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159edo/Interval names and harmonies

Revision as of 03:08, 27 January 2022 by Aura (talk | contribs)

159edo contains all the intervals of 53edo, however, as some of the interpretations differ due 159edo having different mappings for certain primes, those differences show up in how harmonies are constructed. It should be noted that since 159edo does a better job of representing the 2.3.11 subgroup than 24edo, some of the chords listed on the page for 24edo interval names and harmonies carry over to this page, even though the exact sets of enharmonics differ between the two systems.

Table of 159edo intervals
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
  • Approximates the marvel comma
  • 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
  • Approximates 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...
  • Approximates the syntonic comma
  • Approximates the Pythagorean comma
  • Is a dissonance to be avoided 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...
  • 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
  • Used as 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 complicated 11-limit paradiatonic quartertone that is the namesake of 24edo's own Inframinor Second
  • Is the closest approximation of the 31edo Superprime found in this system
  • Is a dissonance to be avoided in 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
  • Used as the destination for a glissando
6 45.2830189 ? ? ? 40/39 192/187 kkm2, Rum2, rU1 Wide Inframinor Second, Narrow Ultraprime, Semilimma Eb↓↓, Dt<\ This interval is particularly likely to be used as a cross between an Ultraprime and an Inframinor Second; furthermore, as the name "Semilimma" suggests, this interval is one half of a Pythagorean Minor Second.
7 52.8301887 ? 33/32 ? 34/33 U1, rKum2 Ultraprime, Narrow Subminor Second Dt<, Edb<↑ By default, this interval is a type of parachromatic quartertone- specifically, the representation of the Al-Farabi Quartertone- and is thus used in much the same way as 24edo's own Ultraprime; what might be surprising is that five of these add up to this system's approximation of the Septimal Subminor Third.
8 60.3773585 28/27 ? ? 88/85 sm2, Kum2, uA1 Lesser Subminor Second, Wide Ultraprime, Infra-Augmented Prime Dt>, Eb↓\ Although this interval can act as a leading tone, it can also act as a trienstone- that is, a third of a tone- since it's one third of the Ptolemaic Major Second.
9 67.9245283 25/24 ? ? 26/25, 27/26 ? km2, RuA1, kkA1 Greater Subminor Second, Diptolemaic Augmented Prime Eb↓, Dt<↑\, D#↓↓ Although this interval frequently acts as the Classic Chroma due to consistently approximating it, it can also act as a trienstone- that is, a third of a tone- since it's one third of the Pythagorean Major Second.
10 75.4716981 ? ? ? 160/153 Rkm2, rKuA1 Wide Subminor Second, Lesser Sub-Augmented Prime Eb↓/, Dt<↑ This interval acts as a type of semitone, however, whether it's a diatonic or chromatic semitone depends on the situation; in addition, it is also the closest approximation of the 31edo Subminor Second found in this system.
11 83.0188679 21/20 22/21 ? ? rm2, KuA1 Narrow Minor Second, Greater Sub-Augmented Prime Eb\, Dt>↑ Not only does this interval serve as a type of leading tone due to it being the approximation of the Septimal Minor Semitone, but it should be noted that six of these add up to a Perfect Fourth.
12 90.5660377 256/243, 135/128 ? ? ? ? m2, kA1 Pythagorean Minor Second, Ptolemaic Augmented Prime Eb, D#↓ As the approximation of both the Pythagorean Minor Second and the Ptolemaic Augmented Prime, this interval is used accordingly; however, it is also worth noting that as a further consequence of the schisma being tempered out in this system, two of these add up to the approximation of the Ptolemaic Major Second.
13 98.1132075 ? 128/121 55/52 18/17 Rm2, RkA1 Artomean Minor Second, Artomean Augmented Prime Eb/, D#↓/ This interval is one of two in this system that are essential in executing the frameshift cadence; it is also the closest approximation of the 12edo Minor Second found in this system.
14 105.6603774 ? ? ? 17/16 rKm2, rA1 Tendomean Minor Second, Tendomean Augmented Prime D#\, Eb↑\ As the approximation of both the octave-reduced seventeenth harmonic and the interval formed from stacking two Ultraprimes, this interval is used accordingly.
15 113.2075472 16/15 ? ? ? ? Km2, A1 Ptolemaic Minor Second, Pythagorean Augmented Prime D#, Eb↑ This interval approximates the Ptolemaic Minor Second- that is, the traditional 5-limit leading tone- as well as the Pythagorean Augmented Prime, and thus, is used accordingly; however, this interval is also useful for evoking the feel of 31edo due to approximating that system's Minor Second, and is also one of two in this system that are essential in executing the frameshift cadence.
16 120.7547170 15/14 275/256 ? ? RKm2, kn2, RA1 Wide Minor Second, Artoretromean Augmented Prime Ed<↓, Eb↑/, D#/ In addition to being the approximation of the Septimal Major Semitone, this interval is also one third of a Lesser Submajor Third in this system, and is thus used accordingly.
17 128.3018868 ? ? 14/13 128/119 kN2, rKA1 Lesser Supraminor Second, Tendoretromean Augmented Prime Ed>↓, D#↑\ In addition to its properties as a type of supraminor second, this interval is also one third of a Ptolemaic Major Third in this system and is thus used accordingly.
18 135.8490566 27/25 ? ? 13/12 ? KKm2, rn2, KA1 Greater Supraminor Second, Diptolemaic Limma, Retroptolemaic Augmented Prime Ed<\, Eb↑↑, D#↑ This interval is not only both two thirds of Pythagorean Major Second and the approximation of the Large Limma or Diptolemaic Limma in this system, but also a type of supraminor second, and is thus used accordingly.
19 143.3962264 ? 88/81 ? ? n2, SA1, kUA1 Artoneutral Second, Lesser Super-Augmented Prime Ed<, Dt#<↓ As one of two neutral seconds in this system, this interval is notable for being half of the approximation of the Neo-Gothic Minor Third, though it is also sometimes used in much the same way as 24edo's own Neutral Second.
20 150.9433962 ? 12/11 ? ? N2, RkUA1 Tendoneutral Second, Greater Super-Augmented Prime Ed>, Dt#>↓ As one of two neutral seconds in this system, this interval is the one that most closely resembles the low-complexity JI neutral second, and thus, it is frequently used in much the same way as 24edo's own Neutral Second.
21 158.4905660 ? ? ? 128/117 561/512, 1024/935 kkM2, RN2, rUA1 Lesser Submajor Second, Diretroptolemaic Augmented Prime Ed>/, E↓↓, Dt#>↓/, D#↑↑ In addition to being a type of Submajor Second and the closest approximation of the 31edo Middle Second found in this system, two of these add up to the approximation of the Ptolemaic Minor Third.
22 166.0377358 ? 11/10 ? ? Kn2, UA1 Greater Submajor Second, Ultra-Augmented Prime Ed<↑, Dt#<, Fb↓/ In addition to its properties as the interval that most closely resembles the Undecimal Submajor Second, this interval serves as both the Ultra-Augmented Prime and as one third of a Perfect Fourth, and is used accordingly.
23 173.5849057 567/512 243/220 ? 425/384 rkM2, KN2 Narrow Major Second Ed>↑, E↓\, Dt#>, Fb\ While this interval is large enough to act as a type of whole tone, it is worth noting that two of these add up to the approximation of the low-complexity JI Neutral Third in this system.
24 181.1320755 10/9 ? 256/231 ? ? kM2 Ptolemaic Major Second E↓, Fb As the approximation of the Ptolemaic Major Second, this interval is used accordingly, though it is worth noting that in this system, two of these add up to the approximation of the thirteenth subharmonic; furthermore, it is also 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".
25 188.6792458 ? ? 143/128 512/459 RkM2 Artomean Major Second E↓/, Fb/ This interval has surprising utility in modulating to keys that are not found on the same circle of fifths owing to both its size and its ease of access through octave-reducing stacks of approximated low-complexity JI intervals.
26 196.2264151 28/25 121/108 ? ? rM2 Tendomean Major Second E\, Fb↑\ In addition to being the closest approximation of the 31edo Major Second found in this system, it is one of two intervals that come the closest to approximating the 12edo Major Second found in this system.
27 203.7735849 9/8 ? ? ? ? M2 Pythagorean Major Second E, Fb↑ This interval is the standard-issue whole tone in this system as it is one of two intervals that come the closest to approximating the 12edo Major Second, and the only one of the two that actually approximates the Pythagorean Major Second; furthermore, it 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.
28 211.3207547 ? ? 44/39 289/256 RM2 Wide Major Second E/, Fd<↓ This interval is interesting on the basis that it is formed by stacking two instances of the octave-reduced approximation of the seventeenth harmonic.
29 218.8679245 ? ? ? 17/15 rKM2 Narrow Supermajor Second E↑\, Fd>↓ This interval is interesting not only because it is utilized in approximations of the 17-odd-limit, but also because it is the whole tone found in this system's Superpyth scale, and is of such quality that two of these add up to this system's approximation of the Septimal Supermajor Third.
30 226.4150943 256/225 ? 154/135 ? ? KM2 Lesser Supermajor Second E↑, Fd<\, Fb↑↑, Dx This interval can be interpreted as a type of second on the basis of it approximating the sum of the syntonic comma and the Pythagorean Major Second; it also appears in approximations of 5-limit Neapolitan scales as the interval formed from stacking two Ptolemaic Minor Seconds, making it double as a type of diminished third, and is likely the smallest interval in this system that can be used in chords without causing crowding.
31 233.9622642 8/7 55/48 ? ? SM2, kUM2 Greater Supermajor Second, Narrow Inframinor Third Fd<, Et<↓, E↑/ As the approximation of the octave-reduced seventh subharmonic- that is, the Septimal Supermajor Second- this interval is used accordingly; in fact, since three of these add up to a Perfect Fifth in this system, there are multiple ways this interval can be used in chords to great effect.
32 241.5094340 ? 1024/891 ? ? um3, RkUM2 Inframinor Third, Wide Supermajor Second Fd>, Et>↓ The 11-limit ratio this interval approximates is the namesake of 24edo's own Inframinor Third; however, in a higher-fidelity system such as this, one will notice that this is a syntactic third that sounds more like a second.
33 249.0566038 ? ? ? 15/13 ? kkm3, KKM2, Rum3, rUM2 Wide Inframinor Third, Narrow Ultramajor Second, Semifourth Fd>/, Et<\, F↓↓, E↑↑ This interval is particularly likely to be used as a cross between an Ultramajor Second and an Inframinor Third; furthermore, as the name "Semifourth" suggests, this interval is one half of a Perfect Fourth, and used in exactly the same way as 24edo's own Semifourth, right down to the low-complexity 13-limit interpretation.
34 256.6037736 ? 297/256 ? ? UM2, rKum3 Ultramajor Second, Narrow Subminor Third Et<, Fd<↑ The 11-limit ratio this interval approximates is the namesake of 24edo's own Ultramajor Second; however, in a higher-fidelity system such as this, one will notice that this is a syntactic second that sounds more like a third.
35 264.1509434 7/6 64/55 ? ? sm3, Kum3 Lesser Subminor Third, Wide Ultramajor Second Et>, Fd>↑, F↓\ As the approximation of the Septimal Subminor Third, 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 other, ambisonant triads framed by the Perfect Fourth; in addition, three of these add up to the Pythagorean Minor Sixth.
36 271.6981132 75/64 ? ? ? ? km3 Greater Subminor Third F↓, Et>/, E#↓↓, Gbb This interval is useful for evoking the feel of 31edo due to approximating that system's Subminor Third, and even approximates the result of subtracting a syntonic comma from a Pythagorean Minor Third; however, it most frequently appears in approximations of 5-limit Harmonic scales as the interval between the Ptolemaic Minor Sixth and the Ptolemaic Major Seventh, making it double as a type of augmented second.
37 279.2452830 ? ? ? 20/17 Rkm3 Wide Subminor Third F↓/, Et<↑ This interval is utilized in approximations of the 17-odd-limit, courtesy of acting as the fourth complement to the Narrow Supermajor Second; it is also good for evoking the feel of 17edo due to approximating that system's Minor Third.
38 286.7924528 ? 33/28 13/11 85/72 rm3 Narrow Minor Third F\, Et>↑ This interval is of particular interest because it is the approximation of the Neo-Gothic Minor Third and is used accordingly; what's more, this interval and the approximation of the Neo-Gothic Major Third add up to make the Perfect Fifth in this system.
39 294.3396226 32/27 ? ? ? ? m3 Pythagorean Minor Third F This interval approximates the Pythagorean Minor Third, and since this system does not temper out the syntonic comma, this interval- in contrast to the Ptolemaic Minor Third- is very useful as an interpretation of the dissonant Minor Third from Medieval music's florid organum, and can thus be used in creating a subtle instability in certain Diatonic harmonies.
40 301.8867925 25/21 144/121 ? ? Rm3 Artomean Minor Third F/ This interval is the closest approximation of the 12edo Minor Third found in this system, and, conveniently enough, it is easily accessed by stacking instances of this system's approximation of the low-complexity JI neutral second.
41 309.4339622 ? ? 512/429 153/128 rKm3 Tendomean Minor Third F↑\ In addition to being the closest approximation of the 31edo Minor Third found in this system, this interval is also half of this system's approximation of the Greater Septimal Tritone and is thus used accordingly as part of a triad.
42 316.9811321 6/5 ? 77/64 ? ? Km3 Ptolemaic Minor Third F↑, E# As the approximation of the Ptolemaic Minor Third- that is, the traditional 5-limit minor third- this interval is one of four imperfect consonances in this system, and, unsurprisingly, is thus used accordingly; however, one should also note that this interval can be reached by stacking three of this system's approximation of the octave-reduced seventeenth harmonic.
43 324.5283019 135/112 ? ? 512/425 RKm3, kn3 Wide Minor Third Ft<↓, F↑/, Gdb< The main thing of note concerning this interval is that two of these add up to this system's approximation of the Paraminor Fifth, thus facilitating the formation of strange-sounding triads
44 332.0754717 ? 40/33, 121/100 ? 144/119, 165/136 kN3, ud4 Lesser Supraminor Third, Infra-Diminished Fourth Ft>↓, Gdb> This interval is mainly of interest due to the fact that it's exactly twice the size of it's fourth complement- the approximation of the Undecimal Submajor Second- and its interesting properties as a type of supraminor third.
45 339.6226415 ? ? ? 39/32 17/14 KKm3, rn3, Rud4 Greater Supraminor Third, Diretroptolemaic Diminished Fourth Ft<\, F↑↑, Gdb<↑\, Gb↓↓ This interval is of interest because not only does it have 13-limit interpretations, but it also has usage as a 17-odd-limit interval, and all while being easily reached by stacking three Ptolemaic Minor Seconds.
46 347.1698113 ? 11/9 ? ? n3, rKud4 Artoneutral Third, Lesser Sub-Diminished Fourth Ft<, Gdb<↑ As one of two neutral thirds in this system, this interval is the one that most closely resembles the low-complexity JI neutral third, and thus, it is frequently used in much the same way as 24edo's own Neutral Third; on top of that, it can be stacked in interesting ways in this system.
47 354.7169811 ? 27/22 ? ? N3, sd4, Kud4 Tendoneutral Third, Greater Sub-Diminished Fourth Ft>, Gdb>↑ As one of two neutral seconds in this system, this interval is notable for being one half of a possible generator for this system's superpyth scale.
48 362.2641509 ? ? ? 16/13 21/17 kkM3, RN3, kd4 Lesser Submajor Third, Retroptolemaic Diminished Fourth Ft>/, F#↓↓, Gb↓ As both the approximation of the octave-reduced thirteenth subharmonic, and ostensibly one of the easiest 13-limit thirds to utilize in chords framed by some type of sharp wolf fifth, this interval is used accordingly.
49 369.8113208 ? ? ? 68/55 Kn3, Rkd4 Greater Submajor Third, Artoretromean Diminished Fourth Ft<↑, Gb↓/ In addition to its properties as a type of submajor third, this interval is also one third of a Pythagorean Major Seventh in this system and is thus used accordingly.
50 377.3584906 56/45 1024/825 ? ? rkM3, KN3, rd4 Narrow Major Third, Tendoretromean Diminished Fourth Ft>↑, F#↓\, Gb\ The main thing of note concerning this interval is that two of these add up to this system's approximation of the Paramajor Fifth, thus facilitating the formation of strange-sounding triads.
51 384.9056604 5/4 ? 96/77 ? ? kM3, d4 Ptolemaic Major Third, Pythagorean Diminished Fourth Gb, F#↓ This interval is none other than the approximation of the octave-reduced fifth harmonic- that is, the traditional 5-limit major third- and thus, it one of four imperfect consonances in this system, and, unsurprisingly, is used accordingly; however, this interval is also the approximation of the Pythagorean Diminished Fourth in this system, which sometimes leads to interesting enharmonic substitutions when building chords for purposes of voice-leading.
52 392.4528302 ? ? ? 64/51 RkM3, Rd4 Artomean Major Third, Artomean Diminished Fourth Gb/, F#↓/ As this interval is situated between the Ptolemaic Major Third on one hand and the familiar major third of 12edo on the other, this interval 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↑\ As none other than the familiar major third of 12edo, this interval is useful for creating the familiar augmented triads of 12edo, performing modulatory maneuvers based around said triads, and evoking the feel of 12edo in other ways.
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 ? ? ? 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
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