Starling chords: Difference between revisions
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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 [[ | 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. | |||
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. | |||
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]], | 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. | ||
[[ | [[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: | [[Category:Triads]] | ||
[[Category: | [[Category:Tetrads]] | ||
[[Category: | [[Category:Pentads]] | ||
[[Category:Starling]] | [[Category:Starling]] | ||
Latest revision as of 09:41, 9 October 2024
Starling chords are essentially tempered dyadic chords tempered by the starling comma, 126/125.
The starling tetrad is an 126/125-tempered chord which in close position (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 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.
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.
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 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.
Equal temperaments with starling chords include 19, 27, 31, 43, 46, 50, 58, 77, 185, and 265c, and using the patent val tuning, 34 and 65.