Fluid just intonation: Difference between revisions
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=== | === 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). | 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). | ||
Going by the ''sheet music's cent values'', [[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. | |||
Going by the ''sheet music's JI ratios'', [[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. | |||
== Influences == | == Influences == | ||
Revision as of 03:37, 28 March 2025
Fluid just intonation[idiosyncratic term] is a subtype of adaptive just intonation developed by composer and music theorist Rosie Sheldon in 2021.
She first used it in her piece Microtonal Composition in "Fluid Just Intonation" (composed 2021, published 2022):
- listen on YouTube
- listen on Bandcamp
- purchase sheet music (includes instructions for configuring a DAW for this tuning method)
Description
Notes are tuned on a chord-by-chord basis.
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.
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
| Scale degree | Ratio | Tuning adjustment (cents) |
|---|---|---|
| 1 | 1/1 | 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 |
| b7 | 7/4 (dom7) | -31 (dom7) |
| 9/5 (m7) | +18 (m7) | |
| 7 | 15/8 | -12 |
| 8ve | 2/1 | 0 |
Based on the cent values
| 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 |
| b7 | 7/4 (dom7) | -31 (dom7) |
| 9/5 (m7) | +18 (m7) | |
| 7 | 15/8 | -12 |
| 8ve | 2/1 | 0 |
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).
Going by the sheet music's cent values, 30afdo 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.
Going by the sheet music's JI ratios, 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.
Influences
Sheldon cited Adam Neely’s version of intonalism as the main inspiration behind the concept, with fluid just intonation being like Neely’s style of intonalism, but with the 12edo skeleton removed and replaced with pure JI.
Sheldon also cited Jacob Collier, David Bruce, Dolores Catherino and Sevish as inspirations for the concept of fluid just intonation.