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Fluid just intonation: Difference between revisions

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→Description: I'm still in the Zoom meeting right now but quickly updated the page during a lull in the meeting to include both versions of the table, original and corrected
BudjarnLambeth (talk | contribs)
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Updated tables based on discussion in Discord
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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.
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]]).


(''Note: Some of the cents values given by the original table - the one included in the sheet music - do not match the actual cents values of the JI values given. So, the "original" column documents the values given by the original table, and the "corrected" column documents the accurate values for each JI interval. It is unclear which of these was used in the piece itself.'')
However, the JI ratios and the cents 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"
{| class="wikitable"
! rowspan="2" | Scale degree!! rowspan="2" | Ratio!! colspan="2" |Tuning adjustment in [[cents]]
! Scale degree!! Ratio
!Tuning adjustment in [[cents]]
|-
|-
!Original
|1||1/1
!Corrected
|0
|-
|b2||16/15
|  +12
|-
|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||8/5
|  +14
|-
|6||5/3
|  -16
|-
| rowspan="2" |b7||7/4 (dom7)
|  -31 (dom7)
|-
|9/5 (m7)
|  +18 (m7)
|-
|7||15/8
|  -12
|-
|8ve||2/1
|0
|}
 
 
'''Based on the cent values'''
 
{| class="wikitable"
! Scale degree!! Ratio!!Tuning adjustment in [[cents]]
|-
|-
|1||1/1||0
|1||1/1||0
|0
|-
|-
|b2||16/15||+5
|b2||17/16||+5
| +12
|-
|-
|2||9/8||+4
|2||9/8||+4
| +4
|-
|-
|b3||6/5||+16
|b3||6/5||+16
| +16
|-
|-
|3||5/4||-14
|3||5/4||-14
| -14
|-
|-
|4||4/3||-2
|4||4/3||-2
| -2
|-
|-
|#4/b5||11/8||-49
|#4/b5||11/8||-49
| -49
|-
|-
|5||3/2||+2
|5||3/2||+2
| +2
|-
|-
|b6||8/5||+41
|b6||13/8||+41
| +14
|-
|-
|6||5/3||+6
|6||27/16||+6
| -16
|-
|-
| rowspan="2" |b7||7/4 (dom7)||-31 (dom7)
| rowspan="2" |b7||7/4 (dom7)||-31 (dom7)
| -31 (dom7)
|-
|-
|9/5 (m7)||+18 (m7)
|9/5 (m7)||+18 (m7)
| +18 (m7)
|-
|-
|7||15/8||-12
|7||15/8||-12
| -12
|-
|-
|8ve||2/1||0
|8ve||2/1||0
|0
|}
|}


== Subsets and supersets ==
== Subsets and supersets ==
Fluid just intonation is a subset of [[11-limit]] just intonation.  
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 [[8afdo]]).
It is also a subset of the [[polymicrotonal]] tuning of ([[15afdo]] and [[16afdo]]).


== Influences ==
== Influences ==
Retrieved from "https://en.xen.wiki/w/Fluid_just_intonation"