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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 Aeolorimic, 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 Aeolorimic
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 BEGian
2143 NAPian
3119 TIKian
3607 WOPian
3851 YILian
3973 ZEHian
2017 MEQian
7-2YES
253 BOSian
1087 GOBian
2591 PUWian
3343 VAJian
3719 XOFian
3907 YUTian
4001 ZIYian
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 Sudhvidhamagini
3781 Gyphian
1969 Zorian
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 Crater Scale
3723 Myptian
3909 Rydian
2001 Gydian
7-22NO
871 Hungarian Romani Minor 4th Mode
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 Heptatonic Chromatic
2111 Heptatonic Chromatic 2
3103 Heptatonic Chromatic 3
3599 Heptatonic Chromatic 4
3847 Heptatonic Chromatic 5
3971 Heptatonic Chromatic 6
4033 Heptatonic Chromatic Descending
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 Major Romani
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: Heptatonic Chromatic - Forte class: 7-1
ScaleAntiscaleSuperantimodes
127 Heptatonic Chromatic3969 Hexatonic Chromatic Descending
3971 Heptatonic Chromatic 6
4033 Heptatonic Chromatic Descending
2111 Heptatonic Chromatic 21985 MEWian
4033 Heptatonic Chromatic Descending
3103 Heptatonic Chromatic 3993 GAVian
NONE
3599 Heptatonic Chromatic 4497 Kadimic
NONE
3847 Heptatonic Chromatic 5249 BOQian
NONE
3971 Heptatonic Chromatic 6125 ATWian
127 Heptatonic Chromatic
4033 Heptatonic Chromatic Descending 63 Hexatonic Chromatic
127 Heptatonic Chromatic
2111 Heptatonic Chromatic 2
Scale family 191: BEGian - Forte class: 7-2
ScaleAntiscaleSuperantimodes
191 BEGian3905 YUSian
NONE
2143 NAPian1953 MACian
2017 MEQian
3119 TIKian977 Kocrimic
NONE
3607 WOPian489 Phrathimic
NONE
3851 YILian245 Raga Dipak
NONE
3973 ZEHian123 ASUian
NONE
2017 MEQian2079 Hexatonic Chromatic 4
2143 NAPian
Scale family 223: BIZian - Forte class: 7-4
ScaleAntiscaleSuperantimodes
223 BIZian3873 YOYian
NONE
2159 NEYian1937 Galimic
NONE
3127 TOPian969 Ionogimic
NONE
3611 WORian485 Stoptimic
NONE
3853 YOMian243 BOMian
NONE
1987 MEXian2109 MUVian
NONE
3041 TANian1055 GIHian
NONE
Scale family 239: BIKian - Forte class: 7-5
ScaleAntiscaleSuperantimodes
239 BIKian3857 Ponimic
NONE
2167 NEDian1929 Aeolycrimic
NONE
3131 TORian965 Ionothimic
NONE
3613 WOSian483 Kygimic
NONE
1927 LUNian2169 NEFian
NONE
3011 SUWian1085 GOZian
NONE
3553 WEHian543 DENian
NONE
Scale family 247: BOPian - Forte class: 7-5
ScaleAntiscaleSuperantimodes
247 BOPian3849 YIKian
NONE
2171 NEGian1925 LUMian
NONE
3133 TOSian963 GACian
NONE
1807 LARian2289 Mocrimic
NONE
2951 SILian1145 Zygimic
NONE
3523 WAPian573 Saptimic
NONE
3809 YELian 287 Gynimic
NONE
Scale family 251: BORian - Forte class: 7-4
ScaleAntiscaleSuperantimodes
251 BORian3845 YIHian
NONE
2173 NEHian1923 LULian
NONE
1567 JOBian2529 PIKian
NONE
2831 RUQian1265 Pynimic
NONE
3463 VOFian633 Kydimic
NONE
3779 YASian 317 Korimic
NONE
3937 ZALian 159 BAMian
NONE
Scale family 253: BOSian - Forte class: 7-2
ScaleAntiscaleSuperantimodes
253 BOSian3843 Hexatonic Chromatic 5
3907 YUTian
1087 GOBian3009 SUVian
NONE
2591 PUWian1505 JEPian
NONE
3343 VAJian753 Kytrimic
NONE
3719 XOFian377 Kathimic
NONE
3907 YUTian 189 BEFian
253 BOSian
4001 ZIYian 95 ARKian
NONE
Scale family 319: Epodian - Forte class: 7-3
ScaleAntiscaleSuperantimodes
319 Epodian3777 YARian
NONE
2207 Mygian1889 LOQian
NONE
3151 Pacrian945 Raga Saravati
1009 Katyptian
3623 Aerocrian473 Aeralimic
NONE
3859 Aeolarian237 BIJian
NONE
3977 Kythian 119 SMOian
NONE
1009 Katyptian3087 Hexatonic Chromatic 3
3151 Pacrian
Scale family 351: Epanian - Forte class: 7-9
ScaleAntiscaleSuperantimodes
351 Epanian3745 XUVian
NONE
2223 Konian1873 Dathimic
NONE
3159 Stocrian937 Stothimic
NONE
3627 Kalian469 Katyrimic
NONE
3861 Phroptian235 BIHian
NONE
1989 Dydian2107 MUTian
NONE
1521 Stanian2575 PUMian
NONE
Scale family 367: Aerodian - Forte class: 7-Z36
ScaleAntiscaleSuperantimodes
367 Aerodian3729 Starimic
NONE
2231 Macrian1865 Thagimic
NONE
3163 Rogian933 Dadimic
NONE
3629 Boptian467 Raga Dhavalangam
NONE
1931 Stogian2165 NECian
NONE
3013 Thynian1083 GOYian
NONE
1777 Saptian2319 ODUian
NONE
Scale family 375: Sodian - Forte class: 7-13
ScaleAntiscaleSuperantimodes
375 Sodian3721 Phragimic
NONE
2235 Bathian1861 Phrygimic
NONE
3165 Mylian931 Raga Kalakanthi
NONE
1815 Godian2281 Rathimic
NONE
2955 Thorian1141 Rynimic
NONE
3525 Zocrian571 Kynimic
NONE
1905 Katacrian2191 Thydimic
NONE
Scale family 379: Aeragian - Forte class: 7-11
ScaleAntiscaleSuperantimodes
379 Aeragian3717 XIDian
3781 Gyphian
2237 Epothian1859 LIXian
NONE
1583 Salian2513 Aerycrimic
NONE
2839 Lyptian1257 Minor Blues
NONE
3467 Sudhvidhamagini629 Aeronimic
NONE
3781 Gyphian 315 Stodimic
379 Aeragian
1969 Zorian2127 NAFian
NONE
Scale family 381: Kogian - Forte class: 7-8
ScaleAntiscaleSuperantimodes
381 Kogian3715 XICian
3723 Myptian
1119 Rarian2977 SOBian
NONE
2607 Aerolian1489 Raga Jyoti
2001 Gydian
3351 Crater Scale745 Kolimic
NONE
3723 Myptian373 Epagimic
381 Kogian
3909 Rydian 187 BEDian
NONE
2001 Gydian2095 MUMian
2607 Aerolian
Scale family 415: Aeoladian - Forte class: 7-6
ScaleAntiscaleSuperantimodes
415 Aeoladian3681 XAHian
NONE
2255 Dylian1841 Thogimic
NONE
3175 Eponian921 Bogimic
NONE
3635 Katygian461 Raga Syamalam
NONE
3865 Starian 231 BIFian
NONE
995 Phrathian3101 TIYian
NONE
2545 Thycrian1551 JORian
NONE
Scale family 431: Epyrian - Forte class: 7-14
ScaleAntiscaleSuperantimodes
431 Epyrian3665 Stalimic
NONE
2263 Lycrian1833 Ionacrimic
NONE
3179 Daptian917 Dygimic
NONE
3637 Raga Rageshri459 Zaptimic
NONE
1933 Mocrian2163 NEBian
NONE
1507 Zynian2589 PUVian
NONE
2801 Zogian1295 HUYian
NONE
Scale family 439: Bythian - Forte class: 7-Z38
ScaleAntiscaleSuperantimodes
439 Bythian3657 Epynimic
NONE
2267 Padian1829 Pathimic
NONE
3181 Rolian915 Raga Kalagada
NONE
1819 Pydian2277 Kagimic
NONE
2957 Thygian1139 Aerygimic
NONE
1763 Katalian2333 Stynimic
NONE
2929 Aeolathian1167 Aerodimic
NONE
Scale family 443: Kothian - Forte class: 7-Z37
ScaleAntiscaleSuperantimodes
443 Kothian3653 Sathimic
NONE
2269 Pygian1827 Katygimic
1891 Thalian
1591 Rodian2505 Mydimic
NONE
2843 Sorian1253 Zolimic
NONE
3469 Monian627 Mogimic
NONE
1891 Thalian2205 Ionocrimic
2269 Pygian
2993 Stythian1103 Lynimic
NONE
Scale family 445: Gocrian - Forte class: 7-11
ScaleAntiscaleSuperantimodes
445 Gocrian3651 WUQian
NONE
1135 Katolian2961 Bygimic
3025 Epycrian
2615 Thoptian1481 Zagimic
NONE
3355 Bagian741 Gathimic
NONE
3725 Kyrian 371 Rythimic
NONE
1955 Sonian2141 NANian
NONE
3025 Epycrian1071 GORian
1135 Katolian
Scale family 463: Zythian - Forte class: 7-7
ScaleAntiscaleSuperantimodes
463 Zythian3633 Daptimic
3641 Thocrian
2279 Dyrian1817 Phrythimic
NONE
3187 Koptian909 Katarimic
NONE
3641 Thocrian 455 Messiaen Mode 5 Rotation 2
967 Mela Salaga
463 Zythian
967 Mela Salaga3129 TOQian
3641 Thocrian
2531 Danian1565 JOZian
NONE
3313 Aeolacrian783 ETUian
NONE
Scale family 471: Dodian - Forte class: 7-15
ScaleAntiscaleSuperantimodes
471 Dodian3625 Podimic
NONE
2283 Aeolyptian1813 Katothimic
1821 Aeradian
3189 Aeolonian907 Tholimic
NONE
1821 Aeradian2275 Messiaen Mode 5
2787 Zyrian
2283 Aeolyptian
1479 Mela Jalarnava2617 Pylimic
NONE
2787 Zyrian1309 Pogimic
1821 Aeradian
3441 Thacrian655 Kataptimic
NONE
Scale family 475: Aeolygian - Forte class: 7-Z38
ScaleAntiscaleSuperantimodes
475 Aeolygian3621 Gylimic
NONE
2285 Aerogian1811 Kyptimic
NONE
1595 Dacrian2501 Ralimic
NONE
2845 Baptian1251 Sylimic
NONE
1735 Mela Navanitam2361 Docrimic
NONE
2915 Aeolydian1181 Katagimic
NONE
3505 Stygian 591 Gaptimic
NONE
Scale family 477: Stacrian - Forte class: 7-13
ScaleAntiscaleSuperantimodes
477 Stacrian3619 Thanimic
NONE
1143 Styrian2953 Ionylimic
NONE
2619 Ionyrian1477 Raga Jaganmohanam
NONE
3357 Phrodian739 Rorimic
NONE
1863 Pycrian2233 Donimic
NONE
2979 Gyptian1117 Raptimic
NONE
3537 Katogian559 Lylimic
NONE
Scale family 487: Dynian - Forte class: 7-7
ScaleAntiscaleSuperantimodes
487 Dynian3609 WOQian
NONE
2291 Zydian1805 LAQian
NONE
3193 Zathian903 FOSian
911 Radian
911 Radian3185 Messiaen Mode 5 Rotation 1
3697 Ionarian
3193 Zathian
2503 Mela Jhalavarali1593 Zogimic
NONE
3299 Syptian797 Katocrimic
NONE
3697 Ionarian 399 Zynimic
911 Radian
Scale family 491: Aeolyrian - Forte class: 7-14
ScaleAntiscaleSuperantimodes
491 Aeolyrian3605 OLKian
NONE
2293 Gorian1803 LAPian
NONE
1597 Aeolodian2499 PIRian
NONE
1423 Doptian2673 Mythimic
NONE
2759 Mela Pavani1337 Epogimic
NONE
3427 Zacrian669 Major Blues
NONE
3761 Raga Madhuri 335 Zanimic
NONE
Scale family 493: Rygian - Forte class: 7-Z36
ScaleAntiscaleSuperantimodes
493 Rygian3603 WOMian
NONE
1147 Epynian2949 SIKian
NONE
2621 Ionogian1475 UFFian
NONE
1679 Kydian2417 Kanimic
NONE
2887 Gaptian1209 Raga Bhanumanjari
NONE
3491 Tharian 605 Dycrimic
NONE
3793 Aeopian 303 Golimic
NONE
Scale family 499: Ionaptian - Forte class: 7-6
ScaleAntiscaleSuperantimodes
499 Ionaptian3597 WIJian
NONE
2297 Thylian1799 LAMian
NONE
799 Lolian3297 ULLian
NONE
2447 Thagian1649 Bolimic
NONE
3271 Mela Raghupriya825 Thyptimic
NONE
3683 Dycrian413 Ganimic
NONE
3889 Parian 207 BEQian
NONE
Scale family 501: Katylian - Forte class: 7-9
ScaleAntiscaleSuperantimodes
501 Katylian3595 WIHian
NONE
1149 Bydian2947 SIJian
NONE
1311 Bynian2785 RONian
NONE
2703 Galian1393 Mycrimic
NONE
3399 Zonian697 Lagimic
NONE
3747 Myrian 349 Borimic
NONE
3921 Pythian 175 BEWian
NONE
Scale family 505: Sanian - Forte class: 7-3
ScaleAntiscaleSuperantimodes
505 Sanian3591 WIFian
3655 Mathian
575 Ionydian3521 WANian
NONE
2335 Epydian1761 KUQian
NONE
3215 Katydian881 Aerothimic
NONE
3655 Mathian441 Thycrimic
505 Sanian
3875 Aeryptian221 BIYian
NONE
3985 Thadian 111 AROian
NONE
Scale family 607: Kadian - Forte class: 7-10
ScaleAntiscaleSuperantimodes
607 Kadian3489 VUVian
NONE
2351 Gynian1745 Raga Vutari
NONE
3223 Thyphian873 Bagimic
NONE
3659 Polian437 Ronimic
NONE
3877 Thanian 219 Istrian
NONE
1993 Katoptian2103 MURian
NONE
761 Ponian3335 VADian
NONE
Scale family 623: Sycrian - Forte class: 7-16
ScaleAntiscaleSuperantimodes
623 Sycrian3473 Lathimic
NONE
2359 Gadian1737 Raga Madhukauns
NONE
3227 Aeolocrian869 Kothimic
NONE
3661 Mixodorian435 Raga Purna Pancama
NONE
1939 Dathian2157 NEXian
NONE
3017 Gacrian1079 GOWian
NONE
889 Borian3207 UCOian
NONE
Scale family 631: Zygian - Forte class: 7-Z17
ScaleAntiscaleSuperantimodes
631 Zygian3465 Katathimic
3529 Stalian
2363 Kataptian1733 Raga Sarasvati
NONE
3229 Aeolaptian867 Phrocrimic
NONE
1831 Pothian2265 Raga Rasamanjari
NONE
2963 Bygian1133 Stycrimic
NONE
3529 Stalian567 Aeoladimic
631 Zygian
953 Mela Yagapriya3143 Polimic
NONE
Scale family 635: Epolian - Forte class: 7-16
ScaleAntiscaleSuperantimodes
635 Epolian3461 VODian
NONE
2365 Sythian1731 KOXian
NONE
1615 Sydian2481 Raga Paraju
NONE
2855 Epocrian1241 Pygimic
NONE
3475 Kylian621 Pyramid Hexatonic
NONE
3785 Epagian 311 Stagimic
NONE
985 Mela Sucaritra3111 TIFian
NONE
Scale family 637: Debussy's Heptatonic - Forte class: 7-10
ScaleAntiscaleSuperantimodes
637 Debussy's Heptatonic3459 VOCian
NONE
1183 Sadian2913 SENian
NONE
2639 Dothian1457 Raga Kamalamanohari
NONE
3367 Moptian729 Stygimic
NONE
3731 Aeryrian 365 Marimic
NONE
3913 Bonian 183 BEBian
NONE
1001 Badian3095 TIVian
NONE
Scale family 671: Stycrian - Forte class: 7-Z12
ScaleAntiscaleSuperantimodes
671 Stycrian3425 VIHian
NONE
2383 Katorian1713 Raga Khamas
NONE
3239 Mela Tanarupi857 Aeolydimic
NONE
3667 Kaptian429 Koptimic
NONE
3881 Morian 215 BIVian
NONE
997 Rycrian3099 TIXian
NONE
1273 Heptatonic Blues2823 RULian
NONE
Scale family 687: Aeolythian - Forte class: 7-24
ScaleAntiscaleSuperantimodes
687 Aeolythian3409 Katanimic
NONE
2391 Molian1705 Raga Manohari
NONE
3243 Mela Rupavati853 Epothimic
NONE
3669 Mothian 427 Raga Suddha Simantini
NONE
1941 Aeranian2155 NEWian
NONE
1509 Ragian2587 PUTian
NONE
1401 Pagian2695 RAKian
NONE
Scale family 695: Sarian - Forte class: 7-27
ScaleAntiscaleSuperantimodes
695 Sarian3401 Palimic
NONE
2395 Zoptian1701 Mixolydian Hexatonic
1765 Lonian
3245 Mela Varunapriya851 Raga Hejjajji
NONE
1835 Byptian2261 Raga Caturangini
NONE
2965 Darian1131 Honchoshi Plagal Form
NONE
1765 Lonian2331 Dylimic
2395 Zoptian
1465 Mela Ragavardhani2631 Macrimic
NONE
Scale family 699: Aerothian - Forte class: 7-26
ScaleAntiscaleSuperantimodes
699 Aerothian3397 Sydimic
NONE
2397 Stagian1699 Raga Rasavali
NONE
1623 Lothian2473 Raga Takka
NONE
2859 Phrycrian1237 Salimic
NONE
3477 Kyptian 619 Double-Phrygian Hexatonic
NONE
1893 Ionylian2203 Dorimic
NONE
1497 Mela Jyotisvarupini2599 Malimic
NONE
Scale family 701: Mixonyphian - Forte class: 7-23
ScaleAntiscaleSuperantimodes
701 Mixonyphian3395 VEPian
NONE
1199 Magian2897 Rycrimic
NONE
2647 Dadian1449 Raga Gopikavasantam
1513 Stathian
3371 Aeolylian725 Raga Yamuna Kalyani
NONE
3733 Gycrian 363 Soptimic
NONE
1957 Pyrian2139 NAMian
NONE
1513 Stathian2583 PURian
2647 Dadian
Scale family 719: Kanian - Forte class: 7-19
ScaleAntiscaleSuperantimodes
719 Kanian3377 Phralimic
NONE
2407 Zylian1689 Lorimic
NONE
3251 Mela Hatakambari845 Raga Neelangi
NONE
3673 Ranian 423 Sogimic
NONE
971 Mela Gavambodhi3125 TONian
NONE
2533 Podian1563 JOYian
NONE
1657 Ionothian2439 PAGian
NONE
Scale family 727: Phradian - Forte class: 7-29
ScaleAntiscaleSuperantimodes
727 Phradian3369 Mixolimic
NONE
2411 Aeolorian1685 Zeracrimic
NONE
3253 Mela Naganandini843 Molimic
NONE
1837 Dalian2259 Raga Mandari
NONE
1483 Mela Bhavapriya2613 Raga Hamsa Vinodini
NONE
2789 Zolian1307 Katorimic
NONE
1721 Mela Vagadhisvari2375 Aeolaptimic
NONE
Scale family 731: Alternating Heptamode - Forte class: 7-31
ScaleAntiscaleSuperantimodes
731 Alternating Heptamode3365 Katolimic
NONE
2413 Harmonic Minor Flat 51683 Raga Malayamarutam
NONE
1627 Hungarian Major 4th Mode2469 Raga Bhinna Pancama
NONE
2861 Hungarian Major 5th Mode1235 Tritone Scale
NONE
1739 Mela Sadvidhamargini2357 Raga Sarasanana
NONE
2917 Nohkan Flute Scale1179 Sonimic
NONE
1753 Hungarian Major2343 Tharimic
NONE
Scale family 733: Donian - Forte class: 7-25
ScaleAntiscaleSuperantimodes
733 Donian3363 Rogimic
NONE
1207 Aeoloptian2889 Thoptimic
NONE
2651 Panian1445 Raga Navamanohari
NONE
3373 Lodian 723 Ionadimic
NONE
1867 Solian2229 Raga Nalinakanti
NONE
2981 Ionolian1115 Superlocrian Hexamirror
NONE
1769 Blues Heptatonic II2327 Epalimic
NONE
Scale family 743: Chromatic Hypophrygian Inverse - Forte class: 7-20
ScaleAntiscaleSuperantimodes
743 Chromatic Hypophrygian Inverse3353 Phraptimic
NONE
2419 Raga Lalita1677 Raga Manavi
NONE
3257 Mela Calanata839 Ionathimic
NONE
919 Chromatic Phrygian Inverse3177 Rothimic
NONE
2507 Todi That1589 Raga Rageshri
NONE
3301 Chromatic Mixolydian Inverse795 Aeologimic
NONE
1849 Chromatic Hypodorian Inverse2247 Raga Vijayasri
NONE
Scale family 747: Lynian - Forte class: 7-28
ScaleAntiscaleSuperantimodes
747 Lynian3349 Aeolocrimic
NONE
2421 Malian1675 Raga Salagavarali
NONE
1629 Synian2467 Raga Padi
NONE
1431 Phragian2665 Messiaen Mode 2 Truncation 1
NONE
2763 Mela Suvarnangi1333 Lyptimic
NONE
3429 Marian 667 Rodimic
NONE
1881 Korian2215 Ranimic
NONE
Scale family 749: Aeologian - Forte class: 7-25
ScaleAntiscaleSuperantimodes
749 Aeologian3347 Synimic
NONE
1211 Ceiling Scale2885 Byrimic
NONE
2653 Sygian1443 Raga Phenadyuti
NONE
1687 Phralian2409 Zacrimic
NONE
2891 Phrogian1205 Raga Siva Kambhoji
NONE
3493 Rathian 603 Aeolygimic
NONE
1897 Ionopian2199 Dyptimic
NONE
Scale family 755: Phrythian - Forte class: 7-Z18
ScaleAntiscaleSuperantimodes
755 Phrythian3341 VAHian
NONE
2425 Rorian1671 KEMian
NONE
815 Bolian3281 Raga Vijayavasanta
NONE
2455 Bothian1641 Bocrimic
NONE
3275 Mela Divyamani821 Aeranimic
NONE
3685 Kodian 411 Lygimic
NONE
1945 Zarian2151 NATian
NONE
Scale family 757: Ionyptian - Forte class: 7-23
ScaleAntiscaleSuperantimodes
757 Ionyptian3339 SMUian
3403 Bylian
1213 Gyrian2883 SAVian
NONE
1327 Zalian2769 Dyrimic
NONE
2711 Stolian1385 Phracrimic
NONE
3403 Bylian 693 Arezzo Major Diatonic Hexachord
757 Ionyptian
3749 Raga Sorati 347 Barimic
NONE
1961 Soptian2135 NAKian
NONE
Scale family 823: Stodian - Forte class: 7-21
ScaleAntiscaleSuperantimodes
823 Stodian3273 Raga Jivantini
3277 Mela Nitimati
2459 Ionocrian1637 Syptimic
NONE
3277 Mela Nitimati 819 Augmented Inverse
1843 Ionygian
883 Ralian
823 Stodian
1843 Ionygian2253 Raga Amarasenapriya
3277 Mela Nitimati
2969 Tholian1127 Eparimic
NONE
883 Ralian3213 Eponimic
3277 Mela Nitimati
2489 Mela Gangeyabhusani1607 Epytimic
NONE
Scale family 827: Mixolocrian - Forte class: 7-21
ScaleAntiscaleSuperantimodes
827 Mixolocrian3269 Raga Malarani
NONE
2461 Sagian1635 Sygimic
1639 Aeolothian
1639 Aeolothian2457 Augmented
3481 Katathian
2521 Mela Dhatuvardhani
2461 Sagian
2867 Major Romani1229 Raga Simharava
NONE
3481 Katathian 615 Schoenberg Hexachord
1639 Aeolothian
947 Mela Gayakapriya3149 Phrycrimic
NONE
2521 Mela Dhatuvardhani1575 Zycrimic
1639 Aeolothian
Scale family 829: Lygian - Forte class: 7-Z18
ScaleAntiscaleSuperantimodes
829 Lygian3267 URFian
NONE
1231 Logian2865 Solimic
NONE
2663 Lalian1433 Dynimic
NONE
3379 Verdi's Scala Enigmatica Descending 717 Raga Vijayanagari
NONE
3737 Phrocrian 359 Bothimic
NONE
979 Mela Dhavalambari3117 TIJian
NONE
2537 Laptian1559 JOWian
NONE
Scale family 847: Ganian - Forte class: 7-19
ScaleAntiscaleSuperantimodes
847 Ganian3249 Raga Tilang
NONE
2471 Mela Ganamurti1625 Hungarian Major No5
NONE
3283 Mela Visvambhari813 Larimic
NONE
3689 Katocrian 407 All-Trichord Hexachord
NONE
973 Mela Syamalangi3123 TOMian
NONE
1267 Katynian2829 RUPian
NONE
2681 Aerycrian1415 IMPian
NONE
Scale family 855: Porian - Forte class: 7-30
ScaleAntiscaleSuperantimodes
855 Porian3241 Dalimic
NONE
2475 Neapolitan Minor1621 Scriabin's Prometheus
NONE
3285 Lydian #6811 Radimic
NONE
1845 Mixolydian Augmented2251 Zodimic
NONE
1485 Minor Romani2611 Raga Vasanta
NONE
1395 Locrian Dominant2701 Hawaiian
NONE
2745 Mela Sulini1351 Aeraptimic
NONE
Scale family 859: Ultralocrian - Forte class: 7-32
ScaleAntiscaleSuperantimodes
859 Ultralocrian3237 Raga Brindabani Sarang
NONE
2477 Harmonic Minor1619 Prometheus Neapolitan
NONE
1643 Locrian Natural 62453 Raga Latika
NONE
2869 Major Augmented1227 Thacrimic
NONE
1741 Lydian Diminished2355 Raga Lalita
NONE
1459 Phrygian Dominant2637 Raga Ranjani
NONE
2777 Aeolian Harmonic1319 Phronimic
NONE
Scale family 861: Rylian - Forte class: 7-28
ScaleAntiscaleSuperantimodes
861 Rylian3235 Pothimic
NONE
1239 Epaptian2857 Stythimic
NONE
2667 Byrian1429 Bythimic
NONE
3381 Katanian 715 T4 Prime Mode
NONE
1869 Katyrian2227 Raga Gaula
NONE
1491 Namanarayani2605 Rylimic
NONE
2793 Eporian1303 Epolimic
NONE
Scale family 871: Hungarian Romani Minor 4th Mode - Forte class: 7-22
ScaleAntiscaleSuperantimodes
871 Hungarian Romani Minor 4th Mode3225 Ionalimic
3289 Lydian Sharp 2 Sharp 6
2483 Double Harmonic1613 Thylimic
NONE
3289 Lydian Sharp 2 Sharp 6807 Raga Suddha Mukhari
871 Hungarian Romani Minor 4th Mode
923 Ultraphrygian3173 Zarimic
NONE
2509 Double Harmonic Minor1587 Raga Rudra Pancama
1651 Asian
1651 Asian2445 Zadimic
2509 Double Harmonic Minor
2873 Ionian Augmented Sharp 21223 Phryptimic
NONE
Scale family 875: Locrian Double-flat 7 - Forte class: 7-32
ScaleAntiscaleSuperantimodes
875 Locrian Double-flat 73221 Bycrimic
NONE
2485 Harmonic Major1611 Dacrimic
NONE
1645 Dorian Flat 52451 Raga Bauli
NONE
1435 Phrygian Flat 42661 Stydimic
NONE
2765 Lydian Flat 31331 Raga Vasantabhairavi
NONE
1715 Harmonic Minor Inverse2381 Takemitsu Linea Mode 1
NONE
2905 Lydian Augmented Sharp 21191 Pyrimic
NONE
Scale family 877: Moravian Pistalkova - Forte class: 7-31
ScaleAntiscaleSuperantimodes
877 Moravian Pistalkova3219 Ionaphimic
NONE
1243 Epylian2853 Baptimic
NONE
2669 Jeths' Mode1427 Lolimic
NONE
1691 Kathian2405 T4 First Rotation
NONE
2893 Lylian1203 Pagimic
NONE
1747 Mela Ramapriya2349 Raga Ghantana
NONE
2921 Pogian1175 Epycrimic
NONE
Scale family 885: Sathian - Forte class: 7-26
ScaleAntiscaleSuperantimodes
885 Sathian3211 Epacrimic
NONE
1245 Lathian2851 Katoptimic
NONE
1335 Elephant Scale2761 Dagimic
NONE
2715 Kynian1381 Padimic
NONE
3405 Stynian 691 Raga Kalavati
NONE
1875 Persichetti Scale2221 Raga Sindhura Kafi
NONE
2985 Epacrian1111 Sycrimic
NONE
Scale family 925: Chromatic Hypodorian - Forte class: 7-20
ScaleAntiscaleSuperantimodes
925 Chromatic Hypodorian3171 Zythimic
NONE
1255 Chromatic Mixolydian2841 African Pentatonic 3
NONE
2675 Chromatic Lydian1421 Raga Trimurti
NONE
3385 Chromatic Phrygian711 Raga Chandrajyoti
NONE
935 Chromatic Dorian3161 Kodimic
NONE
2515 Chromatic Hypolydian1581 Raga Bagesri
NONE
3305 Chromatic Hypophrygian791 Aeoloptimic
NONE
Scale family 939: Mela Senavati - Forte class: 7-30
ScaleAntiscaleSuperantimodes
939 Mela Senavati3157 Zyptimic
NONE
2517 Harmonic Lydian1579 Sagimic
NONE
1653 Minor Romani Inverse2443 Panimic
NONE
1437 Sabach ascending2659 Katynimic
NONE
1383 Pynian2713 Porimic
NONE
2739 Mela Suryakanta1357 Takemitsu Linea Mode 2
NONE
3417 Golian 679 Lanimic
NONE
Scale family 941: Mela Jhankaradhvani - Forte class: 7-29
ScaleAntiscaleSuperantimodes
941 Mela Jhankaradhvani3155 Ladimic
NONE
1259 Stadian2837 Aelothimic
NONE
2677 Thodian1419 Raga Kashyapi
NONE
1693 Dogian2403 Lycrimic
NONE
1447 Mela Ratnangi2649 Aeolythimic
NONE
2771 Marva That1325 Phradimic
NONE
3433 Thonian 663 Phrynimic
NONE
Scale family 949: Mela Mararanjani - Forte class: 7-27
ScaleAntiscaleSuperantimodes
949 Mela Mararanjani3147 Ryrimic
NONE
1261 Modified Blues2835 Ionygimic
2899 Kagian
1339 Kycrian2757 Raga Nishadi
NONE
2717 Epygian1379 Kycrimic
NONE
1703 Mela Vanaspati2393 Zathimic
NONE
2899 Kagian1197 Minor Hexatonic
1261 Modified Blues
3497 Phrolian 599 Thyrimic
NONE
Scale family 981: Mela Kantamani - Forte class: 7-24
ScaleAntiscaleSuperantimodes
981 Mela Kantamani3115 TIHian
NONE
1269 Katythian2827 RUNian
NONE
1341 Madian2755 RIVian
NONE
1359 Aerygian2737 Raga Hari Nata
NONE
2727 Mela Manavati1369 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 Inverse2729 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 Aeroptian2219 Phrydimic
2731 Neapolitan Major
1493 Lydian Minor2603 Gadimic
2731 Neapolitan Major
1397 Major Locrian2699 Sythimic
2731 Neapolitan Major
1373 Storian2723 Raga Jivantika
2731 Neapolitan Major
Scale family 1371: Superlocrian - Forte class: 7-34
ScaleAntiscaleSuperantimodes
1371 Superlocrian2725 Raga Nagagandhari
2733 Melodic Minor Ascending
2733 Melodic Minor Ascending1363 Gygimic
1371 Superlocrian
1707 Dorian Flat 22389 Eskimo Hexatonic 2
2901 Lydian Augmented
2901 Lydian Augmented1195 Raga Gandharavam
1707 Dorian Flat 2
1749 Acoustic2347 Raga Viyogavarali
NONE
1461 Major-Minor2635 Gocrimic
NONE
1389 Minor Locrian2707 Banimic
NONE
Scale family 1387: Locrian - Forte class: 7-35
ScaleAntiscaleSuperantimodes
1387 Locrian2709 Raga Kumud
2741 Major
2773 Lydian
2741 Major1355 Aeolorimic
1387 Locrian
1709 Dorian2387 Paptimic
NONE
1451 Phrygian2645 Raga Mruganandana
2773 Lydian
2773 Lydian1323 Ritsu
1387 Locrian
1451 Phrygian
1717 Mixolydian2379 Raga Gurjari Todi
NONE
1453 Aeolian2643 Raga Hamsanandi
NONE