The Exciting Universe Of Music Theory
presents

Antiscales

It all started, for me, with watching this video by 12tone:

For a primer on what I'll be investigating here, I really recommend you watch that video first, as it was my own introduction to the subject and the basis for everything I'll be doing to follow up on it. Much of the material on this page is merely a reiteration of the same conclusions 12tone came to, but with more verbose examples and not much additional insight.

Antiscales were invented (or discovered, or reported) by Reuben Nebbett-Blades, who sent an email describing them to 12tone in March of 2019. Reuben (according to 12tone) made the observation that some, but not all, diatonic modes had antiscales that were essentially other diatonic modes. This concept was formalized by 12tone in the video above. So, don't get any notions that these are well-established kernels of music theory - this is fresh, hot steaming stuff that just came out of the oven. Also, I didn't invent any of it and have never met any of the folks who did.

For this exploration, I am rejecting my usual definition of a "scale", by allowing scales that contain leaps greater than a major third. While the omisison of leaps makes musical sense, it introduces gaps into the combinatorial permutations and gets in the way when doing mathematical stuff. So here we will consider a "scale" to be any pitch class set that has a root tone, regardless of its intervallic content. A prerequisite for understanding some of the formulas in this article is understanding how I represent scales as binary words; so if this is unfamiliar territory go and read about it now.

Our first step is to figure out how to compute an antiscale. We know that an antiscale is the complement, with an added root. Finding the complement of a scale is done with a bitwise XOR against the Chromatic Scale (111111111111, which is the binary representation of 2^12 or the decimal number 4095). XOR does what we want: for a binary word with 12 bits, it turns all the ON bits OFF, and turns the OFF bits ON.

Once we have the complement, we add a root tone to it. In our numbering of scales, the root tone has the binary digit 1. This means any legit scale (with a root) will be an odd number, and any complement of a scale (lacking a root) will be even. To create an antiscale, the formula is simple: take the complement of the original scale using that binary XOR, and then add 1 to it.

In code, it looks like this:

function antiscale($scalenum) { return (4095 ^ $scalenum) + 1; }

Easy, right? But we can make it even easier.

When we combine a scale and its complement, we get the complete set of 12, aka the 12-tone chromatic scale. The binary number for the chromatic scale is 4095, aka the binary 111111111111. When we combine a scale and its antiscale, we've again constructed the whole set of 12 tones, but with an extra root tone added because it is present in both the scales. So, the sum of a scale and its antiscale is 4095 + 1 = 4096. So the easy formula for an antiscale becomes evident:

function antiscale($scalenum) { return 4096 - $scalenum; }

By this formula it also becomes apparent that every scale will have one and only one antiscale, every antiscale is unique (no scale has more than one antiscale), and the scales and antiscales will be in pairs that sum up to 4096. The relationship is bidirectional: the antiscale of an antiscale of a scale is itself. In the extreme case, the 12 tone chromatic scale (4095) has the antiscale of just a root tone (1), so in essence the antiscale of a 12-note scale is a 1-note scale, and vice-versa.

We can make some more obvious observations about the cardinality of antiscales. For a scale with cardinality d, the cardinality of the complement will be (12 - d), and the cardinality of the antiscale will be ((12 - d) + 1), or more simply (13 - d). Consequently all heptatonic scales will have a hexatonic antiscale, and vice-versa. This relationship of cardinality suffices to show that no scale can ever be its own antiscale, because no scale can have a non-integral cardinality. This assertion is also consistent with the formula A = 4096 - S, because the only S that would satisfy A = S is (4096 / 2) = 2048, which has no root tone (which we can see at a glance because it's an even number) and thus is not a scale.

Now we can look at an example. 12tone sprints through it pretty fast, so let me break it down in steps that you can read at a more leisurely pace.

Scale 2741: MajorScale 1355: Raga BhavaniScale 1387: Locrian



Figure 1 The major scale; its antiscale Raga Bhavani, and Locrian - a diatonic scale which is a mode of Major and a superset of Raga Bhavani. The one note difference between 1355 and 1387 is the perfect 4th interval, highlighted in red.

The Major scale is 2741 . The antiscale of that is 1355 Raga Bhavani , which 12Tone calls "Antimajor". Raga Bhavani is a hexatonic subset of 1387 Locrian ; Raga Bhavani is the Locrian scale with one note removed. And... Locrian is a mode of Major. This is the connection that Reuben observed, 12tone correctly observed that this is pretty neat, and gave the relationship a name: Antiscale Equivalence (AE).

The contrary example given by 12tone is 1453 Aeolian , also known as Natural Minor. The antiscale of 1453 is 2643 Raga Hamsanandi . Raga Hamsanandi is not a hexatonic subset of any of the modes of Aeolian, so therefore Aeolian does not have Antiscale Equivalence.

Scale 1453: AeolianScale 2643: Raga Hamsanandi


Figure 2 The minor scale, and its antiscale Raga Hamsanandi. There is no mode of 1453 that contains all the tones of 2643, thus the scale does not have Antiscale Equivalence.

12tone says the four diatonic modes with Antiscale Equivalence are Major, Locrian, Lydian, and Phrygian. It's true! Here are the antiscales of each diatonic mode, and the diatonic modes that we can achieve by adding one extra tone to the antiscale:

ScaleAntiscaleSubset of:
2741 Major 
1355 Raga Bhavani 
1387 Locrian 
1709 Dorian 
2387 Paptimic 
NONE
1451 Phrygian 
2645 Raga Mruganandana 
2773 Lydian 
2773 Lydian 
1323 Ritsu 
1387 Locrian 
1451 Phrygian 
1717 Mixolydian 
2379 Raga Gurjari Todi 
NONE
1453 Aeolian 
2643 Raga Hamsanandi 
NONE
1387 Locrian 
2709 Raga Kumud 
2741 Major 
2773 Lydian 
Figure 3 The diatonic modes, their antiscales, and diatonic modes that are supersets of those antiscales.

For want of a better term, I'll call these the Superantimodes, and they can be plural. For example, notice that Major and Lydian are the superantimodes of Locrian, and Locrian is the superantimode of both Major and Lydian. Representing the superantimode relationship as an arrow , we can build a network graph showing the superantimode relationships between modes:

Figure 4 The relationship of diatonic Scales to their Superantimodes.

From our example of the diatonic set it's apparent that within a modal family we may see some scales with AE, and some without; some scales - like Locrian - will have multiple superantimodes. And conversely, some modes - like Lydian - will be the superantimode of more than one of its modal siblings. 12tone mentions this plurality in the video at 7:41.

The diagram above might insinuate that there is a smooth continuum from Major to Phrygian, but that would be a misinterpretation. Connection by an arrow in the network graph really means the modes are very different, and where a node has more than one connection, its adjacent nodes are similar to each other in that they are both additions of a single note to a common antiscale. As a case in point, Phrygian and Locrian are similar scales differing only by the alteration of the 5th, and Major and Lydian are similar to each other differing only by the alteration of the 4th.

A fact that we can accept immediately is that AE will only occur for heptatonic scales. For as we determined above, an antiscale has the cardinality 13 - d, and any superset (adding just one tone) will have cardinality (13 - d) + 1. For that superset to be an superantimode, the cardinality of the superset must equal the cardinality of the original scale. So (13 - d) + 1 = d, which solves as d = 7.

Another observation is that like the pairwise relationship of antiscales, superantimodes are always reciprocal. If Scale A has a superantimode B, then Scale B will have a superantimode A. Superantimode relationships are always reciprocal, even if they're not one-to-one.

When a scale has AE, its inverse will also have AE, without exception. We can see in the lists below that pairs of families have the same Forte Class numbers; that's because classes are related by rotation or inversion, whereas our modal families are only related by rotation. For every modal family that has AE scales, its inverted relatives from the same Forte class will have the same pattern. For example, in Figure 5: scale 2143 inverted is 3907, and scale 2017 inverted is 253.


Figure 5 AE pairs from the same Forte pitch class 7-2, but different modal families related by inversion.

When 12tone says "there are 16 sets represented", he isn't talking about modal families, he means 16 different Forte classes, each of which may be invertible or non-invertible. The property that 12tone calls "invertible" has another name: chirality. A chiral scale has an inverse that is different from itself and all its own modes; the inverse can not be produced by rotation. A chiral scale is like a left glove; no matter how you turn it around (excluding turning it inside-out), it cannot be transformed into a right glove. An achiral scale is like a tube sock: it has no left or right handedness, and its reflection looks the same as a rotation of itself. The achiral sets are the ones that have at least one axis of reflective symmetry.

What we see is that in chiral scales (the ones with no symmetry), the AE scales will have an enantiomorph with its own superantimode - like matching fingers on a left and right glove. In scales that are chiral (with symmetry), there is no enantiomorph, and the superantiscales ARE the inverse.

What patterns exist?

After crunching all the numbers, it turns out that most of the superantimode relationships are between two modes, or in a linear cycle of 3 or 4 modes.

There are 12 modal families that contain a single pair of AE scales that are superantimodes of each other. Most of them are chiral, and their enantiomorphs are superantimodes of each other too. In the achiral ones (that have reflective symmetry) - 7-Z37 and 7-Z17 - The AE scales are both inverses and superantimodes of each other.

Forte ClassChiralityModal FamilyAE modes
7-2YES
191 
7-2YES
253 
7-3YES
319 Epodian 
2207 Mygian 
3151 Pacrian 
3623 Aerocrian 
3859 Aeolarian 
3977 Kythian 
1009 Katyptian 
7-3YES
505 Sanian 
575 Ionydian 
2335 Epydian 
3215 Katydian 
3655 Mathian 
3875 Aeryptian 
3985 Thadian 
7-11YES
379 Aeragian 
2237 Epothian 
1583 Salian 
2839 Lyptian 
3467 Katonian 
3781 Gyphian 
1969 Stylian 
7-11YES
445 Gocrian 
1135 Katolian 
2615 Thoptian 
3355 Bagian 
3725 Kyrian 
1955 Sonian 
3025 Epycrian 
7-Z37NO
443 Kothian 
2269 Pygian 
1591 Rodian 
2843 Sorian 
3469 Monian 
1891 Thalian 
2993 Stythian 
7-Z17NO
631 Zygian 
2363 Kataptian 
3229 Aeolaptian 
1831 Pothian 
2963 Bygian 
3529 Stalian 
953 Mela Yagapriya 
7-23YES
701 Mixonyphian 
1199 Magian 
2647 Dadian 
3371 Aeolylian 
3733 Gycrian 
1957 Pyrian 
1513 Stathian 
7-23YES
757 Ionyptian 
1213 Gyrian 
1327 Zalian 
2711 Stolian 
3403 Bylian 
3749 Raga Sorati 
1961 Soptian 
7-27YES
949 Mela Mararanjani 
1261 Modified Blues 
1339 Kycrian 
2717 Epygian 
1703 Mela Vanaspati 
2899 Kagian 
3497 Phrolian 
7-27YES
695 Sarian 
2395 Zoptian 
3245 Mela Varunapriya 
1835 Byptian 
2965 Darian 
1765 Lonian 
1465 Mela Ragavardhani 
Figure 6 All the sets with a single pair of reciprocal superantimodes.

There are three modal families with two connected AE pairs. These sets are all achiral (they have reflective symmetry), and exhibit the interesting pattern that the superantimode pairs aren't inverses of each other, but the pairs have one from each inverted couple. For example, in class 7-8, the scales 381 and 2001 are inverses, as are the scales 3723 and 2607.

Forte ClassChiralityModal FamilyAE modes
7-8NO
381 Kogian 
1119 Rarian 
2607 Aerolian 
3351 Karian 
3723 Myptian 
3909 Rydian 
2001 Gydian 
7-22NO
871 Locrian Double-flat 3 Double-flat 7 
2483 Double Harmonic 
3289 Lydian Sharp 2 Sharp 6 
923 Ultraphrygian 
2509 Double Harmonic Minor 
1651 Asian 
2873 Ionian Augmented Sharp 2 
7-34NO
1371 Superlocrian 
2733 Melodic Minor Ascending 
1707 Dorian Flat 2 
2901 Lydian Augmented 
1749 Acoustic 
1461 Major-Minor 
1389 Minor Locrian 
Figure 7 All the sets with two unconnected pairs of reciprocal superantimodes.

There are three modal families with a linear cycle of 3 modes. The 7-7 class has the predictable chiral relationship between the two modal sets. Set 7-15 is elegant with its scale 1821 being palindromic (so it is its own inverse), and its two superantimodes 2283 and 2787 are inverses of each other.

Forte ClassChiralityModal FamilyAE modes
7-7YES
463 Zythian 
2279 Dyrian 
3187 Koptian 
3641 Thocrian 
967 Mela Salaga 
2531 Danian 
3313 Aeolacrian 
7-7YES
487 Dynian 
2291 Zydian 
3193 Zathian 
911 Radian 
2503 Mela Jhalavarali 
3299 Syptian 
3697 Ionarian 
7-15NO
471 Dodian 
2283 Aeolyptian 
3189 Aeolonian 
1821 Aeradian 
1479 Mela Jalarnava 
2787 Zyrian 
3441 Thacrian 
Figure 8 All the sets with a chain of 3 related superantimodes.

There are two modal families with a linear cycle of 4 modes. It is interesting to note that these are the most evenly-spaced and the least evenly-spaced scales of all the heptatonics, and here we meet with our favourite set, 7-35 the major aka diatonic. Of the four connected scales, the two middle ones with two superantiscales (eg Locrian and Lydian) are inverses of each other, and the two outer ones (eg Major and Phrygian) are also inverses. You won't find the 7-1 class mentioned in the Study of Scales due to its large "leap" (disqualifying it from being called a True Scale) but it's included here for the reasons explained in the intro.

Forte ClassChiralityModal FamilyAE modes
7-1NO
127 
7-35NO
1387 Locrian 
2741 Major 
1709 Dorian 
1451 Phrygian 
2773 Lydian 
1717 Mixolydian 
1453 Aeolian 
Figure 9 All the sets with a chain of 4 related superantimodes.

There are two modal families where one mode is related by AE to 3 other modes. Predictably, they are chiral enantiomorphs of each other, from the same Forte class. The central most-connected mode in each family are inverses; 3277 is the inverse of 1639.

Forte ClassChiralityModal FamilyAE modes
7-21YES
823 Stodian 
2459 Ionocrian 
3277 Mela Nitimati 
1843 Ionygian 
2969 Tholian 
883 Ralian 
2489 Mela Gangeyabhusani 
7-21YES
827 Mixolocrian 
2461 Sagian 
1639 Aeolothian 
2867 Socrian 
3481 Katathian 
947 Mela Gayakapriya 
2521 Mela Dhatuvardhani 
Figure 10 All the sets where one mode has a superantimode relationship with 3 others that are otherwise unrelated.

The last and most impressive modal family is this one. All 7 modes have AE, with Neapolitan Major occupying a central node connected to all others. Its palindromic symmetry means it is its own inverse, and the six others are paired up as inverses too. The elegance of this set is apparent when you observe that it is a whole tone scale with one of the gaps filled. There are six gaps in the whole tone scale, producing 6 scales with similar placement of gaps; but then there is the Neapolitan Major scale where the filled gap acts as the root, allowing the whole tone pattern to shift by a semitone. That shift puts it out of phase with all its siblings, with notes where there are gaps and gaps where there are notes... consequently Neapolitan Major is superantimodal to all its siblings - a quintessential black sheep.

Forte ClassChiralityModal FamilyAE modes
7-33NO
1367 Leading Whole-Tone Inverse 
2731 Neapolitan Major 
3413 Leading Whole-tone 
1877 Aeroptian 
1493 Lydian Minor 
1397 Major Locrian 
1373 Storian 
Figure 11 The 7-33 set includes one mode having a superantimode relationship with all 6 others.

Showing my work

Now with our formula for computing superantimodes (the existence of which signifies AE), we can easily iterate through all the modal families and map out the superantimodes. There are a total of 66 heptatonic modal families. 23 of those modal families contain one or more AE scales, and those families belong to 16 pitch class sets. Seven of those sixteen sets are chiral and comprise two enantiomorphic modal families (making 14), the other nine are achiral. This is the potatoes of this article... every heptatonic modal family, with all the superantimodes shown. Enjoy!

Scale family 127: - Forte class: 7-1
ScaleAntiscaleSuperantimodes
127 3969 
2111 1985 
3103 993 
NONE
3599 497 Kadimic 
NONE
3847 249 
NONE
3971 125 
127 
4033  63 
127 
Scale family 191: - Forte class: 7-2
ScaleAntiscaleSuperantimodes
191 3905 
NONE
2143 1953 
3119 977 Kocrimic 
NONE
3607 489 Phrathimic 
NONE
3851 245 Raga Dipak 
NONE
3973 123 
NONE
2017 2079 
Scale family 223: - Forte class: 7-4
ScaleAntiscaleSuperantimodes
223 3873 
NONE
2159 1937 Galimic 
NONE
3127 969 Ionogimic 
NONE
3611 485 Stoptimic 
NONE
3853 243 
NONE
1987 2109 
NONE
3041 1055 
NONE
Scale family 239: - Forte class: 7-5
ScaleAntiscaleSuperantimodes
239 3857 Ponimic 
NONE
2167 1929 Aeolycrimic 
NONE
3131 965 Ionothimic 
NONE
3613 483 Kygimic 
NONE
1927 2169 
NONE
3011 1085 
NONE
3553 543 
NONE
Scale family 247: - Forte class: 7-5
ScaleAntiscaleSuperantimodes
247 3849 
NONE
2171 1925 
NONE
3133 963 
NONE
1807 2289 Mocrimic 
NONE
2951 1145 Zygimic 
NONE
3523 573 Saptimic 
NONE
3809  287 Gynimic 
NONE
Scale family 251: - Forte class: 7-4
ScaleAntiscaleSuperantimodes
251 3845 
NONE
2173 1923 
NONE
1567 2529 
NONE
2831 1265 Pynimic 
NONE
3463 633 Kydimic 
NONE
3779  317 Korimic 
NONE
3937  159 
NONE
Scale family 253: - Forte class: 7-2
ScaleAntiscaleSuperantimodes
253 3843 
1087 3009 
NONE
2591 1505 
NONE
3343 753 Aeronimic 
NONE
3719 377 Kathimic 
NONE
3907  189 
253 
4001  95 
NONE
Scale family 319: Epodian - Forte class: 7-3
ScaleAntiscaleSuperantimodes
319 Epodian 3777 
NONE
2207 Mygian 1889 
NONE
3151 Pacrian 945 Raga Saravati 
1009 Katyptian 
3623 Aerocrian 473 Aeralimic 
NONE
3859 Aeolarian 237 
NONE
3977 Kythian  119 
NONE
1009 Katyptian 3087 
3151 Pacrian 
Scale family 351: Epanian - Forte class: 7-9
ScaleAntiscaleSuperantimodes
351 Epanian 3745 
NONE
2223 Konian 1873 Dathimic 
NONE
3159 Stocrian 937 Stothimic 
NONE
3627 Kalian 469 Katyrimic 
NONE
3861 Phroptian 235 
NONE
1989 Dydian 2107 
NONE
1521 Stanian 2575 
NONE
Scale family 367: Aerodian - Forte class: 7-Z36
ScaleAntiscaleSuperantimodes
367 Aerodian 3729 Starimic 
NONE
2231 Macrian 1865 Thagimic 
NONE
3163 Rogian 933 Dadimic 
NONE
3629 Boptian 467 Raga Dhavalangam 
NONE
1931 Stogian 2165 
NONE
3013 Thynian 1083 
NONE
1777 Saptian 2319 
NONE
Scale family 375: Sodian - Forte class: 7-13
ScaleAntiscaleSuperantimodes
375 Sodian 3721 Phragimic 
NONE
2235 Bathian 1861 Phrygimic 
NONE
3165 Mylian 931 Raga Kalakanthi 
NONE
1815 Godian 2281 Rathimic 
NONE
2955 Thorian 1141 Rynimic 
NONE
3525 Zocrian 571 Kynimic 
NONE
1905 Katacrian 2191 Thydimic 
NONE
Scale family 379: Aeragian - Forte class: 7-11
ScaleAntiscaleSuperantimodes
379 Aeragian 3717 
3781 Gyphian 
2237 Epothian 1859 
NONE
1583 Salian 2513 Aerycrimic 
NONE
2839 Lyptian 1257 Blues Scale 
NONE
3467 Katonian 629 Aeronimic 
NONE
3781 Gyphian  315 Stodimic 
379 Aeragian 
1969 Stylian 2127 
NONE
Scale family 381: Kogian - Forte class: 7-8
ScaleAntiscaleSuperantimodes
381 Kogian 3715 
3723 Myptian 
1119 Rarian 2977 
NONE
2607 Aerolian 1489 Raga Jyoti 
2001 Gydian 
3351 Karian 745 Kolimic 
NONE
3723 Myptian 373 Epagimic 
381 Kogian 
3909 Rydian  187 
NONE
2001 Gydian 2095 
2607 Aerolian 
Scale family 415: Aeoladian - Forte class: 7-6
ScaleAntiscaleSuperantimodes
415 Aeoladian 3681 
NONE
2255 Dylian 1841 Thogimic 
NONE
3175 Eponian 921 Bogimic 
NONE
3635 Katygian 461 Raga Syamalam 
NONE
3865 Starian  231 
NONE
995 Phrathian 3101 
NONE
2545 Thycrian 1551 
NONE
Scale family 431: Epyrian - Forte class: 7-14
ScaleAntiscaleSuperantimodes
431 Epyrian 3665 Stalimic 
NONE
2263 Lycrian 1833 Ionacrimic 
NONE
3179 Daptian 917 Dygimic 
NONE
3637 Raga Rageshri 459 Zaptimic 
NONE
1933 Mocrian 2163 
NONE
1507 Zynian 2589 
NONE
2801 Zogian 1295 
NONE
Scale family 439: Bythian - Forte class: 7-Z38
ScaleAntiscaleSuperantimodes
439 Bythian 3657 Epynimic 
NONE
2267 Padian 1829 Pathimic 
NONE
3181 Rolian 915 Raga Kalagada 
NONE
1819 Pydian 2277 Kagimic 
NONE
2957 Thygian 1139 Aerygimic 
NONE
1763 Katalian 2333 Stynimic 
NONE
2929 Aeolathian 1167 Aerodimic 
NONE
Scale family 443: Kothian - Forte class: 7-Z37
ScaleAntiscaleSuperantimodes
443 Kothian 3653 Sathimic 
NONE
2269 Pygian 1827 Katygimic 
1891 Thalian 
1591 Rodian 2505 Mydimic 
NONE
2843 Sorian 1253 Zolimic 
NONE
3469 Monian 627 Mogimic 
NONE
1891 Thalian 2205 Ionocrimic 
2269 Pygian 
2993 Stythian 1103 Lynimic 
NONE
Scale family 445: Gocrian - Forte class: 7-11
ScaleAntiscaleSuperantimodes
445 Gocrian 3651 
NONE
1135 Katolian 2961 Bygimic 
3025 Epycrian 
2615 Thoptian 1481 Zagimic 
NONE
3355 Bagian 741 Gathimic 
NONE
3725 Kyrian  371 Rythimic 
NONE
1955 Sonian 2141 
NONE
3025 Epycrian 1071 
1135 Katolian 
Scale family 463: Zythian - Forte class: 7-7
ScaleAntiscaleSuperantimodes
463 Zythian 3633 Daptimic 
3641 Thocrian 
2279 Dyrian 1817 Phrythimic 
NONE
3187 Koptian 909 Katarimic 
NONE
3641 Thocrian  455 Messiaen Mode 5 
967 Mela Salaga 
463 Zythian 
967 Mela Salaga 3129 
3641 Thocrian 
2531 Danian 1565 
NONE
3313 Aeolacrian 783 
NONE
Scale family 471: Dodian - Forte class: 7-15
ScaleAntiscaleSuperantimodes
471 Dodian 3625 Podimic 
NONE
2283 Aeolyptian 1813 Katothimic 
1821 Aeradian 
3189 Aeolonian 907 Tholimic 
NONE
1821 Aeradian 2275 Messiaen Mode 5 
2787 Zyrian 
2283 Aeolyptian 
1479 Mela Jalarnava 2617 Pylimic 
NONE
2787 Zyrian 1309 Pogimic 
1821 Aeradian 
3441 Thacrian 655 Kataptimic 
NONE
Scale family 475: Aeolygian - Forte class: 7-Z38
ScaleAntiscaleSuperantimodes
475 Aeolygian 3621 Gylimic 
NONE
2285 Aerogian 1811 Kyptimic 
NONE
1595 Dacrian 2501 Ralimic 
NONE
2845 Baptian 1251 Sylimic 
NONE
1735 Mela Navanitam 2361 Docrimic 
NONE
2915 Aeolydian 1181 Katagimic 
NONE
3505 Stygian  591 Gaptimic 
NONE
Scale family 477: Stacrian - Forte class: 7-13
ScaleAntiscaleSuperantimodes
477 Stacrian 3619 Thanimic 
NONE
1143 Styrian 2953 Ionylimic 
NONE
2619 Ionyrian 1477 Raga Jaganmohanam 
NONE
3357 Phrodian 739 Rorimic 
NONE
1863 Pycrian 2233 Donimic 
NONE
2979 Gyptian 1117 Raptimic 
NONE
3537 Katogian 559 Lylimic 
NONE
Scale family 487: Dynian - Forte class: 7-7
ScaleAntiscaleSuperantimodes
487 Dynian 3609 
NONE
2291 Zydian 1805 
NONE
3193 Zathian 903 
911 Radian 
911 Radian 3185 Messiaen Mode 5 Inverse 
3697 Ionarian 
3193 Zathian 
2503 Mela Jhalavarali 1593 Zogimic 
NONE
3299 Syptian 797 Katocrimic 
NONE
3697 Ionarian  399 Zynimic 
911 Radian 
Scale family 491: Aeolyrian - Forte class: 7-14
ScaleAntiscaleSuperantimodes
491 Aeolyrian 3605 
NONE
2293 Gorian 1803 
NONE
1597 Aeolodian 2499 
NONE
1423 Doptian 2673 Mythimic 
NONE
2759 Mela Pavani 1337 Epogimic 
NONE
3427 Zacrian 669 Gycrimic 
NONE
3761 Raga Madhuri  335 Zanimic 
NONE
Scale family 493: Rygian - Forte class: 7-Z36
ScaleAntiscaleSuperantimodes
493 Rygian 3603 
NONE
1147 Epynian 2949 
NONE
2621 Ionogian 1475 
NONE
1679 Kydian 2417 Kanimic 
NONE
2887 Gaptian 1209 Raga Bhanumanjari 
NONE
3491 Tharian  605 Dycrimic 
NONE
3793 Aeopian  303 Golimic 
NONE
Scale family 499: Ionaptian - Forte class: 7-6
ScaleAntiscaleSuperantimodes
499 Ionaptian 3597 
NONE
2297 Thylian 1799 
NONE
799 Lolian 3297 
NONE
2447 Thagian 1649 Bolimic 
NONE
3271 Mela Raghupriya 825 Thyptimic 
NONE
3683 Dycrian 413 Ganimic 
NONE
3889 Parian  207 
NONE
Scale family 501: Katylian - Forte class: 7-9
ScaleAntiscaleSuperantimodes
501 Katylian 3595 
NONE
1149 Bydian 2947 
NONE
1311 Bynian 2785 
NONE
2703 Galian 1393 Mycrimic 
NONE
3399 Zonian 697 Lagimic 
NONE
3747 Myrian  349 Borimic 
NONE
3921 Pythian  175 
NONE
Scale family 505: Sanian - Forte class: 7-3
ScaleAntiscaleSuperantimodes
505 Sanian 3591 
3655 Mathian 
575 Ionydian 3521 
NONE
2335 Epydian 1761 
NONE
3215 Katydian 881 Aerothimic 
NONE
3655 Mathian 441 Thycrimic 
505 Sanian 
3875 Aeryptian 221 
NONE
3985 Thadian  111 
NONE
Scale family 607: Kadian - Forte class: 7-10
ScaleAntiscaleSuperantimodes
607 Kadian 3489 
NONE
2351 Gynian 1745 Raga Vutari 
NONE
3223 Thyphian 873 Bagimic 
NONE
3659 Polian 437 Ronimic 
NONE
3877 Thanian  219 Istrian 
NONE
1993 Katoptian 2103 
NONE
761 Ponian 3335 
NONE
Scale family 623: Sycrian - Forte class: 7-16
ScaleAntiscaleSuperantimodes
623 Sycrian 3473 Lathimic 
NONE
2359 Gadian 1737 Raga Madhukauns 
NONE
3227 Aeolocrian 869 Kothimic 
NONE
3661 Mixodorian 435 Raga Purna Pancama 
NONE
1939 Dathian 2157 
NONE
3017 Gacrian 1079 
NONE
889 Borian 3207 
NONE
Scale family 631: Zygian - Forte class: 7-Z17
ScaleAntiscaleSuperantimodes
631 Zygian 3465 Katathimic 
3529 Stalian 
2363 Kataptian 1733 Raga Sarasvati 
NONE
3229 Aeolaptian 867 Phrocrimic 
NONE
1831 Pothian 2265 Raga Rasamanjari 
NONE
2963 Bygian 1133 Stycrimic 
NONE
3529 Stalian 567 Aeoladimic 
631 Zygian 
953 Mela Yagapriya 3143 Polimic 
NONE
Scale family 635: Epolian - Forte class: 7-16
ScaleAntiscaleSuperantimodes
635 Epolian 3461 
NONE
2365 Sythian 1731 
NONE
1615 Sydian 2481 Raga Paraju 
NONE
2855 Epocrain 1241 Pygimic 
NONE
3475 Kylian 621 Pyramid Hexatonic 
NONE
3785 Epagian  311 Stagimic 
NONE
985 Mela Sucaritra 3111 
NONE
Scale family 637: Debussy's Heptatonic - Forte class: 7-10
ScaleAntiscaleSuperantimodes
637 Debussy's Heptatonic 3459 
NONE
1183 Sadian 2913 
NONE
2639 Dothian 1457 Raga Kamalamanohari 
NONE
3367 Moptian 729 Stygimic 
NONE
3731 Aeryrian  365 Marimic 
NONE
3913 Bonian  183 
NONE
1001 Badian 3095 
NONE
Scale family 671: Stycrian - Forte class: 7-Z12
ScaleAntiscaleSuperantimodes
671 Stycrian 3425 
NONE
2383 Katorian 1713 Raga Khamas 
NONE
3239 Mela Tanarupi 857 Aeolydimic 
NONE
3667 Kaptian 429 Koptimic 
NONE
3881 Morian  215 
NONE
997 Rycrian 3099 
NONE
1273 Ronian 2823 
NONE
Scale family 687: Aeolythian - Forte class: 7-24
ScaleAntiscaleSuperantimodes
687 Aeolythian 3409 Katanimic 
NONE
2391 Molian 1705 Raga Manohari 
NONE
3243 Mela Rupavati 853 Epothimic 
NONE
3669 Mothian  427 Raga Suddha Simantini 
NONE
1941 Aeranian 2155 
NONE
1509 Ragian 2587 
NONE
1401 Pagian 2695 
NONE
Scale family 695: Sarian - Forte class: 7-27
ScaleAntiscaleSuperantimodes
695 Sarian 3401 Palimic 
NONE
2395 Zoptian 1701 Dominant Seventh 
1765 Lonian 
3245 Mela Varunapriya 851 Raga Hejjajji 
NONE
1835 Byptian 2261 Raga Caturangini 
NONE
2965 Darian 1131 Honchoshi Plagal Form 
NONE
1765 Lonian 2331 Dylimic 
2395 Zoptian 
1465 Mela Ragavardhani 2631 Macrimic 
NONE
Scale family 699: Aerothian - Forte class: 7-26
ScaleAntiscaleSuperantimodes
699 Aerothian 3397 Sydimic 
NONE
2397 Stagian 1699 Raga Rasavali 
NONE
1623 Lothian 2473 Raga Takka 
NONE
2859 Phrycrian 1237 Salimic 
NONE
3477 Kyptian  619 Double-Phrygian Hexatonic 
NONE
1893 Ionylian 2203 Dorimic 
NONE
1497 Mela Jyotisvarupini 2599 Malimic 
NONE
Scale family 701: Mixonyphian - Forte class: 7-23
ScaleAntiscaleSuperantimodes
701 Mixonyphian 3395 
NONE
1199 Magian 2897 Rycrimic 
NONE
2647 Dadian 1449 Raga Gopikavasantam 
1513 Stathian 
3371 Aeolylian 725 Raga Yamuna Kalyani 
NONE
3733 Gycrian  363 Soptimic 
NONE
1957 Pyrian 2139 
NONE
1513 Stathian 2583 
2647 Dadian 
Scale family 719: Kanian - Forte class: 7-19
ScaleAntiscaleSuperantimodes
719 Kanian 3377 Phralimic 
NONE
2407 Zylian 1689 Lorimic 
NONE
3251 Mela Hatakambari 845 Raga Neelangi 
NONE
3673 Ranian  423 Sogimic 
NONE
971 Mela Gavambodhi 3125 
NONE
2533 Podian 1563 
NONE
1657 Ionothian 2439 
NONE
Scale family 727: Phradian - Forte class: 7-29
ScaleAntiscaleSuperantimodes
727 Phradian 3369 Mixolimic 
NONE
2411 Aeolorian 1685 Zeracrimic 
NONE
3253 Mela Naganandini 843 Molimic 
NONE
1837 Dalian 2259 Raga Mandari 
NONE
1483 Mela Bhavapriya 2613 Raga Hamsa Vinodini 
NONE
2789 Zolian 1307 Katorimic 
NONE
1721 Mela Vagadhisvari 2375 Aeolaptimic 
NONE
Scale family 731: Ionorian - Forte class: 7-31
ScaleAntiscaleSuperantimodes
731 Ionorian 3365 Katolimic 
NONE
2413 Locrian Natural 2 1683 Raga Malayamarutam 
NONE
1627 Zyptian 2469 Raga Bhinna Pancama 
NONE
2861 Katothian 1235 Messiaen Truncated Mode 2 
NONE
1739 Mela Sadvidhamargini 2357 Raga Sarasanana 
NONE
2917 Nohkan Flute Scale 1179 Sonimic 
NONE
1753 Hungarian Major 2343 Tharimic 
NONE
Scale family 733: Donian - Forte class: 7-25
ScaleAntiscaleSuperantimodes
733 Donian 3363 Rogimic 
NONE
1207 Aeoloptian 2889 Thoptimic 
NONE
2651 Panian 1445 Raga Navamanohari 
NONE
3373 Lodian  723 Ionadimic 
NONE
1867 Solian 2229 Raga Nalinakanti 
NONE
2981 Ionolian 1115 Superlocrian Hexamirror 
NONE
1769 Blues Heptatonic II 2327 Epalimic 
NONE
Scale family 743: Chromatic Hypophrygian Inverse - Forte class: 7-20
ScaleAntiscaleSuperantimodes
743 Chromatic Hypophrygian Inverse 3353 Phraptimic 
NONE
2419 Raga Lalita 1677 Raga Manavi 
NONE
3257 Mela Calanata 839 Ionathimic 
NONE
919 Chromatic Phrygian Inverse 3177 Rothimic 
NONE
2507 Todi That 1589 Raga Rageshri 
NONE
3301 Chromatic Mixolydian Inverse 795 Aeologimic 
NONE
1849 Chromatic Hypodorian Inverse 2247 Raga Vijayasri 
NONE
Scale family 747: Lynian - Forte class: 7-28
ScaleAntiscaleSuperantimodes
747 Lynian 3349 Aeolocrimic 
NONE
2421 Malian 1675 Raga Salagavarali 
NONE
1629 Synian 2467 Raga Padi 
NONE
1431 Phragian 2665 Aeradimic 
NONE
2763 Mela Suvarnangi 1333 Lyptimic 
NONE
3429 Marian  667 Rodimic 
NONE
1881 Katorian 2215 Ranimic 
NONE
Scale family 749: Aeologian - Forte class: 7-25
ScaleAntiscaleSuperantimodes
749 Aeologian 3347 Synimic 
NONE
1211 Zadian 2885 Byrimic 
NONE
2653 Sygian 1443 Raga Phenadyuti 
NONE
1687 Phralian 2409 Zacrimic 
NONE
2891 Phrogian 1205 Raga Siva Kambhoji 
NONE
3493 Rathian  603 Aeolygimic 
NONE
1897 Ionopian 2199 Dyptimic 
NONE
Scale family 755: Phrythian - Forte class: 7-Z18
ScaleAntiscaleSuperantimodes
755 Phrythian 3341 
NONE
2425 Rorian 1671 
NONE
815 Bolian 3281 Raga Vijayavasanta 
NONE
2455 Bothian 1641 Bocrimic 
NONE
3275 Mela Divyamani 821 Aeranimic 
NONE
3685 Kodian  411 Lygimic 
NONE
1945 Zarian 2151 
NONE
Scale family 757: Ionyptian - Forte class: 7-23
ScaleAntiscaleSuperantimodes
757 Ionyptian 3339 
3403 Bylian 
1213 Gyrian 2883 
NONE
1327 Zalian 2769 Dyrimic 
NONE
2711 Stolian 1385 Phracrimic 
NONE
3403 Bylian  693 Arezzo Major Diatonic Hexachord 
757 Ionyptian 
3749 Raga Sorati  347 Barimic 
NONE
1961 Soptian 2135 
NONE
Scale family 823: Stodian - Forte class: 7-21
ScaleAntiscaleSuperantimodes
823 Stodian 3273 Raga Jivantini 
3277 Mela Nitimati 
2459 Ionocrian 1637 Syptimic 
NONE
3277 Mela Nitimati  819 Augmented Inverse 
1843 Ionygian 
883 Ralian 
823 Stodian 
1843 Ionygian 2253 Raga Amarasenapriya 
3277 Mela Nitimati 
2969 Tholian 1127 Eparimic 
NONE
883 Ralian 3213 Eponimic 
3277 Mela Nitimati 
2489 Mela Gangeyabhusani 1607 Epytimic 
NONE
Scale family 827: Mixolocrian - Forte class: 7-21
ScaleAntiscaleSuperantimodes
827 Mixolocrian 3269 Raga Malarani 
NONE
2461 Sagian 1635 Sygimic 
1639 Aeolothian 
1639 Aeolothian 2457 Augmented 
3481 Katathian 
2521 Mela Dhatuvardhani 
2461 Sagian 
2867 Socrian 1229 Raga Simharava 
NONE
3481 Katathian  615 Phrothimic 
1639 Aeolothian 
947 Mela Gayakapriya 3149 Phrycrimic 
NONE
2521 Mela Dhatuvardhani 1575 Zycrimic 
1639 Aeolothian 
Scale family 829: Lygian - Forte class: 7-Z18
ScaleAntiscaleSuperantimodes
829 Lygian 3267 
NONE
1231 Logian 2865 Solimic 
NONE
2663 Lalian 1433 Dynimic 
NONE
3379 Verdi's Scala Enigmatica Descending  717 Raga Vijayanagari 
NONE
3737 Phrocrian  359 Bothimic 
NONE
979 Mela Dhavalambari 3117 
NONE
2537 Laptian 1559 
NONE
Scale family 847: Ganian - Forte class: 7-19
ScaleAntiscaleSuperantimodes
847 Ganian 3249 Raga Tilang 
NONE
2471 Mela Ganamurti 1625 Lythimic 
NONE
3283 Mela Visvambhari 813 Larimic 
NONE
3689 Katocrian  407 Zylimic 
NONE
973 Mela Syamalangi 3123 
NONE
1267 Katynian 2829 
NONE
2681 Aerycrian 1415 
NONE
Scale family 855: Porian - Forte class: 7-30
ScaleAntiscaleSuperantimodes
855 Porian 3241 Dalimic 
NONE
2475 Neapolitan Minor 1621 Scriabin's Prometheus 
NONE
3285 Mela Citrambari 811 Radimic 
NONE
1845 Lagian 2251 Zodimic 
NONE
1485 Minor Romani 2611 Raga Vasanta 
NONE
1395 Asian (a) 2701 Hawaiian 
NONE
2745 Mela Sulini 1351 Aeraptimic 
NONE
Scale family 859: Ultralocrian - Forte class: 7-32
ScaleAntiscaleSuperantimodes
859 Ultralocrian 3237 Raga Brindabani Sarang 
NONE
2477 Harmonic Minor 1619 Prometheus Neapolitan 
NONE
1643 Locrian Natural 6 2453 Raga Latika 
NONE
2869 Major Augmented 1227 Thacrimic 
NONE
1741 Lydian Diminished 2355 Raga Lalita 
NONE
1459 Phrygian Dominant 2637 Raga Ranjani 
NONE
2777 Aeolian Harmonic 1319 Phronimic 
NONE
Scale family 861: Rylian - Forte class: 7-28
ScaleAntiscaleSuperantimodes
861 Rylian 3235 Pothimic 
NONE
1239 Epaptian 2857 Stythimic 
NONE
2667 Byrian 1429 Bythimic 
NONE
3381 Katanian  715 Messiaen Truncated Mode 2 
NONE
1869 Katyrian 2227 Raga Gaula 
NONE
1491 Mela Namanarayani 2605 Rylimic 
NONE
2793 Eporian 1303 Epolimic 
NONE
Scale family 871: Locrian Double-flat 3 Double-flat 7 - Forte class: 7-22
ScaleAntiscaleSuperantimodes
871 Locrian Double-flat 3 Double-flat 7 3225 Ionalimic 
3289 Lydian Sharp 2 Sharp 6 
2483 Double Harmonic 1613 Thylimic 
NONE
3289 Lydian Sharp 2 Sharp 6 807 Raga Suddha Mukhari 
871 Locrian Double-flat 3 Double-flat 7 
923 Ultraphrygian 3173 Zarimic 
NONE
2509 Double Harmonic Minor 1587 Raga Rudra Pancama 
1651 Asian 
1651 Asian 2445 Zadimic 
2509 Double Harmonic Minor 
2873 Ionian Augmented Sharp 2 1223 Phryptimic 
NONE
Scale family 875: Locrian Double-flat 7 - Forte class: 7-32
ScaleAntiscaleSuperantimodes
875 Locrian Double-flat 7 3221 Bycrimic 
NONE
2485 Harmonic Major 1611 Dacrimic 
NONE
1645 Dorian Flat 5 2451 Raga Bauli 
NONE
1435 Makam Huzzam 2661 Stydimic 
NONE
2765 Lydian Diminished 1331 Raga Vasantabhairavi 
NONE
1715 Harmonic Minor Inverse 2381 Takemitsu Linea Mode 1 
NONE
2905 Aeolian Flat 1 1191 Pyrimic 
NONE
Scale family 877: Moravian Pistalkova - Forte class: 7-31
ScaleAntiscaleSuperantimodes
877 Moravian Pistalkova 3219 Ionaphimic 
NONE
1243 Epylian 2853 Baptimic 
NONE
2669 Jeths' Mode 1427 Lolimic 
NONE
1691 Kathian 2405 Katalimic 
NONE
2893 Lylian 1203 Pagimic 
NONE
1747 Mela Ramapriya 2349 Raga Ghantana 
NONE
2921 Pogian 1175 Epycrimic 
NONE
Scale family 885: Sathian - Forte class: 7-26
ScaleAntiscaleSuperantimodes
885 Sathian 3211 Epacrimic 
NONE
1245 Lathian 2851 Katoptimic 
NONE
1335 Elephant Scale 2761 Dagimic 
NONE
2715 Kynian 1381 Padimic 
NONE
3405 Stynian  691 Raga Kalavati 
NONE
1875 Persichetti Scale 2221 Raga Sindhura Kafi 
NONE
2985 Epacrian 1111 Sycrimic 
NONE
Scale family 925: Chromatic Hypodorian - Forte class: 7-20
ScaleAntiscaleSuperantimodes
925 Chromatic Hypodorian 3171 Zythimic 
NONE
1255 Chromatic Mixolydian 2841 Sothimic 
NONE
2675 Chromatic Lydian 1421 Raga Trimurti 
NONE
3385 Chromatic Phrygian 711 Raga Chandrajyoti 
NONE
935 Chromatic Dorian 3161 Kodimic 
NONE
2515 Chromatic Hypolydian 1581 Raga Bagesri 
NONE
3305 Chromatic Hypophrygian 791 Aeoloptimic 
NONE
Scale family 939: Mela Senavati - Forte class: 7-30
ScaleAntiscaleSuperantimodes
939 Mela Senavati 3157 Zyptimic 
NONE
2517 Harmonic Lydian 1579 Sagimic 
NONE
1653 Minor Romani Inverse 2443 Panimic 
NONE
1437 Sabach ascending 2659 Katynimic 
NONE
1383 Pynian 2713 Porimic 
NONE
2739 Mela Suryakanta 1357 Takemitsu Linea Mode 2 
NONE
3417 Golian  679 Lanimic 
NONE
Scale family 941: Mela Jhankaradhvani - Forte class: 7-29
ScaleAntiscaleSuperantimodes
941 Mela Jhankaradhvani 3155 Ladimic 
NONE
1259 Stadian 2837 Aelothimic 
NONE
2677 Thodian 1419 Raga Kashyapi 
NONE
1693 Dogian 2403 Lycrimic 
NONE
1447 Mela Ratnangi 2649 Aeolythimic 
NONE
2771 Marva That 1325 Phradimic 
NONE
3433 Thonian  663 Phrynimic 
NONE
Scale family 949: Mela Mararanjani - Forte class: 7-27
ScaleAntiscaleSuperantimodes
949 Mela Mararanjani 3147 Ryrimic 
NONE
1261 Modified Blues 2835 Ionygimic 
2899 Kagian 
1339 Kycrian 2757 Raga Nishadi 
NONE
2717 Epygian 1379 Kycrimic 
NONE
1703 Mela Vanaspati 2393 Zathimic 
NONE
2899 Kagian 1197 Minor Hexatonic 
1261 Modified Blues 
3497 Phrolian  599 Thyrimic 
NONE
Scale family 981: Mela Kantamani - Forte class: 7-24
ScaleAntiscaleSuperantimodes
981 Mela Kantamani 3115 
NONE
1269 Katythian 2827 
NONE
1341 Madian 2755 
NONE
1359 Aerygian 2737 Raga Hari Nata 
NONE
2727 Mela Manavati 1369 Boptimic 
NONE
3411 Enigmatic  685 Raga Suddha Bangala 
NONE
3753 Phraptian  343 Ionorimic 
NONE
Scale family 1367: Leading Whole-Tone Inverse - Forte class: 7-33
ScaleAntiscaleSuperantimodes
1367 Leading Whole-Tone Inverse 2729 Aeragimic 
2731 Neapolitan Major 
2731 Neapolitan Major  1365 Whole Tone 
3413 Leading Whole-tone 
1877 Aeroptian 
1493 Lydian Minor 
1397 Major Locrian 
1373 Storian 
1367 Leading Whole-Tone Inverse 
3413 Leading Whole-tone  683 Stogimic 
2731 Neapolitan Major 
1877 Aeroptian 2219 Phrydimic 
2731 Neapolitan Major 
1493 Lydian Minor 2603 Gadimic 
2731 Neapolitan Major 
1397 Major Locrian 2699 Sythimic 
2731 Neapolitan Major 
1373 Storian 2723 Raga Jivantika 
2731 Neapolitan Major 
Scale family 1371: Superlocrian - Forte class: 7-34
ScaleAntiscaleSuperantimodes
1371 Superlocrian 2725 Raga Nagagandhari 
2733 Melodic Minor Ascending 
2733 Melodic Minor Ascending 1363 Gygimic 
1371 Superlocrian 
1707 Dorian Flat 2 2389 Eskimo Hexatonic 2 
2901 Lydian Augmented 
2901 Lydian Augmented 1195 Raga Gandharavam 
1707 Dorian Flat 2 
1749 Acoustic 2347 Raga Viyogavarali 
NONE
1461 Major-Minor 2635 Gocrimic 
NONE
1389 Minor Locrian 2707 Banimic 
NONE
Scale family 1387: Locrian - Forte class: 7-35
ScaleAntiscaleSuperantimodes
1387 Locrian 2709 Raga Kumud 
2741 Major 
2773 Lydian 
2741 Major 1355 Raga Bhavani 
1387 Locrian 
1709 Dorian 2387 Paptimic 
NONE
1451 Phrygian 2645 Raga Mruganandana 
2773 Lydian 
2773 Lydian 1323 Ritsu 
1387 Locrian 
1451 Phrygian 
1717 Mixolydian 2379 Raga Gurjari Todi 
NONE
1453 Aeolian 2643 Raga Hamsanandi 
NONE