User:FloraC/Quick reference

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 aka 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.
• 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: 38–75
• Large: 76–185
• Mega: 186+