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: Major | Scale 1355: Raga Bhavani | Scale 1387: Locrian |
|---|---|---|
|
|
|
|
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: Aeolian | Scale 2643: Raga Hamsanandi |
|---|---|
|
|
|
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:
| Scale | Antiscale | Subset 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 |
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:
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.
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 Class | Chirality | Modal Family | AE modes |
|---|---|---|---|
| 7-2 | YES | 191 BEGian 2143 NAPian 3119 TIKian 3607 WOPian 3851 YILian 3973 ZEHian 2017 MEQian | |
| 7-2 | YES | 253 BOSian 1087 GOBian 2591 PUWian 3343 VAJian 3719 XOFian 3907 YUTian 4001 ZIYian | |
| 7-3 | YES | 319 Epodian 2207 Mygian 3151 Pacrian 3623 Aerocrian 3859 Aeolarian 3977 Kythian 1009 Katyptian |  |
| 7-3 | YES | 505 Sanian 575 Ionydian 2335 Epydian 3215 Katydian 3655 Mathian 3875 Aeryptian 3985 Thadian |  |
| 7-11 | YES | 379 Aeragian 2237 Epothian 1583 Salian 2839 Lyptian 3467 Sudhvidhamagini 3781 Gyphian 1969 Zorian |  |
| 7-11 | YES | 445 Gocrian 1135 Katolian 2615 Thoptian 3355 Bagian 3725 Kyrian 1955 Sonian 3025 Epycrian |  |
| 7-Z37 | NO | 443 Kothian 2269 Pygian 1591 Rodian 2843 Sorian 3469 Monian 1891 Thalian 2993 Stythian |  |
| 7-Z17 | NO | 631 Zygian 2363 Kataptian 3229 Aeolaptian 1831 Pothian 2963 Bygian 3529 Stalian 953 Mela Yagapriya |  |
| 7-23 | YES | 701 Mixonyphian 1199 Magian 2647 Dadian 3371 Aeolylian 3733 Gycrian 1957 Pyrian 1513 Stathian |  |
| 7-23 | YES | 757 Ionyptian 1213 Gyrian 1327 Zalian 2711 Stolian 3403 Bylian 3749 Raga Sorati 1961 Soptian |  |
| 7-27 | YES | 949 Mela Mararanjani 1261 Modified Blues 1339 Kycrian 2717 Epygian 1703 Mela Vanaspati 2899 Kagian 3497 Phrolian |  |
| 7-27 | YES | 695 Sarian 2395 Zoptian 3245 Mela Varunapriya 1835 Byptian 2965 Darian 1765 Lonian 1465 Mela Ragavardhani |  |
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 Class | Chirality | Modal Family | AE modes |
|---|---|---|---|
| 7-8 | NO | 381 Kogian 1119 Rarian 2607 Aerolian 3351 Crater Scale 3723 Myptian 3909 Rydian 2001 Gydian |  |
| 7-22 | NO | 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 |  |
| 7-34 | NO | 1371 Superlocrian 2733 Melodic Minor Ascending 1707 Dorian Flat 2 2901 Lydian Augmented 1749 Acoustic 1461 Major-Minor 1389 Minor Locrian |  |
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 Class | Chirality | Modal Family | AE modes |
|---|---|---|---|
| 7-7 | YES | 463 Zythian 2279 Dyrian 3187 Koptian 3641 Thocrian 967 Mela Salaga 2531 Danian 3313 Aeolacrian |  |
| 7-7 | YES | 487 Dynian 2291 Zydian 3193 Zathian 911 Radian 2503 Mela Jhalavarali 3299 Syptian 3697 Ionarian |  |
| 7-15 | NO | 471 Dodian 2283 Aeolyptian 3189 Aeolonian 1821 Aeradian 1479 Mela Jalarnava 2787 Zyrian 3441 Thacrian |  |
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 Class | Chirality | Modal Family | AE modes |
|---|---|---|---|
| 7-1 | NO | 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 |  |
| 7-35 | NO | 1387 Locrian 2741 Major 1709 Dorian 1451 Phrygian 2773 Lydian 1717 Mixolydian 1453 Aeolian |  |
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 Class | Chirality | Modal Family | AE modes |
|---|---|---|---|
| 7-21 | YES | 823 Stodian 2459 Ionocrian 3277 Mela Nitimati 1843 Ionygian 2969 Tholian 883 Ralian 2489 Mela Gangeyabhusani |  |
| 7-21 | YES | 827 Mixolocrian 2461 Sagian 1639 Aeolothian 2867 Major Romani 3481 Katathian 947 Mela Gayakapriya 2521 Mela Dhatuvardhani |  |
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 Class | Chirality | Modal Family | AE modes |
|---|---|---|---|
| 7-33 | NO | 1367 Leading Whole-Tone Inverse 2731 Neapolitan Major 3413 Leading Whole-tone 1877 Aeroptian 1493 Lydian Minor 1397 Major Locrian 1373 Storian |  |
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 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 127 Heptatonic Chromatic | 3969 Hexatonic Chromatic Descending | 3971 Heptatonic Chromatic 6 4033 Heptatonic Chromatic Descending | |
| 2111 Heptatonic Chromatic 2 | 1985 MEWian | 4033 Heptatonic Chromatic Descending | |
| 3103 Heptatonic Chromatic 3 | 993 GAVian | NONE | |
| 3599 Heptatonic Chromatic 4 | 497 Kadimic | NONE | |
| 3847 Heptatonic Chromatic 5 | 249 BOQian | NONE | |
| 3971 Heptatonic Chromatic 6 | 125 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 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 191 BEGian | 3905 YUSian | NONE | |
| 2143 NAPian | 1953 MACian | 2017 MEQian | |
| 3119 TIKian | 977 Kocrimic | NONE | |
| 3607 WOPian | 489 Phrathimic | NONE | |
| 3851 YILian | 245 Raga Dipak | NONE | |
| 3973 ZEHian | 123 ASUian | NONE | |
| 2017 MEQian | 2079 Hexatonic Chromatic 4 | 2143 NAPian | |
| Scale family 223: BIZian - Forte class: 7-4 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 223 BIZian | 3873 YOYian | NONE | |
| 2159 NEYian | 1937 Galimic | NONE | |
| 3127 TOPian | 969 Ionogimic | NONE | |
| 3611 WORian | 485 Stoptimic | NONE | |
| 3853 YOMian | 243 BOMian | NONE | |
| 1987 MEXian | 2109 MUVian | NONE | |
| 3041 TANian | 1055 GIHian | NONE | |
| Scale family 239: BIKian - Forte class: 7-5 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 239 BIKian | 3857 Ponimic | NONE | |
| 2167 NEDian | 1929 Aeolycrimic | NONE | |
| 3131 TORian | 965 Ionothimic | NONE | |
| 3613 WOSian | 483 Kygimic | NONE | |
| 1927 LUNian | 2169 NEFian | NONE | |
| 3011 SUWian | 1085 GOZian | NONE | |
| 3553 WEHian | 543 DENian | NONE | |
| Scale family 247: BOPian - Forte class: 7-5 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 247 BOPian | 3849 YIKian | NONE | |
| 2171 NEGian | 1925 LUMian | NONE | |
| 3133 TOSian | 963 GACian | NONE | |
| 1807 LARian | 2289 Mocrimic | NONE | |
| 2951 SILian | 1145 Zygimic | NONE | |
| 3523 WAPian | 573 Saptimic | NONE | |
| 3809 YELian | 287 Gynimic | NONE | |
| Scale family 251: BORian - Forte class: 7-4 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 251 BORian | 3845 YIHian | NONE | |
| 2173 NEHian | 1923 LULian | NONE | |
| 1567 JOBian | 2529 PIKian | NONE | |
| 2831 RUQian | 1265 Pynimic | NONE | |
| 3463 VOFian | 633 Kydimic | NONE | |
| 3779 YASian | 317 Korimic | NONE | |
| 3937 ZALian | 159 BAMian | NONE | |
| Scale family 253: BOSian - Forte class: 7-2 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 253 BOSian | 3843 Hexatonic Chromatic 5 | 3907 YUTian | |
| 1087 GOBian | 3009 SUVian | NONE | |
| 2591 PUWian | 1505 JEPian | NONE | |
| 3343 VAJian | 753 Kytrimic | NONE | |
| 3719 XOFian | 377 Kathimic | NONE | |
| 3907 YUTian | 189 BEFian | 253 BOSian | |
| 4001 ZIYian | 95 ARKian | NONE | |
| Scale family 319: Epodian - Forte class: 7-3 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 319 Epodian | 3777 YARian | NONE | |
| 2207 Mygian | 1889 LOQian | NONE | |
| 3151 Pacrian | 945 Raga Saravati | 1009 Katyptian | |
| 3623 Aerocrian | 473 Aeralimic | NONE | |
| 3859 Aeolarian | 237 BIJian | NONE | |
| 3977 Kythian | 119 SMOian | NONE | |
| 1009 Katyptian | 3087 Hexatonic Chromatic 3 | 3151 Pacrian | |
| Scale family 351: Epanian - Forte class: 7-9 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 351 Epanian | 3745 XUVian | NONE | |
| 2223 Konian | 1873 Dathimic | NONE | |
| 3159 Stocrian | 937 Stothimic | NONE | |
| 3627 Kalian | 469 Katyrimic | NONE | |
| 3861 Phroptian | 235 BIHian | NONE | |
| 1989 Dydian | 2107 MUTian | NONE | |
| 1521 Stanian | 2575 PUMian | NONE | |
| Scale family 367: Aerodian - Forte class: 7-Z36 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 367 Aerodian | 3729 Starimic | NONE | |
| 2231 Macrian | 1865 Thagimic | NONE | |
| 3163 Rogian | 933 Dadimic | NONE | |
| 3629 Boptian | 467 Raga Dhavalangam | NONE | |
| 1931 Stogian | 2165 NECian | NONE | |
| 3013 Thynian | 1083 GOYian | NONE | |
| 1777 Saptian | 2319 ODUian | NONE | |
| Scale family 375: Sodian - Forte class: 7-13 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 379 Aeragian | 3717 XIDian | 3781 Gyphian | |
| 2237 Epothian | 1859 LIXian | NONE | |
| 1583 Salian | 2513 Aerycrimic | NONE | |
| 2839 Lyptian | 1257 Minor Blues | NONE | |
| 3467 Sudhvidhamagini | 629 Aeronimic | NONE | |
| 3781 Gyphian | 315 Stodimic | 379 Aeragian | |
| 1969 Zorian | 2127 NAFian | NONE | |
| Scale family 381: Kogian - Forte class: 7-8 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 381 Kogian | 3715 XICian | 3723 Myptian | |
| 1119 Rarian | 2977 SOBian | NONE | |
| 2607 Aerolian | 1489 Raga Jyoti | 2001 Gydian | |
| 3351 Crater Scale | 745 Kolimic | NONE | |
| 3723 Myptian | 373 Epagimic | 381 Kogian | |
| 3909 Rydian | 187 BEDian | NONE | |
| 2001 Gydian | 2095 MUMian | 2607 Aerolian | |
| Scale family 415: Aeoladian - Forte class: 7-6 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 415 Aeoladian | 3681 XAHian | NONE | |
| 2255 Dylian | 1841 Thogimic | NONE | |
| 3175 Eponian | 921 Bogimic | NONE | |
| 3635 Katygian | 461 Raga Syamalam | NONE | |
| 3865 Starian | 231 BIFian | NONE | |
| 995 Phrathian | 3101 TIYian | NONE | |
| 2545 Thycrian | 1551 JORian | NONE | |
| Scale family 431: Epyrian - Forte class: 7-14 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 431 Epyrian | 3665 Stalimic | NONE | |
| 2263 Lycrian | 1833 Ionacrimic | NONE | |
| 3179 Daptian | 917 Dygimic | NONE | |
| 3637 Raga Rageshri | 459 Zaptimic | NONE | |
| 1933 Mocrian | 2163 NEBian | NONE | |
| 1507 Zynian | 2589 PUVian | NONE | |
| 2801 Zogian | 1295 HUYian | NONE | |
| Scale family 439: Bythian - Forte class: 7-Z38 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 445 Gocrian | 3651 WUQian | 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 NANian | NONE | |
| 3025 Epycrian | 1071 GORian | 1135 Katolian | |
| Scale family 463: Zythian - Forte class: 7-7 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 463 Zythian | 3633 Daptimic | 3641 Thocrian | |
| 2279 Dyrian | 1817 Phrythimic | NONE | |
| 3187 Koptian | 909 Katarimic | NONE | |
| 3641 Thocrian | 455 Messiaen Mode 5 Rotation 2 | 967 Mela Salaga 463 Zythian | |
| 967 Mela Salaga | 3129 TOQian | 3641 Thocrian | |
| 2531 Danian | 1565 JOZian | NONE | |
| 3313 Aeolacrian | 783 ETUian | NONE | |
| Scale family 471: Dodian - Forte class: 7-15 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 487 Dynian | 3609 WOQian | NONE | |
| 2291 Zydian | 1805 LAQian | NONE | |
| 3193 Zathian | 903 FOSian | 911 Radian | |
| 911 Radian | 3185 Messiaen Mode 5 Rotation 1 | 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 491 Aeolyrian | 3605 OLKian | NONE | |
| 2293 Gorian | 1803 LAPian | NONE | |
| 1597 Aeolodian | 2499 PIRian | NONE | |
| 1423 Doptian | 2673 Mythimic | NONE | |
| 2759 Mela Pavani | 1337 Epogimic | NONE | |
| 3427 Zacrian | 669 Major Blues | NONE | |
| 3761 Raga Madhuri | 335 Zanimic | NONE | |
| Scale family 493: Rygian - Forte class: 7-Z36 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 493 Rygian | 3603 WOMian | NONE | |
| 1147 Epynian | 2949 SIKian | NONE | |
| 2621 Ionogian | 1475 UFFian | 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 499 Ionaptian | 3597 WIJian | NONE | |
| 2297 Thylian | 1799 LAMian | NONE | |
| 799 Lolian | 3297 ULLian | NONE | |
| 2447 Thagian | 1649 Bolimic | NONE | |
| 3271 Mela Raghupriya | 825 Thyptimic | NONE | |
| 3683 Dycrian | 413 Ganimic | NONE | |
| 3889 Parian | 207 BEQian | NONE | |
| Scale family 501: Katylian - Forte class: 7-9 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 501 Katylian | 3595 WIHian | NONE | |
| 1149 Bydian | 2947 SIJian | NONE | |
| 1311 Bynian | 2785 RONian | NONE | |
| 2703 Galian | 1393 Mycrimic | NONE | |
| 3399 Zonian | 697 Lagimic | NONE | |
| 3747 Myrian | 349 Borimic | NONE | |
| 3921 Pythian | 175 BEWian | NONE | |
| Scale family 505: Sanian - Forte class: 7-3 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 505 Sanian | 3591 WIFian | 3655 Mathian | |
| 575 Ionydian | 3521 WANian | NONE | |
| 2335 Epydian | 1761 KUQian | NONE | |
| 3215 Katydian | 881 Aerothimic | NONE | |
| 3655 Mathian | 441 Thycrimic | 505 Sanian | |
| 3875 Aeryptian | 221 BIYian | NONE | |
| 3985 Thadian | 111 AROian | NONE | |
| Scale family 607: Kadian - Forte class: 7-10 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 607 Kadian | 3489 VUVian | 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 MURian | NONE | |
| 761 Ponian | 3335 VADian | NONE | |
| Scale family 623: Sycrian - Forte class: 7-16 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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 NEXian | NONE | |
| 3017 Gacrian | 1079 GOWian | NONE | |
| 889 Borian | 3207 UCOian | NONE | |
| Scale family 631: Zygian - Forte class: 7-Z17 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 635 Epolian | 3461 VODian | NONE | |
| 2365 Sythian | 1731 KOXian | NONE | |
| 1615 Sydian | 2481 Raga Paraju | NONE | |
| 2855 Epocrian | 1241 Pygimic | NONE | |
| 3475 Kylian | 621 Pyramid Hexatonic | NONE | |
| 3785 Epagian | 311 Stagimic | NONE | |
| 985 Mela Sucaritra | 3111 TIFian | NONE | |
| Scale family 637: Debussy's Heptatonic - Forte class: 7-10 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 637 Debussy's Heptatonic | 3459 VOCian | NONE | |
| 1183 Sadian | 2913 SENian | NONE | |
| 2639 Dothian | 1457 Raga Kamalamanohari | NONE | |
| 3367 Moptian | 729 Stygimic | NONE | |
| 3731 Aeryrian | 365 Marimic | NONE | |
| 3913 Bonian | 183 BEBian | NONE | |
| 1001 Badian | 3095 TIVian | NONE | |
| Scale family 671: Stycrian - Forte class: 7-Z12 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 671 Stycrian | 3425 VIHian | NONE | |
| 2383 Katorian | 1713 Raga Khamas | NONE | |
| 3239 Mela Tanarupi | 857 Aeolydimic | NONE | |
| 3667 Kaptian | 429 Koptimic | NONE | |
| 3881 Morian | 215 BIVian | NONE | |
| 997 Rycrian | 3099 TIXian | NONE | |
| 1273 Heptatonic Blues | 2823 RULian | NONE | |
| Scale family 687: Aeolythian - Forte class: 7-24 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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 NEWian | NONE | |
| 1509 Ragian | 2587 PUTian | NONE | |
| 1401 Pagian | 2695 RAKian | NONE | |
| Scale family 695: Sarian - Forte class: 7-27 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 695 Sarian | 3401 Palimic | NONE | |
| 2395 Zoptian | 1701 Mixolydian Hexatonic | 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 701 Mixonyphian | 3395 VEPian | 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 NAMian | NONE | |
| 1513 Stathian | 2583 PURian | 2647 Dadian | |
| Scale family 719: Kanian - Forte class: 7-19 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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 TONian | NONE | |
| 2533 Podian | 1563 JOYian | NONE | |
| 1657 Ionothian | 2439 PAGian | NONE | |
| Scale family 727: Phradian - Forte class: 7-29 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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: Alternating Heptamode - Forte class: 7-31 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 731 Alternating Heptamode | 3365 Katolimic | NONE | |
| 2413 Harmonic Minor Flat 5 | 1683 Raga Malayamarutam | NONE | |
| 1627 Hungarian Major 4th Mode | 2469 Raga Bhinna Pancama | NONE | |
| 2861 Hungarian Major 5th Mode | 1235 Tritone Scale | 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 747 Lynian | 3349 Aeolocrimic | NONE | |
| 2421 Malian | 1675 Raga Salagavarali | NONE | |
| 1629 Synian | 2467 Raga Padi | NONE | |
| 1431 Phragian | 2665 Messiaen Mode 2 Truncation 1 | NONE | |
| 2763 Mela Suvarnangi | 1333 Lyptimic | NONE | |
| 3429 Marian | 667 Rodimic | NONE | |
| 1881 Korian | 2215 Ranimic | NONE | |
| Scale family 749: Aeologian - Forte class: 7-25 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 749 Aeologian | 3347 Synimic | NONE | |
| 1211 Ceiling Scale | 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 755 Phrythian | 3341 VAHian | NONE | |
| 2425 Rorian | 1671 KEMian | 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 NATian | NONE | |
| Scale family 757: Ionyptian - Forte class: 7-23 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 757 Ionyptian | 3339 SMUian | 3403 Bylian | |
| 1213 Gyrian | 2883 SAVian | 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 NAKian | NONE | |
| Scale family 823: Stodian - Forte class: 7-21 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 827 Mixolocrian | 3269 Raga Malarani | NONE | |
| 2461 Sagian | 1635 Sygimic | 1639 Aeolothian | |
| 1639 Aeolothian | 2457 Augmented | 3481 Katathian 2521 Mela Dhatuvardhani 2461 Sagian | |
| 2867 Major Romani | 1229 Raga Simharava | NONE | |
| 3481 Katathian | 615 Schoenberg Hexachord | 1639 Aeolothian | |
| 947 Mela Gayakapriya | 3149 Phrycrimic | NONE | |
| 2521 Mela Dhatuvardhani | 1575 Zycrimic | 1639 Aeolothian | |
| Scale family 829: Lygian - Forte class: 7-Z18 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 829 Lygian | 3267 URFian | 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 TIJian | NONE | |
| 2537 Laptian | 1559 JOWian | NONE | |
| Scale family 847: Ganian - Forte class: 7-19 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 847 Ganian | 3249 Raga Tilang | NONE | |
| 2471 Mela Ganamurti | 1625 Hungarian Major No5 | NONE | |
| 3283 Mela Visvambhari | 813 Larimic | NONE | |
| 3689 Katocrian | 407 All-Trichord Hexachord | NONE | |
| 973 Mela Syamalangi | 3123 TOMian | NONE | |
| 1267 Katynian | 2829 RUPian | NONE | |
| 2681 Aerycrian | 1415 IMPian | NONE | |
| Scale family 855: Porian - Forte class: 7-30 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 855 Porian | 3241 Dalimic | NONE | |
| 2475 Neapolitan Minor | 1621 Scriabin's Prometheus | NONE | |
| 3285 Lydian #6 | 811 Radimic | NONE | |
| 1845 Mixolydian Augmented | 2251 Zodimic | NONE | |
| 1485 Minor Romani | 2611 Raga Vasanta | NONE | |
| 1395 Locrian Dominant | 2701 Hawaiian | NONE | |
| 2745 Mela Sulini | 1351 Aeraptimic | NONE | |
| Scale family 859: Ultralocrian - Forte class: 7-32 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 861 Rylian | 3235 Pothimic | NONE | |
| 1239 Epaptian | 2857 Stythimic | NONE | |
| 2667 Byrian | 1429 Bythimic | NONE | |
| 3381 Katanian | 715 T4 Prime Mode | NONE | |
| 1869 Katyrian | 2227 Raga Gaula | NONE | |
| 1491 Namanarayani | 2605 Rylimic | NONE | |
| 2793 Eporian | 1303 Epolimic | NONE | |
| Scale family 871: Hungarian Romani Minor 4th Mode - Forte class: 7-22 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 871 Hungarian Romani Minor 4th Mode | 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 Hungarian Romani Minor 4th Mode | |
| 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 875 Locrian Double-flat 7 | 3221 Bycrimic | NONE | |
| 2485 Harmonic Major | 1611 Dacrimic | NONE | |
| 1645 Dorian Flat 5 | 2451 Raga Bauli | NONE | |
| 1435 Phrygian Flat 4 | 2661 Stydimic | NONE | |
| 2765 Lydian Flat 3 | 1331 Raga Vasantabhairavi | NONE | |
| 1715 Harmonic Minor Inverse | 2381 Takemitsu Linea Mode 1 | NONE | |
| 2905 Lydian Augmented Sharp 2 | 1191 Pyrimic | NONE | |
| Scale family 877: Moravian Pistalkova - Forte class: 7-31 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 877 Moravian Pistalkova | 3219 Ionaphimic | NONE | |
| 1243 Epylian | 2853 Baptimic | NONE | |
| 2669 Jeths' Mode | 1427 Lolimic | NONE | |
| 1691 Kathian | 2405 T4 First Rotation | 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 925 Chromatic Hypodorian | 3171 Zythimic | NONE | |
| 1255 Chromatic Mixolydian | 2841 African Pentatonic 3 | 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 981 Mela Kantamani | 3115 TIHian | NONE | |
| 1269 Katythian | 2827 RUNian | NONE | |
| 1341 Madian | 2755 RIVian | 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 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 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 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 1387 Locrian | 2709 Raga Kumud | 2741 Major 2773 Lydian | |
| 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 | |