159edo/Interval names and harmonies: Difference between revisions

| Perfect Unison

| D

:* Is the basic representation of a given chord's root

:* Is the basic representation of the Tonic

| Wide Prime

| D/

:* Is useful for defining [[11-limit]] subchromatic alterations in the Western-Classical-based functional harmony of this system

:* Can function as both a type of subchroma and a type of reverse diesis in this system

* Is useful for slight dissonances that convey something less than satisfactory

| rK1

| Narrow Superprime

* Approximates the [[ptolemisma]] and the [[biyatisma]]

* Is useful for slight dissonances that create noticeable tension

| K1

| Lesser Superprime

:* Is especially useful as a basis for defining [[5-limit]] subchromatic alterations in the Western-Classical-based functional harmony of this system

:* Can be considered a type of reverse diesis

* Is a dissonance to be avoided in Western-Classical-based harmony unless deliberately used for expressive purposes

:* An appoggiatura

:* An acciaccatura

| S1, kU1

| Greater Superprime, Narrow Inframinor Second

:* Can function as both a type of parachroma and a type of diesis in this system

:* Can be considered a type of parachroma

:* Used for hidden subchromatic voice-leading in the middle voices

:* Used in a contrapuntal passage in which both of the notes separated by this interval in one voice work well against the notes in all other voices

:* Deliberately used for expressive purposes

:* An appoggiatura

:* An acciaccatura

| um2, RkU1

| Inframinor Second, Wide Superprime

* Approximates the [[45/44|Undecimal Fifth-Tone]]

* Approximates a complex 11-limit Paradiatonic quartertone that is the namesake of 24edo's own Inframinor Second  

:* Is capable of being used in progressions reminiscent of that system's [[SpiralProgressions|spiral progressions]]

:* Used for hidden voice-leading in the middle voices

:* Used for tonality-flux-based chord progressions

:* Used in a contrapuntal passage in which both of the notes separated by this interval in one voice work well against the notes in all other voices

:* Deliberately used for expressive purposes

:* A non-chord passing tone

:* The destination for a glissando

| kkm2, Rum2, rU1

| Wide Inframinor Second, Narrow Ultraprime

* Approximates the [[40/39|Tridecimal Minor Diesis]]

::* It has the potential to move directly back down to the Tonic through a parachromatic motion

::* It has the potential to move away from the Tonic towards either a Contralead or Supertonic harmony through a diatonic or paradiatonic motion

::* It cannot occur as the distance between any two notes in a single chord in Western-Classical-based polypedal harmony due to its dissonance

::* It can be used in Western-Classical-based harmony as part of a contrapuntal passage in which both of the notes separated by this interval in one voice work well against the notes in all other voices

::* It can be used in Western-Classical-based harmony for hidden voice-leading in the middle voices

| U1, rKum2

| Ultraprime, Narrow Subminor Second

::* Can be used more overtly in both melodic and harmonic voice-leading in general, though doing so in Western-Classical-based music requires a proper set-up

::* Cannot occur as the distance between any two notes in a single chord in Western-Classical-based polypedal harmony due to its dissonance

::* Has the potential to move away from the Tonic towards either a Contralead or Supertonic harmony through a type of Diatonic or Paradiatonic semitone motion

* Is one fifth of this system's approximation of the Septimal Subminor Third

:* Can be used in Superpyth-based melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

:* Follows similar interval arithmetic logic in relation to Pythagorean intervals, albeit with caveats, since the rastma is not tempered out

* Is one of the more important intervals for use in tonality-flux-based chord progressions

| sm2, Kum2, uA1

| Lesser Subminor Second, Wide Ultraprime, Infra-Augmented Prime

:* Is the narrowest interval that can be used in Western-Classical-based harmony and Neo-Medieval harmony as a proper leading tone

::* Compared to other options, it has a markedly more tense feel

:* Can be used as an unexpected option for a chromatic-type semitone in Western-Classical-based harmony

:* Is capable of being used for similar modulatory moves, albeit with caveats, since such moves on their own don't work the exact same way in this system

* Is one third of this system's approximation of the Ptolemaic Major Second

| km2, RuA1, kkA1

| Greater Subminor Second, Diptolemaic Augmented Prime

:* It frequently acts as a chromatic semitone in Western-Classical-based harmony

:* It demonstrates third-tone functionality- especially in relation to this system's approximation of the Pythagorean Major Second- due to the combination of commas tempered out in this system

:* Is capable of being used for similar modulatory moves, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| Rkm2, rKuA1

| Wide Subminor Second, Lesser Sub-Augmented Prime

:* In Western-Classical-based harmony as part of the simul cadence due to it providing a smooth option for both voice-leading and chord construction

:* As an unexpected option for a chromatic-type semitone in Western-Classical-based harmony

:* Is capable of being used in certain similar melodic and harmonic gestures, albeit with caveats, since such moves on their own don't work the exact same way in this system

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| rm2, KuA1

| Narrow Minor Second, Greater Sub-Augmented Prime

:* It serves as a type of leading tone when resolving septimal harmony constructions to classic harmony constructions

:* It serves as a type of small chromatic semitone in undecimal harmony constructions

* Is one sixth of this system's approximation of the Perfect Fourth

| m2, kA1

| Pythagorean Minor Second, Ptolemaic Augmented Prime

:* Can be used readily in both melodic and harmonic voice-leading in general

:* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this causes dissonance, and thus requires resolution

::* Has the potential to move directly back down to the Tonic as a Contralead, though in non-meantone systems like this one, such a gesture using this interval has a slightly more tense feel

::* Can serve as a possible interval between the Tonic and the root of a Neapolitan chord

::* It separates Pythagorean Major intervals from Ptolemaic Minor Intervals, and likewise separates Ptolemaic Major intervals from Pythagorean Minor intervals

* Is one half of this system's approximation of the Classic Major Second as a consequence of the [[schisma]] being tempered out in this system

:* Can be used in [[Warped diatonic|Warped Diatonic]] gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| Rm2, RkA1

| Artomean Minor Second, Artomean Augmented Prime  

:* Can be used as an unexpected option for a chromatic-type semitone in Western-Classical-based harmony

:* Can be used as a type of Diatonic semitone in undecimal harmony

:* Is one of two in this system that are essential in executing the [[Frameshift comma #Frameshift cedence|frameshift cadence]]  

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| rKm2, rA1

| Tendomean Minor Second, Tendomean Augmented Prime  

:* Can be used as an unexpected option for a Diatonic-type semitone in Western-Classical-based harmony

:* Can be used as a type of chromatic semitone in undecimal harmony

:* Can be used in Faux-Classical-based melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since the biyatisma is not tempered out

:* Can be used in Warped Diatonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

| Km2, A1

| Ptolemaic Minor Second, Pythagorean Augmented Prime

:* Is one of the staples of both melodic and harmonic voice-leading

:* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this causes crowding, and thus requires resolution

::* Has the potential to move directly back down to the Tonic as a Contralead, though in non-meantone systems like this one, such a gesture using this interval has a slightly more lax and natural feel

::* Has close affinities with the Serviant due to being located at roughly a Ptolemaic Major Third away from it

::* Can serve as a possible interval between the Tonic and the root of a Neapolitan chord

:* Is generally the interval that defines the default value of [[Wikipedia: Sharp (music)|sharps]] and [[Wikipedia: Flat (music)|flats]] in this system, and is thus very helpful as a reference interval

:* Is one of two in this system that are essential in executing the frameshift cadence

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| RKm2, kn2, RA1

| Wide Minor Second, Artoretromean Augmented Prime

:* It functions as both a type of chromatic semitone and a type of Diatonic semitone in septimal harmony

* Is one third of this system's approximation of the Octave-Reduced Thirteenth Subharmonic

:* Can be used in Warped Diatonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system  

|-

| kN2, rKA1

| Lesser Supraminor Second, Tendoretromean Augmented Prime

:* It can be thought of as something along the lines of a "wide semitone" in voice-leading

:* It demonstrates trienthird functionality- namely in relation to this system's approximation of the Classic Major Third- due to the combination of commas tempered out in this system

:* As an unexpected option for a Diatonic-type semitone in Western-Classical-based harmony

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, since such moves on their own don't work the exact same way in this system

|-

| KKm2, rn2, KA1

| Greater Supraminor Second, Diptolemaic Limma, Retroptolemaic Augmented Prime

:* It frequently acts as a Diatonic semitone in Western-Classical-based harmony

:* It demonstrates two-third-tone functionality- especially in relation to this system's approximation of the Pythagorean Major Second- due to the combination of commas tempered out in this system

:* It demonstrates trienthird functionality- namely in relation to this system's approximation of the Pythagorean Major Third- due to the combination of commas tempered out in this system

| n2, SA1

| Artoneutral Second, Lesser Super-Augmented Prime

:* It can be thought of as something along the lines of a "wide semitone" in voice-leading

:* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this causes dissonance, and thus requires resolution

::* Has the potential to move to the Pythagorean Minor Third through a Paradiatonic "narrow whole tone" motion  

::* Has the potential to move to the Lesser Subminor Second through a type of Chromatic semitone motion  

* Is one half of this system's approximation of the Neo-Gothic Minor Third

* Is one third of this system's approximation of the Classic Diminished Fourth

:* Is capable of being used for similar modulatory moves, albeit with caveats, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| N2, RkUA1

| Tendoneutral Second, Greater Super-Augmented Prime

:* It can be thought of as something along the lines of a "narrow whole tone" in voice-leading

:* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this causes crowding, and thus requires resolution

::* Has the potential to move to the Pythagorean Minor Third through a Paradiatonic "wide semitone" motion  

::* Has the potential to move to the Lesser Subminor Second through a type of Chromatic semitone motion

* Is one fifth of this system's approximation of the Just Paramajor Fifth

:* Follows similar interval arithmetic logic in relation to Pythagorean intervals, albeit with caveats, since the rastma is not tempered out

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

| kkM2, RN2, rUA1

| Lesser Submajor Second, Diretroptolemaic Augmented Prime

* Is one half of this system's approximation of the Classic Minor Third

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

* Is found in 53edo as that system's Submajor Second, and can thus be used to create identical-sounding melodic and harmonic gestures in this system  

| Kn2, UA1

| Greater Submajor Second, Ultra-Augmented Prime

:* It can be thought of as something along the lines of a "narrow whole tone" in voice-leading

:* It can be thought of as a type of sesquichroma when acting in this capacity

* Is one third of this system's approximation of the Perfect Fourth

:* Can be used in Faux-Classical-based melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| rkM2, KN2

| Narrow Major Second

* Is one half of the approximation of the traditional, [[low-complexity JI|low complexity]] Undecimal Neutral Third in this system

* Is one third of the approximation of the Classic Acute Fourth in this system

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| kM2

| Ptolemaic Major Second

:* Can be used readily in both melodic and harmonic voice-leading in general

:* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this causes crowding, and thus requires resolution

:* Is one the intervals in this system that are essential in executing any sort of variation on Jacob Collier's "Four Magical chords" from his rendition of "In the Bleak Midwinter"  

::* It has close affinities with the Serviant due to being located at roughly a Ptolemaic Minor Third away from it

* Is one half of this system's approximation of the Octave-Reduced Thirteenth Subharmonic

* Is one fifth of this system's approximation of the Pythagorean Major Sixth

:* Can be used in Warped Diatonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system  

|-

| RkM2

| Artomean Major Second

:* Is useful for modulating to keys that are not found on the same circle of fifths

* Is one third of this system's approximation of the Classic Augmented Fourth

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, since such moves on their own don't work the exact same way in this system

|-

| rM2

| Tendomean Major Second

* Approximates the [[28/25|Middle Major Second]]

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, since such moves on their own don't work the exact same way in this system

|-

| M2

| Pythagorean Major Second

:* Is one of the staples of both melodic and harmonic voice-leading

:* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this causes crowding, and thus requires resolution

::* It functions as a Double Dominant due to being the result of stacking two Perfect Fifths and octave-reducing

::* It sees usage in Paradiatonic and Parachromatic harmonies in addition to the more obvious Diatonic-related uses

* Is one fourth of this system's approximation of the Classic Minor Sixth as a consequence of the schisma being tempered out in this system

* Is reachable through stacking three of this system's approximation of the Septimal Subfourth and octave-reducing

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| RM2

| Wide Major Second

:* It is very likely to be treated as a type of whole tone when working in Neo-Medieval harmony

* Is reachable through stacking two of this system's approximation of the Octave-Reduced Seventeenth Harmonic

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system  

|-

| rKM2

| Narrow Supermajor Second

:* Can be used as an unexpected option for a diminished third in Western-Classical-based harmony

:* It can be thought of as a type of whole tone when acting in this capacity

* Is one half of this system's approximation of the Septimal Supermajor Third

* Is reachable through stacking two of this system's approximation of the Septendecimal Fifth and octave-reducing

:* Can be used in Superpyth-based melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| KM2

| Lesser Supermajor Second

:* It readily appears in approximations of 5-limit Neapolitan scales as the interval formed from stacking two Ptolemaic Minor Seconds

:* It can be thought of as a type of second when acting in this capacity

* Is likely the smallest interval in this system that can be used in chords without causing crowding

:* Is capable of being used in certain similar melodic and harmonic gestures, albeit with caveats, since such moves on their own don't work the exact same way in this system   

|-

| SM2, kUM2

| Greater Supermajor Second, Narrow Inframinor Third

::* Since three of these add up to this system's approximation of the Perfect Fifth, there are multiple ways it can be used in chords to great effect

::* This causes ambisonance, so chords that utilize it are prone to decomposition

::* It functions as a Contravaricant due to its semiambitonal properties relative to the Diatonic scale

* Is one half of this system's approximation of the Septimal Subfourth

:* Is capable of being used in certain similar melodic and harmonic gestures, albeit with caveats, since such moves on their own don't work the exact same way in this system  

|-

| um3, RkUM2

| Inframinor Third, Wide Supermajor Second

:* It has the potential to move back down to the Supertonic through a diatonic or paradiatonic motion

:* It has the potential to move up towards a Mediant harmony through a parachromatic motion

* Is one fourth of this system's approximation of the Octave-Reduced Seventh Harmonic

:* Can be used in Warped Diatonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| kkm3, KKM2, Rum3, rUM2

| Wide Inframinor Third, Narrow Ultramajor Second, Semifourth

:* It can be used both in triads framed by a Perfect Fourth and in triads Framed by a Perfect Fifth

* Is one half of a Perfect Fourth in this system

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, since such moves on their own don't work the exact same way in this system

:* Is capable of being used in certain similar melodic and harmonic gestures, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| UM2, rKum3

| Ultramajor Second, Narrow Subminor Third

:* It has the potential to move back down to the Supertonic through a parachromatic motion

:* It has the potential to move up towards a Mediant harmony through a diatonic or paradiatonic motion

| sm3, Kum3

| Lesser Subminor Third, Wide Ultramajor Second

::* This causes ambisonance, so chords that utilize it are prone to decomposition

::* It functions as a Contravaricant due to its semiambitonal properties relative to the Diatonic scale

::* It is useful in forming not only strident-sounding triads framed by the Perfect Fifth, but also other, ambisonant triads framed by the Perfect Fourth

| km3

| Greater Subminor Third

:* It most frequently appears in approximations of 5-limit Harmonic scales as the interval between the Ptolemaic Minor Sixth and the Ptolemaic Major Seventh

:* It can be thought of as a type of third when acting in this capacity

:* Can be used in Superpyth-based melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

:* Is capable of being used in certain similar melodic and harmonic gestures, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| Rkm3

| Wide Subminor Third

* Approximates the [[20/17|Septendecimal Minor Third]]

:* Can be used in Warped Diatonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| rm3

| Narrow Minor Third

:* Can be used in Western-Classical-based harmony and Neo-Medieval harmony very easily

::* When it is found in what is otherwise the traditional Diatonic context of a Minor key

* Is one third of this system's approximation of the Greater Tridecimal Neutral Sixth  

| Pythagorean Minor Third

| F

:* Is one of the staples of both melodic and harmonic motion in general

:* Readily occurs as the distance between two notes in a single chord in Western-Classical-based polypedal harmony

::* It is very useful as an interpretation of the dissonant Minor Third from [[Wikipedia: Medieval music #Early_polyphony: organum|Medieval music's florid organum]]  

::* It can be used in creating a subtle instability in certain Diatonic harmonies

| Artomean Minor Third

| F/

::* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

* Is one half of this system's approximation of the Larger Septendecimal Tritone

| rKm3

| Tendomean Minor Third  

* Approximates the [[153/128|Septendecimal Tendomean Minor Third]]

:* Is used accordingly as part of a diminished triad

* Is reachable through stacking two of this system's approximation of the Just Paramajor Fifth and octave-reducing

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

* Can easily be used in modulatory maneuvers similar to those performed by Jacob Collier

| Km3

| Ptolemaic Minor Third

::* It is a staple interval in Western-Classical-based Diatonic scales

:* Readily occurs as the distance between two notes in a single chord in Western-Classical-based polypedal harmony

::* It is one of four imperfect consonances in this system, rendering it extremely suitable for use in a Tonic triad in Western-Classical-based polypedal harmony

* Is reachable through stacking three of this system's approximation of the Octave-Reduced Seventeenth Harmonic

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, since such moves on their own don't work the exact same way in this system

|-

| RKm3, kn3

| Wide Minor Third

:* Is the widest interval that can reasonably be used in Western-Classical-based harmony and Neo-Medieval harmony as a type of Minor Third

* Is one half of this system's approximation of the Just Paraminor Fifth

* Is one third of this system's approximation of the Neapolitan Augmented Sixth as a consequence of the [[hemimage comma]] being tempered out in this system

:* Can be used in Faux-Classical-based melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| kN3, ud4

| Lesser Supraminor Third, Infra-Diminished Fourth

:* It functions as the [[fourth complement]] to this system's approximation of the Undecimal Submajor Second

* Is one half of this system's approximation of the Undecimal Acute Ultra-Diminished Fifth

| KKm3, rn3, Rud4

| Greater Supraminor Third, Diretroptolemaic Diminished Fourth

:* It serves as the [[fifth complement]] of the Octave-Reduced Thirteenth Subharmonic

:* Is very useful for essentially tempered chords such as [[273/272|tannic chords]]

* Is reachable through stacking three of this system's approximation of the Classic Minor Second

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

* Is found in 53edo as that system's Supraminor Third, and can thus be used to create identical-sounding melodic and harmonic gestures in this system  

| n3, rKud4

| Artoneutral Third, Lesser Sub-Diminished Fourth

:* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this causes dissonance, and thus requires resolution

:* It is a staple interval of the Western-Classical based Paradiatonic scale in this system

::* Has the potential to move to the Perfect Fourth through a Paradiatonic "narrow whole tone" motion  

::* Has the potential to move to the Lesser Subminor Third through a type of Chromatic semitone motion

:* Follows similar interval arithmetic logic in relation to Pythagorean intervals, albeit with caveats, since the rastma is not tempered out

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system  

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since the rastma is not tempered out

|-

| N3, sd4, Kud4

| Tendoneutral Third, Greater Sub-Diminished Fourth

:* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this causes dissonance, and thus requires resolution

::* Has the potential to move to the Perfect Fourth through a Paradiatonic "wide semitone" motion  

::* Has the potential to move to the Lesser Subminor Third through a type of Chromatic semitone motion

* Is one half of this system's approximation of the Septendecimal Fifth, which is a a possible generator for this system's Superpyth scale

:* Is capable of being used for similar modulatory moves, albeit with caveats, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| kkM3, RN3, kd4

| Lesser Submajor Third, Retroptolemaic Diminished Fourth

| This interval

:* Is ostensibly one of the easiest 13-limit thirds to utilize in chords framed by either a Grave Fifth or an Acute Fifth

* Is one third of this system's approximation of the Classic Major Seventh

:* Can be used in Warped Diatonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

* Is found in 53edo as that system's Submajor Third, and can thus be used to create identical-sounding melodic and harmonic gestures in this system   

| Kn3, Rkd4

| Greater Submajor Third, Artoretromean Diminished Fourth

:* Serves as the fourth complement to this system's approximation of the Tridecimal Supraminor Second

* Is one third of this system's approximation of the Pythagorean Major Seventh

:* Can be used in Warped Diatonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system  

|-

| rkM3, KN3, rd4

| Narrow Major Third, Tendoretromean Diminished Fourth

:* Is the narrowest interval that can reasonably be used in Western-Classical-based harmony and Neo-Medieval harmony as a type of Major Third

* Is one half of this system's approximation of the Just Paramajor Fifth

:* Is capable of being used in certain similar melodic and harmonic gestures, albeit with caveats, since such moves on their own don't work the exact same way in this system

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, since such moves on their own don't work the exact same way in this system

|-

| kM3, d4

| Ptolemaic Major Third, Pythagorean Diminished Fourth

::* It is a staple interval in Western-Classical-based Diatonic scales

:* Readily occurs as the distance between two notes in a single chord in Western-Classical-based polypedal harmony

::* It is one of four imperfect consonances in this system, rendering it extremely suitable for use in a Tonic triad in Western-Classical-based polypedal harmony

:* Serves as an enharmonic substitution for the Classic Major Third when building chords for purposes of voice-leading, in which case it counts as an unresolved interval

:* Can be used in Faux-Classical-based melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system  

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| RkM3, Rd4

| Artomean Major Third, Artomean Diminished Fourth

* Approximates the [[64/51|Septendecimal Artomean Major Third]]

* Is reachable through stacking two of this system's approximation of the Middle Major Second  

| rM3, rKd4

| Tendomean Major Third, Tendomean Diminished Fourth

* Approximates the [[63/50|Quasi-Tempered Major Third]]

::* Creating the familiar augmented triads of 12edo

::* Performing modulatory maneuvers based around the aforementioned triads

:* It just so happens that stacking this interval with this system's approximation of the Quasi-Tempered Minor Third makes triads of just this sort in the [[27-odd-limit]]

|-

| M3, Kd4

| Pythagorean Major Third, Ptolemaic Diminished Fourth

::* It is a useful interval in Western-Classical-based Diatonic scales

:* Can easily occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony

::* It is very useful as an interpretation of the dissonant Major Third from Medieval music's florid organum  

::* It can be used in creating a subtle instability in certain Diatonic harmonies

:* Leads to this interval being useful in forming oddly charming augmented triads

* Moving up by seven of these with two octave-reductions is an unexpected alternative means for exploiting the frameshift comma, though this system's approximation of the Axirabian Limma remains essential to the process even in this case

| RM3, kUd4

| Wide Major Third, Lesser Super-Diminished Fourth

:* Can be used in Western-Classical-based harmony and Neo-Medieval harmony very easily

::* When it is found in what is otherwise the traditional Diatonic context of a Major key

:* Can be used to make augmented triads framed by this system's closest approximation of [[acoustic phi]]

* Is reachable through stacking five of this system's approximation of the Septimal Minor Semitone

| rKM3, RkUd4

| Narrow Supermajor Third, Greater Super-Diminished Fourth

* Approximates the [[51/40|Septendecimal Major Third]]

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| KM3, rUd4, KKd4

| Lesser Supermajor Third, Diptolemaic Diminished Fourth

:* It is easily very useful when it comes to building chords despite- or perhaps even because of- its dissonance

:* It can be thought of as a type of third when acting in this capacity

* Is one half of this system's approximation of the Greater Tridecimal Neutral Sixth  

| SM3, kUM3, rm4, Ud4

| Greater Supermajor Third, Ultra-Diminished Fourth

:* Can occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, though this causes dissonance, and thus requires resolution  

::* It is useful in forming not only strident-sounding triads framed by the Perfect Fifth, but also different types of augmented and superaugmented triad

* Is one half of this system's approximation of the Marvelous Minor Sixth as a consequence of the hemimage comma being tempered out in this system

:* Can be used in Superpyth-based melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| m4, RkUM3

| Paraminor Fourth, Wide Supermajor Third

::* It functions as a Misoserviant due to its dissonance and its properties relative to the Diatonic scale

::* It has the potential to move back down to the Tonic harmony through a Paradiatonic motion

::* It has the potential to move up towards an Intersubiant harmony through a Parachromatic semitone-type motion, with this move granting additional follow-up options

* Follows after the pattern of inframinor and ultramajor intervals sounding like members of the adjacent interval classes- specifically, the paraminor fourth sounds more like a third than a fourth

:* Is capable of being used for similar modulatory moves, albeit with caveats, since such moves on their own don't work the exact same way in this system  

|-

| Rm4, KKM3, rUM3

| Wide Paraminor Fourth, Narrow Ultramajor Third

* Approximates the [[13/10|Tridecimal Semisixth]]

:* Is capable of being used in certain similar melodic and harmonic gestures, albeit with caveats, since such moves on their own don't work the exact same way in this system  

* Is very useful for essentially tempered chords such as [[island chords]]

| UM3, rKm4

| Ultramajor Third, Narrow Grave Fourth

:* It has the potential to move up to the Intersubiant harmony through Paradiatonic motion

:* It has the potential to move back down to a Mediant harmony through a type of Chromatic or Parachromatic semitone motion

* Is reachable through stacking four of this system's approximation of the Neo-Gothic Major Third and octave-reducing  

:* Can be used in Warped Diatonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| s4, Km4

| Lesser Grave Fourth, Wide Ultramajor Third

:* Is really useful for forming suspensions on account of its dissonance

* Is one half of this system's approximation of the Septimal Supermajor Sixth  

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| k4

| Greater Grave Fourth

* Approximates a complex 5-limit interval formed by subtracting a syntonic comma from a Perfect Fourth

* Is one half of this system's approximation of the Tridecimal Semitwelfth

| Rk4

| Wide Grave Fourth

* Is one half of this system's approximation of the Octave-Reduced Seventh Harmonic

:* Can be used in Warped Diatonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

* Is one of two intervals that can generate a Diatonic MOS with a more extreme hardness than that seen in Ultrapyth temperament

| Narrow Fourth

| G\

:* Is one of two intervals that can generate a Diatonic MOS with a sound and feel akin to that seen in Superpyth temperament

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

:* Can be used in both Superpyth-based and Faux-Classical-based melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system  

|-

| Perfect Fourth

| G

:::* It is one of two intervals that can generate this system's approximation of the Pythagorean Diatonic MOS

:* Can easily occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony  

::* It is the basic interval for framing a standard tetrachord in this system

:* Is one of four perfect consonances in this system

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

:* A chain of 53 Perfect Fourths closing at the octave due to [[Mercator's comma]] being tempered out

:* Virtually all of its functionality in the realm of Western-Classical-based Diatonic scales and Diatonic functional harmony

:* New approaches enabled by this system supporting temperaments such as [[sextilififths]]

:* A sizable chunk of its functionality in the realm of Western-Classical-based Paradiatonic functional harmony

| Wide Fourth

| G/

:* Is one of two intervals that can generate a Diatonic MOS with a sound and feel akin to that seen in Flattone temperament

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| rK4

| Narrow Acute Fourth

:* Is one of two intervals that can generate a Diatonic MOS with a softness so extreme as to be quasi-equalized

* Is reachable through stacking four of this system's approximation of the Tridecimal Supraminor Second

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| K4

| Lesser Acute Fourth

:* Is one of two xenharmonic intervals that appear in the otherwise traditional settings of Western-Classical-based Diatonic scales

::* Specifically, it is found between the Major Third and Major Sixth in the Lydian Mode of the familiar [[Zarlino|Ptolemaic Sequence]], and is ideally in the exact same position for both Ionian and Mixolydian modes, though this technically results in there being Diatonic scales of different varieties- namely the Bilawal and Myxian scale types

| S4, kM4

| Greater Acute Fourth

* Is reachable through stacking two of this system's approximation of the Septimal Subminor Third

* Is reachable through stacking five of this system's approximation of the Large Septendecimal Semitone

:* Is capable of being used in certain similar melodic and harmonic gestures, albeit with caveats, since such moves on their own don't work the exact same way in this system  

|-

| RkM4, ud5

| Wide Acute Fourth, Infra-Diminished Fifth

:* Is extremely useful as an imperfect dissonance in Western-Classical-based Paradiatonic functional harmony

:* Has interesting functions in undecimal harmony in which it can act as both an acute fourth and an infra-augmented fourth

:* It can be thought of as a type of sesquiflat-fifth when acting in this capacity  

* Is one half of this system's approximation of the Tridecimal Submajor Seventh

| rM4, Rud5

| Narrow Paramajor Fourth, Diretroptolemaic Diminished Fifth

:* Can be used in Superpyth-based melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

:* Is capable of being used in certain similar melodic and harmonic gestures, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| M4, rKud5

| Paramajor Fourth, Lesser Sub-Diminished Fifth

::* It functions as an Intersubiant due to its ambisonance and its properties relative to the Diatonic scale

::* It has the potential to move up towards to the Dominant harmony through a Paradiatonic motion

::* It has the potential to move up towards an Interregnant harmony through a Paradiatonic semitone-type motion, with this move granting additional follow-up options

* Is reachable through stacking eight of this system's approximation of the Septendecimal Whole Tone and octave-reducing

:* Can be used in Warped Diatonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system  

:* Follows similar interval arithmetic logic in relation to Pythagorean intervals, albeit with caveats, since the rastma is not tempered out

:* Is capable of being used in certain similar melodic and harmonic gestures, albeit with caveats, since such moves on their own don't work the exact same way in this system

| RM4, uA4, Kud5

| Infra-Augmented Fourth, Greater Sub-Diminished Fifth

:* It can be thought of as a type of fifth when acting in this capacity

:* It can be thought of as a type of fourth when acting in this capacity

* Is one half of this system's approximation of the Undecimal Major Seventh

| kkA4, RuA4, kd5

| Diptolemaic Augmented Fourth, Retroptolemaic Diminished Fifth

:* It frequently acts as an Augmented Fourth in Western-Classical-based harmony

:* It acts as an Augmented Fourth in Western-Classical-based Paradiatonic harmony

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system  

|-

| rKuA4, Rkd5

| Lesser Sub-Augmented Fourth, Artoretromean Diminished Fifth

:* It can be thought of as a type of fourth when acting in this capacity

* Is one half of this system's approximation of the Undecimal Infraoctave

| KuA4, rd5

| Greater Sub-Augmented Fourth, Tendoretromean Diminished Fifth

:* It occurs frequently in septimal harmony, especially in harmonic seventh chords

* Is reachable through stacking eleven of this system's approximation of the Al-Farabi Quartertone

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| kA4, d5

| Ptolemaic Augmented Fourth, Pythagorean Diminished Fifth

:* Is one of only two intervals in the tritonic region that is allowed to be built directly on top of the Tonic in Western-Classical-based harmony

:* It functions as an Augmented Fourth in Western-Classical-based functional harmony by default, and is the signature interval of 5-limit Lydian Mode

:* It functions as a Diminished Fifth when acting in this capacity, though this usually only occurs due to voice-leading or the stacking of Pythagorean intervals

* Is reachable through stacking three of this system's approximation of the Middle Major Second

| RkA4, Rd5

| Artomean Augmented Fourth, Artomean Diminished Fifth

:* It can be thought of as a type of augmented fourth when acting in this capacity

* Is reachable through stacking fourteen of this system's approximation of the Tridecimal Supraminor Second and octave-reducing

:* Can be used in melodic and harmonic gestures reminiscent of those found in 10edo, 12edo and 22edo, albeit with caveats, since such moves on their own don't work the exact same way in this system

* Is very useful for essentially tempered chords such as ainic chords

| rKd5, rA4

| Tendomean Diminished Fifth, Tendomean Augmented Fourth

:* It can be thought of as a type of diminished fifth when acting in this capacity

* Is reachable through stacking four of this system's approximation of the Low-Complexity JI Neutral Second

:* Can be used in melodic and harmonic gestures reminiscent of those found in 10edo, 12edo and 22edo, albeit with caveats, since such moves on their own don't work the exact same way in this system

* Is very useful for essentially tempered chords such as ainic chords

| Kd5, A4

| Ptolemaic Diminished Fifth, Pythagorean Augmented Fourth

:* Is one of only two intervals in the tritonic region that is allowed to be built directly on top of the Tonic in Western-Classical-based harmony

:* It functions as a Diminished Fifth in Western-Classical-based functional harmony by default, and is the signature interval of 5-limit Locrian Mode

:* It functions as an Augmented Fourth when acting in this capacity, though this usually only occurs due to voice-leading or the stacking of Pythagorean intervals

* Is reachable through stacking three of this system's approximation of the Larger Septendecimal Tritone and octave-reducing

| kUd5, RA4

| Lesser Super-Diminished Fifth, Artoretromean Augmented Fourth

:* It occurs frequently in septimal harmony, especially in inversions of harmonic seventh chords

* Is reachable through stacking four of this system's approximation of the Just Paramajor Fifth and octave-reducing

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

|-

| RkUd5, rKA4

| Greater Super-Diminished Fifth, Tendoretromean Augmented Fourth

:* It can be thought of as a type of fifth when acting in this capacity

* Is one half of this system's approximation of the Undecimal Ultraoctave

| KKd5, rUDd5, KA4

| Diptolemaic Diminished Fifth, Retroptolemaic Augmented Fourth

:* It frequently acts as a Diminished Fifth in Western-Classical-based harmony

:* It acts as a Diminished Fifth in Western-Classical-based Paradiatonic harmony

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system

:* Can be used in melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system  

|-

| rm5, Ud5, kUA4

| Ultra-Diminished Fifth, Lesser Super-Augmented Fourth

:* It can be thought of as a type of fourth when acting in this capacity

:* It can be thought of as a type of fifth when acting in this capacity

* Is reachable through stacking five of this system's approximation of the Tridecimal Supraminor Second

| m5, RkUA4

| Paraminor Fifth, Greater Super-Augmented Fourth

::* It functions as an Interregnant due to its ambisonance and its properties relative to the Diatonic scale

::* It has the potential to move back down to a Serviant harmony through a Paradiatonic motion

::* It has the potential to move back down to an Intersubiant harmony through a Paradiatonic semitone-type motion, with this move granting additional follow-up options

* Is reachable through stacking five of this system's approximation of the Tridecimal Submajor Third and octave-reducing

:* Can be used in Warped Diatonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system  

:* Follows similar interval arithmetic logic in relation to Pythagorean intervals, albeit with caveats, since the rastma is not tempered out

:* Is capable of being used in certain similar melodic and harmonic gestures, albeit with caveats, since such moves on their own don't work the exact same way in this system

| Rm5, rUA4

| Wide Paraminor Fifth, Diretroptolemaic Augmented Fourth

* Is reachable through stacking three of this system's approximation of the Septendecimal Whole Tone

:* Can be used in Superpyth-based melodic and harmonic gestures reminiscent of those found in that system, albeit with caveats, since such moves on their own don't work the exact same way in this system