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 Ultra-Alt 67 2143 Alt ♮7𝄫34𝄫♭56 3119 Alt ♮7♯6𝄫345 3607 Alt ♮7♯6𝄪5𝄫3 3851 Phrygian +𝄪5♯𝄪4 3973 Superlydian Augmented ♮2𝄪5♯𝄪34 2017 Dominant +𝄪34♯𝄪2 | |
| 7-2 | YES | 253 Alt ♮2𝄫5𝄫♭6𝄫𝄫7 1087 Infra-Alt 5♭7𝄫𝄫6 2591 Alt ♮67𝄫34𝄫♭5 3343 Phrygian +𝄫34 3719 Phrygian+𝄫3𝄪45 3907 Superlydian Augmented ♭2𝄪35♯𝄪4 4001 Superlydian Augmented 𝄪5♯𝄪234 | |
| 7-3 | YES | 319 Ultra-Alt 6 2207 Alt ♮7𝄫346𝄫♭5 3151 Alt ♮7♯6𝄫34 3623 Ionian ♭2♯6𝄫3𝄪5 3859 Ionian ♭2♯6𝄪5♯𝄪4 3977 Superlydian Augmented 𝄪5♯𝄪34 1009 Lydian ♭6♯3𝄪2𝄫7 |  |
| 7-3 | YES | 505 Major Locrian ♯2𝄫6𝄫♭7 575 Infra-Alt 5𝄫𝄫6 2335 Byzantine 3215 Neapoitan Major ♯6𝄫34 3655 Phrygian +𝄪5𝄫3 3875 Superlydian Augmented ♭2𝄪5♯𝄪4 3985 Superlydian Augmented 𝄪25♯𝄪34 |  |
| 7-11 | YES | 379 Alt 𝄫5𝄫♭67 2237 Alt ♮27𝄫56 1583 Alt ♮6𝄫345 2839 Neapolitan Major ♭4♯5𝄫3 3467 Phrygian +𝄪4 3781 Ionian ♯6𝄪345 1969 Dominant +♯3𝄪24 |  |
| 7-11 | YES | 445 Alt ♮2𝄫56𝄫♭7 1135 Alt 𝄫345𝄫♭6 2615 Alt ♮67𝄫35 3355 Phrygian +♭4 3725 Melodic ♯6𝄪45 1955 Dominant +♭2♯3𝄪4 3025 Ionian +𝄪234 |  |
| 7-Z37 | NO | 443 Alt 𝄫56𝄫♭7 2269 Nomadic minor 1591 Alt ♮6𝄫35 2843 Neapolitan Major ♭4♯5 3469 Melodic +♯6𝄪4 1891 Lydian 7+♭2♯3 2993 Ionian +♯3𝄪24 |  |
| 7-Z17 | NO | 631 Infra-Alt 6♭4 2363 Unorthodox 3229 Melodic ♯6♭4 1831 Dominant +♭2𝄫3 2963 Ionian +♭2𝄪4 3529 Superlydian Augmented 𝄪34 953 Mela Yagapriya |  |
| 7-23 | YES | 701 Alt ♮2𝄫567 1199 Alt 𝄫3456 2647 Bohemian 3371 Neapoitan Major ♯56 3733 Ionian ♯6𝄪45 1957 Dominant +♯3𝄪4 1513 Lydian 7♭6♯23 |  |
| 7-23 | YES | 757 Major Locrian 𝄫67 1213 Alt ♮2𝄫56 1327 Alt 𝄫345 2711 Erratic 3403 Phrygian + 3749 Raga Sorati 1961 Dominant +♯23𝄪4 |  |
| 7-27 | YES | 949 Mela Mararanjani 1261 Aeolian ♭5𝄫6 1339 Alt 𝄫5 2717 Melodic ♭4 1703 Mela Vanaspati 2899 Lydian +♭2 3497 Superlydian Augmented 𝄪4 |  |
| 7-27 | YES | 695 Alt 𝄫3567 2395 Alt ♮7 3245 Melodic ♯6 1835 Dorian +♭2 2965 Ionian +𝄪4 1765 Lydian 7♯3 1465 Dominant ♭6♯2 |  |
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 Alt ♮2𝄫5𝄫♭67 1119 Infra-Alt 56♭7 2607 Alt ♮67𝄫345 3351 Alt ♮7♯56𝄫3 3723 Phrygian +𝄪45 3909 Superlydian Augmented ♮2𝄪35♯𝄪4 2001 Dominant +𝄪234 |  |
| 7-22 | NO | 871 Hungarian Romani Minor 4th Mode 2483 Double Harmonic 3289 Lydian ♯26 923 Alt ♮5𝄫7 2509 Double Harmonic Minor 1651 Asian 2873 Ionian Augmented ♯2 |  |
| 7-34 | NO | 1371 Superlocrian 2733 Melodic Minor Ascending 1707 Dorian ♭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 Infra-Alt 7♭5 2279 Apathetic minor 3187 Ionian ♭25♯6 3641 Ionian ♯26𝄪5 967 Mela Salaga 2531 Lydian ♭26♯3 3313 Lydian ♯36𝄪2 |  |
| 7-7 | YES | 487 Locrian 𝄫36𝄫♭7 2291 Pacific 3193 Ionian ♭5♯26 911 Phrygian 𝄫347 2503 Lydian ♭26𝄫3 3299 Lydian ♭2♯36 3697 Superlydian Augmented 𝄪25 |  |
| 7-15 | NO | 471 Alt 𝄫36𝄫♭7 2283 Pacific minor 3189 Ionian ♭5♯6 1821 Dorian +♭4 1479 Phrygian ♯4𝄫3 2787 Lydian ♭2♯3 3441 Superlydian Augmented 𝄪2 |  |
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 Alt ♮7𝄫34𝄫♭5𝄫𝄫6 3103 Alt ♮7♯6𝄫34𝄫♭5 3599 Heptatonic Chromatic 4 3847 Heptatonic Chromatic 5 3971 Superlydian Augmented ♭2𝄪5♯𝄪34 4033 Alt-Maximus |  |
| 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 Alt 𝄫357 2459 Neapoitan Minor ♭4 3277 Lydian ♭3♯6 1843 Dominant +♭2 2969 Ionian +♯2𝄪4 883 Locrian ♮3𝄫7 2489 Ionian ♯2♭6 |  |
| 7-21 | YES | 827 Alt 𝄫57 2461 Harmonic minor ♭4 1639 Locrian ♮6𝄫3 2867 Ionian +♭2 3481 Ionian +♯26𝄪4 947 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 Lydian +♯6 1877 Lydian 7+ 1493 Lydian Minor 1397 Major Locrian 1373 Alt ♮2 |  |
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 Superlydian Augmented ♭2𝄪5♯𝄪34 4033 Alt-Maximus | |
| 2111 Alt ♮7𝄫34𝄫♭5𝄫𝄫6 | 1985 MEWian | 4033 Alt-Maximus | |
| 3103 Alt ♮7♯6𝄫34𝄫♭5 | 993 GAVian | NONE | |
| 3599 Heptatonic Chromatic 4 | 497 Kadimic | NONE | |
| 3847 Heptatonic Chromatic 5 | 249 BOQian | NONE | |
| 3971 Superlydian Augmented ♭2𝄪5♯𝄪34 | 125 ATWian | 127 Heptatonic Chromatic | |
| 4033 Alt-Maximus | 63 Hexatonic Chromatic | 127 Heptatonic Chromatic 2111 Alt ♮7𝄫34𝄫♭5𝄫𝄫6 | |
| Scale family 191: Ultra-Alt 67 - Forte class: 7-2 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 191 Ultra-Alt 67 | 3905 YUSian | NONE | |
| 2143 Alt ♮7𝄫34𝄫♭56 | 1953 MACian | 2017 Dominant +𝄪34♯𝄪2 | |
| 3119 Alt ♮7♯6𝄫345 | 977 Kocrimic | NONE | |
| 3607 Alt ♮7♯6𝄪5𝄫3 | 489 Phrathimic | NONE | |
| 3851 Phrygian +𝄪5♯𝄪4 | 245 Raga Dipak | NONE | |
| 3973 Superlydian Augmented ♮2𝄪5♯𝄪34 | 123 ASUian | NONE | |
| 2017 Dominant +𝄪34♯𝄪2 | 2079 Hexatonic Chromatic 4 | 2143 Alt ♮7𝄫34𝄫♭56 | |
| Scale family 223: Ultra-Alt 7 - Forte class: 7-4 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 223 Ultra-Alt 7 | 3873 YOYian | NONE | |
| 2159 Alt ♮7𝄫345𝄫♭6 | 1937 Galimic | NONE | |
| 3127 Alt ♮7♯6𝄫35 | 969 Ionogimic | NONE | |
| 3611 Alt ♮7♯6𝄪5 | 485 Stoptimic | NONE | |
| 3853 Melodic ♯6𝄪5♯𝄪4 | 243 BOMian | NONE | |
| 1987 Dominant +♭2𝄪34 | 2109 MUVian | NONE | |
| 3041 Superlydian Augmented ♮6𝄪34♯𝄪2 | 1055 GIHian | NONE | |
| Scale family 239: Infra-Alt 6𝄫𝄫7 - Forte class: 7-5 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 239 Infra-Alt 6𝄫𝄫7 | 3857 Ponimic | NONE | |
| 2167 Alt ♮7𝄫35𝄫♭6 | 1929 Aeolycrimic | NONE | |
| 3131 Alt ♮7♯6𝄫5 | 965 Ionothimic | NONE | |
| 3613 Melodic ♭4♯6𝄪5 | 483 Kygimic | NONE | |
| 1927 Alt ♮6♯5𝄫3𝄪4 | 2169 NEFian | NONE | |
| 3011 Ionian +♭2𝄪34 | 1085 GOZian | NONE | |
| 3553 Superlydian Augmented 𝄪34♯𝄪2 | 543 DENian | NONE | |
| Scale family 247: Infra-Alt 6♭4𝄫𝄫7 - Forte class: 7-5 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 247 Infra-Alt 6♭4𝄫𝄫7 | 3849 YIKian | NONE | |
| 2171 Alt ♮7𝄫5𝄫♭6 | 1925 LUMian | NONE | |
| 3133 Melodic ♭4♯6𝄫5 | 963 GACian | NONE | |
| 1807 Alt ♮6♯5𝄫34 | 2289 Mocrimic | NONE | |
| 2951 Neapolitan Major ♯5𝄫3𝄪4 | 1145 Zygimic | NONE | |
| 3523 Superlydian Augmented ♭2𝄪34 | 573 Saptimic | NONE | |
| 3809 Superlydian Augmented 𝄪345♯𝄪2 | 287 Gynimic | NONE | |
| Scale family 251: Alt 𝄫5𝄫♭6𝄫𝄫7 - Forte class: 7-4 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 251 Alt 𝄫5𝄫♭6𝄫𝄫7 | 3845 YIHian | NONE | |
| 2173 Alt ♮27𝄫5𝄫♭6 | 1923 LULian | NONE | |
| 1567 Alt ♮6𝄫34𝄫♭5 | 2529 PIKian | NONE | |
| 2831 Alt ♮67♯5𝄫34 | 1265 Pynimic | NONE | |
| 3463 Phrygian +𝄫3𝄪4 | 633 Kydimic | NONE | |
| 3779 Superlydian Augmented ♭2𝄪345 | 317 Korimic | NONE | |
| 3937 Superlydian Augmented 𝄪35♯𝄪24 | 159 BAMian | NONE | |
| Scale family 253: Alt ♮2𝄫5𝄫♭6𝄫𝄫7 - Forte class: 7-2 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 253 Alt ♮2𝄫5𝄫♭6𝄫𝄫7 | 3843 Hexatonic Chromatic 5 | 3907 Superlydian Augmented ♭2𝄪35♯𝄪4 | |
| 1087 Infra-Alt 5♭7𝄫𝄫6 | 3009 SUVian | NONE | |
| 2591 Alt ♮67𝄫34𝄫♭5 | 1505 JEPian | NONE | |
| 3343 Phrygian +𝄫34 | 753 Kytrimic | NONE | |
| 3719 Phrygian+𝄫3𝄪45 | 377 Kathimic | NONE | |
| 3907 Superlydian Augmented ♭2𝄪35♯𝄪4 | 189 BEFian | 253 Alt ♮2𝄫5𝄫♭6𝄫𝄫7 | |
| 4001 Superlydian Augmented 𝄪5♯𝄪234 | 95 ARKian | NONE | |
| Scale family 319: Ultra-Alt 6 - Forte class: 7-3 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 319 Ultra-Alt 6 | 3777 YARian | NONE | |
| 2207 Alt ♮7𝄫346𝄫♭5 | 1889 LOQian | NONE | |
| 3151 Alt ♮7♯6𝄫34 | 945 Raga Saravati | 1009 Lydian ♭6♯3𝄪2𝄫7 | |
| 3623 Ionian ♭2♯6𝄫3𝄪5 | 473 Aeralimic | NONE | |
| 3859 Ionian ♭2♯6𝄪5♯𝄪4 | 237 BIJian | NONE | |
| 3977 Superlydian Augmented 𝄪5♯𝄪34 | 119 SMOian | NONE | |
| 1009 Lydian ♭6♯3𝄪2𝄫7 | 3087 Hexatonic Chromatic 3 | 3151 Alt ♮7♯6𝄫34 | |
| Scale family 351: Infra-Alt 567 - Forte class: 7-9 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 351 Infra-Alt 567 | 3745 XUVian | NONE | |
| 2223 Arcadian minor | 1873 Dathimic | NONE | |
| 3159 Alt ♮7♯6𝄫3 | 937 Stothimic | NONE | |
| 3627 Neapoitan Major ♯6𝄪5 | 469 Katyrimic | NONE | |
| 3861 Ionian ♯6𝄪5♯𝄪4 | 235 BIHian | NONE | |
| 1989 Dominant +𝄪34 | 2107 MUTian | NONE | |
| 1521 Lydian 7♭6♯3𝄪2 | 2575 PUMian | NONE | |
| Scale family 367: Infra-Alt 67 - Forte class: 7-Z36 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 367 Infra-Alt 67 | 3729 Starimic | NONE | |
| 2231 Arcadian | 1865 Thagimic | NONE | |
| 3163 Alt ♮7♯6 | 933 Dadimic | NONE | |
| 3629 Melodic ♯6𝄪5 | 467 Raga Dhavalangam | NONE | |
| 1931 Dorian +♭2𝄪4 | 2165 NECian | NONE | |
| 3013 Ionian +𝄪34 | 1083 GOYian | NONE | |
| 1777 Lydian 7♯3𝄪2 | 2319 ODUian | NONE | |
| Scale family 375: Infra-Alt 67♭4 - Forte class: 7-13 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 375 Infra-Alt 67♭4 | 3721 Phragimic | NONE | |
| 2235 Exotic minor | 1861 Phrygimic | NONE | |
| 3165 Alt ♮27♯6 | 931 Raga Kalakanthi | NONE | |
| 1815 Alt ♮6♯5𝄫3 | 2281 Rathimic | NONE | |
| 2955 Neapoitan Major ♯5𝄪4 | 1141 Rynimic | NONE | |
| 3525 Ionian +♯6𝄪34 | 571 Kynimic | NONE | |
| 1905 Lydian 7+♯3𝄪2 | 2191 Thydimic | NONE | |
| Scale family 379: Alt 𝄫5𝄫♭67 - Forte class: 7-11 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 379 Alt 𝄫5𝄫♭67 | 3717 XIDian | 3781 Ionian ♯6𝄪345 | |
| 2237 Alt ♮27𝄫56 | 1859 LIXian | NONE | |
| 1583 Alt ♮6𝄫345 | 2513 Aerycrimic | NONE | |
| 2839 Neapolitan Major ♭4♯5𝄫3 | 1257 Minor Blues | NONE | |
| 3467 Phrygian +𝄪4 | 629 Aeronimic | NONE | |
| 3781 Ionian ♯6𝄪345 | 315 Stodimic | 379 Alt 𝄫5𝄫♭67 | |
| 1969 Dominant +♯3𝄪24 | 2127 NAFian | NONE | |
| Scale family 381: Alt ♮2𝄫5𝄫♭67 - Forte class: 7-8 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 381 Alt ♮2𝄫5𝄫♭67 | 3715 XICian | 3723 Phrygian +𝄪45 | |
| 1119 Infra-Alt 56♭7 | 2977 SOBian | NONE | |
| 2607 Alt ♮67𝄫345 | 1489 Raga Jyoti | 2001 Dominant +𝄪234 | |
| 3351 Alt ♮7♯56𝄫3 | 745 Kolimic | NONE | |
| 3723 Phrygian +𝄪45 | 373 Epagimic | 381 Alt ♮2𝄫5𝄫♭67 | |
| 3909 Superlydian Augmented ♮2𝄪35♯𝄪4 | 187 BEDian | NONE | |
| 2001 Dominant +𝄪234 | 2095 MUMian | 2607 Alt ♮67𝄫345 | |
| Scale family 415: Infra-Alt 57 - Forte class: 7-6 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 415 Infra-Alt 57 | 3681 XAHian | NONE | |
| 2255 Alt ♮7𝄫346 | 1841 Thogimic | NONE | |
| 3175 Locrian ♮7♯6𝄫3 | 921 Bogimic | NONE | |
| 3635 Ionian ♭2♯6𝄪5 | 461 Raga Syamalam | NONE | |
| 3865 Ionian ♯26𝄪5♯𝄪4 | 231 BIFian | NONE | |
| 995 Lydian ♭26♯3𝄫7 | 3101 TIYian | NONE | |
| 2545 Lydian ♭6♯3𝄪2 | 1551 JORian | NONE | |
| Scale family 431: Infra-Alt 7 - Forte class: 7-14 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 431 Infra-Alt 7 | 3665 Stalimic | NONE | |
| 2263 Phlegmatic minor | 1833 Ionacrimic | NONE | |
| 3179 Locrian ♮7♯6 | 917 Dygimic | NONE | |
| 3637 Ionian ♯6𝄪5 | 459 Zaptimic | NONE | |
| 1933 Dorian +𝄪4 | 2163 NEBian | NONE | |
| 1507 Lydian 7♭26♯3 | 2589 PUVian | NONE | |
| 2801 Lydian ♯3𝄪2 | 1295 HUYian | NONE | |
| Scale family 439: Infra-Alt 7♭4 - Forte class: 7-Z38 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 439 Infra-Alt 7♭4 | 3657 Epynimic | NONE | |
| 2267 Exotic | 1829 Pathimic | NONE | |
| 3181 Melodic ♭5♯6 | 915 Raga Kalagada | NONE | |
| 1819 Alt ♮6♯5 | 2277 Kagimic | NONE | |
| 2957 Melodic +𝄪4 | 1139 Aerygimic | NONE | |
| 1763 Lydian 7♭2♯3 | 2333 Stynimic | NONE | |
| 2929 Lydian +♯3𝄪2 | 1167 Aerodimic | NONE | |
| Scale family 443: Alt 𝄫56𝄫♭7 - Forte class: 7-Z37 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 443 Alt 𝄫56𝄫♭7 | 3653 Sathimic | NONE | |
| 2269 Nomadic minor | 1827 Katygimic | 1891 Lydian 7+♭2♯3 | |
| 1591 Alt ♮6𝄫35 | 2505 Mydimic | NONE | |
| 2843 Neapolitan Major ♭4♯5 | 1253 Zolimic | NONE | |
| 3469 Melodic +♯6𝄪4 | 627 Mogimic | NONE | |
| 1891 Lydian 7+♭2♯3 | 2205 Ionocrimic | 2269 Nomadic minor | |
| 2993 Ionian +♯3𝄪24 | 1103 Lynimic | NONE | |
| Scale family 445: Alt ♮2𝄫56𝄫♭7 - Forte class: 7-11 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 445 Alt ♮2𝄫56𝄫♭7 | 3651 WUQian | NONE | |
| 1135 Alt 𝄫345𝄫♭6 | 2961 Bygimic | 3025 Ionian +𝄪234 | |
| 2615 Alt ♮67𝄫35 | 1481 Zagimic | NONE | |
| 3355 Phrygian +♭4 | 741 Gathimic | NONE | |
| 3725 Melodic ♯6𝄪45 | 371 Rythimic | NONE | |
| 1955 Dominant +♭2♯3𝄪4 | 2141 NANian | NONE | |
| 3025 Ionian +𝄪234 | 1071 GORian | 1135 Alt 𝄫345𝄫♭6 | |
| Scale family 463: Infra-Alt 7♭5 - Forte class: 7-7 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 463 Infra-Alt 7♭5 | 3633 Daptimic | 3641 Ionian ♯26𝄪5 | |
| 2279 Apathetic minor | 1817 Phrythimic | NONE | |
| 3187 Ionian ♭25♯6 | 909 Katarimic | NONE | |
| 3641 Ionian ♯26𝄪5 | 455 Messiaen Mode 5 Rotation 2 | 967 Mela Salaga 463 Infra-Alt 7♭5 | |
| 967 Mela Salaga | 3129 TOQian | 3641 Ionian ♯26𝄪5 | |
| 2531 Lydian ♭26♯3 | 1565 JOZian | NONE | |
| 3313 Lydian ♯36𝄪2 | 783 ETUian | NONE | |
| Scale family 471: Alt 𝄫36𝄫♭7 - Forte class: 7-15 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 471 Alt 𝄫36𝄫♭7 | 3625 Podimic | NONE | |
| 2283 Pacific minor | 1813 Katothimic | 1821 Dorian +♭4 | |
| 3189 Ionian ♭5♯6 | 907 Tholimic | NONE | |
| 1821 Dorian +♭4 | 2275 Messiaen Mode 5 | 2787 Lydian ♭2♯3 2283 Pacific minor | |
| 1479 Phrygian ♯4𝄫3 | 2617 Pylimic | NONE | |
| 2787 Lydian ♭2♯3 | 1309 Pogimic | 1821 Dorian +♭4 | |
| 3441 Superlydian Augmented 𝄪2 | 655 Kataptimic | NONE | |
| Scale family 475: Alt 𝄫6𝄫♭7 - Forte class: 7-Z38 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 475 Alt 𝄫6𝄫♭7 | 3621 Gylimic | NONE | |
| 2285 Supine | 1811 Kyptimic | NONE | |
| 1595 Alt ♮6𝄫5 | 2501 Ralimic | NONE | |
| 2845 Melodic +♭4 | 1251 Sylimic | NONE | |
| 1735 Lydian 7♭2𝄫3 | 2361 Docrimic | NONE | |
| 2915 Lydian +♭2♯3 | 1181 Katagimic | NONE | |
| 3505 Superlydian Augmented 𝄪24 | 591 Gaptimic | NONE | |
| Scale family 477: Alt ♮2𝄫6𝄫♭7 - Forte class: 7-13 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 477 Alt ♮2𝄫6𝄫♭7 | 3619 Thanimic | NONE | |
| 1143 Alt 𝄫35𝄫♭6 | 2953 Ionylimic | NONE | |
| 2619 Alt ♮67𝄫5 | 1477 Raga Jaganmohanam | NONE | |
| 3357 Melodic +♯6♭4 | 739 Rorimic | NONE | |
| 1863 Lydian 7+♭2𝄫3 | 2233 Donimic | NONE | |
| 2979 Ionian +♭2♯3𝄪4 | 1117 Raptimic | NONE | |
| 3537 Superlydian Augmented 𝄪234 | 559 Lylimic | NONE | |
| Scale family 487: Locrian 𝄫36𝄫♭7 - Forte class: 7-7 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 487 Locrian 𝄫36𝄫♭7 | 3609 WOQian | NONE | |
| 2291 Pacific | 1805 LAQian | NONE | |
| 3193 Ionian ♭5♯26 | 903 FOSian | 911 Phrygian 𝄫347 | |
| 911 Phrygian 𝄫347 | 3185 Messiaen Mode 5 Rotation 1 | 3697 Superlydian Augmented 𝄪25 3193 Ionian ♭5♯26 | |
| 2503 Lydian ♭26𝄫3 | 1593 Zogimic | NONE | |
| 3299 Lydian ♭2♯36 | 797 Katocrimic | NONE | |
| 3697 Superlydian Augmented 𝄪25 | 399 Zynimic | 911 Phrygian 𝄫347 | |
| Scale family 491: Locrian 𝄫6𝄫♭7 - Forte class: 7-14 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 491 Locrian 𝄫6𝄫♭7 | 3605 OLKian | NONE | |
| 2293 Bucolic | 1803 LAPian | NONE | |
| 1597 Dorian ♭4𝄫5 | 2499 PIRian | NONE | |
| 1423 Alt ♮5𝄫34 | 2673 Mythimic | NONE | |
| 2759 Lydian ♭2𝄫3 | 1337 Epogimic | NONE | |
| 3427 Phrygian +♯3 | 669 Major Blues | NONE | |
| 3761 Raga Madhuri | 335 Zanimic | NONE | |
| Scale family 493: Locrian ♮2𝄫6𝄫♭7 - Forte class: 7-Z36 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 493 Locrian ♮2𝄫6𝄫♭7 | 3603 WOMian | NONE | |
| 1147 Alt 𝄫5𝄫♭6 | 2949 SIKian | NONE | |
| 2621 Euphoric | 1475 UFFian | NONE | |
| 1679 Dorian ♭2𝄫34 | 2417 Kanimic | NONE | |
| 2887 Neapolitan Major ♯45𝄫3 | 1209 Raga Bhanumanjari | NONE | |
| 3491 Superlydian Augmented ♭2𝄪4 | 605 Dycrimic | NONE | |
| 3793 Superlydian Augmented 𝄪2345 | 303 Golimic | NONE | |
| Scale family 499: Major Locrian ♭2𝄫6𝄫♭7 - Forte class: 7-6 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 499 Major Locrian ♭2𝄫6𝄫♭7 | 3597 WIJian | NONE | |
| 2297 Ionian ♭5♯2𝄫6 | 1799 LAMian | NONE | |
| 799 Infra-Alt 5♭6 | 3297 ULLian | NONE | |
| 2447 Alt ♮57𝄫34 | 1649 Bolimic | NONE | |
| 3271 Mela Raghupriya | 825 Thyptimic | NONE | |
| 3683 Phrygian +♯3𝄪5 | 413 Ganimic | NONE | |
| 3889 Superlydian Augmented 𝄪25♯𝄪4 | 207 BEQian | NONE | |
| Scale family 501: Major Locrian 𝄫6𝄫♭7 - Forte class: 7-9 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 501 Major Locrian 𝄫6𝄫♭7 | 3595 WIHian | NONE | |
| 1149 Alt ♮2𝄫5𝄫♭6 | 2947 SIJian | NONE | |
| 1311 Alt 𝄫34𝄫♭5 | 2785 RONian | NONE | |
| 2703 Erratic minor | 1393 Mycrimic | NONE | |
| 3399 Phrygian +𝄫3 | 697 Lagimic | NONE | |
| 3747 Superlydian Augmented ♭2𝄪45 | 349 Borimic | NONE | |
| 3921 Superlydian Augmented 𝄪235♯𝄪4 | 175 BEWian | NONE | |
| Scale family 505: Major Locrian ♯2𝄫6𝄫♭7 - Forte class: 7-3 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 505 Major Locrian ♯2𝄫6𝄫♭7 | 3591 WIFian | 3655 Phrygian +𝄪5𝄫3 | |
| 575 Infra-Alt 5𝄫𝄫6 | 3521 WANian | NONE | |
| 2335 Byzantine | 1761 KUQian | NONE | |
| 3215 Neapoitan Major ♯6𝄫34 | 881 Aerothimic | NONE | |
| 3655 Phrygian +𝄪5𝄫3 | 441 Thycrimic | 505 Major Locrian ♯2𝄫6𝄫♭7 | |
| 3875 Superlydian Augmented ♭2𝄪5♯𝄪4 | 221 BIYian | NONE | |
| 3985 Superlydian Augmented 𝄪25♯𝄪34 | 111 AROian | NONE | |
| Scale family 607: Infra-Alt 56 - Forte class: 7-10 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 607 Infra-Alt 56 | 3489 VUVian | NONE | |
| 2351 Alt ♮7𝄫345 | 1745 Raga Vutari | NONE | |
| 3223 Alt ♮57♯6𝄫3 | 873 Bagimic | NONE | |
| 3659 Phrygian +𝄪5 | 437 Ronimic | NONE | |
| 3877 Ionian ♯36𝄪5♯𝄪4 | 219 Istrian | NONE | |
| 1993 Dominant +♯2𝄪34 | 2103 MURian | NONE | |
| 761 Major Locrian ♯2𝄫67 | 3335 VADian | NONE | |
| Scale family 623: Infra-Alt 6 - Forte class: 7-16 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 623 Infra-Alt 6 | 3473 Lathimic | NONE | |
| 2359 Unorthodox minor | 1737 Raga Madhukauns | NONE | |
| 3227 Neapoitan Major ♭4♯6 | 869 Kothimic | NONE | |
| 3661 Melodic ♯46𝄪5 | 435 Raga Purna Pancama | NONE | |
| 1939 Dominant +♭2𝄪4 | 2157 NEXian | NONE | |
| 3017 Ionian +♯2𝄪34 | 1079 GOWian | NONE | |
| 889 Major Locrian ♯2𝄫7 | 3207 UCOian | NONE | |
| Scale family 631: Infra-Alt 6♭4 - Forte class: 7-Z17 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 631 Infra-Alt 6♭4 | 3465 Katathimic | 3529 Superlydian Augmented 𝄪34 | |
| 2363 Unorthodox | 1733 Raga Sarasvati | NONE | |
| 3229 Melodic ♯6♭4 | 867 Phrocrimic | NONE | |
| 1831 Dominant +♭2𝄫3 | 2265 Raga Rasamanjari | NONE | |
| 2963 Ionian +♭2𝄪4 | 1133 Stycrimic | NONE | |
| 3529 Superlydian Augmented 𝄪34 | 567 Aeoladimic | 631 Infra-Alt 6♭4 | |
| 953 Mela Yagapriya | 3143 Polimic | NONE | |
| Scale family 635: Alt 𝄫57𝄫♭6 - Forte class: 7-16 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 635 Alt 𝄫57𝄫♭6 | 3461 VODian | NONE | |
| 2365 Alt ♮27𝄫5 | 1731 KOXian | NONE | |
| 1615 Alt ♮6𝄫34 | 2481 Raga Paraju | NONE | |
| 2855 Ionian +♭2𝄫3 | 1241 Pygimic | NONE | |
| 3475 Enigmatic 𝄪4 | 621 Pyramid Hexatonic | NONE | |
| 3785 Superlydian Augmented 𝄪345 | 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 Infra-Alt 5♭7 | 2913 SENian | NONE | |
| 2639 Alt ♮67𝄫34 | 1457 Raga Kamalamanohari | NONE | |
| 3367 Neapolitan Major ♯56𝄫3 | 729 Stygimic | NONE | |
| 3731 Phrygian +♮3𝄪45 | 365 Marimic | NONE | |
| 3913 Bonian | 183 BEBian | NONE | |
| 1001 Lydian ♯23♭6𝄫7 | 3095 TIVian | NONE | |
| Scale family 671: Infra-Alt 5 - Forte class: 7-Z12 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 671 Infra-Alt 5 | 3425 VIHian | NONE | |
| 2383 Alt ♮7𝄫34 | 1713 Raga Khamas | NONE | |
| 3239 Ionian ♭2♯6𝄫3 | 857 Aeolydimic | NONE | |
| 3667 Lydian ♭2♯6𝄪5 | 429 Koptimic | NONE | |
| 3881 Superlydian Augmented 𝄪5♯𝄪4 | 215 BIVian | NONE | |
| 997 Lydian ♭6♯3𝄫7 | 3099 TIXian | NONE | |
| 1273 Dominant ♭5♯2𝄫6 | 2823 RULian | NONE | |
| Scale family 687: Alt 𝄫34567 - Forte class: 7-24 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 687 Alt 𝄫34567 | 3409 Katanimic | NONE | |
| 2391 Phlegmatic | 1705 Raga Manohari | NONE | |
| 3243 Neapoitan Major ♯6 | 853 Epothimic | NONE | |
| 3669 Lydian ♯6𝄪5 | 427 Raga Suddha Simantini | NONE | |
| 1941 Dominant +𝄪4 | 2155 NEWian | NONE | |
| 1509 Lydian minor ♯3 | 2587 PUTian | NONE | |
| 1401 Major Locrian ♯2 | 2695 RAKian | NONE | |
| Scale family 695: Alt 𝄫3567 - Forte class: 7-27 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 695 Alt 𝄫3567 | 3401 Palimic | NONE | |
| 2395 Alt ♮7 | 1701 Mixolydian Hexatonic | 1765 Lydian 7♯3 | |
| 3245 Melodic ♯6 | 851 Raga Hejjajji | NONE | |
| 1835 Dorian +♭2 | 2261 Raga Caturangini | NONE | |
| 2965 Ionian +𝄪4 | 1131 Honchoshi Plagal Form | NONE | |
| 1765 Lydian 7♯3 | 2331 Dylimic | 2395 Alt ♮7 | |
| 1465 Dominant ♭6♯2 | 2631 Macrimic | NONE | |
| Scale family 699: Alt 𝄫567 - Forte class: 7-26 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 699 Alt 𝄫567 | 3397 Sydimic | NONE | |
| 2397 Eccentric | 1699 Raga Rasavali | NONE | |
| 1623 Alt ♮6𝄫3 | 2473 Raga Takka | NONE | |
| 2859 Neapolitan Major ♯5 | 1237 Salimic | NONE | |
| 3477 Ionian +♯6𝄪4 | 619 Hexatonic Double Phrygian | NONE | |
| 1893 Lydian 7+♯3 | 2203 Dorimic | NONE | |
| 1497 Mela Jyotisvarupini | 2599 Malimic | NONE | |
| Scale family 701: Alt ♮2𝄫567 - Forte class: 7-23 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 701 Alt ♮2𝄫567 | 3395 VEPian | NONE | |
| 1199 Alt 𝄫3456 | 2897 Rycrimic | NONE | |
| 2647 Bohemian | 1449 Raga Gopikavasantam | 1513 Lydian 7♭6♯23 | |
| 3371 Neapoitan Major ♯56 | 725 Raga Yamuna Kalyani | NONE | |
| 3733 Ionian ♯6𝄪45 | 363 Soptimic | NONE | |
| 1957 Dominant +♯3𝄪4 | 2139 NAMian | NONE | |
| 1513 Lydian 7♭6♯23 | 2583 PURian | 2647 Bohemian | |
| Scale family 719: Alt 𝄫3467 - Forte class: 7-19 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 719 Alt 𝄫3467 | 3377 Phralimic | NONE | |
| 2407 Apathetic | 1689 Lorimic | NONE | |
| 3251 Mela Hatakambari | 845 Raga Neelangi | NONE | |
| 3673 Lydian ♯26𝄪5 | 423 Sogimic | NONE | |
| 971 Mela Gavambodhi | 3125 TONian | NONE | |
| 2533 Lydian ♯3♭6 | 1563 JOYian | NONE | |
| 1657 Dominant ♭5♯2 | 2439 PAGian | NONE | |
| Scale family 727: Alt 𝄫367 - Forte class: 7-29 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 727 Alt 𝄫367 | 3369 Mixolimic | NONE | |
| 2411 Locrian ♮7 | 1685 Zeracrimic | NONE | |
| 3253 Mela Naganandini | 843 Molimic | NONE | |
| 1837 Dorian + | 2259 Raga Mandari | NONE | |
| 1483 Phrygian ♯4 | 2613 Raga Hamsa Vinodini | NONE | |
| 2789 Lydian ♯3 | 1307 Katorimic | NONE | |
| 1721 Dominant ♯2 | 2375 Aeolaptimic | NONE | |
| Scale family 731: Alternating Heptamode - Forte class: 7-31 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 731 Alternating Heptamode | 3365 Katolimic | NONE | |
| 2413 Harmonic Minor ♭5 | 1683 Raga Malayamarutam | NONE | |
| 1627 Alt ♮6 | 2469 Raga Bhinna Pancama | NONE | |
| 2861 Melodic + | 1235 Tritone Scale | NONE | |
| 1739 Dorian ♭2♯4 | 2357 Raga Sarasanana | NONE | |
| 2917 Nohkan Flute Scale | 1179 Sonimic | NONE | |
| 1753 Hungarian Major | 2343 Tharimic | NONE | |
| Scale family 733: Alt ♮2𝄫67 - Forte class: 7-25 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 733 Alt ♮2𝄫67 | 3363 Rogimic | NONE | |
| 1207 Alt 𝄫356 | 2889 Thoptimic | NONE | |
| 2651 Dysphoric | 1445 Raga Navamanohari | NONE | |
| 3373 Melodic +♯6 | 723 Ionadimic | NONE | |
| 1867 Lydian 7+♭23 | 2229 Raga Nalinakanti | NONE | |
| 2981 Ionian +♯3𝄪4 | 1115 Superlocrian Hexamirror | NONE | |
| 1769 Lydian 7♯23 | 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 Alt ♮5𝄫37 | 3177 Rothimic | NONE | |
| 2507 Neapoitan Minor ♯4 | 1589 Raga Rageshri | NONE | |
| 3301 Lydian ♯36 | 795 Aeologimic | NONE | |
| 1849 Chromatic Hypodorian Inverse | 2247 Raga Vijayasri | NONE | |
| Scale family 747: Locrian 𝄫67 - Forte class: 7-28 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 747 Locrian 𝄫67 | 3349 Aeolocrimic | NONE | |
| 2421 Harmonic Major ♭5 | 1675 Raga Salagavarali | NONE | |
| 1629 Synian | 2467 Raga Padi | NONE | |
| 1431 Phragian | 2665 Messiaen Mode 2 Truncation 1 | NONE | |
| 2763 Neapolitan Major ♯4 | 1333 Lyptimic | NONE | |
| 3429 Lydian +♯36 | 667 Rodimic | NONE | |
| 1881 Lydian 7+♯2 | 2215 Ranimic | NONE | |
| Scale family 749: Locrian ♮2𝄫67 - Forte class: 7-25 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 749 Locrian ♮2𝄫67 | 3347 Synimic | NONE | |
| 1211 Ceiling Scale | 2885 Byrimic | NONE | |
| 2653 Nomadic | 1443 Raga Phenadyuti | NONE | |
| 1687 Dorian ♭24𝄫3 | 2409 Zacrimic | NONE | |
| 2891 Lydian +♭23 | 1205 Raga Siva Kambhoji | NONE | |
| 3493 Ionian +♯36𝄪4 | 603 Aeolygimic | NONE | |
| 1897 Lydian 7+♯23 | 2199 Dyptimic | NONE | |
| Scale family 755: Ionian ♭25𝄫67 - Forte class: 7-Z18 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 755 Ionian ♭25𝄫67 | 3341 VAHian | NONE | |
| 2425 Harm. Maj ♭5♯2 | 1671 KEMian | NONE | |
| 815 Alt 𝄫3457 | 3281 Raga Vijayavasanta | NONE | |
| 2455 Bohemian minor | 1641 Bocrimic | NONE | |
| 3275 Mela Divyamani | 821 Aeranimic | NONE | |
| 3685 Lydian ♯36𝄪5 | 411 Lygimic | NONE | |
| 1945 Dominant +♯2𝄪4 | 2151 NATian | NONE | |
| Scale family 757: Major Locrian 𝄫67 - Forte class: 7-23 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 757 Major Locrian 𝄫67 | 3339 SMUian | 3403 Phrygian + | |
| 1213 Alt ♮2𝄫56 | 2883 SAVian | NONE | |
| 1327 Alt 𝄫345 | 2769 Dyrimic | NONE | |
| 2711 Erratic | 1385 Phracrimic | NONE | |
| 3403 Phrygian + | 693 Arezzo Major Diatonic Hexachord | 757 Major Locrian 𝄫67 | |
| 3749 Raga Sorati | 347 Barimic | NONE | |
| 1961 Dominant +♯23𝄪4 | 2135 NAKian | NONE | |
| Scale family 823: Alt 𝄫357 - Forte class: 7-21 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 823 Alt 𝄫357 | 3273 Raga Jivantini | 3277 Lydian ♭3♯6 | |
| 2459 Neapoitan Minor ♭4 | 1637 Syptimic | NONE | |
| 3277 Lydian ♭3♯6 | 819 Augmented Inverse | 1843 Dominant +♭2 883 Locrian ♮3𝄫7 823 Alt 𝄫357 | |
| 1843 Dominant +♭2 | 2253 Raga Amarasenapriya | 3277 Lydian ♭3♯6 | |
| 2969 Ionian +♯2𝄪4 | 1127 Eparimic | NONE | |
| 883 Locrian ♮3𝄫7 | 3213 Eponimic | 3277 Lydian ♭3♯6 | |
| 2489 Ionian ♯2♭6 | 1607 Epytimic | NONE | |
| Scale family 827: Alt 𝄫57 - Forte class: 7-21 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 827 Alt 𝄫57 | 3269 Raga Malarani | NONE | |
| 2461 Harmonic minor ♭4 | 1635 Sygimic | 1639 Locrian ♮6𝄫3 | |
| 1639 Locrian ♮6𝄫3 | 2457 Augmented | 3481 Ionian +♯26𝄪4 2521 Mela Dhatuvardhani 2461 Harmonic minor ♭4 | |
| 2867 Ionian +♭2 | 1229 Raga Simharava | NONE | |
| 3481 Ionian +♯26𝄪4 | 615 Schoenberg Hexachord | 1639 Locrian ♮6𝄫3 | |
| 947 Mela Gayakapriya | 3149 Phrycrimic | NONE | |
| 2521 Mela Dhatuvardhani | 1575 Zycrimic | 1639 Locrian ♮6𝄫3 | |
| Scale family 829: Alt ♮2𝄫57 - Forte class: 7-Z18 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 829 Alt ♮2𝄫57 | 3267 URFian | NONE | |
| 1231 Alt 𝄫346 | 2865 Solimic | NONE | |
| 2663 Supine minor | 1433 Dynimic | NONE | |
| 3379 Verdi's Scala Enigmatica Descending | 717 Raga Vijayanagari | NONE | |
| 3737 Ionian ♯26𝄪45 | 359 Bothimic | NONE | |
| 979 Mela Dhavalambari | 3117 TIJian | NONE | |
| 2537 Lydian ♭6♯23 | 1559 JOWian | NONE | |
| Scale family 847: Alt 𝄫347 - Forte class: 7-19 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 847 Alt 𝄫347 | 3249 Raga Tilang | NONE | |
| 2471 Neapolitan minor 𝄫3 | 1625 Hungarian Major No5 | NONE | |
| 3283 Mela Visvambhari | 813 Larimic | NONE | |
| 3689 Superlydian Augmented 𝄪5 | 407 All-Trichord Hexachord | NONE | |
| 973 Mela Syamalangi | 3123 TOMian | NONE | |
| 1267 Locrian ♮3𝄫6 | 2829 RUPian | NONE | |
| 2681 Ionian ♭5♯2 | 1415 IMPian | NONE | |
| Scale family 855: Alt 𝄫37 - Forte class: 7-30 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 855 Alt 𝄫37 | 3241 Dalimic | NONE | |
| 2475 Neapolitan Minor | 1621 Scriabin's Prometheus | NONE | |
| 3285 Lydian #6 | 811 Radimic | NONE | |
| 1845 Mixolydian Augmented | 2251 Zodimic | NONE | |
| 1485 Aeolian ♯4 | 2611 Raga Vasanta | NONE | |
| 1395 Locrian Dominant | 2701 Hawaiian | NONE | |
| 2745 Ionian ♯2 | 1351 Aeraptimic | NONE | |
| Scale family 859: Alt 𝄫7 - Forte class: 7-32 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 859 Alt 𝄫7 | 3237 Raga Brindabani Sarang | NONE | |
| 2477 Harmonic Minor | 1619 Prometheus Neapolitan | NONE | |
| 1643 Locrian ♮6 | 2453 Raga Latika | NONE | |
| 2869 Major Augmented | 1227 Thacrimic | NONE | |
| 1741 Dorian ♯4 | 2355 Raga Lalita | NONE | |
| 1459 Phrygian Dominant | 2637 Raga Ranjani | NONE | |
| 2777 Aeolian Harmonic | 1319 Phronimic | NONE | |
| Scale family 861: Alt ♮2𝄫7 - Forte class: 7-28 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 861 Alt ♮2𝄫7 | 3235 Pothimic | NONE | |
| 1239 Alt 𝄫36 | 2857 Stythimic | NONE | |
| 2667 Neapolitan Major ♭5 | 1429 Bythimic | NONE | |
| 3381 Ionian +♯6 | 715 T4 Prime Mode | NONE | |
| 1869 Lydian 7+♭3 | 2227 Raga Gaula | NONE | |
| 1491 Lydian minor ♭2 | 2605 Rylimic | NONE | |
| 2793 Lydian ♯23 | 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 ♯26 | |
| 2483 Double Harmonic | 1613 Thylimic | NONE | |
| 3289 Lydian ♯26 | 807 Raga Suddha Mukhari | 871 Hungarian Romani Minor 4th Mode | |
| 923 Alt ♮5𝄫7 | 3173 Zarimic | NONE | |
| 2509 Double Harmonic Minor | 1587 Raga Rudra Pancama | 1651 Asian | |
| 1651 Asian | 2445 Zadimic | 2509 Double Harmonic Minor | |
| 2873 Ionian Augmented ♯2 | 1223 Phryptimic | NONE | |
| Scale family 875: Locrian 𝄫7 - Forte class: 7-32 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 875 Locrian 𝄫7 | 3221 Bycrimic | NONE | |
| 2485 Harmonic Major | 1611 Dacrimic | NONE | |
| 1645 Dorian ♭5 | 2451 Raga Bauli | NONE | |
| 1435 Phrygian ♭4 | 2661 Stydimic | NONE | |
| 2765 Lydian ♭3 | 1331 Raga Vasantabhairavi | NONE | |
| 1715 Dominant ♭2 | 2381 Takemitsu Linea Mode 1 | NONE | |
| 2905 Lydian Augmented ♯2 | 1191 Pyrimic | NONE | |
| Scale family 877: Locrian ♮2𝄫7 - Forte class: 7-31 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 877 Locrian ♮2𝄫7 | 3219 Ionaphimic | NONE | |
| 1243 Alt 𝄫6 | 2853 Baptimic | NONE | |
| 2669 Melodic ♭5 | 1427 Lolimic | NONE | |
| 1691 Dorian ♭24 | 2405 T4 First Rotation | NONE | |
| 2893 Lydian +♭3 | 1203 Pagimic | NONE | |
| 1747 Lydian 7♭2 | 2349 Raga Ghantana | NONE | |
| 2921 Lydian +♯23 | 1175 Epycrimic | NONE | |
| Scale family 885: Major Locrian 𝄫7 - Forte class: 7-26 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 885 Major Locrian 𝄫7 | 3211 Epacrimic | NONE | |
| 1245 Alt ♮2𝄫6 | 2851 Katoptimic | NONE | |
| 1335 Elephant Scale | 2761 Dagimic | NONE | |
| 2715 Neapolitan Major ♭4 | 1381 Padimic | NONE | |
| 3405 Phrygian +♮2 | 691 Raga Kalavati | NONE | |
| 1875 Lydian 7+♭2 | 2221 Raga Sindhura Kafi | NONE | |
| 2985 Ionian +♯23𝄪4 | 1111 Sycrimic | NONE | |
| Scale family 925: Alt ♮25𝄫7 - Forte class: 7-20 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 925 Alt ♮25𝄫7 | 3171 Zythimic | NONE | |
| 1255 Locrian 𝄫36 | 2841 African Pentatonic 3 | NONE | |
| 2675 Persian ♮6 | 1421 Raga Trimurti | NONE | |
| 3385 Chromatic Phrygian | 711 Raga Chandrajyoti | NONE | |
| 935 Locrian ♮5𝄫37 | 3161 Kodimic | NONE | |
| 2515 Chromatic Hypolydian | 1581 Raga Bagesri | NONE | |
| 3305 Lydian ♯236 | 791 Aeoloptimic | NONE | |
| Scale family 939: Phrygian 𝄫7 - Forte class: 7-30 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 939 Phrygian 𝄫7 | 3157 Zyptimic | NONE | |
| 2517 Harm. Major ♯4 | 1579 Sagimic | NONE | |
| 1653 Dominant ♭5 | 2443 Panimic | NONE | |
| 1437 Sabach ascending | 2659 Katynimic | NONE | |
| 1383 Locrian 𝄫3 | 2713 Porimic | NONE | |
| 2739 Ionian ♭2 | 1357 Takemitsu Linea Mode 2 | NONE | |
| 3417 Lydian +♯26 | 679 Lanimic | NONE | |
| Scale family 941: Aeolian 𝄫7 - Forte class: 7-29 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 941 Aeolian 𝄫7 | 3155 Ladimic | NONE | |
| 1259 Locrian 𝄫6 | 2837 Aelothimic | NONE | |
| 2677 Ionian ♭5 | 1419 Raga Kashyapi | NONE | |
| 1693 Dorian ♭4 | 2403 Lycrimic | NONE | |
| 1447 Mela Ratnangi | 2649 Aeolythimic | NONE | |
| 2771 Lydian ♭2 | 1325 Phradimic | NONE | |
| 3433 Super Lydian Augmented | 663 Phrynimic | NONE | |
| Scale family 949: Mela Mararanjani - Forte class: 7-27 | |||
|---|---|---|---|
| |||
| Scale | Antiscale | Superantimodes | |
| 949 Mela Mararanjani | 3147 Ryrimic | NONE | |
| 1261 Aeolian ♭5𝄫6 | 2835 Ionygimic | 2899 Lydian +♭2 | |
| 1339 Alt 𝄫5 | 2757 Raga Nishadi | NONE | |
| 2717 Melodic ♭4 | 1379 Kycrimic | NONE | |
| 1703 Mela Vanaspati | 2393 Zathimic | NONE | |
| 2899 Lydian +♭2 | 1197 Minor Hexatonic | 1261 Aeolian ♭5𝄫6 | |
| 3497 Superlydian Augmented 𝄪4 | 599 Thyrimic | NONE | |
| Scale family 981: Mela Kantamani - Forte class: 7-24 | |||
|---|---|---|---|
| Scale | Antiscale | Superantimodes | |
| 981 Mela Kantamani | 3115 TIHian | NONE | |
| 1269 Major Locrian 𝄫6 | 2827 RUNian | NONE | |
| 1341 Alt ♮2𝄫5 | 2755 RIVian | NONE | |
| 1359 Alt 𝄫34 | 2737 Raga Hari Nata | NONE | |
| 2727 Neapolitan Major 𝄫3 | 1369 Boptimic | NONE | |
| 3411 Enigmatic | 685 Raga Suddha Bangala | NONE | |
| 3753 Superlydian Augmented 𝄪45 | 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 Lydian +♯6 1877 Lydian 7+ 1493 Lydian Minor 1397 Major Locrian 1373 Alt ♮2 1367 Leading Whole-Tone Inverse | |
| 3413 Lydian +♯6 | 683 Stogimic | 2731 Neapolitan Major | |
| 1877 Lydian 7+ | 2219 Phrydimic | 2731 Neapolitan Major | |
| 1493 Lydian Minor | 2603 Gadimic | 2731 Neapolitan Major | |
| 1397 Major Locrian | 2699 Sythimic | 2731 Neapolitan Major | |
| 1373 Alt ♮2 | 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 ♭2 | 2389 Eskimo Hexatonic 2 | 2901 Lydian Augmented | |
| 2901 Lydian Augmented | 1195 Raga Gandharavam | 1707 Dorian ♭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 | |