Chords of orwell: Difference between revisions
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Below is a complete list of all [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[orwell|orwell 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 subminor third [[generator]]s above the root. | Below is a complete list of all [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[orwell|orwell 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 subminor third [[generator]]s above the root. | ||
Typing the chords requires consideration of the fact that orwell equates certain [[11-odd-limit]] consonances – it conflates [[14/11]] with [[9/7]], [[11/7]] with [[14/9]], [[12/11]] with [[11/10]], and [[11/6]] with [[20/11]]. If a [[transversal]] can be found which shows the chord to be [[dyadic chord #Essentially tempered dyadic chord|essentially just]], that transversal is listed along with a typing as [[otonal]], [[utonal]], or [[ambitonal]]. Sometimes multiple such transversals exist, in which case the chord is a [[plurichord]], and the type is given for all possible interpretations. If the chord is [[dyadic chord #Essentially tempered dyadic chord|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 9/7 and 11/10 over the root. | Typing the chords requires consideration of the fact that orwell equates certain [[11-odd-limit]] consonances – it conflates [[14/11]] with [[9/7]], [[11/7]] with [[14/9]], [[12/11]] with [[11/10]], and [[11/6]] with [[20/11]]. If a [[transversal]] can be found which shows the chord to be [[dyadic chord #Essentially tempered dyadic chord|essentially just]], that transversal is listed along with a typing as [[otonal]], [[utonal]], or [[ambitonal]]. Sometimes multiple such transversals exist, in which case the chord is a [[plurichord]], and the type is given for all possible interpretations. If the chord is [[dyadic chord #Essentially tempered dyadic chord|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 9/7 and 11/10 over the root. | ||
Those requiring tempering only by [[225/224]] are labeled [[marvel chords|marvel]], by [[99/98]] [[mothwellsmic chords|mothwellsmic]], by [[121/120]] [[biyatismic chords|biyatismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], by [[385/384]] [[keenanismic chords|keenanismic]], and by [[540/539]] [[swetismic chords|swetismic]]. If it requires any two of 99/98, 176/175 and 225/224, it is labeled [[minerva chords|minerva]], any two of 99/98, 121/120 or 540/539, [[big brother chords|big brother]], any two of 121/120, 176/175 or 385/384, [[zeus chords|zeus]], any two of 225/224, 385/384 or 540/539, [[undecimal marvel chords| | Those requiring tempering only by [[225/224]] are labeled [[marvel chords|marvel]], by [[99/98]] [[mothwellsmic chords|mothwellsmic]], by [[121/120]] [[biyatismic chords|biyatismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], by [[385/384]] [[keenanismic chords|keenanismic]], and by [[540/539]] [[swetismic chords|swetismic]]. If it requires any two of 99/98, 176/175 and 225/224, it is labeled [[minerva chords|minerva]], any two of 99/98, 121/120 or 540/539, [[big brother chords|big brother]], any two of 121/120, 176/175 or 385/384, [[zeus chords|zeus]], any two of 225/224, 385/384 or 540/539, [[undecimal marvel chords|marvel11]]. If it requires both 99/98 and 385/384 it is labeled [[orwellian chords|orwellian]], and if it requires three independent commas among those discussed above, it is labeled [[orwell chords|orwell]]. | ||
Orwell has [[mos]] of size 5, 9, 13, 22 and 31. The complaint is often made that orwell is lacking in low-complexity harmonies; however, even the orwell pentatonic scale has three triads and a tetrad. The 9-note mos is of course much better supplied, and with 13 notes we are rolling in chords and tossing them in the air, finding plenty of chords including even the inexorable [[4:5:6|major triad]]. | Orwell has [[mos]] of size 5, 9, 13, 22 and 31. The complaint is often made that orwell is lacking in low-complexity harmonies; however, even the orwell pentatonic scale has three triads and a tetrad. The 9-note mos is of course much better supplied, and with 13 notes we are rolling in chords and tossing them in the air, finding plenty of chords including even the inexorable [[4:5:6|major triad]]. | ||
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| 0–1–3–6 | | 0–1–3–6 | ||
| 1–7/6–9/7–8/5 | | 1–7/6–9/7–8/5 | ||
| | | Marvel11 | ||
| | | | ||
| [[File:Orwell_0_1_3_6_22edo.mp3]] | | [[File:Orwell_0_1_3_6_22edo.mp3]] | ||
| Line 359: | Line 360: | ||
| 0–3–5–6 | | 0–3–5–6 | ||
| 1–11/10–9/7–8/5 | | 1–11/10–9/7–8/5 | ||
| | | Marvel11 | ||
| | | | ||
| [[File:Orwell_0_3_5_6_22edo.mp3]] | | [[File:Orwell_0_3_5_6_22edo.mp3]] | ||
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| 0–2–3–14 | | 0–2–3–14 | ||
| 1–9/8–11/8–8/5 | | 1–9/8–11/8–8/5 | ||
| | | Marvel11 | ||
| | | | ||
| | | | ||
| Line 828: | Line 829: | ||
| 0–11–12–14 | | 0–11–12–14 | ||
| 1–9/8–7/5–18/11 | | 1–9/8–7/5–18/11 | ||
| | | Marvel11 | ||
| | | | ||
| | | | ||
| Line 1,269: | Line 1,270: | ||
| 0–3–5–6–17 | | 0–3–5–6–17 | ||
| 1–11/10–9/7–8/5–9/5 | | 1–11/10–9/7–8/5–9/5 | ||
| | | Marvel11 | ||
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|- | |- | ||
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| 0–11–12–14–17 | | 0–11–12–14–17 | ||
| 1–9/8–7/5–18/11–9/5 | | 1–9/8–7/5–18/11–9/5 | ||
| | | Marvel11 | ||
| | | | ||
|} | |} | ||