View source for Starling and thrush

'''Starling''' is a [[rank-3 temperament|rank-3]] [[regular temperament|temperament]] with the same [[lattice]] structure as 5-limit JI, while identifying the [[7/4|harmonic seventh (7/4)]] as a stack of a [[3/2|perfect fifth (3/2)]] and three [[5/3|classical major sixths (5/3)]] octave-reduced, [[tempering out]] [[126/125]]. It is the head of the [[starling family]], and its best [[11-limit]] [[extension]], '''thrush''', adding [[176/175]] and [[441/440]] to the comma list, makes it a member of both [[valinorsmic clan]] and [[werckismic temperaments]]. 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<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_6385.html Yahoo! Tuning Group | ''Meantone and "starling" scale with slightly stretched octaves'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3732.html Yahoo! Tuning Group | ''Starling temperament mapping'']</ref>, and thrush was named by [[Gene Ward Smith]] in 2004<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_8625.html Yahoo! Tuning Group | ''11-limit Starling'']</ref>. 

See [[Starling family #Thrush]] for technical details. 

== Interval lattice ==
<gallery>
File:Lattice Thrush.png|11-limit thrush
File:Lattice Thrush13.png|13-limit thrush
</gallery>

== 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. 

{| class="wikitable center-1 center-3"
|+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-v<sup>3</sup>A#
|-
| 11/8
| Quintuple-down double-augmented third
| C-v<sup>5</sup>Ex
|-
| 13/8
| Quintuple-down double-augmented fifth
| C-v<sup>5</sup>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 chord]]s of [[Starling chords|starling]], [[Valinorsmic chords|valinorsmic]], [[Werckismic chords|werckismic]], and [[Thrush chords|thrush]]. Extending the temperament to the 13-limit enables chords of [[Mynucumic chords|mynucumic]], [[Ratwolfsmic chords|ratwolfsmic]] and [[Minthmic chords|minthmic]]. 

== Scales ==
=== Starling hobbit scales ===
* [[Starling7]]
* [[Starling8]]
* [[Starling9]]
* [[Starling11]]
* [[Starling12]]
* [[Starling15]]
* [[Starling16]]
* [[Starling17]]
* [[Starling19]]

=== Thrush hobbit scales ===
* [[Thrush12]]
* [[Thrush15]]

=== Other scales ===
* [[Starling diatonic]]
* [[Starling chromatic]]
* [[Starling wholetone]]

== Music ==
; [[Jake Freivald]]
* [https://soundcloud.com/jdfreivald/a-seed-planted-starling-pure ''A Seed Planted''] (2013) – the melody depends on tempering out 126/125.

== Notes ==

[[Category:Starling| ]] <!-- main article -->
[[Category:Thrush| ]] <!-- main article -->
[[Category:Rank-3 temperaments]]
[[Category:Starling family]]
[[Category:Valinorsmic clan]]
[[Category:Werckismic temperaments]]