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'''Starling chords''' are [[Dyadic chord #Essentially tempered dyadic chords|essentially tempered dyadic chords]] tempered by the starling comma, [[126/125]].  
'''Starling chords''' are [[Dyadic chord #Essentially tempered dyadic chords|essentially tempered dyadic chords]] tempered by the starling comma, [[126/125]].  


The starling [[tetrad]] is an 126/125-tempered [[chord]] which in close position ([[octave reduction|reduced to an octave]]) consists of a chain of three approximate [[6/5]] minor thirds and an approximate [[7/6]] subminor third, in a tuning which [[Tempering out|tempers out]] the starling comma, 126/125, and hence causes it to close on the [[octave]]. That is, it is a starling-tempered 6/5-6/5-6/5-7/6, which may also be regarded as a tempered 1-6/5-10/7-12/7; it is also known as the septimal semicomma diminished seventh chord. In a [[meantone]] tuning the starling tetrad is three minor thirds and an augmented second, which is the traditional diminished seventh chord of common practice music in the meantone era.  
The starling [[tetrad]] is an 126/125-tempered [[chord]] which in close position ([[octave reduction|reduced to an octave]]) consists of a chain of three approximate [[6/5]] minor thirds and an approximate [[7/6]] subminor third, in a tuning which [[tempering out|tempers out]] the starling comma, 126/125, and hence causes it to close on the [[octave]]. That is, it is a starling-tempered  
* 1–6/5–10/7–12/7, with steps 6/5, 6/5, 6/5, 7/6.  


Also familiar from the music of common practice is the diminished [[triad]], a tempering of 1-6/5-10/7 with steps 6/5-6/5-7/5 when understood [[7-limit|septimally]]. Other essentially tempered starling triads are the 1-5/4-7/5 chord with steps 5/4-10/9-10/7 and its inversion, 1-5/4-9/5 with steps 5/4-10/7-10/9.  
It is also known as the septimal semicomma diminished seventh chord. In a [[meantone]] tuning the starling tetrad is three minor thirds and an augmented second, which is the traditional diminished seventh chord of common practice music in the meantone era.  


For starling tetrads, we also have the 1-5/4-3/2-9/5 chord with steps 5/4-6/5-6/5-10/9 and its inversion, 1-6/5-3/2-5/3; the 1-5/4-7/5-7/4 chord with steps of 5/4-10/9-5/4-8/7; the 1-5/4-7/5-9/5 chord with steps of 5/4-10/9-9/7-10/9; and the 1-9/8-5/4-9/5 chord with steps of 9/8-10/9-10/7-10/9.
Also familiar from the music of common practice is the diminished [[triad]], a tempering of
* 1–6/5–10/7 with steps 6/5, 6/5, 7/5,


There is also a unique starling [[pentad]], 1-9/8-5/4-3/2-9/5, with steps of 9/8-10/9-6/5-6/5-10/9, a modified complete ninth chord. In the transposition 1-6/5-4/3-3/2-5/3 with steps 6/5-10/9-9/8-10/9-6/5 we can more easily see that the steps are symmetrical around 9/8.
when understood [[7-limit|septimally]]. Other essentially tempered starling triads are
* 1–5/4–7/5 with steps 5/4, 10/9, 10/7 and its inversion,
* 1–5/4–9/5 with steps 5/4, 10/7, 10/9.
 
For starling tetrads, we also have
* 1–5/4–3/2–9/5 with steps 5/4, 6/5, 6/5, 10/9 and its inversion,
* 1–6/5–3/2–5/3 with steps 6/5, 5/4, 10/9, 6/5;
* 1–5/4–7/5–7/4 with steps 5/4, 10/9, 5/4, 8/7;
* 1–5/4–7/5–9/5 with steps 5/4, 10/9, 9/7, 10/9;
* 1–9/8–5/4–9/5 with steps 9/8, 10/9, 10/7, 10/9.
 
There is also a unique starling [[pentad]], a modified complete ninth chord,
* 1–9/8–5/4–3/2–9/5, with steps 9/8, 10/9, 6/5, 6/5, 10/9,  
 
In the transposition 1–6/5–4/3–3/2–5/3 with steps 6/5, 10/9, 9/8, 10/9, 6/5 we can more easily see that the steps are symmetrical around 9/8.


Starling chords come to triads: 3, tetrads: 6, pentads: 1, for a total of 10.
Starling chords come to triads: 3, tetrads: 6, pentads: 1, for a total of 10.


[[EDO|Equal temperaments]] with starling chords include [[19edo|19]], [[27edo|27]], [[31edo|31]], [[43edo|43]], [[46edo|46]], [[50edo|50]], [[58edo|58]], [[77edo|77]], [[185edo|185]] and [[265edo|265c]], and using the [[patent val]] tuning, [[34edo|34]] and [[65edo|65]].
[[Equal temperament]]s with starling chords include {{EDOs| 19, 27, 31, 43, 46, 50, 58, 77, 185, and 265c }}, and using the [[patent val]] tuning, [[34edo|34]] and [[65edo|65]].


[[Category:7-odd-limit]]
[[Category:7-odd-limit chords]]
[[Category:9-odd-limit]]
[[Category:9-odd-limit chords]]
[[Category:Essentially tempered chords]]
[[Category:Essentially tempered chords]]
[[Category:Triads]]
[[Category:Triads]]
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