User:FloraC/Quick reference: Difference between revisions
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** JI purism: this school recognizes that the acoustic quality of JI is of top importance. Some consider music as a platonic ideal object that cannot be approximated at all. Meanwhile, its weaker version is characterized by being maximally strict about JI approximation. | ** JI purism: this school recognizes that the acoustic quality of JI is of top importance. Some consider music as a platonic ideal object that cannot be approximated at all. Meanwhile, its weaker version is characterized by being maximally strict about JI approximation. | ||
*** Primodality: I don't feel entitled to define this. | *** Primodality: I don't feel entitled to define this. | ||
*** Stacking based | *** Stacking based a.k.a. lattice based: a more traditional approach to JI. They recognize both the acoustic quality and the algebraic structure of JI. | ||
** JI approximabilism: this school recognizes that the acoustic quality of JI and the algebraic structure of tuning systems are similarly important, and therefore accepts a tradeoff. | ** JI approximabilism: this school recognizes that the acoustic quality of JI and the algebraic structure of tuning systems are similarly important, and therefore accepts a tradeoff. | ||
*** RTT: this school encompasses stacking based JI and applies approximation for custom structures. | *** RTT: this school encompasses stacking based JI and applies approximation for custom structures. | ||
| Line 47: | Line 47: | ||
* Exo: 0–9 | * Exo: 0–9 | ||
* Small: 10–37 | * Small: 10–37 | ||
* Medium: | * Medium: 38–79 | ||
* Large: | * Large: 80–185 | ||
* Mega: 186+ | * Mega: 186+ | ||
Revision as of 14:57, 10 August 2025
Taxonomy of tuning approaches
- Tuning rationalism
- JI purism: this school recognizes that the acoustic quality of JI is of top importance. Some consider music as a platonic ideal object that cannot be approximated at all. Meanwhile, its weaker version is characterized by being maximally strict about JI approximation.
- Primodality: I don't feel entitled to define this.
- Stacking based a.k.a. lattice based: a more traditional approach to JI. They recognize both the acoustic quality and the algebraic structure of JI.
- JI approximabilism: this school recognizes that the acoustic quality of JI and the algebraic structure of tuning systems are similarly important, and therefore accepts a tradeoff.
- RTT: this school encompasses stacking based JI and applies approximation for custom structures.
- JI agnosticism: this school suspends the question whether the acoustic quality of JI is of importance. It tends to focus on algebraic structures such as mos scales and generalizations.
- JI indifferentism: this school does not believe the acoustic quality of JI is of importance. Practice in this school is orthogonal to the influence of JI.
- JI purism: this school recognizes that the acoustic quality of JI is of top importance. Some consider music as a platonic ideal object that cannot be approximated at all. Meanwhile, its weaker version is characterized by being maximally strict about JI approximation.
- Tuning empiricism
- Tuning stochasticism
Important prime limits
- 3-limit (rank-2)
- Essential interval functions
- 13-limit (rank-6)
- Essential interval colors
- Tonality: tonal and microtonal
- Categorical characteristics: pivotal, ambitonal, and semiambitonal
- Mode 8
- 23-limit (rank-9)
- Limit of classical functional harmony
- Limit of classical concordance
- Tonality: pseudotonal and pseudomicrotonal
- Categorical characteristics: pseudoambitonal
- Mode 12
- Followed by a record prime gap
- 31-limit (rank-11)
- Mode 16
- 37-limit (rank-12)
- 47-limit (rank-15)
- Mode 24
- 61-limit (rank-18)
- Mode 32
- 89-limit (rank-24)
- Mode 48
- Followed by a record prime gap
Edo sizes
- Exo: 0–9
- Small: 10–37
- Medium: 38–79
- Large: 80–185
- Mega: 186+