Chords of magic: Difference between revisions
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Below | Below is a complete list of the [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[magic|magic temperament]]. Note that there are many common chords, for example [[8:10:12:15]], which are not listed; in this case due to [[15/8]] not being in the 11-odd-limit. Every chord listed has multiple [[chord #Inversion|inversions]]; only one is listed, that being the inversion where all notes are a nonnegative number of major third [[generator]]s above the root. | ||
Typing the chords requires consideration of the fact that magic conflates [[10/9]] and [[11/10]] and so also [[9/5]] and [[20/11]]. If a [[transversal]] can be found which shows the chord to be essentially just, that transversal is listed along with a typing as [[otonal]], [[utonal]], or [[ambitonal]]. If the chord is essentially tempered, it is analyzed in terms of the transversal that requires the minimum amount of commas to be tempered out; if there is a tie between multiple transversals, it is analyzed in terms of the transversal which employs 10/9 and 9/5. | |||
Magic has [[mos scale]]s of | Chords requiring tempering only by [[225/224]] are labeled [[marvel chords|marvel]], by [[245/243]] [[sensamagic chords|sensamagic]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[896/891]] [[pentacircle chords|pentacircle]], by [[385/384]] [[keenanismic chords|keenanismic]], and by [[540/539]] [[swetismic chords|swetismic]]. Those requiring any two of 100/99, 225/224 or 896/891 are labeled [[apollo chords|apollo]], any two of 100/99, 245/243 or 540/539 [[octarod chords|octarod]], any two of 245/243, 896/891 or 385/384 [[undecimal sensamagic chords|sensamagic11]], any two of 225/224, 385/384, or 540/539 [[undecimal marvel chords|marvel11]]. Chords requiring both 100/99 and 385/384 are labeled [[keemic chords|keemic]]. Finally, anything requiring three independent commas among those discussed above is labeled [[magic chords|magic]]. | ||
Magic has [[mos scale]]s of 7, 10, 13, 16, 19, and 22 notes. It may be seen that even the 7-note mos is not without a few harmonic resources, and the larger ones do much better. | |||
[[Kite Giedraitis]] has named the chords using arrows (ups and downs), as described in [[Kite's thoughts on pergens]]. The pergen is (P8, P12/5) fifth-of-a-twelfth, #37 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf list of pergens]. One up is 19 generators, octave-reduced. The generator is {{nowrap| vM3 {{=}} 380{{c}} + ''c''/5 }}, where ''c'' is the amount in cents the tempered fifth exceeds 700{{c}}. The [[Kite's thoughts on enharmonic unisons in ups and downs notation|enharmonic unison]] is ^<sup>5</sup>dd2, thus {{nowrap|^<sup>5</sup>C {{=}} Bx}}. To simplify the chord names, slashes (lifts and drops) are also used. One lift is -22 generators, octave-reduced. Thus {{nowrap|/1 {{=}} −25''G'' + 3''G'' {{=}} m2 + ^^d8 {{=}} ^^d2}}. Thus a lift equals two ups minus a tempered pythagorean comma, so {{nowrap| /C {{=}} ^^Dbb }}, {{nowrap| \C {{=}} vvB# }}, {{nowrap| ^^C {{=}} /B# }}, and {{nowrap| vvC {{=}} \Dbb }}. The cents values of sharps, ups and lifts vary greatly, as this table shows. Note that if the fifth is wider than 22edo's fifth, a lift will actually be descending. Furthermore, if the fifth is narrower than 19edo's, an up will be descending. | [[Kite Giedraitis]] has named the chords using arrows (ups and downs), as described in [[Kite's thoughts on pergens]]. The pergen is (P8, P12/5) fifth-of-a-twelfth, #37 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf list of pergens]. One up is 19 generators, octave-reduced. The generator is {{nowrap| vM3 {{=}} 380{{c}} + ''c''/5 }}, where ''c'' is the amount in cents the tempered fifth exceeds 700{{c}}. The [[Kite's thoughts on enharmonic unisons in ups and downs notation|enharmonic unison]] is ^<sup>5</sup>dd2, thus {{nowrap|^<sup>5</sup>C {{=}} Bx}}. To simplify the chord names, slashes (lifts and drops) are also used. One lift is -22 generators, octave-reduced. Thus {{nowrap|/1 {{=}} −25''G'' + 3''G'' {{=}} m2 + ^^d8 {{=}} ^^d2}}. Thus a lift equals two ups minus a tempered pythagorean comma, so {{nowrap| /C {{=}} ^^Dbb }}, {{nowrap| \C {{=}} vvB# }}, {{nowrap| ^^C {{=}} /B# }}, and {{nowrap| vvC {{=}} \Dbb }}. The cents values of sharps, ups and lifts vary greatly, as this table shows. Note that if the fifth is wider than 22edo's fifth, a lift will actually be descending. Furthermore, if the fifth is narrower than 19edo's, an up will be descending. | ||
| Line 892: | Line 894: | ||
| 0–1–2–13 | | 0–1–2–13 | ||
| 1–12/11–5/4–14/9 | | 1–12/11–5/4–14/9 | ||
| | | Marvel11 | ||
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| Line 969: | Line 971: | ||
| 0–1–11–13 | | 0–1–11–13 | ||
| 1–12/11–5/4–7/5 | | 1–12/11–5/4–7/5 | ||
| | | Marvel11 | ||
| | | | ||
| | | | ||
| Line 1,004: | Line 1,006: | ||
| 0–2–12–13 | | 0–2–12–13 | ||
| 1–12/11–14/9–7/4 | | 1–12/11–14/9–7/4 | ||
| | | Marvel11 | ||
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| Line 1,032: | Line 1,034: | ||
| 0–11–12–13 | | 0–11–12–13 | ||
| 1–12/11–7/5–7/4 | | 1–12/11–7/5–7/4 | ||
| | | Marvel11 | ||
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| Line 1,046: | Line 1,048: | ||
| 0–7–8–18 | | 0–7–8–18 | ||
| 1–7/6–16/11–18/11 | | 1–7/6–16/11–18/11 | ||
| | | Marvel11 | ||
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| Line 1,109: | Line 1,111: | ||
| 0–10–11–18 | | 0–10–11–18 | ||
| 1–9/8–7/5–18/11 | | 1–9/8–7/5–18/11 | ||
| | | Marvel11 | ||
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| Line 1,512: | Line 1,514: | ||
| 0–1–2–11–13 | | 0–1–2–11–13 | ||
| 1–12/11–5/4–7/5–14/9 | | 1–12/11–5/4–7/5–14/9 | ||
| | | Marvel11 | ||
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| Line 1,547: | Line 1,549: | ||
| 0–1–2–12–13 | | 0–1–2–12–13 | ||
| 1–12/11–5/4–14/9–7/4 | | 1–12/11–5/4–14/9–7/4 | ||
| | | Marvel11 | ||
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| Line 1,589: | Line 1,591: | ||
| 0–1–11–12–13 | | 0–1–11–12–13 | ||
| 1–12/11–5/4–7/5–7/4 | | 1–12/11–5/4–7/5–7/4 | ||
| | | Marvel11 | ||
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| Line 1,596: | Line 1,598: | ||
| 0–2–11–12–13 | | 0–2–11–12–13 | ||
| 1–12/11–7/5–14/9–7/4 | | 1–12/11–7/5–14/9–7/4 | ||
| | | Marvel11 | ||
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| Line 1,813: | Line 1,815: | ||
| 0–2–12–13–20 | | 0–2–12–13–20 | ||
| 1–12/11–14/11–14/9–7/4 | | 1–12/11–14/11–14/9–7/4 | ||
| | | Marvel11 | ||
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| Line 1,834: | Line 1,836: | ||
| 0–7–8–18–20 | | 0–7–8–18–20 | ||
| 1–7/6–14/11–16/11–18/11 | | 1–7/6–14/11–16/11–18/11 | ||
| | | Marvel11 | ||
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| Line 1,945: | Line 1,947: | ||
| 0–1–2–11–12–13 | | 0–1–2–11–12–13 | ||
| 1–12/11–5/4–7/5–14/9–7/4 | | 1–12/11–5/4–7/5–14/9–7/4 | ||
| | | Marvel11 | ||
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