159edo/Interval names and harmonies: Difference between revisions
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| Ultraprime, Narrow Subminor Second | | Ultraprime, Narrow Subminor Second | ||
| Dt<, Edb<↑ | | Dt<, Edb<↑ | ||
| By default, this interval is a type of parachromatic quartertone and is thus used in much the same way as 24edo's own Ultraprime | | By default, this interval is a type of parachromatic quartertone- specifically, the representation of the Al-Farabi Quartertone- and is thus used in much the same way as 24edo's own Ultraprime; what might be surprising is that five of these add up to this system's approximation of the Septimal Subminor Third. | ||
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| 8 | | 8 | ||
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| Tendomean Minor Second, Tendomean Augmented Prime | | Tendomean Minor Second, Tendomean Augmented Prime | ||
| D#\, Eb↑\ | | D#\, Eb↑\ | ||
| As the approximation of both the seventeenth harmonic and the interval formed from stacking two Ultraprimes, this interval is used accordingly. | | As the approximation of both the [[octave-reduced]] seventeenth harmonic and the interval formed from stacking two Ultraprimes, this interval is used accordingly. | ||
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| 15 | | 15 | ||
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| Wide Major Second | | Wide Major Second | ||
| E/, Fd<↓ | | E/, Fd<↓ | ||
| This interval is interesting on the basis that it is formed by stacking two instances of the | | This interval is interesting on the basis that it is formed by stacking two instances of the octave-reduced approximation of the seventeenth harmonic. | ||
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| 29 | | 29 | ||
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| Narrow Supermajor Second | | Narrow Supermajor Second | ||
| E↑\, Fd>↓ | | E↑\, Fd>↓ | ||
| This interval is of note because it is utilized in approximations of the [[17-odd-limit]]; what's more, it is also the whole tone in this system's superpyth diatonic scale, and | | This interval is of note because it is utilized in approximations of the [[17-odd-limit]]; what's more, it is also the whole tone in this system's superpyth diatonic scale, and in fact, two of these add up to the approximation of the Septimal Supermajor Third in this system. | ||
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| 30 | | 30 | ||
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| Lesser Supermajor Second | | Lesser Supermajor Second | ||
| E↑, Dx | | E↑, Dx | ||
| This interval can be interpreted as a type of second on the basis of it approximating the sum of the syntonic comma and the Pythagorean Major Second; it also appears in approximations of [[5-limit]] Neapolitan scales as the interval formed from stacking two Ptolemaic Minor Seconds, making it double as a type of diminished third. | | This interval can be interpreted as a type of second on the basis of it approximating the sum of the syntonic comma and the Pythagorean Major Second; it also appears in approximations of [[5-limit]] Neapolitan scales as the interval formed from stacking two Ptolemaic Minor Seconds, making it double as a type of diminished third, and is likely the smallest interval in this system that can be used in chords without causing crowding. | ||
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| 31 | | 31 | ||
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| Greater Supermajor Second, Narrow Inframinor Third | | Greater Supermajor Second, Narrow Inframinor Third | ||
| Fd<, Et<↓, E↑/ | | Fd<, Et<↓, E↑/ | ||
| As the approximation of the seventh subharmonic, this interval is used accordingly | | As the approximation of the octave-reduced seventh subharmonic- that is, the Septimal Supermajor Second- this interval is used accordingly; in fact, since three of these add up to a Perfect Fifth in this system, there are multiple ways this interval can be used in chords to great effect. | ||
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| 32 | | 32 | ||
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| ? | | ? | ||
| ? | | ? | ||
| | | sm3, Kum3 | ||
| | | Lesser Subminor Third, Wide Ultramajor Second | ||
| | | Et>, Fd>↑, F↓\ | ||
| | | As the approximation of the Septimal Subminor Third, this interval is used accordingly; what's more, due in part to both the [[keenanisma]] being tempered out and the fact that three of these add up to the Pythagorean Minor Sixth, this interval can be used to great effect in chords. | ||
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| 36 | | 36 | ||
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| ? | | ? | ||
| ? | | ? | ||
| | | km3 | ||
| | | Greater Subminor Third | ||
| | | F↓, Gbb | ||
| | | This interval can be interpreted as a type of third on the basis of it approximating result of subtracting a syntonic comma from a Pythagorean Minor Third; however, it most frequently appears in approximations of [[5-limit]] Harmonic scales as the interval between the Ptolemaic Minor Sixth and the Ptolemaic Major Seventh, making it double as a type of augmented second. | ||
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| 37 | | 37 | ||
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| ? | | ? | ||
| [[20/17]] | | [[20/17]] | ||
| | | Rkm3 | ||
| | | Wide Subminor Third | ||
| | | This interval is utilized in approximations of the [[17-odd-limit]], courtesy of acting as the [[fourth complement]] to the Narrow Supermajor Second. | ||
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