Starling and thrush

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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


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.

Starling/thrush nomenclature for selected intervals
Ratio Nominal Example
3/2 Perfect fifth C-G
5/4 Down major third C-vE
7/4 Triple-down augmented sixth C-v3A#
11/8 Quintuple-down double-augmented third C-v5Ex
13/8 Quintuple-down double-augmented fifth C-v5Gx

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.


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.


Starling hobbit scales

Thrush hobbit scales


Jake Freivald
  • A Seed Planted (2013) – the melody depends on tempering out 126/125.