Starling and thrush: Difference between revisions

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'''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]].

{{Infobox regtemp

| Title = Starling; thrush

| Subgroups = 2.3.5.7, 2.3.5.7.11

| Comma basis = [[126/125]] (7-limit); <br>[[126/125]], [[176/175]] (11-limit)

| Edo join 1 = 12 | Edo join 2 = 15 | Edo join 3 = 31

| Mapping = 1; 1 0 -2 -2; 0 1 3 5

| Generators = 3/2, 5/4

| Generators tuning = 701.6, 390.9

| Optimization method = CWE

| Odd limit 1 = 9 | Mistuning 1 = 4.60 | Complexity 1 = ?

| Odd limit 2 = 11-limit 21 | Mistuning 2 = 5.27 | Complexity 2 = ?

}}

'''Starling''' is a [[rank-3 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]].

In starling, classical minor thirds and major sixths are low-complexity intervals. A suitable 5-limit scale to temper via starling will be one where there are chains of minor thirds. Starling has a 6/5, 6/5, 6/5, 7/6 version of the [[diminished seventh chord]], which is very characteristic of it. Since this is a chord of [[meantone]] in wide use in Western {{w|common practice}} harmony long before [[12edo]] established itself as the standard tuning, it is arguably more authentic to tune it as three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds.

Starling's 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>.

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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 and harmony ==

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 ==

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* [[Starling chromatic]]

* [[Starling wholetone]]

== Tunings ==

{| class="wikitable mw-collapsible mw-collapsed"

|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings

|-

! rowspan="2" |

! colspan="3" | Euclidean

|-

! Constrained

! Constrained & skewed

! Destretched

|-

! Tenney

| CTE: ~3/2 = 700.9120{{c}}, ~5/4 = 389.6713{{c}}

| CWE: ~3/2 = 701.0811{{c}}, ~5/4 = 389.8833{{c}}

| POTE: ~3/2 = 701.2515{{c}}, ~5/4 = 390.0970{{c}}

|}

{| class="wikitable mw-collapsible mw-collapsed"

|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings

|-

! rowspan="2" |

! colspan="3" | Euclidean

|-

! Constrained

! Constrained & skewed

! Destretched

|-

! Tenney

| CTE: ~3/2 = 701.1852{{c}}, ~5/4 = 390.3842{{c}}

| CWE: ~3/2 = 701.6298{{c}}, ~5/4 = 390.8558{{c}}

| POTE: ~3/2 = 701.9454{{c}}, ~5/4 = 391.1906{{c}}

|}

== Music ==

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

== ~~Notes~~ ==

== References ==

~~[[Category:Temperaments]]~~

[[Category:Starling| ]]

[[Category:Thrush| ]]

[[Category:Rank-3 temperaments]]

[[Category:Starling family]]

[[Category:Valinorsmic clan]]

[[Category:Werckismic temperaments]]

@@ Line 1: / Line 1: @@
-'''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]].
+{{Infobox regtemp
+| Title = Starling; thrush
+| Subgroups = 2.3.5.7, 2.3.5.7.11
+| Comma basis = [[126/125]] (7-limit); <br>[[126/125]], [[176/175]] (11-limit)
+| Edo join 1 = 12 | Edo join 2 = 15 | Edo join 3 = 31
+| Mapping = 1; 1 0 -2 -2; 0 1 3 5
+| Generators = 3/2, 5/4
+| Generators tuning = 701.6, 390.9
+| Optimization method = CWE
+| Odd limit 1 = 9 | Mistuning 1 = 4.60 | Complexity 1 = ?
+| Odd limit 2 = 11-limit 21 | Mistuning 2 = 5.27 | Complexity 2 = ?
+}}
+'''Starling''' is a [[rank-3 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]].
+In starling, classical minor thirds and major sixths are low-complexity intervals. A suitable 5-limit scale to temper via starling will be one where there are chains of minor thirds. Starling has a 6/5, 6/5, 6/5, 7/6 version of the [[diminished seventh chord]], which is very characteristic of it. Since this is a chord of [[meantone]] in wide use in Western {{w|common practice}} harmony long before [[12edo]] established itself as the standard tuning, it is arguably more authentic to tune it as three stacked minor thirds and an augmented second, which is what it is in meantone, than as the modern version of four stacked very flat minor thirds.
+Starling's 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>.
@@ Line 43: / Line 59: @@
 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 and harmony ==
 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 ==
@@ Line 66: / Line 82: @@
 * [[Starling chromatic]]
 * [[Starling wholetone]]
+== Tunings ==
+{| class="wikitable mw-collapsible mw-collapsed"
+|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
+|-
+! rowspan="2" |
+! colspan="3" | Euclidean
+|-
+! Constrained
+! Constrained & skewed
+! Destretched
+|-
+! Tenney
+| CTE: ~3/2 = 700.9120{{c}}, ~5/4 = 389.6713{{c}}
+| CWE: ~3/2 = 701.0811{{c}}, ~5/4 = 389.8833{{c}}
+| POTE: ~3/2 = 701.2515{{c}}, ~5/4 = 390.0970{{c}}
+|}
+{| class="wikitable mw-collapsible mw-collapsed"
+|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings
+|-
+! rowspan="2" |
+! colspan="3" | Euclidean
+|-
+! Constrained
+! Constrained & skewed
+! Destretched
+|-
+! Tenney
+| CTE: ~3/2 = 701.1852{{c}}, ~5/4 = 390.3842{{c}}
+| CWE: ~3/2 = 701.6298{{c}}, ~5/4 = 390.8558{{c}}
+| POTE: ~3/2 = 701.9454{{c}}, ~5/4 = 391.1906{{c}}
+|}
 == Music ==
@@ Line 71: / Line 120: @@
 * [https://soundcloud.com/jdfreivald/a-seed-planted-starling-pure ''A Seed Planted''] (2013) – the melody depends on tempering out 126/125.
-== Notes ==
+== References ==
-[[Category:Temperaments]]
 [[Category:Starling| ]] <!-- main article -->
 [[Category:Thrush| ]] <!-- main article -->
+[[Category:Rank-3 temperaments]]
 [[Category:Starling family]]
 [[Category:Valinorsmic clan]]
 [[Category:Werckismic temperaments]]