Starling and thrush
Starling is the rank-3 temperament tempering out 126/125, the starling comma. Its best 11-limit extension, thrush, adds 176/175 and 441/440 to the comma list. It also has an obvious 13-limit extension tempering out 196/195, 351/350, and 352/351.
Starling was named by Herman Miller in 1999^{[1]}^{[2]}, and thrush was named by Gene Ward Smith in 2004^{[3]}.
See Starling family #Thrush for technical details.
Interval lattice
Notation
Starling/thrush can be notated the same as 5-limit just intonation since they share the same lattice structure. One way to do this is to take the conventional circle-of-fifths notation with an additional module of accidentals for the 81/80 comma. In this system, 5/4 is a major third, 7/4 an augmented sixth, and 11/8 a double diminished 5th.
Ratio | Nominal | Example |
---|---|---|
3/2 | Perfect fifth | C-G |
5/4 | Down major third | C-vE |
7/4 | Triple-down augmented sixth | C-v^{3}A# |
11/8 | Quintuple-down double-augmented third | C-v^{5}Ex |
13/8 | Quintuple-down double-augmented fifth | C-v^{5}Gx |
Alternatively, it can be notated the same as full prime-limit just intonation, with a distinct accidental pair for each prime. That makes some intervals more intuitive, at the cost of hiding the structure of starling/thrush tempering. For example, it is customary of the 5/4 to be a major third, and 7/4 to be a minor seventh. As a result, the fact that the 12/7 is a stack of three 6/5's is not revealed, and the related chords can be less convenient.
Chords
Starling/thrush enables essentially tempered chords of starling, valinorsmic, werckismic, and thrush. Extending the temperament to the 13-limit enables chords of mynucumic, ratwolfsmic and minthmic.
Scales
Starling hobbit scales
Thrush hobbit scales
Music
- A Seed Planted (2013) – the melody depends on tempering out 126/125.