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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | '''Starling chords''' are [[Dyadic chord #Essentially tempered dyadic chords|essentially tempered dyadic chords]] tempered by the starling comma, [[126/125]]. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:csvargas31|csvargas31]] and made on <tt>2013-10-06 20:02:52 UTC</tt>.<br>
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| : The original revision id was <tt>457318970</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">//Starling chords// are [[Dyadic chord#Essentially%20tempered%20dyadic%20chords|essentially tempered dyadic chords]] tempered by the staring 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 third 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 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. 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.
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| 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. 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.
| | 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. |
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| 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.
| | 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. |
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| | 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, |
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| | 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. |
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| | 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. |
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| | 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, |
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| | 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. |
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| 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. |
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| 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.</pre></div> | | [[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]]. |
| <h4>Original HTML content:</h4>
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| <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>starling chords</title></head><body><em>Starling chords</em> are <a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords">essentially tempered dyadic chords</a> tempered by the staring 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 third 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 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. 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.<br />
| | [[Category:7-odd-limit chords]] |
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| | [[Category:9-odd-limit chords]] |
| 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. 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.<br />
| | [[Category:Essentially tempered chords]] |
| <br />
| | [[Category:Triads]] |
| 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.<br />
| | [[Category:Tetrads]] |
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| | [[Category:Pentads]] |
| Starling chords come to triads: 3, tetrads: 6, pentads: 1, for a total of 10.<br /> | | [[Category:Starling]] |
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| 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.</body></html></pre></div>
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