Starling and thrush: Difference between revisions
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'''Starling''' is a [[rank-3 | {{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. | 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. | ||
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* [[Starling chromatic]] | * [[Starling chromatic]] | ||
* [[Starling wholetone]] | * [[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 == | == 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. | * [https://soundcloud.com/jdfreivald/a-seed-planted-starling-pure ''A Seed Planted''] (2013) – the melody depends on tempering out 126/125. | ||
== | == References == | ||
[[Category:Starling| ]] <!-- main article --> | [[Category:Starling| ]] <!-- main article --> | ||