Heptatonic Chord List

[GoesThump]

Thanks for thinking about this. Yes C(12, 7) is a good way to start estimating the size. Unique scales would be 792/7=117 families, I think.
But you are also permitting patterns that arent very musical like Epodian that have gaps of 4 notes, hence why the simple C is big, but the useful number of families ,at leaset to my taste is around 10, so 70 scales.

OK - that makes sense to me. In other words we need to split scales from sets, with scales (being defined by both order & content) being derived from sets (being defined by content only.)

Of those 792 sets, once we eliminate all the rotations/transpositions, we're down to Forte's 38.

Forgive me if I'm a bit plodding here, but most of the names you listed are new to me (A quick search reveals that the name Epodian seems to have originated with William Zeitler - published after my time so to speak. ) I have done a lot of musical set theory in the past & a bucketload of experimentation with scales, microtunings, etc, but always in the framework of 20th century theory like Rahn, Forte, Perle, etc. "Epodian" = 7-3 in the Forte system, as near as I can tell.

Whereas all scales are sets, not all sets are scales. The unusual grouping of 7-3/Epodian is not particularly scale like, true. (I hesitate a bit at calling it not very musical - certainly guys like Ligeti & Xenakis made it work, but in decidedly non-tonal settings. )

Question : how many gaps (intervals larger than a major 2d) and/or clusters (more than 2 semitones in a row) should we allow in a 7 note collection before disqualifying something as being "not a scale"? If we can establish that, it would be easier to come up w/a comprehensive list of scales that fit your definition, above. The interval vectors would give the answer quickly on what meets those criteria.

I don't know if you're familiar w/this tool, but it is one I often recommend to my theory students when they ask about non-traditional note groupings:

PC Set Calculator

Interesting discussion - glad you brought it up!

GT

 

[logdrum]

Even for someone like me who is pretty good with jazz extensions not only on bass but monophonic instruments and a student of the diminished scale, and studied Hindustani music, the list is not that much of use.

The explanation of the binary value is a head scratcher for sure. If you used HEX, then it makes more sense.

0AB5 for Major
06AD. for Ionian
makes more sense to me



In jazz extension of dominant 7th chords you can create scales that can utilize 11 notes but of course in context of what the voicing is, maximum useable is 8 (counting the root once.) is what is usually useful

Mastery of the diminished scale is more useful IMO .

But thanks for putting it up.

 

[IamGroot]

OK - that makes sense to me. In other words we need to split scales from sets, with scales (being defined by both order & content) being derived from sets (being defined by content only.)

Of those 792 sets, once we eliminate all the rotations/transpositions, we're down to Forte's 38.

Forgive me if I'm a bit plodding here, but most of the names you listed are new to me (A quick search reveals that the name Epodian seems to have originated with William Zeitler - published after my time so to speak. ) I have done a lot of musical set theory in the past & a bucketload of experimentation with scales, microtunings, etc, but always in the framework of 20th century theory like Rahn, Forte, Perle, etc. "Epodian" = 7-3 in the Forte system, as near as I can tell.

Whereas all scales are sets, not all sets are scales. The unusual grouping of 7-3/Epodian is not particularly scale like, true. (I hesitate a bit at calling it not very musical - certainly guys like Ligeti & Xenakis made it work, but in decidedly non-tonal settings. )

Question : how many gaps (intervals larger than a major 2d) and/or clusters (more than 2 semitones in a row) should we allow in a 7 note collection before disqualifying something as being "not a scale"? If we can establish that, it would be easier to come up w/a comprehensive list of scales that fit your definition, above. The interval vectors would give the answer quickly on what meets those criteria.

I don't know if you're familiar w/this tool, but it is one I often recommend to my theory students when they ask about non-traditional note groupings:

PC Set Calculator

Interesting discussion - glad you brought it up!

GT

Wow, thanks for the reference! I made my own spreadsheet to do this, but the PC Set site
is way easier for some things.

Im using mostly Ian Rings site for my naming convention. Frankly, Once I have a binary number, thats all I need to exactly identify the scale and the intervals.

I disqualify at 2 consecutive half steps or interval greater than 1.5. Hence why my "top favorites list " is much smaller than C(12/7)

 

[IamGroot]

Even for someone like me who is pretty good with jazz extensions not only on bass but monophonic instruments and a student of the diminished scale, and studied Hindustani music, the list is not that much of use.

The explanation of the binary value is a head scratcher for sure. If you used HEX, then it makes more sense.

0AB5 for Major
06AD. for Ionian
makes more sense to me



In jazz extension of dominant 7th chords you can create scales that can utilize 11 notes but of course in context of what the voicing is, maximum useable is 8 (counting the root once.) is what is usually useful

Mastery of the diminished scale is more useful IMO .

But thanks for putting it up.

Take a scale number like that for C Major and covert it to binary. What do you see?

Why are 5 and 7 note scales different from the 4,6 and 8 note scales?

 

[IamGroot]

OK - that makes sense to me. In other words we need to split scales from sets, with scales (being defined by both order & content) being derived from sets (being defined by content only.)

Of those 792 sets, once we eliminate all the rotations/transpositions, we're down to Forte's 38.

Forgive me if I'm a bit plodding here, but most of the names you listed are new to me (A quick search reveals that the name Epodian seems to have originated with William Zeitler - published after my time so to speak. ) I have done a lot of musical set theory in the past & a bucketload of experimentation with scales, microtunings, etc, but always in the framework of 20th century theory like Rahn, Forte, Perle, etc. "Epodian" = 7-3 in the Forte system, as near as I can tell.

Whereas all scales are sets, not all sets are scales. The unusual grouping of 7-3/Epodian is not particularly scale like, true. (I hesitate a bit at calling it not very musical - certainly guys like Ligeti & Xenakis made it work, but in decidedly non-tonal settings. )

Question : how many gaps (intervals larger than a major 2d) and/or clusters (more than 2 semitones in a row) should we allow in a 7 note collection before disqualifying something as being "not a scale"? If we can establish that, it would be easier to come up w/a comprehensive list of scales that fit your definition, above. The interval vectors would give the answer quickly on what meets those criteria.

I don't know if you're familiar w/this tool, but it is one I often recommend to my theory students when they ask about non-traditional note groupings:

PC Set Calculator

Interesting discussion - glad you brought it up!

GT

Here is every one of those 792 Heptatonic scales. If you see more than two consecutive zeros or ones in the binary code, its not good form. As you can see, most of the 792 are foo schist.

127 1111111
191 10111111
223 11011111
239 11101111
247 11110111
251 11111011
253 11111101
254 11111110
319 100111111 319 Epodian
351 101011111 351 Epanian
367 101101111 367 Aerodian
375 101110111 375 Sodian
379 101111011 379 Aeragian
381 101111101 381 Kogian
382 101111110
415 110011111 415 Aeoladian
431 110101111 431 Epyrian
439 110110111 439 Bythian
443 110111011 443 Kothian
445 110111101
446 110111110
463 111001111 463 Zythian
471 111010111 471 Dodian
475 111011011
477 111011101
478 111011110
487 111100111
491 111101011
493 111101101
494 111101110
499 111110011
501 111110101
502 111110110
505 111111001
506 111111010
508 111111100
575 1000111111
607 1001011111 607 Kadian
623 1001101111 623 Sycrian
631 1001110111 631 Zygian
635 1001111011
637 1001111101
638 1001111110
671 1010011111 671 Stycrian
687 1010101111 687 Aeolythian
695 1010110111 695 Sarian
699 1010111011 699 Aerothian
701 1010111101 701 Mixonyphian
702 1010111110
719 1011001111 719 Kanian
727 1011010111 727 Phradian
731 1011011011 731 Alternating Heptamode
733 1011011101 733 Donian
734 1011011110
743 1011100111 743 Chromatic Hypophrygian Inverse
747 1011101011 747 Lynian
749 1011101101
750 1011101110
755 1011110011 755 Phrythian
757 1011110101
758 1011110110
761 1011111001 761 Ponian
762 1011111010
764 1011111100 763 Doryllic
799 1100011111
815 1100101111 815 Bolian
823 1100110111 823 Stodian
827 1100111011
829 1100111101
830 1100111110
847 1101001111
855 1101010111 855 Porian
859 1101011011 859 Ultralocrian
861 1101011101
862 1101011110
871 1101100111 871 Hungarian Romani Minor 4th Mode
875 1101101011
877 1101101101
878 1101101110
883 1101110011 883 Ralian
885 1101110101
886 1101110110
889 1101111001 889 Borian
890 1101111010
892 1101111100
911 1110001111
919 1110010111 919 Chromatic Phrygian Inverse
923 1110011011 923 Ultraphrygian
925 1110011101
926 1110011110
935 1110100111
939 1110101011
941 1110101101
942 1110101110
947 1110110011
949 1110110101
950 1110110110
953 1110111001 953 Mela Yagapriya
954 1110111010
956 1110111100
967 1111000111 967 Mela Salaga
971 1111001011 971 Mela Gavambodhi
973 1111001101
974 1111001110
979 1111010011
981 1111010101
982 1111010110
985 1111011001
986 1111011010
988 1111011100
995 1111100011 995 Phrathian
997 1111100101 997 Rycrian
998 1111100110
1001 1111101001
1002 1111101010
1004 1111101100
1009 1111110001 1009 Katyptian
1010 1111110010
1012 1111110100
1016 1111111000
1087 10000111111
1119 10001011111 1119 Rarian
1135 10001101111
1143 10001110111
1147 10001111011
1149 10001111101
1150 10001111110
1183 10010011111
1199 10010101111 1199 Magian
1207 10010110111 1207 Aeoloptian
1211 10010111011
1213 10010111101
1214 10010111110
1231 10011001111
1239 10011010111
1243 10011011011
1245 10011011101
1246 10011011110
1255 10011100111
1259 10011101011
1261 10011101101
1262 10011101110
1267 10011110011
1269 10011110101
1270 10011110110
1273 10011111001 1273 Heptatonic Blues
1274 10011111010
1276 10011111100
1311 10100011111
1327 10100101111
1335 10100110111
1339 10100111011
1341 10100111101
1342 10100111110
1359 10101001111
1367 10101010111 1367 Leading Whole-Tone Inverse
1371 10101011011 1371 Superlocrian
1373 10101011101 1373 Storian
1374 10101011110
1383 10101100111
1387 10101101011 1387 Locrian
1389 10101101101 1389 Aeolian b5
1390 10101101110
1395 10101110011 1395 Locrian Dominant
1397 10101110101 1397 Major Locrian
1398 10101110110
1401 10101111001 1401 Pagian
1402 10101111010
1404 10101111100
1423 10110001111
1431 10110010111 1431 Phragian
1435 10110011011
1437 10110011101
1438 10110011110
1447 10110100111
1451 10110101011 1451 Phrygian
1453 10110101101 1453 Aeolian
1454 10110101110
1459 10110110011 1459 Phrygian Dominant
1461 10110110101 1461 Mixolydian b6
1462 10110110110
1465 10110111001 1465 Mela Ragavardhani
1466 10110111010
1468 10110111100
1479 10111000111 1479 Mela Jalarnava
1483 10111001011 1483 Mela Bhavapriya
1485 10111001101 1485 Minor Romani
1486 10111001110 1485 Minor Romani
1491 10111010011 1489 Raga Jyoti
1493 10111010101 1493 Lydian Minor
1494 10111010110 1493 Lydian Minor
1497 10111011001 1497 Mela Jyotisvarupini
1498 10111011010 1497 Mela Jyotisvarupini
1500 10111011100 1497 Mela Jyotisvarupini
1507 10111100011 1507 Zynian
1509 10111100101 1509 Ragian
1510 10111100110 1509 Ragian
1513 10111101001 1513 Stathian
1514 10111101010 1513 Stathian
1516 10111101100 1515 Phrygian/Locrian Mixed
1521 10111110001 1521 Stanian
1522 10111110010 1521 Stanian
1524 10111110100 1523 Zothyllic
1528 10111111000 1525 Sodyllic
1567 11000011111 1535 Mixodyllian
1583 11000101111 1583 Salian
1591 11000110111 1591 Rodian
1595 11000111011 1591 Rodian
1597 11000111101 1591 Rodian
1598 11000111110 1591 Rodian
1615 11001001111 1613 Thylimic
1623 11001010111 1623 Lothian
1627 11001011011 1627 Hungarian Major 4th Mode
1629 11001011101 1629 Synian
1630 11001011110 1629 Synian
1639 11001100111 1637 Syptimic
1643 11001101011 1643 Locrian Natural 6
1645 11001101101 1643 Locrian Natural 6
1646 11001101110 1643 Locrian Natural 6
1651 11001110011 1651 Asian
1653 11001110101 1651 Asian
1654 11001110110 1651 Asian
1657 11001111001 1657 Ionothian
1658 11001111010 1657 Ionothian
1660 11001111100 1657 Ionothian
1679 11010001111 1675 Raga Salagavarali
1687 11010010111 1685 Zeracrimic
1691 11010011011 1689 Lorimic
1693 11010011101 1689 Lorimic
1694 11010011110 1689 Lorimic
1703 11010100111 1701 Mixolydian Hexatonic
1707 11010101011 1707 Dorian Flat 2
1709 11010101101 1709 Dorian
1710 11010101110 1709 Dorian
1715 11010110011 1713 Raga Khamas
1717 11010110101 1717 Mixolydian
1718 11010110110 1717 Mixolydian
1721 11010111001 1721 Mela Vagadhisvari
1722 11010111010 1721 Mela Vagadhisvari
1724 11010111100 1721 Mela Vagadhisvari
1735 11011000111 1733 Raga Sarasvati
1739 11011001011 1739 Mela Sadvidhamargini
1741 11011001101 1741 Lydian Diminished
1742 11011001110 1741 Lydian Diminished
1747 11011010011 1745 Raga Vutari
1749 11011010101 1749 Lydian Dominant
1750 11011010110 1749 Lydian Dominant
1753 11011011001 1753 Hungarian Major
1754 11011011010 1753 Hungarian Major
1756 11011011100 1755 Octatonic
1763 11011100011 1763 Katalian
1765 11011100101 1765 Lonian
1766 11011100110 1765 Lonian
1769 11011101001 1769 Blues Heptatonic II
1770 11011101010 1769 Blues Heptatonic II
1772 11011101100 1771 Stylyllic
1777 11011110001 1777 Saptian
1778 11011110010 1777 Saptian
1780 11011110100 1779 Aerythyllic
1784 11011111000 1781 Lydian/Mixolydian Mixed
1807 11100001111 1791 Aerygyllian
1815 11100010111 1815 Godian
1819 11100011011 1819 Pydian
1821 11100011101 1821 Aeradian
1822 11100011110 1821 Aeradian
1831 11100100111 1831 Pothian
1835 11100101011 1835 Byptian
1837 11100101101 1837 Dalian
1838 11100101110 1837 Dalian
1843 11100110011 1843 Ionygian
1845 11100110101 1845 Lagian
1846 11100110110 1845 Lagian
1849 11100111001 1849 Chromatic Hypodorian Inverse
1850 11100111010 1849 Chromatic Hypodorian Inverse
1852 11100111100 1851 Zacryllic
1863 11101000111 1861 Phrygimic
1867 11101001011 1867 Solian
1869 11101001101 1867 Solian
1870 11101001110 1867 Solian
1875 11101010011 1867 Solian
1877 11101010101 1877 Aeroptian
1878 11101010110 1877 Aeroptian
1881 11101011001 1881 Korian
1882 11101011010 1881 Korian
1884 11101011100 1883 Mixopyryllic
1891 11101100011 1891 Thalian
1893 11101100101 1893 Ionylian
1894 11101100110
1897 11101101001
1898 11101101010
1900 11101101100
1905 11101110001 1905 Katacrian
1906 11101110010
1908 11101110100
1912 11101111000
1927 11110000111
1931 11110001011 1931 Stogian
1933 11110001101 1933 Mocrian
1934 11110001110
1939 11110010011 1939 Dathian
1941 11110010101 1941 Aeranian
1942 11110010110
1945 11110011001 1945 Zarian
1946 11110011010
1948 11110011100
1955 11110100011
1957 11110100101 1957 Pyrian
1958 11110100110
1961 11110101001
1962 11110101010
1964 11110101100
1969 11110110001 1969 Zorian
1970 11110110010
1972 11110110100
1976 11110111000
1987 11111000011
1989 11111000101 1989 Dydian
1990 11111000110
1993 11111001001 1993 Katoptian
1994 11111001010
1996 11111001100
2001 11111010001 2001 Gydian
2002 11111010010 2001 Gydian
2004 11111010100
2008 11111011000
2017 11111100001
2018 11111100010
2020 11111100100
2024 11111101000
2032 11111110000
2111 100000111111
2143 100001011111
2159 100001101111
2167 100001110111
2171 100001111011
2173 100001111101
2174 100001111110
2207 100010011111 2207 Mygian
2223 100010101111 2223 Konian
2231 100010110111 2231 Macrian
2235 100010111011 2235 Bathian
2237 100010111101 2237 Epothian
2238 100010111110
2255 100011001111 2255 Dylian
2263 100011010111 2263 Lycrian
2267 100011011011 2267 Padian
2269 100011011101 2269 Pygian
2270 100011011110
2279 100011100111 2279 Dyrian
2283 100011101011 2283 Aeolyptian
2285 100011101101
2286 100011101110
2291 100011110011
2293 100011110101
2294 100011110110
2297 100011111001
2298 100011111010
2300 100011111100
2335 100100011111
2351 100100101111 2351 Gynian
2359 100100110111 2359 Gadian
2363 100100111011 2363 Kataptian
2365 100100111101
2366 100100111110
2383 100101001111 2383 Katorian
2391 100101010111 2391 Molian
2395 100101011011 2395 Zoptian
2397 100101011101 2397 Stagian
2398 100101011110
2407 100101100111 2407 Zylian
2411 100101101011 2411 Aeolorian
2413 100101101101 2413 Harmonic Minor Flat 5
2414 100101101110 2413 Harmonic Minor Flat 5
2419 100101110011 2419 Raga Lalita
2421 100101110101 2421 Malian
2422 100101110110
2425 100101111001 2425 Rorian
2426 100101111010
2428 100101111100
2447 100110001111
2455 100110010111 2455 Bothian
2459 100110011011 2459 Ionocrian
2461 100110011101
2462 100110011110
2471 100110100111
2475 100110101011 2475 Neapolitan Minor
2477 100110101101 2477 Harmonic Minor
2478 100110101110
2483 100110110011 2483 Double Harmonic
2485 100110110101
2486 100110110110
2489 100110111001 2489 Mela Gangeyabhusani
2490 100110111010
2492 100110111100
2503 100111000111
2507 100111001011 2507 Todi That
2509 100111001101 2509 Double Harmonic Minor
2510 100111001110
2515 100111010011
2517 100111010101
2518 100111010110
2521 100111011001
2522 100111011010
2524 100111011100
2531 100111100011 2531 Danian
2533 100111100101 2533 Podian
2534 100111100110
2537 100111101001
2538 100111101010
2540 100111101100
2545 100111110001 2545 Thycrian
2546 100111110010
2548 100111110100
2552 100111111000
2591 101000011111
2607 101000101111 2607 Aerolian
2615 101000110111
2619 101000111011
2621 101000111101
2622 101000111110
2639 101001001111
2647 101001010111 2647 Dadian
2651 101001011011 2651 Panian
2653 101001011101
2654 101001011110
2663 101001100111
2667 101001101011
2669 101001101101
2670 101001101110
2675 101001110011
2677 101001110101
2678 101001110110
2681 101001111001
2682 101001111010
2684 101001111100
2703 101010001111
2711 101010010111
2715 101010011011
2717 101010011101
2718 101010011110
2727 101010100111
2731 101010101011 2731 Neapolitan Major
2733 101010101101 2733 Melodic Minor Ascending
2734 101010101110
2739 101010110011
2741 101010110101 2741 Major
2742 101010110110
2745 101010111001 2745 Mela Sulini
2746 101010111010
2748 101010111100
2759 101011000111
2763 101011001011 2763 Mela Suvarnangi
2765 101011001101
2766 101011001110
2771 101011010011
2773 101011010101 2773 Lydian
2774 101011010110 2773 Lydian
2777 101011011001 2777 Aeolian Harmonic
2778 101011011010
2780 101011011100
2787 101011100011 2787 Zyrian
2789 101011100101 2789 Zolian
2790 101011100110
2793 101011101001
2794 101011101010
2796 101011101100
2801 101011110001 2801 Zogian
2802 101011110010
2804 101011110100
2808 101011111000
2831 101100001111
2839 101100010111 2839 Lyptian
2843 101100011011 2843 Sorian
2845 101100011101
2846 101100011110
2855 101100100111
2859 101100101011 2859 Phrycrian
2861 101100101101 2861 Hungarian Major 5th Mode
2862 101100101110
2867 101100110011
2869 101100110101 2869 Major Augmented
2870 101100110110
2873 101100111001 2873 Ionian Augmented Sharp 2
2874 101100111010
2876 101100111100
2887 101101000111
2891 101101001011
2893 101101001101
2894 101101001110
2899 101101010011
2901 101101010101 2901 Lydian Augmented
2902 101101010110
2905 101101011001
2906 101101011010
2908 101101011100
2915 101101100011
2917 101101100101 2917 Nohkan Flute Scale
2918 101101100110
2921 101101101001
2922 101101101010
2924 101101101100
2929 101101110001 2929 Aeolathian
2930 101101110010
2932 101101110100
2936 101101111000
2951 101110000111
2955 101110001011 2955 Thorian
2957 101110001101 2957 Thygian
2958 101110001110
2963 101110010011 2963 Bygian
2965 101110010101 2965 Darian
2966 101110010110
2969 101110011001 2969 Tholian
2970 101110011010
2972 101110011100
2979 101110100011
2981 101110100101 2981 Ionolian
2982 101110100110
2985 101110101001
2986 101110101010
2988 101110101100
2993 101110110001 2993 Stythian
2994 101110110010
2996 101110110100
3000 101110111000
3011 101111000011
3013 101111000101 3013 Thynian
3014 101111000110
3017 101111001001 3017 Gacrian
3018 101111001010
3020 101111001100
3025 101111010001
3026 101111010010
3028 101111010100
3032 101111011000
3041 101111100001
3042 101111100010
3044 101111100100
3048 101111101000
3056 101111110000
3103 110000011111
3119 110000101111
3127 110000110111
3131 110000111011
3133 110000111101
3134 110000111110
3151 110001001111 3151 Pacrian
3159 110001010111 3159 Stocrian
3163 110001011011 3163 Rogian
3165 110001011101 3165 Mylian
3166 110001011110
3175 110001100111 3175 Eponian
3179 110001101011 3179 Daptian
3181 110001101101 3181 Rolian
3182 110001101110
3187 110001110011 3187 Koptian
3189 110001110101 3189 Aeolonian
3190 110001110110
3193 110001111001
3194 110001111010
3196 110001111100
3215 110010001111
3223 110010010111 3223 Thyphian
3227 110010011011 3227 Aeolocrian
3229 110010011101 3229 Aeolaptian
3230 110010011110
3239 110010100111 3239 Mela Tanarupi
3243 110010101011 3243 Mela Rupavati
3245 110010101101 3245 Mela Varunapriya
3246 110010101110
3251 110010110011 3251 Mela Hatakambari
3253 110010110101 3253 Mela Naganandini
3254 110010110110
3257 110010111001 3257 Mela Calanata
3258 110010111010
3260 110010111100
3271 110011000111
3275 110011001011 3275 Mela Divyamani
3277 110011001101 3277 Mela Nitimati
3278 110011001110
3283 110011010011
3285 110011010101 3285 Mela Citrambari
3286 110011010110
3289 110011011001 3289 Lydian Sharp 2 Sharp 6
3290 110011011010
3292 110011011100
3299 110011100011
3301 110011100101 3301 Chromatic Mixolydian Inverse
3302 110011100110
3305 110011101001
3306 110011101010
3308 110011101100
3313 110011110001 3313 Aeolacrian
3314 110011110010
3316 110011110100
3320 110011111000
3343 110100001111
3351 110100010111 3351 Crater Scale
3355 110100011011
3357 110100011101
3358 110100011110
3367 110100100111
3371 110100101011 3371 Aeolylian
3373 110100101101 3373 Lodian
3374 110100101110
3379 110100110011
3381 110100110101
3382 110100110110
3385 110100111001
3386 110100111010
3388 110100111100
3399 110101000111
3403 110101001011
3405 110101001101
3406 110101001110
3411 110101010011
3413 110101010101 3413 Leading Whole-tone
3414 110101010110
3417 110101011001
3418 110101011010
3420 110101011100
3427 110101100011
3429 110101100101 3429 Marian
3430 110101100110
3433 110101101001
3434 110101101010
3436 110101101100
3441 110101110001 3441 Thacrian
3442 110101110010
3444 110101110100
3448 110101111000
3463 110110000111
3467 110110001011 3467 Sudhvidhamagini
3469 110110001101 3469 Monian
3470 110110001110
3475 110110010011
3477 110110010101 3477 Kyptian
3478 110110010110
3481 110110011001
3482 110110011010
3484 110110011100
3491 110110100011
3493 110110100101
3494 110110100110
3497 110110101001
3498 110110101010
3500 110110101100
3505 110110110001
3506 110110110010
3508 110110110100
3512 110110111000
3523 110111000011
3525 110111000101 3525 Zocrian
3526 110111000110
3529 110111001001 3529 Stalian
3530 110111001010
3532 110111001100
3537 110111010001
3538 110111010010
3540 110111010100
3544 110111011000
3553 110111100001
3554 110111100010
3556 110111100100
3560 110111101000
3568 110111110000
3599 111000001111
3607 111000010111
3611 111000011011
3613 111000011101
3614 111000011110
3623 111000100111 3623 Aerocrian
3627 111000101011 3627 Kalian
3629 111000101101 3629 Boptian
3630 111000101110
3635 111000110011 3635 Katygian
3637 111000110101 3637 Raga Rageshri
3638 111000110110
3641 111000111001 3641 Thocrian
3642 111000111010
3644 111000111100
3655 111001000111
3659 111001001011 3659 Polian
3661 111001001101 3661 Mixodorian
3662 111001001110
3667 111001010011 3667 Kaptian
3669 111001010101 3669 Mothian
3670 111001010110
3673 111001011001 3673 Ranian
3674 111001011010
3676 111001011100
3683 111001100011
3685 111001100101 3685 Kodian
3686 111001100110
3689 111001101001
3690 111001101010
3692 111001101100
3697 111001110001
3698 111001110010
3700 111001110100
3704 111001111000
3719 111010000111
3723 111010001011 3723 Myptian
3725 111010001101
3726 111010001110
3731 111010010011
3733 111010010101 3733 Gycrian
3734 111010010110
3737 111010011001
3738 111010011010
3740 111010011100
3747 111010100011
3749 111010100101
3750 111010100110
3753 111010101001
3754 111010101010
3756 111010101100
3761 111010110001
3762 111010110010
3764 111010110100
3768 111010111000
3779 111011000011
3781 111011000101 3781 Gyphian
3782 111011000110
3785 111011001001
3786 111011001010
3788 111011001100
3793 111011010001
3794 111011010010
3796 111011010100
3800 111011011000
3809 111011100001
3810 111011100010
3812 111011100100
3816 111011101000
3824 111011110000
3847 111100000111
3851 111100001011
3853 111100001101
3854 111100001110
3859 111100010011 3859 Aeolarian
3861 111100010101 3861 Phroptian
3862 111100010110
3865 111100011001 3865 Starian
3866 111100011010
3868 111100011100
3875 111100100011
3877 111100100101 3877 Thanian
3878 111100100110
3881 111100101001 3881 Morian
3882 111100101010
3884 111100101100
3889 111100110001
3890 111100110010
3892 111100110100
3896 111100111000
3907 111101000011
3909 111101000101 3909 Rydian
3910 111101000110
3913 111101001001
3914 111101001010
3916 111101001100
3921 111101010001
3922 111101010010
3924 111101010100
3928 111101011000
3937 111101100001
3938 111101100010
3940 111101100100
3944 111101101000
3952 111101110000
3971 111110000011
3973 111110000101
3974 111110000110
3977 111110001001 3977 Kythian
3978 111110001010
3980 111110001100
3985 111110010001
3986 111110010010
3988 111110010100
3992 111110011000
4001 111110100001
4002 111110100010
4004 111110100100
4008 111110101000
4016 111110110000
4033 111111000001
4034 111111000010
4036 111111000100
4040 111111001000
4048 111111010000
4064 111111100000

 

[Evilheim]

Just my two cents here, although it's a good thing to organize scales, specially knowing that sometimes the information you can find on the internet is not properly explained (or related), even whatever related to music theory, like for example chords and arpeggios, those things can get really messy in your head if you don't understand the terms "Scale Family", or "Chord Types" by invertions and voicings to organize them properly. I mean, most of the time I see all those things being shown/taught separately (even when I studied Musicology).

But I think that is also cool and very helpful to understand/explain even very briefly the background of each scale/family, (even tho I understand that the amounth of scale families still is quite intimidating): where it comes from, what it is used for, if it is vital for understanding modern music (like the major scale's modes AKA Diatonic Scale Family).

That's because, if you know a bit of the background of the scale and what it is mainly used for, you can actually use it properly and try to harmoize it, make chord progressions for a song or whatever, like happen when actually knowing the background of the harmonic and melodic minors. Instead of having a bunch of scales that you know are there but you don't know nothing about it, just theplacement of the notes.

I also think that is important to point out/clarify (and people very often forget) that some scales are not "literal translations" into the western 12 semitone system, because that on different cultures and eras, people have used a big variety of musical systems, like 24-tone system, or even different types or what we can be considered as "microtonal". So we've translated some of those scales (sonorities), by using the closest intervals of our 12 tone system of those "microtonal" ones.

 

[Papageno]

Here is every one of those 792 Heptatonic scales. If you see more than two consecutive zeros or ones in the binary code, its not good form. As you can see, most of the 792 are foo schist.

127 1111111
191 10111111
223 11011111
239 11101111
247 11110111
251 11111011
253 11111101
254 11111110
319 100111111 319 Epodian
351 101011111 351 Epanian
367 101101111 367 Aerodian
375 101110111 375 Sodian
379 101111011 379 Aeragian
381 101111101 381 Kogian
382 101111110
415 110011111 415 Aeoladian
431 110101111 431 Epyrian
439 110110111 439 Bythian
443 110111011 443 Kothian
445 110111101
446 110111110
463 111001111 463 Zythian
471 111010111 471 Dodian
475 111011011
477 111011101
478 111011110
487 111100111
491 111101011
493 111101101
494 111101110
499 111110011
501 111110101
502 111110110
505 111111001
506 111111010
508 111111100
575 1000111111
607 1001011111 607 Kadian
623 1001101111 623 Sycrian
631 1001110111 631 Zygian
635 1001111011
637 1001111101
638 1001111110
671 1010011111 671 Stycrian
687 1010101111 687 Aeolythian
695 1010110111 695 Sarian
699 1010111011 699 Aerothian
701 1010111101 701 Mixonyphian
702 1010111110
719 1011001111 719 Kanian
727 1011010111 727 Phradian
731 1011011011 731 Alternating Heptamode
733 1011011101 733 Donian
734 1011011110
743 1011100111 743 Chromatic Hypophrygian Inverse
747 1011101011 747 Lynian
749 1011101101
750 1011101110
755 1011110011 755 Phrythian
757 1011110101
758 1011110110
761 1011111001 761 Ponian
762 1011111010
764 1011111100 763 Doryllic
799 1100011111
815 1100101111 815 Bolian
823 1100110111 823 Stodian
827 1100111011
829 1100111101
830 1100111110
847 1101001111
855 1101010111 855 Porian
859 1101011011 859 Ultralocrian
861 1101011101
862 1101011110
871 1101100111 871 Hungarian Romani Minor 4th Mode
875 1101101011
877 1101101101
878 1101101110
883 1101110011 883 Ralian
885 1101110101
886 1101110110
889 1101111001 889 Borian
890 1101111010
892 1101111100
911 1110001111
919 1110010111 919 Chromatic Phrygian Inverse
923 1110011011 923 Ultraphrygian
925 1110011101
926 1110011110
935 1110100111
939 1110101011
941 1110101101
942 1110101110
947 1110110011
949 1110110101
950 1110110110
953 1110111001 953 Mela Yagapriya
954 1110111010
956 1110111100
967 1111000111 967 Mela Salaga
971 1111001011 971 Mela Gavambodhi
973 1111001101
974 1111001110
979 1111010011
981 1111010101
982 1111010110
985 1111011001
986 1111011010
988 1111011100
995 1111100011 995 Phrathian
997 1111100101 997 Rycrian
998 1111100110
1001 1111101001
1002 1111101010
1004 1111101100
1009 1111110001 1009 Katyptian
1010 1111110010
1012 1111110100
1016 1111111000
1087 10000111111
1119 10001011111 1119 Rarian
1135 10001101111
1143 10001110111
1147 10001111011
1149 10001111101
1150 10001111110
1183 10010011111
1199 10010101111 1199 Magian
1207 10010110111 1207 Aeoloptian
1211 10010111011
1213 10010111101
1214 10010111110
1231 10011001111
1239 10011010111
1243 10011011011
1245 10011011101
1246 10011011110
1255 10011100111
1259 10011101011
1261 10011101101
1262 10011101110
1267 10011110011
1269 10011110101
1270 10011110110
1273 10011111001 1273 Heptatonic Blues
1274 10011111010
1276 10011111100
1311 10100011111
1327 10100101111
1335 10100110111
1339 10100111011
1341 10100111101
1342 10100111110
1359 10101001111
1367 10101010111 1367 Leading Whole-Tone Inverse
1371 10101011011 1371 Superlocrian
1373 10101011101 1373 Storian
1374 10101011110
1383 10101100111
1387 10101101011 1387 Locrian
1389 10101101101 1389 Aeolian b5
1390 10101101110
1395 10101110011 1395 Locrian Dominant
1397 10101110101 1397 Major Locrian
1398 10101110110
1401 10101111001 1401 Pagian
1402 10101111010
1404 10101111100
1423 10110001111
1431 10110010111 1431 Phragian
1435 10110011011
1437 10110011101
1438 10110011110
1447 10110100111
1451 10110101011 1451 Phrygian
1453 10110101101 1453 Aeolian
1454 10110101110
1459 10110110011 1459 Phrygian Dominant
1461 10110110101 1461 Mixolydian b6
1462 10110110110
1465 10110111001 1465 Mela Ragavardhani
1466 10110111010
1468 10110111100
1479 10111000111 1479 Mela Jalarnava
1483 10111001011 1483 Mela Bhavapriya
1485 10111001101 1485 Minor Romani
1486 10111001110 1485 Minor Romani
1491 10111010011 1489 Raga Jyoti
1493 10111010101 1493 Lydian Minor
1494 10111010110 1493 Lydian Minor
1497 10111011001 1497 Mela Jyotisvarupini
1498 10111011010 1497 Mela Jyotisvarupini
1500 10111011100 1497 Mela Jyotisvarupini
1507 10111100011 1507 Zynian
1509 10111100101 1509 Ragian
1510 10111100110 1509 Ragian
1513 10111101001 1513 Stathian
1514 10111101010 1513 Stathian
1516 10111101100 1515 Phrygian/Locrian Mixed
1521 10111110001 1521 Stanian
1522 10111110010 1521 Stanian
1524 10111110100 1523 Zothyllic
1528 10111111000 1525 Sodyllic
1567 11000011111 1535 Mixodyllian
1583 11000101111 1583 Salian
1591 11000110111 1591 Rodian
1595 11000111011 1591 Rodian
1597 11000111101 1591 Rodian
1598 11000111110 1591 Rodian
1615 11001001111 1613 Thylimic
1623 11001010111 1623 Lothian
1627 11001011011 1627 Hungarian Major 4th Mode
1629 11001011101 1629 Synian
1630 11001011110 1629 Synian
1639 11001100111 1637 Syptimic
1643 11001101011 1643 Locrian Natural 6
1645 11001101101 1643 Locrian Natural 6
1646 11001101110 1643 Locrian Natural 6
1651 11001110011 1651 Asian
1653 11001110101 1651 Asian
1654 11001110110 1651 Asian
1657 11001111001 1657 Ionothian
1658 11001111010 1657 Ionothian
1660 11001111100 1657 Ionothian
1679 11010001111 1675 Raga Salagavarali
1687 11010010111 1685 Zeracrimic
1691 11010011011 1689 Lorimic
1693 11010011101 1689 Lorimic
1694 11010011110 1689 Lorimic
1703 11010100111 1701 Mixolydian Hexatonic
1707 11010101011 1707 Dorian Flat 2
1709 11010101101 1709 Dorian
1710 11010101110 1709 Dorian
1715 11010110011 1713 Raga Khamas
1717 11010110101 1717 Mixolydian
1718 11010110110 1717 Mixolydian
1721 11010111001 1721 Mela Vagadhisvari
1722 11010111010 1721 Mela Vagadhisvari
1724 11010111100 1721 Mela Vagadhisvari
1735 11011000111 1733 Raga Sarasvati
1739 11011001011 1739 Mela Sadvidhamargini
1741 11011001101 1741 Lydian Diminished
1742 11011001110 1741 Lydian Diminished
1747 11011010011 1745 Raga Vutari
1749 11011010101 1749 Lydian Dominant
1750 11011010110 1749 Lydian Dominant
1753 11011011001 1753 Hungarian Major
1754 11011011010 1753 Hungarian Major
1756 11011011100 1755 Octatonic
1763 11011100011 1763 Katalian
1765 11011100101 1765 Lonian
1766 11011100110 1765 Lonian
1769 11011101001 1769 Blues Heptatonic II
1770 11011101010 1769 Blues Heptatonic II
1772 11011101100 1771 Stylyllic
1777 11011110001 1777 Saptian
1778 11011110010 1777 Saptian
1780 11011110100 1779 Aerythyllic
1784 11011111000 1781 Lydian/Mixolydian Mixed
1807 11100001111 1791 Aerygyllian
1815 11100010111 1815 Godian
1819 11100011011 1819 Pydian
1821 11100011101 1821 Aeradian
1822 11100011110 1821 Aeradian
1831 11100100111 1831 Pothian
1835 11100101011 1835 Byptian
1837 11100101101 1837 Dalian
1838 11100101110 1837 Dalian
1843 11100110011 1843 Ionygian
1845 11100110101 1845 Lagian
1846 11100110110 1845 Lagian
1849 11100111001 1849 Chromatic Hypodorian Inverse
1850 11100111010 1849 Chromatic Hypodorian Inverse
1852 11100111100 1851 Zacryllic
1863 11101000111 1861 Phrygimic
1867 11101001011 1867 Solian
1869 11101001101 1867 Solian
1870 11101001110 1867 Solian
1875 11101010011 1867 Solian
1877 11101010101 1877 Aeroptian
1878 11101010110 1877 Aeroptian
1881 11101011001 1881 Korian
1882 11101011010 1881 Korian
1884 11101011100 1883 Mixopyryllic
1891 11101100011 1891 Thalian
1893 11101100101 1893 Ionylian
1894 11101100110
1897 11101101001
1898 11101101010
1900 11101101100
1905 11101110001 1905 Katacrian
1906 11101110010
1908 11101110100
1912 11101111000
1927 11110000111
1931 11110001011 1931 Stogian
1933 11110001101 1933 Mocrian
1934 11110001110
1939 11110010011 1939 Dathian
1941 11110010101 1941 Aeranian
1942 11110010110
1945 11110011001 1945 Zarian
1946 11110011010
1948 11110011100
1955 11110100011
1957 11110100101 1957 Pyrian
1958 11110100110
1961 11110101001
1962 11110101010
1964 11110101100
1969 11110110001 1969 Zorian
1970 11110110010
1972 11110110100
1976 11110111000
1987 11111000011
1989 11111000101 1989 Dydian
1990 11111000110
1993 11111001001 1993 Katoptian
1994 11111001010
1996 11111001100
2001 11111010001 2001 Gydian
2002 11111010010 2001 Gydian
2004 11111010100
2008 11111011000
2017 11111100001
2018 11111100010
2020 11111100100
2024 11111101000
2032 11111110000
2111 100000111111
2143 100001011111
2159 100001101111
2167 100001110111
2171 100001111011
2173 100001111101
2174 100001111110
2207 100010011111 2207 Mygian
2223 100010101111 2223 Konian
2231 100010110111 2231 Macrian
2235 100010111011 2235 Bathian
2237 100010111101 2237 Epothian
2238 100010111110
2255 100011001111 2255 Dylian
2263 100011010111 2263 Lycrian
2267 100011011011 2267 Padian
2269 100011011101 2269 Pygian
2270 100011011110
2279 100011100111 2279 Dyrian
2283 100011101011 2283 Aeolyptian
2285 100011101101
2286 100011101110
2291 100011110011
2293 100011110101
2294 100011110110
2297 100011111001
2298 100011111010
2300 100011111100
2335 100100011111
2351 100100101111 2351 Gynian
2359 100100110111 2359 Gadian
2363 100100111011 2363 Kataptian
2365 100100111101
2366 100100111110
2383 100101001111 2383 Katorian
2391 100101010111 2391 Molian
2395 100101011011 2395 Zoptian
2397 100101011101 2397 Stagian
2398 100101011110
2407 100101100111 2407 Zylian
2411 100101101011 2411 Aeolorian
2413 100101101101 2413 Harmonic Minor Flat 5
2414 100101101110 2413 Harmonic Minor Flat 5
2419 100101110011 2419 Raga Lalita
2421 100101110101 2421 Malian
2422 100101110110
2425 100101111001 2425 Rorian
2426 100101111010
2428 100101111100
2447 100110001111
2455 100110010111 2455 Bothian
2459 100110011011 2459 Ionocrian
2461 100110011101
2462 100110011110
2471 100110100111
2475 100110101011 2475 Neapolitan Minor
2477 100110101101 2477 Harmonic Minor
2478 100110101110
2483 100110110011 2483 Double Harmonic
2485 100110110101
2486 100110110110
2489 100110111001 2489 Mela Gangeyabhusani
2490 100110111010
2492 100110111100
2503 100111000111
2507 100111001011 2507 Todi That
2509 100111001101 2509 Double Harmonic Minor
2510 100111001110
2515 100111010011
2517 100111010101
2518 100111010110
2521 100111011001
2522 100111011010
2524 100111011100
2531 100111100011 2531 Danian
2533 100111100101 2533 Podian
2534 100111100110
2537 100111101001
2538 100111101010
2540 100111101100
2545 100111110001 2545 Thycrian
2546 100111110010
2548 100111110100
2552 100111111000
2591 101000011111
2607 101000101111 2607 Aerolian
2615 101000110111
2619 101000111011
2621 101000111101
2622 101000111110
2639 101001001111
2647 101001010111 2647 Dadian
2651 101001011011 2651 Panian
2653 101001011101
2654 101001011110
2663 101001100111
2667 101001101011
2669 101001101101
2670 101001101110
2675 101001110011
2677 101001110101
2678 101001110110
2681 101001111001
2682 101001111010
2684 101001111100
2703 101010001111
2711 101010010111
2715 101010011011
2717 101010011101
2718 101010011110
2727 101010100111
2731 101010101011 2731 Neapolitan Major
2733 101010101101 2733 Melodic Minor Ascending
2734 101010101110
2739 101010110011
2741 101010110101 2741 Major
2742 101010110110
2745 101010111001 2745 Mela Sulini
2746 101010111010
2748 101010111100
2759 101011000111
2763 101011001011 2763 Mela Suvarnangi
2765 101011001101
2766 101011001110
2771 101011010011
2773 101011010101 2773 Lydian
2774 101011010110 2773 Lydian
2777 101011011001 2777 Aeolian Harmonic
2778 101011011010
2780 101011011100
2787 101011100011 2787 Zyrian
2789 101011100101 2789 Zolian
2790 101011100110
2793 101011101001
2794 101011101010
2796 101011101100
2801 101011110001 2801 Zogian
2802 101011110010
2804 101011110100
2808 101011111000
2831 101100001111
2839 101100010111 2839 Lyptian
2843 101100011011 2843 Sorian
2845 101100011101
2846 101100011110
2855 101100100111
2859 101100101011 2859 Phrycrian
2861 101100101101 2861 Hungarian Major 5th Mode
2862 101100101110
2867 101100110011
2869 101100110101 2869 Major Augmented
2870 101100110110
2873 101100111001 2873 Ionian Augmented Sharp 2
2874 101100111010
2876 101100111100
2887 101101000111
2891 101101001011
2893 101101001101
2894 101101001110
2899 101101010011
2901 101101010101 2901 Lydian Augmented
2902 101101010110
2905 101101011001
2906 101101011010
2908 101101011100
2915 101101100011
2917 101101100101 2917 Nohkan Flute Scale
2918 101101100110
2921 101101101001
2922 101101101010
2924 101101101100
2929 101101110001 2929 Aeolathian
2930 101101110010
2932 101101110100
2936 101101111000
2951 101110000111
2955 101110001011 2955 Thorian
2957 101110001101 2957 Thygian
2958 101110001110
2963 101110010011 2963 Bygian
2965 101110010101 2965 Darian
2966 101110010110
2969 101110011001 2969 Tholian
2970 101110011010
2972 101110011100
2979 101110100011
2981 101110100101 2981 Ionolian
2982 101110100110
2985 101110101001
2986 101110101010
2988 101110101100
2993 101110110001 2993 Stythian
2994 101110110010
2996 101110110100
3000 101110111000
3011 101111000011
3013 101111000101 3013 Thynian
3014 101111000110
3017 101111001001 3017 Gacrian
3018 101111001010
3020 101111001100
3025 101111010001
3026 101111010010
3028 101111010100
3032 101111011000
3041 101111100001
3042 101111100010
3044 101111100100
3048 101111101000
3056 101111110000
3103 110000011111
3119 110000101111
3127 110000110111
3131 110000111011
3133 110000111101
3134 110000111110
3151 110001001111 3151 Pacrian
3159 110001010111 3159 Stocrian
3163 110001011011 3163 Rogian
3165 110001011101 3165 Mylian
3166 110001011110
3175 110001100111 3175 Eponian
3179 110001101011 3179 Daptian
3181 110001101101 3181 Rolian
3182 110001101110
3187 110001110011 3187 Koptian
3189 110001110101 3189 Aeolonian
3190 110001110110
3193 110001111001
3194 110001111010
3196 110001111100
3215 110010001111
3223 110010010111 3223 Thyphian
3227 110010011011 3227 Aeolocrian
3229 110010011101 3229 Aeolaptian
3230 110010011110
3239 110010100111 3239 Mela Tanarupi
3243 110010101011 3243 Mela Rupavati
3245 110010101101 3245 Mela Varunapriya
3246 110010101110
3251 110010110011 3251 Mela Hatakambari
3253 110010110101 3253 Mela Naganandini
3254 110010110110
3257 110010111001 3257 Mela Calanata
3258 110010111010
3260 110010111100
3271 110011000111
3275 110011001011 3275 Mela Divyamani
3277 110011001101 3277 Mela Nitimati
3278 110011001110
3283 110011010011
3285 110011010101 3285 Mela Citrambari
3286 110011010110
3289 110011011001 3289 Lydian Sharp 2 Sharp 6
3290 110011011010
3292 110011011100
3299 110011100011
3301 110011100101 3301 Chromatic Mixolydian Inverse
3302 110011100110
3305 110011101001
3306 110011101010
3308 110011101100
3313 110011110001 3313 Aeolacrian
3314 110011110010
3316 110011110100
3320 110011111000
3343 110100001111
3351 110100010111 3351 Crater Scale
3355 110100011011
3357 110100011101
3358 110100011110
3367 110100100111
3371 110100101011 3371 Aeolylian
3373 110100101101 3373 Lodian
3374 110100101110
3379 110100110011
3381 110100110101
3382 110100110110
3385 110100111001
3386 110100111010
3388 110100111100
3399 110101000111
3403 110101001011
3405 110101001101
3406 110101001110
3411 110101010011
3413 110101010101 3413 Leading Whole-tone
3414 110101010110
3417 110101011001
3418 110101011010
3420 110101011100
3427 110101100011
3429 110101100101 3429 Marian
3430 110101100110
3433 110101101001
3434 110101101010
3436 110101101100
3441 110101110001 3441 Thacrian
3442 110101110010
3444 110101110100
3448 110101111000
3463 110110000111
3467 110110001011 3467 Sudhvidhamagini
3469 110110001101 3469 Monian
3470 110110001110
3475 110110010011
3477 110110010101 3477 Kyptian
3478 110110010110
3481 110110011001
3482 110110011010
3484 110110011100
3491 110110100011
3493 110110100101
3494 110110100110
3497 110110101001
3498 110110101010
3500 110110101100
3505 110110110001
3506 110110110010
3508 110110110100
3512 110110111000
3523 110111000011
3525 110111000101 3525 Zocrian
3526 110111000110
3529 110111001001 3529 Stalian
3530 110111001010
3532 110111001100
3537 110111010001
3538 110111010010
3540 110111010100
3544 110111011000
3553 110111100001
3554 110111100010
3556 110111100100
3560 110111101000
3568 110111110000
3599 111000001111
3607 111000010111
3611 111000011011
3613 111000011101
3614 111000011110
3623 111000100111 3623 Aerocrian
3627 111000101011 3627 Kalian
3629 111000101101 3629 Boptian
3630 111000101110
3635 111000110011 3635 Katygian
3637 111000110101 3637 Raga Rageshri
3638 111000110110
3641 111000111001 3641 Thocrian
3642 111000111010
3644 111000111100
3655 111001000111
3659 111001001011 3659 Polian
3661 111001001101 3661 Mixodorian
3662 111001001110
3667 111001010011 3667 Kaptian
3669 111001010101 3669 Mothian
3670 111001010110
3673 111001011001 3673 Ranian
3674 111001011010
3676 111001011100
3683 111001100011
3685 111001100101 3685 Kodian
3686 111001100110
3689 111001101001
3690 111001101010
3692 111001101100
3697 111001110001
3698 111001110010
3700 111001110100
3704 111001111000
3719 111010000111
3723 111010001011 3723 Myptian
3725 111010001101
3726 111010001110
3731 111010010011
3733 111010010101 3733 Gycrian
3734 111010010110
3737 111010011001
3738 111010011010
3740 111010011100
3747 111010100011
3749 111010100101
3750 111010100110
3753 111010101001
3754 111010101010
3756 111010101100
3761 111010110001
3762 111010110010
3764 111010110100
3768 111010111000
3779 111011000011
3781 111011000101 3781 Gyphian
3782 111011000110
3785 111011001001
3786 111011001010
3788 111011001100
3793 111011010001
3794 111011010010
3796 111011010100
3800 111011011000
3809 111011100001
3810 111011100010
3812 111011100100
3816 111011101000
3824 111011110000
3847 111100000111
3851 111100001011
3853 111100001101
3854 111100001110
3859 111100010011 3859 Aeolarian
3861 111100010101 3861 Phroptian
3862 111100010110
3865 111100011001 3865 Starian
3866 111100011010
3868 111100011100
3875 111100100011
3877 111100100101 3877 Thanian
3878 111100100110
3881 111100101001 3881 Morian
3882 111100101010
3884 111100101100
3889 111100110001
3890 111100110010
3892 111100110100
3896 111100111000
3907 111101000011
3909 111101000101 3909 Rydian
3910 111101000110
3913 111101001001
3914 111101001010
3916 111101001100
3921 111101010001
3922 111101010010
3924 111101010100
3928 111101011000
3937 111101100001
3938 111101100010
3940 111101100100
3944 111101101000
3952 111101110000
3971 111110000011
3973 111110000101
3974 111110000110
3977 111110001001 3977 Kythian
3978 111110001010
3980 111110001100
3985 111110010001
3986 111110010010
3988 111110010100
3992 111110011000
4001 111110100001
4002 111110100010
4004 111110100100
4008 111110101000
4016 111110110000
4033 111111000001
4034 111111000010
4036 111111000100
4040 111111001000
4048 111111010000
4064 111111100000

Any "scale" that has an even number in your list lacks the tonic and therefore does not qualify as a scale according to Ian Ring. So you should keep only odd-numbered scales.

Next, if you are interested in music rather than math, you may want to restrict this set further by limiting the number of consecutive half-steps, and also the maximum interval between consecutive notes.

Here is what you get: (heptatonic scales only)
1. No consecutive half-steps, maximum interval = 2 half-steps.
You have 2 scales (and their modes): Major (1 2 3 4 5 6 7), Melodic minor (1 2 b3 4 5 6 7)

2. No consecutive half-steps, maximum interval = 3 half steps.
You have 2 more scales (and their modes): Harmonic minor (1 2 b 3 4 5 b6 7), Harmonic major (1 2 3 4 5 b6 7).

3. Up to 2 consecutive half-steps, maximum interval = 2 half steps.
You get 1 more scale (and its modes): Whole tone scale with leading tone (1 2 3 #4 b6 b7 7)

4. Up to 2 consecutive half-steps, maximum interval = 3 half-steps.
You get 4 more scales (and their modes): Harmonic minor b2 (1 b2 b3 4 5 b6 7), double harmonic (1 b2 3 4 5 b6 7), melodic minor bebop without 2 (1 b3 4 5 b6 6 7), aeolian bebop without 2 (1 b3 4 5 b6 b7 7).

5. Up to 2 consecutive half-steps, maximum interval = 4 half-steps.
You get 1 more scale: bebop major without 2 (1 3 4 5 b6 6 7).

For me, there is no need to consider more scales. You will notice that the more you go down the list, the less used the scales are.

 

[IamGroot]

Any "scale" that has an even number in your list lacks the tonic and therefore does not qualify as a scale according to Ian Ring. So you should keep only odd-numbered scales.

Next, if you are interested in music rather than math, you may want to restrict this set further by limiting the number of consecutive half-steps, and also the maximum interval between consecutive notes.

Here is what you get: (heptatonic scales only)
1. No consecutive half-steps, maximum interval = 2 half-steps.
You have 2 scales (and their modes): Major (1 2 3 4 5 6 7), Melodic minor (1 2 b3 4 5 6 7)

2. No consecutive half-steps, maximum interval = 3 half steps.
You have 2 more scales (and their modes): Harmonic minor (1 2 b 3 4 5 b6 7), Harmonic major (1 2 3 4 5 b6 7).

3. Up to 2 consecutive half-steps, maximum interval = 2 half steps.
You get 1 more scale (and its modes): Whole tone scale with leading tone (1 2 3 #4 b6 b7 7)

4. Up to 2 consecutive half-steps, maximum interval = 3 half-steps.
You get 4 more scales (and their modes): Harmonic minor b2 (1 b2 b3 4 5 b6 7), double harmonic (1 b2 3 4 5 b6 7), melodic minor bebop without 2 (1 b3 4 5 b6 6 7), aeolian bebop without 2 (1 b3 4 5 b6 b7 7).

5. Up to 2 consecutive half-steps, maximum interval = 4 half-steps.
You get 1 more scale: bebop major without 2 (1 3 4 5 b6 6 7).

For me, there is no need to consider more scales. You will notice that the more you go down the list, the less used the scales are.

Exactly. Basically your 5 points are what I rediscovered on my own. There are actually very few "useable"" scales out of 792 heptatonic. Maybe 70 you would recognize. . And 7 of them are the ones we use frequently. Maybe not even that if you play country.

 

[Evilheim]

Exactly. Basically your 5 points are what I rediscovered on my own. There are actually very few "useable"" scales out of 792 heptatonic. Maybe 70 you would recognize. . And 7 of them are the ones we use frequently. Maybe not even that if you play country.

That was exactly what I was trying to say althought is quite interesting to organize scales and find the relations between them but we forget to relate all of that to their relative musical lenguage. we won't see any country song using a chord progression based for example on the Locrian Dominant scale. But you would find exotic scales on for example Jazz-fusion music, but used on a more experimental fashion.

In other words, in order to use exotic scales you need to know the musical language of those certain scales, or, but more difficult, to understand first functional harmony quite well to then, "break the law" find a way to play coherently with those new tensions from those scales.

That also apply for octotonic scales, like bebop, you can use one of them and play with extra-note as a new tension.

 

[Bob_Ross]

if you are interested in music rather than math, you may want to restrict this set further by limiting the number of consecutive half-steps, and also the maximum interval between consecutive notes.

I would vociferously argue that one can indeed create engaging music using pitch collections that don't limit the number of consecutive half-steps and/or the maximum interval between consecutive notes.

Most of those collections won't be pitch-class collections (as you'll quickly exceed the octave if your collection includes more than a tiny handful of wide interval steps between consecutive pitches) and so can't be properly categorized as "scales" ...but to dismiss them as "unmusical" would be presumtuous or short-sighted.

 

[IamGroot]

I listen to a lot of scales, try to put them in a framework that I can memorize and recall as needed and sneak em in on the fills on a blues gig and act like nothing happened once that acoustic fart has launched.

 

[Papageno]

I would vociferously argue that one can indeed create engaging music using pitch collections that don't limit the number of consecutive half-steps and/or the maximum interval between consecutive notes.

Most of those collections won't be pitch-class collections (as you'll quickly exceed the octave if your collection includes more than a tiny handful of wide interval steps between consecutive pitches) and so can't be properly categorized as "scales" ...but to dismiss them as "unmusical" would be presumtuous or short-sighted.

Sure you're right that one can make interesting music out of any set of pitches. I did not intend to dismiss any kind of music.

Yet, when making music, you usually make stylistic choices, but these choices are highly personnal. That's why I wrote "You may want to restrict...".

This is different if your intention is to perform a comprehensive classication of the scales, without actually using them for creating music.

 

[IamGroot]

Sure you're right that one can make interesting music out of any set of pitches. I did not intend to dismiss any kind of music.

Yet, when making music, you usually make stylistic choices, but these choices are highly personnal. That's why I wrote "You may want to restrict...".

This is different if your intention is to perform a comprehensive classication of the scales, without actually using them for creating music.

Like a lunch and learn seminar for mathematicians with free pizza?

 

[GoesThump]

Like a lunch and learn seminar for mathematicians with free pizza?

My ex was a mathematician.

Take my advice on this one : don't. To us, it's pizza. To them? An invitation to an endless series of pi jokes.

... don't say I didn't warn you.

GT

 

[IamGroot]

My ex was a mathematician.

Take my advice on this one : don't. To us, it's pizza. To them? An invitation to an endless series of pi jokes.

... don't say I didn't warn you.

GT

On long car trips, I make my wife listen to endless facts about Pi.

So the set of all Real numbers can be broken down into two categories; Rational and Irrational. Rational numbers can be expressed as the ration of two integers and irrationals can't. It turns out that there are way more irrational numbers than rational numbers because irrationals contain a special set of numbers called transcendental numbers that can not be put into one-to-one correspondence with the integers. Transcendentals include Pi. The guy who figured all this out died in an insane asylum.

Invalid Link Removed

 

[SteveCS]

I listen to a lot of scales, try to put them in a framework that I can memorize and recall as needed and sneak em in on the fills on a blues gig and act like nothing happened once that acoustic fart has launched.

Somewhere in there is an accidental band name, or at least an album title. Maybe even both ^^

 

[IamGroot]

Somewhere in there is an accidental band name, or at least an album title. Maybe even both ^^

Accidental Band Name? How about Cbb

 

[IamGroot]

I apologize for not warning folks about an important detail.

When you read a scale as a binary, you read from right to left, not right to left. That may have confused some of you, and I am sorry for that.

As an example, for Dorian = 1709, the binary is 0 1 1 0 1 0 1 0 1 1 0 1
But, reading from right to left, its 1 0 1 1 0 1 0 1 0 1 1 0 = 1 2 b3 4 5 6 b7 = WHWWWHW.

 

[mambo4]

Here is every one of those 792 Heptatonic scales.

Liking just because you actually posted all of them.
For me this is certainly a case of interesting > useful

"how any combinations of 7 out of 12 half steps are there?" is a mathematical question
But when we start discussing "which ones are actually useful, and what qualities do they share?" it gets more fun and practical

 

[IamGroot]

Liking just because you actually posted all of them.
For me this is certainly a case of interesting > useful

"how any combinations of 7 out of 12 half steps are there?" is a mathematical question
But when we start discussing "which ones are actually useful, and what qualities do they share?" it gets more fun and practical

Less than 10% of the possibilities for 7 notes sound good to my ears. I will post the full picture for all the scales later, but right now, I am buying more rent houses plus had a tenant sneak out on me and am doing a 4 day turnaround. Plus drafting a contract for fencing .