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- this really should not surprising considering that this interval represents the Al-Farabi Quartertone.
| 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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| 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
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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 approximated seventeenth harmonic.
| 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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| 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 is likely the smallest interval in this system that can be used in chords without causing crowding.
| 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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| 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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| 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- 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.
| 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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| ?
| ?
| ?
| ?
|  
| 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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| ?
| ?
| ?
| ?
|  
| 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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| ?
| ?
| [[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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