Step
|
Cents
|
5 limit
|
7 limit
|
11 limit
|
13 limit
|
17 limit
|
Interval Names
|
Notes
|
0
|
0
|
1/1
|
P1
|
Perfect Unison
|
D
|
This interval...
- Is the basic representation of a given chord's root
- Is the basic representation of the Tonic
- Is one of four perfect consonances in this system
|
1
|
7.5471698
|
|
225/224
|
243/242
|
196/195, 351/350
|
256/255
|
R1
|
Wide Prime
|
D/
|
This interval...
- Approximates the rastma, and thus...
- 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
- Can only be approached in melodic lines indirectly with one or more intervening notes
- Can add to the bandwidth of a sound
|
2
|
15.0943396
|
|
?
|
121/120, 100/99
|
144/143
|
120/119
|
rK1
|
Narrow Superprime
|
D↑\
|
This interval...
- Approximates the ptolemisma and the biyatisma
- Is useful for slight dissonances that create noticeable tension
- Can only be approached in melodic lines indirectly with one or more intervening notes
|
3
|
22.6415094
|
81/80
|
?
|
?
|
78/77
|
85/84
|
K1
|
Lesser Superprime
|
D↑
|
This interval...
- 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
- Is useful in melody as...
- An appoggiatura
- An acciaccatura
- Part of a series of quick passing tones
|
4
|
30.1886792
|
|
64/63
|
56/55, 55/54
|
?
|
52/51
|
S1, kU1
|
Greater Superprime, Narrow Inframinor Second
|
Edb<, Dt<↓
|
This interval...
- Can function as both a type of parachroma and a type of diesis in this system
- Can be considered a type of parachroma
- Is a dissonance to be avoided in Western-Classical-based harmony unless...
- 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
- Is useful in melody as...
- An appoggiatura
- An acciaccatura
- Part of a series of quick passing tones
- The destination for a glissando
|
5
|
37.7358491
|
|
?
|
45/44
|
?
|
51/50
|
um2, RkU1
|
Inframinor Second, Wide Superprime
|
Edb>, Dt>↓
|
This interval...
- Approximates the Undecimal Fifth-Tone
- Approximates a complex 11-limit Paradiatonic quartertone that is the namesake of 24edo's own Inframinor Second
- Is the closest approximation of 31edo's own Superprime found in this system, and thus...
- Is a dissonance to be avoided in Western-Classical-based harmony unless...
- 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
- Is useful in melody as...
- A non-chord passing tone
- The destination for a glissando
|
6
|
45.2830189
|
?
|
?
|
?
|
40/39
|
192/187
|
kkm2, Rum2, rU1
|
Wide Inframinor Second, Narrow Ultraprime
|
Eb↓↓, Dt<\
|
This interval...
- It functions like an Ultraprime in that...
- 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 functions like an Inframinor Second in that...
- 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
- Is one of the more important intervals for use in tonality-flux-based chord progressions
|
7
|
52.8301887
|
|
?
|
33/32
|
?
|
34/33
|
U1, rKum2
|
Ultraprime, Narrow Subminor Second
|
Dt<, Edb<↑
|
This interval...
- It functions as the default parachromatic quartertone in Western-Classical-based Paradiatonic functional harmony, and thus...
- 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 directly back down to the Tonic through a Parachromatic quartertone motion
- 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
- Is the closest approximation of 22edo's Lesser Minor Second in this system, and thus...
- 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 the closest approximation of 24edo's own Ultraprime in this system, and thus...
- 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
|
8
|
60.3773585
|
|
28/27
|
?
|
?
|
88/85
|
sm2, Kum2, uA1
|
Lesser Subminor Second, Wide Ultraprime, Infra-Augmented Prime
|
Dt>, Eb↓\
|
This interval...
- 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 the closest approximation of 19edo's Augmented Prime found in this system, and thus...
- 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
- Can be used for tonality-flux-based chord progressions
|
9
|
67.9245283
|
25/24
|
?
|
?
|
26/25, 27/26
|
?
|
km2, RuA1, kkA1
|
Greater Subminor Second, Diptolemaic Augmented Prime
|
Eb↓, Dt<↑\, D#↓↓
|
This interval...
- 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 the closest approximation of 17edo's Minor Second found in this system, and thus...
- 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
|
10
|
75.4716981
|
|
?
|
?
|
?
|
160/153
|
Rkm2, rKuA1
|
Wide Subminor Second, Lesser Sub-Augmented Prime
|
Eb↓/, Dt<↑
|
This interval...
- Approximates multiple complex 17-limit intervals relative to the Tonic and can be used...
- 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 the closest approximation of 31edo's Subminor Second found in this system, and thus...
- 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 the closest approximation of 16edo's Subminor Second found in this system, and thus...
- 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
|
11
|
83.0188679
|
|
21/20
|
22/21
|
?
|
?
|
rm2, KuA1
|
Narrow Minor Second, Greater Sub-Augmented Prime
|
Eb\, Dt>↑
|
This interval...
- 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
|
12
|
90.5660377
|
256/243, 135/128
|
?
|
?
|
?
|
?
|
m2, kA1
|
Pythagorean Minor Second, Ptolemaic Augmented Prime
|
Eb, D#↓
|
This interval...
- 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
- It serves as a Diatonic semitone in both Western-Classical-based functional harmony and Neo-Medieval harmony in general, and thus...
- 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
- Approximates the Major Chroma or Ptolemaic Augmented Prime, and as such...
- It serves as a chromatic semitone in the 5-limit Diatonic settings that are common to Western-Classical-based harmony, and thus...
- 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
- Is the closest approximation of 13edo's own Minor Second in this system, and thus...
- 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
|
13
|
98.1132075
|
|
?
|
128/121
|
55/52
|
18/17
|
Rm2, RkA1
|
Artomean Minor Second, Artomean Augmented Prime
|
Eb/, D#↓/
|
This interval...
- 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 cadence
- Is the closest approximation of the 12edo Minor Second found in this system, and thus...
- 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
|
14
|
105.6603774
|
|
?
|
?
|
?
|
17/16
|
rKm2, rA1
|
Tendomean Minor Second, Tendomean Augmented Prime
|
D#\, Eb↑\
|
This interval...
- 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
- Is the closest approximation of 22edo's Greater Minor Second in this system, and thus...
- 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
|
15
|
113.2075472
|
16/15
|
?
|
?
|
?
|
?
|
Km2, A1
|
Ptolemaic Minor Second, Pythagorean Augmented Prime
|
D#, Eb↑
|
This interval...
- 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 readily serves as the traditional leading tone in 5-limit Western-Classical-based functional harmony and thus...
- 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
- Approximates the Apotome or Pythagorean Augmented Prime, and thus...
- Is generally the interval that defines the default value of sharps and 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
- Is the closest approximation of 31edo's own Minor Second found in this system, and thus...
- 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
|
16
|
120.7547170
|
|
15/14
|
275/256
|
?
|
?
|
RKm2, kn2, RA1
|
Wide Minor Second, Artoretromean Augmented Prime
|
Ed<↓, Eb↑/, D#/
|
This interval...
- 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
- Is the closest approximation of 10edo's Minor Second, and thus...
- 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
|
17
|
128.3018868
|
|
?
|
?
|
14/13
|
128/119
|
kN2, rKA1
|
Lesser Supraminor Second, Tendoretromean Augmented Prime
|
Ed>↓, D#↑\
|
This interval...
- Approximates the Tridecimal Supraminor Second and a similar 11-limit interval that acts as the Supraminor counterpart to the Undecimal Submajor Second, and thus...
- 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
- Approximates a complex yet uprooted 17-limit interval relative to the Tonic and can be used...
- As an unexpected option for a Diatonic-type semitone in Western-Classical-based harmony
- Is the closest approximation of 19edo's Minor Second found in this system, and thus...
- 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
|
18
|
135.8490566
|
27/25
|
?
|
?
|
13/12
|
?
|
KKm2, rn2, KA1
|
Greater Supraminor Second, Diptolemaic Limma, Retroptolemaic Augmented Prime
|
Ed<\, Eb↑↑, D#↑
|
This interval...
- 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
- Is found in 53edo as that system's Supraminor Second, and can thus be used to create identical-sounding melodic and harmonic gestures in this system
|
19
|
143.3962264
|
|
?
|
88/81
|
?
|
?
|
n2, SA1, kUA1
|
Artoneutral Second, Lesser Super-Augmented Prime
|
Ed<, Dt#<↓
|
This interval...
- 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
- It serves as the smaller and more dissonant of two Neutral Seconds in Western-Classical-based Paradiatonic functional harmony, and thus...
- 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 the closest approximation of 17edo's Neutral Second found in this system, and thus...
- 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
|
20
|
150.9433962
|
|
?
|
12/11
|
?
|
?
|
N2, RkUA1
|
Tendoneutral Second, Greater Super-Augmented Prime
|
Ed>, Dt#>↓
|
This interval...
- 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
- It serves as the larger and more consonant of two Neutral Seconds in Western-Classical-based Paradiatonic functional harmony, and thus...
- 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
- Is the closest approximation of 24edo's own Neutral Second in this system, and thus...
- 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
|
21
|
158.4905660
|
?
|
?
|
?
|
128/117
|
561/512, 1024/935
|
kkM2, RN2, rUA1
|
Lesser Submajor Second, Diretroptolemaic Augmented Prime
|
Ed>/, E↓↓, Dt#>↓/, D#↑↑
|
This interval...
- Is one half of this system's approximation of the Classic Minor Third
- Is the closest approximation of 31edo's own Middle Second found in this system, and thus...
- 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
|
22
|
166.0377358
|
|
?
|
11/10
|
?
|
?
|
Kn2, UA1
|
Greater Submajor Second, Ultra-Augmented Prime
|
Ed<↑, Dt#<, Fb↓/
|
This interval...
- Approximates the Undecimal Submajor Second and a similar 13-limit interval that acts as the Submajor counterpart to the Tridecimal Supraminor Second, and thus...
- It can be thought of as something along the lines of a "narrow whole tone" in voice-leading
- Approximates a complex 11-limit Parachromatic interval formed by stacking an Al-Farabi Quartertone on top of an Apotome, and thus...
- 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
- Is the closest approximation of 22edo's Lesser Major Second in this system, and thus...
- 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
|
23
|
173.5849057
|
|
567/512
|
243/220
|
?
|
425/384
|
rkM2, KN2
|
Narrow Major Second
|
Ed>↑, E↓\, Dt#>, Fb\
|
This interval...
- Is one half of the approximation of the traditional, low complexity Undecimal Neutral Third in this system
- Is one third of the approximation of the Acute Fourth in this system
- Is the closest approximation of the 7edo Second found in this system, and thus...
- 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
|
24
|
181.1320755
|
10/9
|
?
|
256/231
|
?
|
?
|
kM2
|
Ptolemaic Major Second
|
E↓, Fb
|
This interval...
- 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 readily serves as a Diatonic whole tone in Western-Classical-based functional harmony, since...
- 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
- Is the closest approximation of 13edo's own Major Second in this system, and thus...
- 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
|
25
|
188.6792458
|
|
?
|
?
|
143/128
|
512/459
|
RkM2
|
Artomean Major Second
|
E↓/, Fb/
|
This interval...
- 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
- Is the closest approximation of 19edo's Major Second found in this system, and thus...
- 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
|
26
|
196.2264151
|
|
28/25
|
121/108
|
?
|
?
|
rM2
|
Tendomean Major Second
|
E\, Fb↑\
|
This interval...
- Approximates the Middle Major Second
- Is one of two intervals that serve as the closest approximation of the 12edo Major Second found in this system, and thus...
- 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 the closest approximation of 31edo's Major Second found in this system, and thus...
- 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
|
27
|
203.7735849
|
9/8
|
?
|
?
|
?
|
?
|
M2
|
Pythagorean Major Second
|
E, Fb↑
|
This interval...
- 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 readily serves as a Diatonic whole tone in both Western-Classical-based functional harmony and Neo-Medieval harmony in general, since...
- It functions as a Double Dominant due to being the result of stacking two Perfect Fifths and octave-reducing
- Is the whole tone that is used as a reference interval in diatonic-and-chromatic-style interval logic in this system as it pertains to both semitones and quartertones, and thus...
- 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
- Is one of two intervals that serve as the closest approximation of the 12edo Major Second found in this system, and thus...
- 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
|
28
|
211.3207547
|
|
?
|
?
|
44/39
|
289/256
|
RM2
|
Wide Major Second
|
E/, Fd<↓
|
This interval...
- 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
- Is the closest approximation of 17edo's Major Second found in this system, and thus...
- 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
|
29
|
218.8679245
|
|
?
|
?
|
?
|
17/15
|
rKM2
|
Narrow Supermajor Second
|
E↑\, Fd>↓
|
This interval...
- Can be used as an unexpected option for a diminished third in Western-Classical-based harmony
- Approximates a complex 11-limit interval formed by stacking an Parapotome on top of a Classic Minor Second, and thus...
- 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
- Is the closest approximation of 22edo's Greater Major Second in this system, and thus...
- 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
|
30
|
226.4150943
|
256/225
|
?
|
154/135
|
?
|
?
|
KM2
|
Lesser Supermajor Second
|
E↑, Fd<\, Fb↑↑, Dx
|
This interval...
- It readily appears in approximations of 5-limit Neapolitan scales as the interval formed from stacking two Ptolemaic Minor Seconds
- Approximates a complex 5-limit interval formed by stacking a syntonic comma on top of a Pythagorean Major Second, and thus...
- 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 the closest approximation of 16edo's Supermajor Second found in this system, and thus...
- 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
|
31
|
233.9622642
|
|
8/7
|
55/48
|
?
|
?
|
SM2, kUM2
|
Greater Supermajor Second, Narrow Inframinor Third
|
Fd<, Et<↓, E↑/
|
This interval...
- Can readily occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, as per this system's version of the Dinner Party Rules[1], and it should be noted that...
- 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 readily serves as one of the key Paradiatonic intervals in Western-Classical-based Paradiatonic functional harmony, since...
- 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 the closest approximation of 31edo's Supermajor Second found in this system, and thus...
- 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
|
32
|
241.5094340
|
|
?
|
1024/891
|
?
|
?
|
um3, RkUM2
|
Inframinor Third, Wide Supermajor Second
|
Fd>, Et>↓
|
This interval...
- Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic third that sounds more like a second, and as such...
- 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
- Is the closest approximation of 10edo's Major Second slash Minor Third, and thus...
- 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
|
33
|
249.0566038
|
?
|
?
|
?
|
15/13
|
?
|
kkm3, KKM2, Rum3, rUM2
|
Wide Inframinor Third, Narrow Ultramajor Second, Semifourth
|
Fd>/, Et<\, F↓↓, E↑↑
|
This interval...
- 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
- Is the closest approximation of 19edo's Semifourth found in this system, and thus...
- 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 the closest approximation of 24edo's Semifourth, and thus...
- 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
|
34
|
256.6037736
|
|
?
|
297/256
|
?
|
?
|
UM2, rKum3
|
Ultramajor Second, Narrow Subminor Third
|
Et<, Fd<↑
|
This interval...
- Approximates a complex 11-limit Paradiatonic interval that functions as a syntactic second that sounds more like a third, and as such...
- 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
- Is one third of this system's approximation of the Classic Augmented Fifth
- Is reachable through stacking two of this system's approximation of the Tridecimal Supraminor Second
|
35
|
264.1509434
|
|
7/6
|
64/55
|
?
|
?
|
sm3, Kum3
|
Lesser Subminor Third, Wide Ultramajor Second
|
Et>, Fd>↑, F↓\
|
This interval...
- Can readily occur as the distance between two notes in a single chord in Western-Classical-based polypedal harmony, as per this system's version of the Dinner Party Rules, and it should be noted that...
- This causes ambisonance, so chords that utilize it are prone to decomposition
- It readily serves as one of the key Paradiatonic intervals in Western-Classical-based Paradiatonic functional harmony, since...
- 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
|
36
|
271.6981132
|
75/64
|
?
|
?
|
?
|
?
|
km3
|
Greater Subminor Third
|
F↓, Et>/, E#↓↓, Gbb
|
This interval...
- It most frequently appears in approximations of 5-limit Harmonic scales as the interval between the Ptolemaic Minor Sixth and the Ptolemaic Major Seventh
- Approximates a complex 5-limit interval formed by subtracting a syntonic comma from a Pythagorean Minor Third, and thus...
- It can be thought of as a type of third when acting in this capacity
- Is the closest approximation of 22edo's Lesser Minor Third in this system, and thus...
- 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 the closest approximation of 31edo's Subminor Third found in this system, and thus...
- 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
|
37
|
279.2452830
|
|
?
|
?
|
?
|
20/17
|
Rkm3
|
Wide Subminor Third
|
F↓/, Et<↑
|
This interval...
- Is the closest approximation of 13edo's Minor Third found in this system, and thus...
- 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 the closest approximation of 17edo's Minor Third found in this system, and thus...
- 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
|
38
|
286.7924528
|
|
?
|
33/28
|
13/11
|
85/72
|
rm3
|
Narrow Minor Third
|
F\, Et>↑
|
This interval...
- Can be used in Western-Classical-based harmony and Neo-Medieval harmony very easily
- Has additional applications in Paradiatonic harmony, particularly...
- When it is found in what is otherwise the traditional Diatonic context of a Minor key
|
39
|
294.3396226
|
32/27
|
?
|
?
|
?
|
?
|
m3
|
Pythagorean Minor Third
|
F
|
This interval...
- 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 differs from the Ptolemaic Minor Third in that...
- It is very useful as an interpretation of the dissonant Minor Third from Medieval music's florid organum
- It can be used in creating a subtle instability in certain Diatonic harmonies
- Is one third of this system's approximation of the Classic Major 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 Axirabian Limma
|
40
|
301.8867925
|
|
25/21
|
144/121
|
?
|
?
|
Rm3
|
Artomean Minor Third
|
F/
|
This interval...
- It is the closest approximation of 12edo's Minor Third found in this system, and thus...
- 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
- Is reachable through stacking two of this system's approximation of the low-complexity JI neutral second
|
41
|
309.4339622
|
|
?
|
?
|
512/429
|
153/128
|
rKm3
|
Tendomean Minor Third
|
F↑\
|
This interval...
- 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
- Is the closest approximation of 31edo's Minor Third found in this system, and thus...
- 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
|
42
|
316.9811321
|
6/5
|
?
|
77/64
|
?
|
?
|
Km3
|
Ptolemaic Minor Third
|
F↑, E#
|
This interval...
- Is one of the staples of both melodic and harmonic motion in general, and in particular...
- 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 differs from the Pythagorean Minor Third in that...
- 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
- Is the closest approximation of 19edo's Minor Third found in this system, and thus...
- 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
|
43
|
324.5283019
|
|
135/112
|
?
|
?
|
512/425
|
RKm3, kn3
|
Wide Minor Third
|
Ft<↓, F↑/, Gdb<
|
This interval...
- 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
- Is the closest approximation of 22edo's Greater Minor Third in this system, and thus...
- 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
|
44
|
332.0754717
|
|
?
|
40/33, 121/100
|
?
|
144/119, 165/136
|
kN3, ud4
|
Lesser Supraminor Third, Infra-Diminished Fourth
|
Ft>↓, Gdb>
|
This interval...
- 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 Diminished Fifth
- Is one third of this system's approximation of the Pythagorean Minor Seventh
|
45
|
339.6226415
|
?
|
?
|
?
|
39/32
|
17/14
|
KKm3, rn3, Rud4
|
Greater Supraminor Third, Diretroptolemaic Diminished Fourth
|
Ft<\, F↑↑, Gdb<↑\, Gb↓↓
|
This interval...
- Is very useful for essentially tempered chords such as tannic chords
- Is reachable through stacking three of this system's approximation of the Classic Minor Second
- Is the closest approximation of the 7edo Third found in this system, and thus...
- 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
|
46
|
347.1698113
|
|
?
|
11/9
|
?
|
?
|
n3, rKud4
|
Artoneutral Third, Lesser Sub-Diminished Fourth
|
Ft<, Gdb<↑
|
This interval...
- 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
- It serves as the smaller and more consonant of two Neutral Thirds in Western-Classical-based Paradiatonic functional harmony, and thus...
- 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
- Is the closest approximation of 24edo's own Neutral Third in this system, and thus...
- 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
- Is the closest approximation of 31edo's own Middle Third in this system, and thus...
- 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
|
47
|
354.7169811
|
|
?
|
27/22
|
?
|
?
|
N3, sd4, Kud4
|
Tendoneutral Third, Greater Sub-Diminished Fourth
|
Ft>, Gdb>↑
|
This interval...
- 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 serves as the larger and more dissonant of two Neutral Thirds in Western-Classical-based Paradiatonic functional harmony, and thus...
- 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 the closest approximation of 17edo's Neutral Third found in this system, and thus...
- 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
|
48
|
362.2641509
|
?
|
?
|
?
|
16/13
|
21/17
|
kkM3, RN3, kd4
|
Lesser Submajor Third, Retroptolemaic Diminished Fourth
|
Ft>/, F#↓↓, Gb↓
|
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
- Is the closest approximation of 10edo's Major Third, and thus...
- 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
|
49
|
369.8113208
|
|
?
|
?
|
26/21
|
68/55
|
Kn3, Rkd4
|
Greater Submajor Third, Artoretromean Diminished Fourth
|
Ft<↑, Gb↓/
|
This interval...
- Approximates the Tridecimal Submajor Third and a similar 11-limit interval that acts as the Submajor counterpart to the Undecimal Supraminor Third, and thus...
- 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
- Is the closest approximation of 13edo's Minor Third found in this system, and thus...
- 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
|
50
|
377.3584906
|
|
56/45
|
1024/825
|
?
|
?
|
rkM3, KN3, rd4
|
Narrow Major Third, Tendoretromean Diminished Fourth
|
Ft>↑, F#↓\, Gb\
|
This interval...
- 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 the closest approximation of 16edo's Major Third found in this system, and thus...
- 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 the closest approximation of 19edo's Major Third found in this system, and thus...
- 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
|
51
|
384.9056604
|
5/4
|
?
|
96/77
|
?
|
?
|
kM3, d4
|
Ptolemaic Major Third, Pythagorean Diminished Fourth
|
Gb, F#↓
|
This interval...
- Is one of the staples of both melodic and harmonic motion in general, and in particular...
- 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 differs from the Pythagorean Major Third in that...
- 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
- Is the closest approximation of 22edo's Lesser Major Third in this system, and thus...
- 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
- Is the closest approximation of 31edo's Major Third found in this system, and thus...
- 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
|
52
|
392.4528302
|
|
?
|
?
|
?
|
64/51
|
RkM3, Rd4
|
Artomean Major Third, Artomean Diminished Fourth
|
Gb/, F#↓/
|
This interval...
- Approximates the Septendecimal Artomean Major Third
- Is reachable through stacking two of this system's approximation of the Middle Major Second
- Can easily be used in modulatory maneuvers similar to those performed by Jacob Collier
|
53
|
400
|
|
63/50
|
121/96
|
?
|
?
|
rM3, rKd4
|
Tendomean Major Third, Tendomean Diminished Fourth
|
F#\, Gb↑\
|
This interval...
- It is useful for evoking the feel of 12edo in various ways, such as...
- Creating the familiar augmented triads of 12edo
- Being stacked with this system's approximation of the Quasi-Tempered Minor Third to make chords similar in sound to those of 12edo
- Performing modulatory maneuvers based around the aforementioned chords
|
54
|
407.5471698
|
81/64
|
?
|
?
|
?
|
?
|
M3, Kd4
|
Pythagorean Major Third, Ptolemaic Diminished Fourth
|
F#, Gb↑
|
This interval approximates the Pythagorean Major Third, and, since this system does not temper out the syntonic comma, this interval- in contrast to the Ptolemaic Major Third- is very useful as an interpretation of the dissonant Major Third from Medieval music's florid organum, and can thus be used in creating a subtle instability in certain Diatonic harmonies, though it's also useful in building oddly-charming augmented triads.
|
55
|
415.0943396
|
|
?
|
14/11
|
33/26
|
108/85
|
RM3, kUd4
|
Wide Major Third, Lesser Super-Diminished Fourth
|
F#/, Gd<↓, Gb↑/
|
This interval is of particular interest because it is the approximation of the Neo-Gothic Major Third and is used accordingly; what's more, this interval has additional applications in Paradiatonic harmony, particularly when such harmony is found in what is otherwise the traditional Diatonic context of a Major key.
|
56
|
422.6415094
|
|
?
|
?
|
143/112
|
51/40
|
rKM3, RkUd4
|
Narrow Supermajor Third, Greater Super-Diminished Fourth
|
F#↑\, Gd>↓
|
This interval is useful for evoking the feel of 31edo due to approximating that system's Supermajor Third, and is even better for evoking the feel of 17edo due to approximating that system's Major Third.
|
57
|
430.1886792
|
32/25
|
?
|
?
|
?
|
?
|
KM3, rUd4, KKd4
|
Lesser Supermajor Third, Diptolemaic Diminished Fourth
|
F#↑, Gd<\, Gb↑↑
|
This interval is easily very useful due to it being a consistent approximation of the Classic Diminished Fourth; despite its dissonance- or perhaps even because of said dissonance- this interval is even useful when it comes to building chords.
|
58
|
437.7358491
|
|
9/7
|
165/128
|
?
|
?
|
SM3, kUM3, rm4, Ud4
|
Greater Supermajor Third, Ultra-Diminished Fourth
|
Gd<, F#↑/
|
This interval is the approximation of the Septimal Supermajor Third and is directly on this system's Superpyth scale as well; those who are not already familiar with septimal harmony will find this interval useful in forming not only strident-sounding triads framed by the Perfect Fifth, but also different types of augmented and superaugmented triad.
|
59
|
445.2830189
|
|
?
|
128/99
|
?
|
22/17
|
m4, RkUM3
|
Paraminor Fourth, Wide Supermajor Third
|
Gd>, Ft#>↓
|
Although this interval is not found on the Paradiatonic scale, it is nevertheless important for usage in Parachromatic gestures and in various types of harmony based on such gestures; it is the namesake of 24edo's own Paraminor Fourth interval, and, just like that interval, it tends to want to be followed up by either the Unison, the Perfect Fourth, or, its Paramajor counterpart- the latter having additional follow-up options.
|
60
|
452.8301887
|
?
|
?
|
?
|
13/10
|
?
|
|
|
|
|
61
|
460.3773585
|
|
?
|
176/135
|
?
|
?
|
|
|
|
|
62
|
467.9245283
|
|
21/16
|
55/42, 72/55
|
?
|
17/13
|
|
|
|
|
63
|
475.4716981
|
320/243, 675/512
|
?
|
?
|
?
|
?
|
|
|
|
|
64
|
483.0188679
|
|
?
|
33/25
|
?
|
45/34
|
|
|
|
|
65
|
490.5660377
|
|
?
|
?
|
?
|
85/64
|
|
|
|
|
66
|
498.1132075
|
4/3
|
?
|
?
|
?
|
?
|
|
|
|
|
67
|
505.6603774
|
|
75/56
|
162/121
|
?
|
?
|
|
|
|
|
68
|
513.2075472
|
|
?
|
121/90
|
?
|
?
|
|
|
|
|
69
|
520.7547170
|
27/20
|
?
|
?
|
104/77
|
?
|
|
|
|
|
70
|
528.3018868
|
|
?
|
110/81
|
?
|
?
|
|
|
|
|
71
|
535.8490566
|
|
?
|
15/11
|
?
|
?
|
|
|
|
|
72
|
543.3962264
|
?
|
?
|
?
|
160/117
|
256/187
|
|
|
|
|
73
|
550.9433962
|
|
?
|
11/8
|
?
|
?
|
|
|
|
|
74
|
558.4905660
|
|
112/81
|
?
|
?
|
?
|
|
|
|
|
75
|
566.0377358
|
25/18
|
?
|
?
|
18/13
|
?
|
|
|
|
|
76
|
573.5849057
|
|
?
|
?
|
?
|
357/256
|
|
|
|
|
77
|
581.1320755
|
|
7/5
|
?
|
?
|
?
|
|
|
|
|
78
|
588.6792458
|
1024/729, 45/32
|
?
|
?
|
?
|
?
|
|
|
|
|
79
|
596.2264151
|
|
?
|
?
|
?
|
24/17
|
|
|
|
|
80
|
603.7735849
|
|
?
|
?
|
?
|
17/12
|
|
|
|
|
81
|
611.3207547
|
729/512, 64/45
|
?
|
?
|
?
|
?
|
|
|
|
|
82
|
618.8679245
|
|
10/7
|
?
|
?
|
?
|
|
|
|
|
83
|
626.4150943
|
|
?
|
?
|
?
|
512/357
|
|
|
|
|
84
|
633.9622642
|
36/25
|
?
|
?
|
13/9
|
?
|
|
|
|
|
85
|
641.5094340
|
|
81/56
|
?
|
?
|
?
|
|
|
|
|
86
|
649.0566038
|
|
?
|
16/11
|
?
|
?
|
|
|
|
|
87
|
656.6037736
|
?
|
?
|
?
|
117/80
|
187/128
|
|
|
|
|
88
|
664.1509434
|
|
?
|
22/15
|
?
|
?
|
|
|
|
|
89
|
671.6981132
|
|
?
|
81/55
|
?
|
?
|
|
|
|
|
90
|
679.2452830
|
40/27
|
?
|
?
|
77/52
|
?
|
|
|
|
|
91
|
686.7924528
|
|
?
|
180/121
|
?
|
?
|
|
|
|
|
92
|
694.3396226
|
|
112/75
|
121/81
|
?
|
?
|
|
|
|
|
93
|
701.8867925
|
3/2
|
?
|
?
|
?
|
?
|
|
|
|
|
94
|
709.4339622
|
|
?
|
?
|
?
|
128/85
|
|
|
|
|
95
|
716.9811321
|
|
?
|
50/33
|
?
|
68/45
|
|
|
|
|
96
|
724.5283019
|
243/160, 1024/675
|
?
|
?
|
?
|
?
|
|
|
|
|
97
|
732.0754717
|
|
32/21
|
84/55, 55/36
|
?
|
26/17
|
|
|
|
|
98
|
739.6226415
|
|
?
|
135/88
|
?
|
?
|
|
|
|
|
99
|
747.1698113
|
?
|
?
|
?
|
20/13
|
?
|
|
|
|
|
100
|
754.7169811
|
|
?
|
99/64
|
?
|
17/11
|
|
|
|
|
101
|
762.2641509
|
|
14/9
|
256/165
|
?
|
?
|
|
|
|
|
102
|
769.8113208
|
25/16
|
?
|
?
|
?
|
?
|
|
|
|
|
103
|
777.3584906
|
|
?
|
?
|
224/143
|
80/51
|
|
|
|
|
104
|
784.9056604
|
|
?
|
11/7
|
52/33
|
85/54
|
|
|
|
|
105
|
792.4528302
|
128/81
|
?
|
?
|
?
|
?
|
|
|
|
|
106
|
800
|
|
100/63
|
192/121
|
?
|
?
|
|
|
|
|
107
|
807.5471698
|
|
?
|
?
|
?
|
51/32
|
|
|
|
|
108
|
815.0943396
|
8/5
|
?
|
77/48
|
?
|
?
|
|
|
|
|
109
|
822.6415094
|
|
45/28
|
825/512
|
?
|
?
|
|
|
|
|
110
|
830.1886792
|
|
?
|
?
|
21/13
|
55/34
|
|
|
|
|
111
|
837.7358491
|
?
|
?
|
?
|
13/8
|
34/21
|
|
|
|
|
112
|
845.2830189
|
|
?
|
44/27
|
?
|
?
|
|
|
|
|
113
|
852.8301887
|
|
?
|
18/11
|
?
|
?
|
|
|
|
|
114
|
860.3773585
|
?
|
?
|
?
|
64/39
|
28/17
|
|
|
|
|
115
|
867.9245283
|
|
?
|
33/20, 200/121
|
?
|
119/72, 272/165
|
|
|
|
|
116
|
875.4716981
|
|
224/135
|
?
|
?
|
425/256
|
|
|
|
|
117
|
883.0188679
|
5/3
|
?
|
128/77
|
?
|
?
|
|
|
|
|
118
|
890.5660377
|
|
?
|
?
|
429/256
|
256/153
|
|
|
|
|
119
|
898.1132075
|
|
42/25
|
121/72
|
?
|
?
|
|
|
|
|
120
|
905.6603774
|
27/16
|
?
|
?
|
?
|
?
|
|
|
|
|
121
|
913.2075472
|
|
?
|
56/33
|
22/13
|
144/85
|
|
|
|
|
122
|
920.7547170
|
|
?
|
?
|
?
|
17/10
|
|
|
|
|
123
|
928.3018868
|
128/75
|
?
|
?
|
?
|
?
|
|
|
|
|
124
|
935.8490566
|
|
12/7
|
55/32
|
?
|
?
|
|
|
|
|
125
|
943.3962264
|
|
?
|
512/297
|
?
|
?
|
|
|
|
|
126
|
950.9433962
|
?
|
?
|
?
|
26/15
|
?
|
|
|
|
|
127
|
958.4905660
|
|
?
|
891/512
|
?
|
?
|
|
|
|
|
128
|
966.0377358
|
|
7/4
|
96/55
|
?
|
?
|
|
|
|
|
129
|
973.5849057
|
225/128
|
?
|
135/77
|
?
|
?
|
|
|
|
|
130
|
981.1320755
|
|
?
|
?
|
?
|
30/17
|
|
|
|
|
131
|
988.6792458
|
|
?
|
?
|
39/22
|
512/289
|
|
|
|
|
132
|
996.2264151
|
16/9
|
?
|
?
|
?
|
?
|
|
|
|
|
133
|
1003.7735849
|
|
25/14
|
216/121
|
?
|
?
|
|
|
|
|
134
|
1011.3207547
|
|
?
|
?
|
256/143
|
459/256
|
|
|
|
|
135
|
1018.8679245
|
9/5
|
?
|
231/128
|
?
|
?
|
|
|
|
|
136
|
1026.4150943
|
|
1024/567
|
440/243
|
?
|
768/425
|
|
|
|
|
137
|
1033.9622642
|
|
?
|
20/11
|
?
|
?
|
|
|
|
|
138
|
1041.5094340
|
?
|
?
|
?
|
117/64
|
1024/561, 935/512
|
|
|
|
|
139
|
1049.0566038
|
|
?
|
11/6
|
?
|
?
|
|
|
|
|
140
|
1056.6037736
|
|
?
|
81/44
|
?
|
?
|
|
|
|
|
141
|
1064.1509434
|
50/27
|
?
|
?
|
24/13
|
?
|
|
|
|
|
142
|
1071.6981132
|
|
?
|
?
|
13/7
|
119/64
|
|
|
|
|
143
|
1079.2452830
|
|
28/15
|
512/275
|
?
|
?
|
|
|
|
|
144
|
1086.7924528
|
15/8
|
?
|
?
|
?
|
?
|
|
|
|
|
145
|
1094.3396226
|
|
?
|
?
|
?
|
32/17
|
|
|
|
|
146
|
1101.8867925
|
|
?
|
121/64
|
104/55
|
17/9
|
|
|
|
|
147
|
1109.4339622
|
243/128, 256/135
|
?
|
?
|
?
|
?
|
|
|
|
|
148
|
1116.9811321
|
|
40/21
|
21/11
|
?
|
?
|
|
|
|
|
149
|
1124.5283019
|
|
?
|
?
|
?
|
153/80
|
|
|
|
|
150
|
1132.0754717
|
48/25
|
?
|
?
|
25/13, 52/27
|
?
|
|
|
|
|
151
|
1139.6226415
|
|
27/14
|
?
|
?
|
85/44
|
|
|
|
|
152
|
1147.1698113
|
|
?
|
64/33
|
?
|
33/17
|
|
|
|
|
153
|
1154.7169811
|
?
|
?
|
?
|
39/20
|
187/96
|
|
|
|
|
154
|
1162.2641509
|
|
?
|
88/45
|
?
|
100/51
|
|
|
|
|
155
|
1169.8113208
|
|
63/32
|
55/28, 108/55
|
?
|
51/26
|
|
|
|
|
156
|
1177.3584906
|
160/81
|
?
|
?
|
77/39
|
168/85
|
|
|
|
|
157
|
1184.9056604
|
|
?
|
240/121, 99/50
|
143/72
|
119/60
|
|
|
|
|
158
|
1192.4528302
|
|
448/225
|
484/243
|
195/98, 700/351
|
255/128
|
|
|
|
|
159
|
1200
|
2/1
|
P8
|
Perfect Octave
|
D
|
This interval...
- Is the reduplication of a chord's root
- Is the reduplication of the Tonic
- Is one of four perfect consonances in this system
|