. The tuning of the common note stays exactly the same, and all other notes of the new chord are tuned in pure [[JI]] ratios relative to the common note.
-The allowed ratios, and how much they differ from their [[12edo]] tempered version, are listed in the following table:
+=== Allowed ratios ===
+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 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.
+'''Based on the JI ratios'''
 {| class="wikitable"
-! Scale Degree!! Ratio!!Tuning adjustment in [[cents]]
+! Scale degree
+! Ratio
+! Tuning adjustment (cents)
 |-
-|1||1/1||-
+|  1
+| [[1/1]]
+|  0
 |-
-|b2||16/15||5
+|  b2
+| [[16/15]]
+|  +12
 |-
-|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 (subdominant)
+|  4
+| [[4/3]]
+|  -2
 |-
-|#4/b5||11/8||-49
+|  #4/b5
+| [[11/8]]
+|  -49
 |-
-|5||3/2||2
+|  5
+| [[3/2]]
+|  +2
 |-
-|b6||8/5||41
+|  b6
+| [[8/5]]
+|  +14
 |-
-|6||5/3||6
+|  6
+| [[5/3]]
+|  -16
 |-
-| 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||-
+|  8ve
+| [[2/1]]
+|  0
 |}
-== Subsets and supersets ==
-Fluid just intonation is a subset of [[11-limit]] just intonation.
-It is also a subset of the [[polymicrotonal]] tuning of ([[15afdo]] and [[8afdo]]).
+'''Based on the cent values'''
+{| class="wikitable"
+! Scale degree!! Ratio!!Tuning adjustment (cents)
+|-
+|1||[[1/1]]||0
+|-
+|b2||[[17/16]]||+5
+|-
+|2||[[9/8]]||+4
+|-
+|b3||[[6/5]]||+16
+|-
+|3||[[5/4]]||-14
+|-
+|4||[[4/3]]||-2
+|-
+|#4/b5||[[11/8]]||-49
+|-
+|5||[[3/2]]||+2
+|-
+|b6||[[13/8]]||+41
+|-
+|6||[[27/16]]||+6
+|-
+| rowspan="2" |b7||[[7/4]] (''dom7'')||-31 (''dom7'')
+|-
+|[[9/5]] (''m7'')||+18 (''m7'')
+|-
+|7||[[15/8]]||-12
+|-
+|8ve||[[2/1]]||0
+|}
+=== Relationship to other tunings ===
+'''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 ==