User:FloraC/Quick reference
Jump to navigation
Jump to search
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
- 2-limit (rank-1)
- Essential equivalence
- Completes the harmonic series for the first octave
- 3-limit (rank-2)
- Essential interval functions
- Completes the harmonic series for the first 2 octaves
- Rank is a highly composite number
- 5-limit (rank-3)
- Completes the harmonic series for the first 2 octaves and a fifth
- 7-limit (rank-4)
- Tonality: tonal
- Categorical characteristics: pivotal and semiambitonal
- Completes the harmonic series for the first 3 octaves
- Rank is a highly composite number
- 11-limit (rank-5)
- Completes the harmonic series for the first 3 octaves and a fifth
- 13-limit (rank-6)
- Essential interval colors
- Tonality: microtonal
- Categorical characteristics: ambitonal and semiambitonal
- Completes the harmonic series for the first 4 octaves
- Rank is a highly composite number
- 23-limit (rank-9)
- Limit of classical functional harmony
- Limit of classical concordance
- Tonality: pseudotonal and pseudomicrotonal
- Categorical characteristics: pseudoambitonal
- Completes the harmonic series for the first 4 octaves and a fifth
- Followed by a record prime gap
- 31-limit (rank-11)
- Completes the harmonic series for the first 5 octaves
- 37-limit (rank-12)
- Rank is a highly composite number
- 47-limit (rank-15)
- Completes the harmonic series for the first 5 octaves and a fifth
- 61-limit (rank-18)
- Completes the harmonic series for the first 6 octaves
- 89-limit (rank-24)
- Completes the harmonic series for the first 6 octaves and a fifth
- Followed by a record prime gap
- Rank is a highly composite number
Edo sizes
- Exo: 0–9
- Small: 10–38
- Semitonic: 10–14
- Subsemitonic: 15–26
- Dietic: 27–38
- Medium: 39–79
- Commatic: 39–67
- Subcommatic: 68–79
- Large: 80–190
- Hemicommatic: 80–132
- Codettic: 133–137
- Kleismatic: 138–190
- Mega: 191+
- Subkleismatic
- Hemikleismatic
- …