Sensamagic dominant chord: Difference between revisions
Respell the 140/81 as 12/7 and elaborate on this equivalence |
I'd love to share an undecimal variant |
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The '''sensamagic dominant chord''' (or '''Canovian chord''' since it was first explored by [[Flora Canou]]) refers to the sensamagic tempered chord of ratios 1-[[9/7]]-[[12/7]]. It features two instances of voice leading by [[28/27]] in the resolution to the tonic. | The '''sensamagic dominant chord''' (or '''Canovian chord''' since it was first explored by [[Flora Canou]]) refers to the [[sensamagic]] tempered chord of ratios 1-[[9/7]]-[[12/7]]. It features two instances of voice leading by [[28/27]] in the resolution to the tonic. | ||
[[File:Canovian Chord 19-ET.png|thumb|right|Canovian chord notated in 19-ET]] | [[File:Canovian Chord 19-ET.png|thumb|right|Canovian chord notated in 19-ET]] | ||
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== Construction == | == Construction == | ||
The chord consists of a tempered 1-9/7-12/7, usually built on the fifth note of a diatonic scale – it is a dominant chord after all. The root is [[3/2]] above the tone to which it desires to resolve. The 9/7 is 28/27 below the tonic. By the tempering of sensamagic, the 12/7 is simultaneously 140/81, which is 28/27 above [[5/3]], the latter being [[5/4]] with respect to the tonic. For this reason the 12/7~140/81 is a supermajor sixth in terms of chord construction, and an inframinor seventh in terms of voice leading. The 140/81 spelling is arguably preferable for staff notation as it highlights the voice leading, shown on the right. The progression with respect to the tonic is | The chord consists of a tempered 1-9/7-12/7, usually built on the fifth note of a diatonic scale – it is a dominant chord after all. The root is [[3/2]] above the tone to which it desires to resolve. The 9/7 is 28/27 below the tonic. By the tempering of sensamagic, the 12/7 is simultaneously 140/81, which is 28/27 above [[5/3]], the latter being [[5/4]] with respect to the tonic. For this reason the 12/7~140/81 is a supermajor sixth in terms of chord construction, and an inframinor seventh in terms of voice leading. The 140/81 spelling is arguably preferable for staff notation as it highlights the voice leading, shown on the right. The progression with respect to the tonic is | ||
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Not tempering out the comma implies either giving up the voice leading by 28/27 or introducing wolf intervals. The lower voice leading calls for 9/7, a supermajor third. The upper voice leading calls for 140/81, an inframinor seventh. The interval between them is [[980/729]] at 512 cents, called the complex sensamagic fourth. It sounds only mildly wolf in JI, and [[12edo]] ears should be accustomed to a 14-cent-sharp interval anyway. But some tunings can make it much worse. For example, in [[31edo]], it is tuned to 542 cents – same as [[11/8]] – so the chord sounds highly dissonant and disturbing. | Not tempering out the comma implies either giving up the voice leading by 28/27 or introducing wolf intervals. The lower voice leading calls for 9/7, a supermajor third. The upper voice leading calls for 140/81, an inframinor seventh. The interval between them is [[980/729]] at 512 cents, called the complex sensamagic fourth. It sounds only mildly wolf in JI, and [[12edo]] ears should be accustomed to a 14-cent-sharp interval anyway. But some tunings can make it much worse. For example, in [[31edo]], it is tuned to 542 cents – same as [[11/8]] – so the chord sounds highly dissonant and disturbing. | ||
The negative harmony version of the chord consists of a tempered 1-[[7/6]]-[[7/4]] built on the subdominant, with 7/4 simultaneously acting as [[243/140]]. The 243/140 spelling is arguably preferable for staff notation for the same reason discussed above. The progression with respect to the tonic is | |||
<math>\text {(Sensamagic) } 2/3–7/6–14/9 \rightarrow 1–6/5–3/2</math> | |||
It should be noted that the 7/6 is simultaneously [[81/70]], and the voice leading of 81/70 → 6/5 is characterized by 28/27, just as of 14/9 → 3/2. | |||
== Theory == | == Theory == | ||
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== Variations == | == Variations == | ||
There is an undecimal variant, dubbed the '''semiporwellismic dominant chord''', with the voice leading characterized by [[33/32]] instead. It works in undecimal sensamagic as well. It is built by 1-[[128/99]]-[[55/32]]. The progression with respect to the tonic is | |||
<math>\text {( | <math>\text {(Semiporwellismic) } 3/4–32/33–128/99 \rightarrow 1–5/4–3/2</math> | ||
With the voice leading of 32/33 → 1 and 128/99 → 5/4 characterized by 33/32. | |||
== External links == | == External links == | ||