Starling and thrush: Difference between revisions
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'''Starling''' is | '''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. | 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. | See [[Starling family #Thrush]] for technical details. | ||
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== Interval lattice == | == Interval lattice == | ||
<gallery> | <gallery> | ||
File:Lattice Thrush.png | File:Lattice Thrush.png|11-limit thrush | ||
File:Lattice Thrush13.png|13-limit thrush | |||
</gallery> | </gallery> | ||
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| Quintuple-down double-augmented third | | Quintuple-down double-augmented third | ||
| C-v<sup>5</sup>Ex | | 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. | 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 == | == Chords == | ||
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* [[Thrush12]] | * [[Thrush12]] | ||
* [[Thrush15]] | * [[Thrush15]] | ||
=== Other scales === | |||
* [[Starling diatonic]] | |||
* [[Starling chromatic]] | |||
* [[Starling wholetone]] | |||
== Music == | == Music == | ||
; [[Jake Freivald]] | ; [[Jake Freivald]] | ||
* [https://soundcloud.com/jdfreivald/a-seed-planted-starling-pure ''A Seed Planted''] – the melody depends on tempering out 126/125. | * [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:Starling| ]] <!-- main article --> | ||
[[Category:Thrush| ]] <!-- main article --> | [[Category:Thrush| ]] <!-- main article --> | ||
[[Category:Rank-3 temperaments]] | |||
[[Category:Starling family]] | [[Category:Starling family]] | ||
[[Category:Valinorsmic clan]] | [[Category:Valinorsmic clan]] | ||
[[Category:Werckismic temperaments]] | [[Category:Werckismic temperaments]] | ||
Latest revision as of 09:54, 29 April 2025
Starling is a rank-3 temperament with the same lattice structure as 5-limit JI, while identifying the harmonic seventh (7/4) as a stack of a perfect fifth (3/2) and three 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[1][2], and thrush was named by Gene Ward Smith in 2004[3].
See Starling family #Thrush for technical details.
Interval lattice
-
11-limit thrush -
13-limit thrush
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-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.
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
Other scales
Music
- A Seed Planted (2013) – the melody depends on tempering out 126/125.