Compound Scales

I was inspired by one of Rich Cochrane's books, where he lists many scales with names that are a compound of two or more common triads or seventh chords. But it seemed like Cochrane was pragmatic, only using the compound formulas when there was no other traditional scale name to call upon. What a missed opportunity.

I figured, with my scale computation software wouldn't it be easy for me to generate the complete collection of all scales that could be represented as a union of two common chords?

The methodology was simple, because the problem space was relatively small and computable. I started by defining the following chord patterns:

chord	pattern	symbol
major triad	{0,4,7}	1MA
minor triad	{0,3,7}	1MI
diminished triad	{0,3,6}	1◦
augmented triad	{0,4,8}	1+
sus4 triad	{0,5,7}	1SUS4
dominant seventh	{0,4,7,10}	17
diminished seventh	{0,3,6,9}	1◦7
half-diminished seventh	{0,3,6,10}	1∅7
major seventh.	{0,4,7,11}	1∆7

Then I generated the binary mask for those patterns on every scale degree from 0 to 11. Then I nested two loops through each list, and observed every combination. I threw out any combinations that did not have a root tone on 0, and discarded any where the two ingredients collided. Then I passed through all the results and removed obvious duplicates. For example, order doesn't matter: "1◦ & ♭2◦" is the same as "♭2◦ & 1◦". Then removed more duplications where the same diminished sevenths appeared 4 times, and augmented triads appeared 3 times. Unsurprisingly, many pitch class sets can be constructed in multiple ways.

Cochrane's scale list includes a few that are made from 3 ingredients, but I thought for this experiment it should suffice to stop at two.

Chords are indicated here using typical jazz chart symbolism, with "black key" tonics as flat alterations of the major diatonic. For example, the pitch class 1 is called "2"

Keeners will be thrilled to know that if I allowed tone collisions, there are 715 scales that can be created, via 2015 unique chord combinations. Removing the combinations where tones collide, the numbers are lower: 421 scales, created in 746 ways. Looking at which scales can be built the most number of ways: In the former list where collisions were allowed, there were two scales that could be built in 13 different ways! They were scales 819 and 2457. It should be unsurprising that these two scales are modes of each other, seeing as the species of chord ingredients are invariant under rotation (same chords, but rooted on different tones).

In the latter list without collisions, there are 16 scales tied for first place with 5 different chord combinations. They comprise two families, Forte classes 7-32 and 8-28:

(along with all their rotations and reflections)

Here are the results. I'm publishing the list with no tone collisions, because it's a more manageable size and I think it's more interesting.

Combined Scale Number	Combined Scale Bracelet	Name	Ingredient 1	Ingredient 2
219		1◦ & ♭2◦	1◦	♭2◦
347		1◦ & ♭2MI	1◦	♭2MI
363		1◦ & ♭2MA	1◦	♭2MA
365		1◦ & 2◦	1◦	2◦
399		5SUS4 & ♭6SUS4	5SUS4	♭6SUS4
407		5SUS4 & ♭2MI	5SUS4	♭2MI
411		1MA & ♭6SUS4	1MA	♭6SUS4
		1MI & ♭2MI	1MI	♭2MI
		♭2◦ & ♭6MA	♭2◦	♭6MA
423		5SUS4 & ♭2MA	5SUS4	♭2MA
427		1MI & ♭2MA	1MI	♭2MA
		1SUS4 & ♭6SUS4	1SUS4	♭6SUS4
429		1MI & 2◦	1MI	2◦
435		1MA & ♭2MA	1MA	♭2MA
		1SUS4 & ♭2MI	1SUS4	♭2MI
		4MI & ♭2◦	4MI	♭2◦
437		1MA & 2◦	1MA	2◦
439		2∅7 & ♭2◦	2∅7	♭2◦
455		5SUS4 & ♭2SUS4	5SUS4	♭2SUS4
459		1MI & ♭2SUS4	1MI	♭2SUS4
467		1MA & ♭2SUS4	1MA	♭2SUS4
475		♭2◦ & ♭67	♭2◦	♭67
483		1SUS4 & ♭2SUS4	1SUS4	♭2SUS4
603		1◦ & 6MA	1◦	6MA
605		1◦ & 6SUS4	1◦	6SUS4
619		1◦ & ♭2+	1◦	♭2+
621		1◦ & 2MI	1◦	2MI
663		5SUS4 & 6MA	5SUS4	6MA
667		1MI & 6MA	1MI	6MA
		6◦ & ♭2◦	6◦	♭2◦
669		1MI & 6SUS4	1MI	6SUS4
679		5SUS4 & ♭2+	5SUS4	♭2+
683		1MI & ♭2+	1MI	♭2+
685		1MI & 2MI	1MI	2MI
691		1MA & ♭2+	1MA	♭2+
		1SUS4 & 6MA	1SUS4	6MA
		4MA & ♭2◦	4MA	♭2◦
693		1MA & 2MI	1MA	2MI
		1SUS4 & 6SUS4	1SUS4	6SUS4
699		47 & ♭2◦	47	♭2◦
711		5SUS4 & ♭5MI	5SUS4	♭5MI
715		1MI & ♭5MI	1MI	♭5MI
717		1MI & 2MA	1MI	2MA
		1◦ & 2SUS4	1◦	2SUS4
		5SUS4 & ♭3◦	5SUS4	♭3◦
719		1MI & 2∆7	1MI	2∆7
		5SUS4 & ♭3∅7	5SUS4	♭3∅7
723		1MA & ♭5MI	1MA	♭5MI
		♭2◦ & ♭5◦	♭2◦	♭5◦
725		1MA & 2MA	1MA	2MA
727		1MA & 2∆7	1MA	2∆7
		27 & ♭2◦	27	♭2◦
729		1MA & ♭3◦	1MA	♭3◦
731		1MA & ♭3∅7	1MA	♭3∅7
		1◦ & 67	1◦	67
		1◦7 & ♭2◦	1◦7	♭2◦
739		1SUS4 & ♭5MI	1SUS4	♭5MI
741		1SUS4 & 2MA	1SUS4	2MA
743		1SUS4 & 2∆7	1SUS4	2∆7
745		1SUS4 & ♭3◦	1SUS4	♭3◦
747		1SUS4 & ♭3∅7	1SUS4	♭3∅7
795		6◦ & ♭2MI	6◦	♭2MI
		6MA & ♭6MA	6MA	♭6MA
		6MI & ♭6SUS4	6MI	♭6SUS4
797		6SUS4 & ♭6MA	6SUS4	♭6MA
811		6◦ & ♭2MA	6◦	♭2MA
		♭2+ & ♭6MA	♭2+	♭6MA
		4MA & ♭6SUS4	4MA	♭6SUS4
813		2MI & ♭6MA	2MI	♭6MA
		2◦ & 6◦	2◦	6◦
819		1+ & ♭2+	1+	♭2+
		6MI & ♭2MA	6MI	♭2MA
		4MA & ♭2MI	4MA	♭2MI
		4MI & 6MA	4MI	6MA
821		1+ & 2MI	1+	2MI
		2◦ & 6MI	2◦	6MI
		4MI & 6SUS4	4MI	6SUS4
823		6SUS4 & ♭2∆7	6SUS4	♭2∆7
		2∅7 & 6MA	2∅7	6MA
827		47 & ♭2MI	47	♭2MI
		4∆7 & ♭6SUS4	4∆7	♭6SUS4
843		6◦ & ♭2SUS4	6◦	♭2SUS4
		♭5MI & ♭6MA	♭5MI	♭6MA
		♭5◦ & ♭6SUS4	♭5◦	♭6SUS4
845		2MA & ♭6MA	2MA	♭6MA
847		2∆7 & ♭6MA	2∆7	♭6MA
		27 & ♭6SUS4	27	♭6SUS4
851		1+ & ♭5MI	1+	♭5MI
		♭2MI & ♭5◦	♭2MI	♭5◦
		6MI & ♭2SUS4	6MI	♭2SUS4
853		1+ & 2MA	1+	2MA
855		1+ & 2∆7	1+	2∆7
		27 & ♭2MI	27	♭2MI
857		1+ & ♭3◦	1+	♭3◦
859		1+ & ♭3∅7	1+	♭3∅7
		1◦ & 6∆7	1◦	6∆7
		1◦7 & ♭2MI	1◦7	♭2MI
		♭5∅7 & ♭6SUS4	♭5∅7	♭6SUS4
		6MA & ♭67	6MA	♭67
861		6SUS4 & ♭67	6SUS4	♭67
867		♭2MA & ♭5◦	♭2MA	♭5◦
		4MA & ♭2SUS4	4MA	♭2SUS4
		4MI & ♭5MI	4MI	♭5MI
869		2MA & 4MI	2MA	4MI
		2◦ & ♭5◦	2◦	♭5◦
871		27 & ♭2MA	27	♭2MA
		2MA & ♭2∆7	2MA	♭2∆7
		2∆7 & 4MI	2∆7	4MI
		2∅7 & ♭5MI	2∅7	♭5MI
873		4MI & ♭3◦	4MI	♭3◦
875		1◦7 & ♭2MA	1◦7	♭2MA
		♭2+ & ♭67	♭2+	♭67
		47 & ♭2SUS4	47	♭2SUS4
		♭2∆7 & ♭3◦	♭2∆7	♭3◦
		4MI & ♭3∅7	4MI	♭3∅7
877		1◦7 & 2◦	1◦7	2◦
		2MI & ♭67	2MI	♭67
		2∅7 & ♭3◦	2∅7	♭3◦
879		2∅7 & ♭3∅7	2∅7	♭3∅7
883		♭2MA & ♭5∅7	♭2MA	♭5∅7
		4∆7 & ♭2SUS4	4∆7	♭2SUS4
885		2◦ & ♭5∅7	2◦	♭5∅7
909		2SUS4 & ♭6MA	2SUS4	♭6MA
917		1+ & 2SUS4	1+	2SUS4
919		5SUS4 & 6∆7	5SUS4	6∆7
923		1MI & 6∆7	1MI	6∆7
		6∅7 & ♭2MI	6∅7	♭2MI
		67 & ♭6MA	67	♭6MA
		6MA & ♭6∆7	6MA	♭6∆7
925		6SUS4 & ♭6∆7	6SUS4	♭6∆7
933		2SUS4 & 4MI	2SUS4	4MI
935		2SUS4 & ♭2∆7	2SUS4	♭2∆7
939		6∅7 & ♭2MA	6∅7	♭2MA
		♭2+ & ♭6∆7	♭2+	♭6∆7
941		2MI & ♭6∆7	2MI	♭6∆7
		2◦ & 6∅7	2◦	6∅7
947		1SUS4 & 6∆7	1SUS4	6∆7
		4MI & 67	4MI	67
951		2∅7 & 67	2∅7	67
971		6∅7 & ♭2SUS4	6∅7	♭2SUS4
		♭5MI & ♭6∆7	♭5MI	♭6∆7
973		2MA & ♭6∆7	2MA	♭6∆7
		2SUS4 & ♭67	2SUS4	♭67
975		2∆7 & ♭6∆7	2∆7	♭6∆7
987		67 & ♭67	67	♭67
1115		1◦ & ♭7◦	1◦	♭7◦
1131		1◦ & ♭7MI	1◦	♭7MI
1133		1◦ & ♭7MA	1◦	♭7MA
1175		5SUS4 & ♭7◦	5SUS4	♭7◦
1179		1MI & ♭7◦	1MI	♭7◦
1191		5SUS4 & ♭7MI	5SUS4	♭7MI
1195		1MI & ♭7MI	1MI	♭7MI
1197		1MI & ♭7MA	1MI	♭7MA
		5SUS4 & ♭7SUS4	5SUS4	♭7SUS4
1203		1MA & ♭7MI	1MA	♭7MI
		1SUS4 & ♭7◦	1SUS4	♭7◦
		4SUS4 & ♭2◦	4SUS4	♭2◦
1205		1MA & ♭7MA	1MA	♭7MA
1209		1MA & ♭7SUS4	1MA	♭7SUS4
1223		5SUS4 & ♭5MA	5SUS4	♭5MA
1227		1MI & ♭5MA	1MI	♭5MA
		1◦ & 5◦	1◦	5◦
1229		1MI & 2+	1MI	2+
		1◦ & 5MI	1◦	5MI
		5SUS4 & ♭3MI	5SUS4	♭3MI
1235		1MA & ♭5MA	1MA	♭5MA
1237		1MA & 2+	1MA	2+
1239		5SUS4 & ♭57	5SUS4	♭57
1241		1MA & ♭3MI	1MA	♭3MI
		1◦ & 3◦	1◦	3◦
1243		1MI & ♭57	1MI	♭57
		1◦ & ♭2◦7	1◦	♭2◦7
		1∅7 & ♭2◦	1∅7	♭2◦
1245		1◦ & 3∅7	1◦	3∅7
1251		1SUS4 & ♭5MA	1SUS4	♭5MA
1253		1SUS4 & 2+	1SUS4	2+
1255		5SUS4 & ♭5∆7	5SUS4	♭5∆7
1257		1SUS4 & ♭3MI	1SUS4	♭3MI
1259		1MI & ♭5∆7	1MI	♭5∆7
		1◦ & 5∅7	1◦	5∅7
1267		1MA & ♭5∆7	1MA	♭5∆7
		1SUS4 & ♭57	1SUS4	♭57
1307		♭6MA & ♭7◦	♭6MA	♭7◦
1323		4SUS4 & ♭6SUS4	4SUS4	♭6SUS4
		♭6MA & ♭7MI	♭6MA	♭7MI
1325		♭6MA & ♭7MA	♭6MA	♭7MA
1331		1+ & ♭7MI	1+	♭7MI
		4SUS4 & ♭2MI	4SUS4	♭2MI
		4MI & ♭7◦	4MI	♭7◦
1333		1+ & ♭7MA	1+	♭7MA
1335		2∅7 & ♭7◦	2∅7	♭7◦
1337		1+ & ♭7SUS4	1+	♭7SUS4
1355		♭5MA & ♭6MA	♭5MA	♭6MA
1357		2+ & ♭6MA	2+	♭6MA
1363		1+ & ♭5MA	1+	♭5MA
1365		1+ & 2+	1+	2+
1369		1+ & ♭3MI	1+	♭3MI
1371		1◦ & ♭7∅7	1◦	♭7∅7
		1∅7 & ♭2MI	1∅7	♭2MI
		♭57 & ♭6MA	♭57	♭6MA
		♭67 & ♭7◦	♭67	♭7◦
1379		4SUS4 & ♭2SUS4	4SUS4	♭2SUS4
		4MI & ♭5MA	4MI	♭5MA
1381		2+ & 4MI	2+	4MI
1383		2+ & ♭2∆7	2+	♭2∆7
		2∅7 & ♭5MA	2∅7	♭5MA
1385		4MI & ♭3MI	4MI	♭3MI
1387		1∅7 & ♭2MA	1∅7	♭2MA
		♭2∆7 & ♭3MI	♭2∆7	♭3MI
		♭5∆7 & ♭6MA	♭5∆7	♭6MA
		♭67 & ♭7MI	♭67	♭7MI
1389		1◦ & ♭77	1◦	♭77
		1∅7 & 2◦	1∅7	2◦
		2∅7 & ♭3MI	2∅7	♭3MI
		♭67 & ♭7MA	♭67	♭7MA
1395		1+ & ♭5∆7	1+	♭5∆7
		4MI & ♭57	4MI	♭57
1399		2∅7 & ♭57	2∅7	♭57
1419		5◦ & ♭6MA	5◦	♭6MA
1421		5SUS4 & ♭3SUS4	5SUS4	♭3SUS4
		5MI & ♭6MA	5MI	♭6MA
1427		1+ & 5◦	1+	5◦
1429		1+ & 5MI	1+	5MI
1431		5SUS4 & ♭7∅7	5SUS4	♭7∅7
1433		1MA & ♭3SUS4	1MA	♭3SUS4
		1+ & ♭3MA	1+	♭3MA
		3◦ & ♭6MA	3◦	♭6MA
1435		1MI & ♭7∅7	1MI	♭7∅7
		1+ & ♭37	1+	♭37
		17 & ♭6SUS4	17	♭6SUS4
		♭2◦7 & ♭6MA	♭2◦7	♭6MA
		♭6∆7 & ♭7◦	♭6∆7	♭7◦
1437		1+ & ♭3∆7	1+	♭3∆7
		3∅7 & ♭6MA	3∅7	♭6MA
1443		4MI & 5◦	4MI	5◦
1445		4MI & 5MI	4MI	5MI
1447		5MI & ♭2∆7	5MI	♭2∆7
		2∅7 & 5◦	2∅7	5◦
1449		1SUS4 & ♭3SUS4	1SUS4	♭3SUS4
		4MI & ♭3MA	4MI	♭3MA
1451		♭2∆7 & ♭3MA	♭2∆7	♭3MA
		4MI & ♭37	4MI	♭37
		5∅7 & ♭6MA	5∅7	♭6MA
		♭6∆7 & ♭7MI	♭6∆7	♭7MI
1453		1MI & ♭77	1MI	♭77
		2∅7 & ♭3MA	2∅7	♭3MA
		4MI & ♭3∆7	4MI	♭3∆7
		♭6∆7 & ♭7MA	♭6∆7	♭7MA
1455		♭2∆7 & ♭3∆7	♭2∆7	♭3∆7
		2∅7 & ♭37	2∅7	♭37
1457		3◦ & 4MI	3◦	4MI
1459		1+ & 5∅7	1+	5∅7
		1SUS4 & ♭7∅7	1SUS4	♭7∅7
		17 & ♭2MA	17	♭2MA
		3◦ & ♭2∆7	3◦	♭2∆7
		4MI & ♭2◦7	4MI	♭2◦7
1461		1MA & ♭77	1MA	♭77
		17 & 2◦	17	2◦
		2∅7 & 3◦	2∅7	3◦
		3∅7 & 4MI	3∅7	4MI
1463		3∅7 & ♭2∆7	3∅7	♭2∆7
		2∅7 & ♭2◦7	2∅7	♭2◦7
1483		♭5MA & ♭6∆7	♭5MA	♭6∆7
		5◦ & ♭67	5◦	♭67
1485		2+ & ♭6∆7	2+	♭6∆7
		5MI & ♭67	5MI	♭67
1491		17 & ♭2SUS4	17	♭2SUS4
1497		3◦ & ♭67	3◦	♭67
1499		♭2◦7 & ♭67	♭2◦7	♭67
		♭57 & ♭6∆7	♭57	♭6∆7
1501		3∅7 & ♭67	3∅7	♭67
1515		♭5∆7 & ♭6∆7	♭5∆7	♭6∆7
		5∅7 & ♭67	5∅7	♭67
1563		6◦ & ♭7◦	6◦	♭7◦
1579		6◦ & ♭7MI	6◦	♭7MI
1581		6◦ & ♭7MA	6◦	♭7MA
1587		4MA & ♭7◦	4MA	♭7◦
		4SUS4 & 6MA	4SUS4	6MA
		6MI & ♭7MI	6MI	♭7MI
1589		4SUS4 & 6SUS4	4SUS4	6SUS4
		6MI & ♭7MA	6MI	♭7MA
1593		6MI & ♭7SUS4	6MI	♭7SUS4
1595		47 & ♭7◦	47	♭7◦
1611		6◦ & ♭5MA	6◦	♭5MA
1613		2+ & 6◦	2+	6◦
1619		6MI & ♭5MA	6MI	♭5MA
		♭5◦ & ♭7◦	♭5◦	♭7◦
1621		2+ & 6MI	2+	6MI
1623		27 & ♭7◦	27	♭7◦
1625		6MI & ♭3MI	6MI	♭3MI
1627		1∅7 & 6MA	1∅7	6MA
		1◦7 & ♭7◦	1◦7	♭7◦
		6◦ & ♭57	6◦	♭57
1629		1∅7 & 6SUS4	1∅7	6SUS4
1635		4MA & ♭5MA	4MA	♭5MA
		4SUS4 & ♭5MI	4SUS4	♭5MI
		♭5◦ & ♭7MI	♭5◦	♭7MI
1637		2MA & 4SUS4	2MA	4SUS4
		2+ & 4MA	2+	4MA
		♭5◦ & ♭7MA	♭5◦	♭7MA
1639		2∆7 & 4SUS4	2∆7	4SUS4
		27 & ♭7MI	27	♭7MI
1641		4MA & ♭3MI	4MA	♭3MI
		4SUS4 & ♭3◦	4SUS4	♭3◦
		♭5◦ & ♭7SUS4	♭5◦	♭7SUS4
1643		1∅7 & ♭2+	1∅7	♭2+
		1◦7 & ♭7MI	1◦7	♭7MI
		4SUS4 & ♭3∅7	4SUS4	♭3∅7
		47 & ♭5MA	47	♭5MA
		6◦ & ♭5∆7	6◦	♭5∆7
1645		1◦ & ♭7∆7	1◦	♭7∆7
		1∅7 & 2MI	1∅7	2MI
		1◦7 & ♭7MA	1◦7	♭7MA
		2+ & 47	2+	47
		27 & ♭7SUS4	27	♭7SUS4
1651		4MA & ♭57	4MA	♭57
		4∆7 & ♭5MA	4∆7	♭5MA
		6MI & ♭5∆7	6MI	♭5∆7
		♭5∅7 & ♭7MI	♭5∅7	♭7MI
1653		2+ & 4∆7	2+	4∆7
		♭5∅7 & ♭7MA	♭5∅7	♭7MA
1657		4∆7 & ♭3MI	4∆7	♭3MI
		♭5∅7 & ♭7SUS4	♭5∅7	♭7SUS4
1659		47 & ♭57	47	♭57
1675		5◦ & 6◦	5◦	6◦
1677		5MI & 6◦	5MI	6◦
1683		5◦ & 6MI	5◦	6MI
1685		5MI & 6MI	5MI	6MI
1689		6MI & ♭3MA	6MI	♭3MA
		3◦ & 6◦	3◦	6◦
1691		6◦ & ♭2◦7	6◦	♭2◦7
		6MI & ♭37	6MI	♭37
		6∅7 & ♭7◦	6∅7	♭7◦
1693		6MI & ♭3∆7	6MI	♭3∆7
		3∅7 & 6◦	3∅7	6◦
1699		4MA & 5◦	4MA	5◦
1701		2SUS4 & 4SUS4	2SUS4	4SUS4
		4MA & 5MI	4MA	5MI
1705		4MA & ♭3MA	4MA	♭3MA
1707		4MA & ♭37	4MA	♭37
		47 & 5◦	47	5◦
		5∅7 & 6◦	5∅7	6◦
		6∅7 & ♭7MI	6∅7	♭7MI
1709		1MI & ♭7∆7	1MI	♭7∆7
		4MA & ♭3∆7	4MA	♭3∆7
		47 & 5MI	47	5MI
		6∅7 & ♭7MA	6∅7	♭7MA
1713		3◦ & 4MA	3◦	4MA
1715		17 & ♭2+	17	♭2+
		4MA & ♭2◦7	4MA	♭2◦7
		4SUS4 & 67	4SUS4	67
		4∆7 & 5◦	4∆7	5◦
		5∅7 & 6MI	5∅7	6MI
1717		1MA & ♭7∆7	1MA	♭7∆7
		17 & 2MI	17	2MI
		3∅7 & 4MA	3∅7	4MA
		4∆7 & 5MI	4∆7	5MI
1721		4∆7 & ♭3MA	4∆7	♭3MA
		3◦ & 47	3◦	47
1723		47 & ♭2◦7	47	♭2◦7
		4∆7 & ♭37	4∆7	♭37
1725		4∆7 & ♭3∆7	4∆7	♭3∆7
		3∅7 & 47	3∅7	47
1731		5◦ & ♭5◦	5◦	♭5◦
1733		5MI & ♭5◦	5MI	♭5◦
1735		27 & 5◦	27	5◦
1737		♭3MA & ♭5◦	♭3MA	♭5◦
1739		1◦7 & 5◦	1◦7	5◦
		♭37 & ♭5◦	♭37	♭5◦
		6∅7 & ♭5MA	6∅7	♭5MA
1741		1∅7 & 2SUS4	1∅7	2SUS4
		1◦7 & 5MI	1◦7	5MI
		2+ & 6∅7	2+	6∅7
		27 & ♭3MA	27	♭3MA
		♭3∆7 & ♭5◦	♭3∆7	♭5◦
1743		27 & ♭37	27	♭37
1745		3◦ & ♭5◦	3◦	♭5◦
1747		17 & ♭5MI	17	♭5MI
		♭2◦7 & ♭5◦	♭2◦7	♭5◦
		5◦ & ♭5∅7	5◦	♭5∅7
1749		17 & 2MA	17	2MA
		27 & 3◦	27	3◦
		3∅7 & ♭5◦	3∅7	♭5◦
		5MI & ♭5∅7	5MI	♭5∅7
1751		17 & 2∆7	17	2∆7
		27 & ♭2◦7	27	♭2◦7
1753		17 & ♭3◦	17	♭3◦
		1◦7 & 3◦	1◦7	3◦
		♭3MA & ♭5∅7	♭3MA	♭5∅7
1755		1∅7 & 67	1∅7	67
		17 & ♭3∅7	17	♭3∅7
		1◦7 & ♭2◦7	1◦7	♭2◦7
		♭37 & ♭5∅7	♭37	♭5∅7
		6∅7 & ♭57	6∅7	♭57
1757		1◦7 & 3∅7	1◦7	3∅7
		♭3∆7 & ♭5∅7	♭3∆7	♭5∅7
1763		5∅7 & ♭5◦	5∅7	♭5◦
1767		27 & 5∅7	27	5∅7
1771		1◦7 & 5∅7	1◦7	5∅7
		6∅7 & ♭5∆7	6∅7	♭5∆7
1779		5∅7 & ♭5∅7	5∅7	♭5∅7
1817		6MI & ♭3SUS4	6MI	♭3SUS4
1819		6◦ & ♭7∅7	6◦	♭7∅7
1833		4MA & ♭3SUS4	4MA	♭3SUS4
1837		♭6MA & ♭7∆7	♭6MA	♭7∆7
		6◦ & ♭77	6◦	♭77
1843		4MA & ♭7∅7	4MA	♭7∅7
		4SUS4 & 6∆7	4SUS4	6∆7
1845		1+ & ♭7∆7	1+	♭7∆7
		6MI & ♭77	6MI	♭77
1849		4∆7 & ♭3SUS4	4∆7	♭3SUS4
1851		47 & ♭7∅7	47	♭7∅7
1865		♭3SUS4 & ♭5◦	♭3SUS4	♭5◦
1869		27 & ♭3SUS4	27	♭3SUS4
1875		♭5◦ & ♭7∅7	♭5◦	♭7∅7
1879		27 & ♭7∅7	27	♭7∅7
1881		♭3SUS4 & ♭5∅7	♭3SUS4	♭5∅7
1883		1∅7 & 6∆7	1∅7	6∆7
		1◦7 & ♭7∅7	1◦7	♭7∅7
1893		♭5◦ & ♭77	♭5◦	♭77
1901		1◦7 & ♭77	1◦7	♭77
		♭67 & ♭7∆7	♭67	♭7∆7
1909		♭5∅7 & ♭77	♭5∅7	♭77
1947		6∅7 & ♭7∅7	6∅7	♭7∅7
1965		♭6∆7 & ♭7∆7	♭6∆7	♭7∆7
		6∅7 & ♭77	6∅7	♭77
2157		1◦ & 7◦	1◦	7◦
2221		1MI & 7◦	1MI	7◦
2229		1MA & 7◦	1MA	7◦
2247		5SUS4 & ♭5SUS4	5SUS4	♭5SUS4
2251		1MI & ♭5SUS4	1MI	♭5SUS4
2253		1MI & 7MI	1MI	7MI
		1◦ & 5MA	1◦	5MA
		5SUS4 & 7MA	5SUS4	7MA
2259		1MA & ♭5SUS4	1MA	♭5SUS4
2261		1MA & 7MI	1MA	7MI
		5SUS4 & 7SUS4	5SUS4	7SUS4
2265		1MA & 7MA	1MA	7MA
		1MI & 7SUS4	1MI	7SUS4
		1◦ & 3MI	1◦	3MI
2267		1◦ & ♭2∅7	1◦	♭2∅7
2275		1SUS4 & ♭5SUS4	1SUS4	♭5SUS4
2277		1SUS4 & 7MI	1SUS4	7MI
2281		1SUS4 & 7MA	1SUS4	7MA
2285		1◦ & 57	1◦	57
2289		1SUS4 & 7SUS4	1SUS4	7SUS4
2349		7◦ & ♭6MA	7◦	♭6MA
2357		1+ & 7◦	1+	7◦
2379		♭5SUS4 & ♭6MA	♭5SUS4	♭6MA
2381		1◦ & ♭6◦	1◦	♭6◦
		7MI & ♭6MA	7MI	♭6MA
2387		1+ & ♭5SUS4	1+	♭5SUS4
2389		1+ & 7MI	1+	7MI
2393		1+ & 7MA	1+	7MA
		1◦ & 3MA	1◦	3MA
		7SUS4 & ♭6MA	7SUS4	♭6MA
2397		1◦ & 37	1◦	37
2403		4MI & ♭5SUS4	4MI	♭5SUS4
2405		4MI & 7MI	4MI	7MI
2407		7MI & ♭2∆7	7MI	♭2∆7
		2∅7 & ♭5SUS4	2∅7	♭5SUS4
2409		1◦ & 4◦	1◦	4◦
		4MI & 7MA	4MI	7MA
2411		1◦ & ♭27	1◦	♭27
		7MA & ♭2∆7	7MA	♭2∆7
2413		1◦ & 2◦7	1◦	2◦7
		2∅7 & 7MA	2∅7	7MA
		7◦ & ♭67	7◦	♭67
2417		4MI & 7SUS4	4MI	7SUS4
2419		7SUS4 & ♭2∆7	7SUS4	♭2∆7
2421		2∅7 & 7SUS4	2∅7	7SUS4
2445		1MI & ♭6◦	1MI	♭6◦
		5MA & ♭6MA	5MA	♭6MA
		5SUS4 & ♭6MI	5SUS4	♭6MI
2453		1MA & ♭6◦	1MA	♭6◦
		1+ & 5MA	1+	5MA
		3MA & 5SUS4	3MA	5SUS4
2457		1MA & ♭6MI	1MA	♭6MI
		1MI & 3MA	1MI	3MA
		1+ & ♭3+	1+	♭3+
		3MI & ♭6MA	3MI	♭6MA
2459		1∆7 & ♭6SUS4	1∆7	♭6SUS4
		♭2∅7 & ♭6MA	♭2∅7	♭6MA
2461		1MI & 37	1MI	37
		3∆7 & 5SUS4	3∆7	5SUS4
2469		1SUS4 & ♭6◦	1SUS4	♭6◦
		4MI & 5MA	4MI	5MA
		4◦ & 5SUS4	4◦	5SUS4
2471		5MA & ♭2∆7	5MA	♭2∆7
		5SUS4 & ♭27	5SUS4	♭27
2473		1MI & 4◦	1MI	4◦
		1SUS4 & ♭6MI	1SUS4	♭6MI
		4MI & ♭3+	4MI	♭3+
2475		1MI & ♭27	1MI	♭27
		♭2∆7 & ♭3+	♭2∆7	♭3+
2477		1MI & 2◦7	1MI	2◦7
		2∅7 & ♭3+	2∅7	♭3+
		4∅7 & 5SUS4	4∅7	5SUS4
		57 & ♭6MA	57	♭6MA
		7◦ & ♭6∆7	7◦	♭6∆7
2481		1MA & 4◦	1MA	4◦
		1SUS4 & 3MA	1SUS4	3MA
		3MI & 4MI	3MI	4MI
2483		1MA & ♭27	1MA	♭27
		1∆7 & ♭2MA	1∆7	♭2MA
		3MI & ♭2∆7	3MI	♭2∆7
		4MI & ♭2∅7	4MI	♭2∅7
2485		1MA & 2◦7	1MA	2◦7
		1+ & 57	1+	57
		1SUS4 & 37	1SUS4	37
		1∆7 & 2◦	1∆7	2◦
		2∅7 & 3MI	2∅7	3MI
2487		2∅7 & ♭2∅7	2∅7	♭2∅7
2489		1MA & 4∅7	1MA	4∅7
		1SUS4 & 3∆7	1SUS4	3∆7
2507		♭5SUS4 & ♭6∆7	♭5SUS4	♭6∆7
2509		1MI & ♭6∅7	1MI	♭6∅7
		5MA & ♭67	5MA	♭67
		5∆7 & ♭6MA	5∆7	♭6MA
		7MI & ♭6∆7	7MI	♭6∆7
2515		1∆7 & ♭2SUS4	1∆7	♭2SUS4
2517		1MA & ♭6∅7	1MA	♭6∅7
		1+ & 5∆7	1+	5∆7
2521		3MI & ♭67	3MI	♭67
		7SUS4 & ♭6∆7	7SUS4	♭6∆7
2523		♭2∅7 & ♭67	♭2∅7	♭67
2533		1SUS4 & ♭6∅7	1SUS4	♭6∅7
		4MI & 5∆7	4MI	5∆7
2535		5∆7 & ♭2∆7	5∆7	♭2∆7
2541		57 & ♭67	57	♭67
2605		6◦ & 7◦	6◦	7◦
2613		6MI & 7◦	6MI	7◦
2635		6◦ & ♭5SUS4	6◦	♭5SUS4
2637		6◦ & 7MI	6◦	7MI
2643		6MI & ♭5SUS4	6MI	♭5SUS4
2645		6MI & 7MI	6MI	7MI
2649		1◦ & 3SUS4	1◦	3SUS4
		6MI & 7MA	6MI	7MA
		6◦ & 7SUS4	6◦	7SUS4
2659		4MA & ♭5SUS4	4MA	♭5SUS4
2661		4MA & 7MI	4MA	7MI
		7◦ & ♭5◦	7◦	♭5◦
2665		4MA & 7MA	4MA	7MA
2667		47 & ♭5SUS4	47	♭5SUS4
2669		1◦ & 7∅7	1◦	7∅7
		1◦7 & 7◦	1◦7	7◦
		47 & 7MI	47	7MI
2673		4MA & 7SUS4	4MA	7SUS4
2675		4∆7 & ♭5SUS4	4∆7	♭5SUS4
2677		4∆7 & 7MI	4∆7	7MI
		7◦ & ♭5∅7	7◦	♭5∅7
2681		4∆7 & 7MA	4∆7	7MA
		47 & 7SUS4	47	7SUS4
2701		5MA & 6◦	5MA	6◦
2709		3SUS4 & 5SUS4	3SUS4	5SUS4
		5MA & 6MI	5MA	6MI
2713		1MI & 3SUS4	1MI	3SUS4
		6MI & ♭3+	6MI	♭3+
		3MI & 6◦	3MI	6◦
2715		6◦ & ♭2∅7	6◦	♭2∅7
2725		4MA & 5MA	4MA	5MA
2729		4MA & ♭3+	4MA	♭3+
2733		1MI & 7∅7	1MI	7∅7
		47 & 5MA	47	5MA
		57 & 6◦	57	6◦
		6∅7 & 7◦	6∅7	7◦
2737		1SUS4 & 3SUS4	1SUS4	3SUS4
		3MI & 4MA	3MI	4MA
2739		1∆7 & ♭2+	1∆7	♭2+
		4MA & ♭2∅7	4MA	♭2∅7
2741		1MA & 7∅7	1MA	7∅7
		1∆7 & 2MI	1∆7	2MI
		4∆7 & 5MA	4∆7	5MA
		57 & 6MI	57	6MI
2745		4∆7 & ♭3+	4∆7	♭3+
		3MI & 47	3MI	47
2747		47 & ♭2∅7	47	♭2∅7
2757		5MA & ♭5◦	5MA	♭5◦
2761		♭3+ & ♭5◦	♭3+	♭5◦
2763		6∅7 & ♭5SUS4	6∅7	♭5SUS4
2765		1◦7 & 5MA	1◦7	5MA
		27 & ♭3+	27	♭3+
		5SUS4 & 77	5SUS4	77
		5∆7 & 6◦	5∆7	6◦
		6∅7 & 7MI	6∅7	7MI
2769		3MI & ♭5◦	3MI	♭5◦
2771		1∆7 & ♭5MI	1∆7	♭5MI
		♭2∅7 & ♭5◦	♭2∅7	♭5◦
2773		1∆7 & 2MA	1∆7	2MA
		27 & 3MI	27	3MI
		5MA & ♭5∅7	5MA	♭5∅7
		5∆7 & 6MI	5∆7	6MI
2775		1∆7 & 2∆7	1∆7	2∆7
		27 & ♭2∅7	27	♭2∅7
2777		1MA & 77	1MA	77
		1∆7 & ♭3◦	1∆7	♭3◦
		1◦7 & 3MI	1◦7	3MI
		♭3+ & ♭5∅7	♭3+	♭5∅7
		6∅7 & 7SUS4	6∅7	7SUS4
2779		1∆7 & ♭3∅7	1∆7	♭3∅7
		1◦7 & ♭2∅7	1◦7	♭2∅7
2789		4MA & 5∆7	4MA	5∆7
		57 & ♭5◦	57	♭5◦
2793		1SUS4 & 77	1SUS4	77
2797		1◦7 & 57	1◦7	57
		47 & 5∆7	47	5∆7
2805		4∆7 & 5∆7	4∆7	5∆7
		57 & ♭5∅7	57	♭5∅7
2829		6◦ & ♭6◦	6◦	♭6◦
2837		6MI & ♭6◦	6MI	♭6◦
2841		3MA & 6◦	3MA	6◦
		3SUS4 & ♭6MA	3SUS4	♭6MA
		6MI & ♭6MI	6MI	♭6MI
2845		37 & 6◦	37	6◦
2853		4MA & ♭6◦	4MA	♭6◦
2857		4MA & ♭6MI	4MA	♭6MI
		4◦ & 6◦	4◦	6◦
2859		6◦ & ♭27	6◦	♭27
2861		2◦7 & 6◦	2◦7	6◦
		47 & ♭6◦	47	♭6◦
		7∅7 & ♭6MA	7∅7	♭6MA
2865		3MA & 4MA	3MA	4MA
		3SUS4 & 4MI	3SUS4	4MI
		4◦ & 6MI	4◦	6MI
2867		3SUS4 & ♭2∆7	3SUS4	♭2∆7
		6MI & ♭27	6MI	♭27
2869		1+ & 7∅7	1+	7∅7
		2∅7 & 3SUS4	2∅7	3SUS4
		2◦7 & 6MI	2◦7	6MI
		37 & 4MA	37	4MA
		4∆7 & ♭6◦	4∆7	♭6◦
2873		3MA & 47	3MA	47
		3∆7 & 4MA	3∆7	4MA
		4∆7 & ♭6MI	4∆7	♭6MI
		4∅7 & 6MI	4∅7	6MI
2877		37 & 47	37	47
2885		♭5◦ & ♭6◦	♭5◦	♭6◦
2889		♭5◦ & ♭6MI	♭5◦	♭6MI
2893		1◦7 & ♭6◦	1◦7	♭6◦
		27 & ♭6MI	27	♭6MI
		6◦ & ♭6∅7	6◦	♭6∅7
2897		3MA & ♭5◦	3MA	♭5◦
2901		27 & 3MA	27	3MA
		37 & ♭5◦	37	♭5◦
		♭5∅7 & ♭6◦	♭5∅7	♭6◦
		6MI & ♭6∅7	6MI	♭6∅7
2905		1+ & 77	1+	77
		1◦7 & 3MA	1◦7	3MA
		3SUS4 & ♭67	3SUS4	♭67
		3∆7 & ♭5◦	3∆7	♭5◦
		♭5∅7 & ♭6MI	♭5∅7	♭6MI
2909		1◦7 & 37	1◦7	37
		27 & 3∆7	27	3∆7
2913		4◦ & ♭5◦	4◦	♭5◦
2915		♭27 & ♭5◦	♭27	♭5◦
2917		27 & 4◦	27	4◦
		2◦7 & ♭5◦	2◦7	♭5◦
		4MA & ♭6∅7	4MA	♭6∅7
2919		27 & ♭27	27	♭27
2921		1◦7 & 4◦	1◦7	4◦
		4MI & 77	4MI	77
		4∅7 & ♭5◦	4∅7	♭5◦
2923		1◦7 & ♭27	1◦7	♭27
		77 & ♭2∆7	77	♭2∆7
2925		1◦7 & 2◦7	1◦7	2◦7
		2∅7 & 77	2∅7	77
		27 & 4∅7	27	4∅7
		47 & ♭6∅7	47	♭6∅7
		7∅7 & ♭67	7∅7	♭67
2929		4◦ & ♭5∅7	4◦	♭5∅7
2931		♭27 & ♭5∅7	♭27	♭5∅7
2933		2◦7 & ♭5∅7	2◦7	♭5∅7
		4∆7 & ♭6∅7	4∆7	♭6∅7
2937		4∅7 & ♭5∅7	4∅7	♭5∅7
2957		6∅7 & ♭6◦	6∅7	♭6◦
2969		3MA & 6∅7	3MA	6∅7
		3SUS4 & ♭6∆7	3SUS4	♭6∆7
2973		37 & 6∅7	37	6∅7
2985		4◦ & 6∅7	4◦	6∅7
2987		6∅7 & ♭27	6∅7	♭27
2989		2◦7 & 6∅7	2◦7	6∅7
		7∅7 & ♭6∆7	7∅7	♭6∆7
3021		6∅7 & ♭6∅7	6∅7	♭6∅7
3171		4SUS4 & ♭5SUS4	4SUS4	♭5SUS4
3173		4SUS4 & 7MI	4SUS4	7MI
3177		4SUS4 & 7MA	4SUS4	7MA
3181		1∅7 & 7◦	1∅7	7◦
3185		4SUS4 & 7SUS4	4SUS4	7SUS4
3237		4SUS4 & 5MA	4SUS4	5MA
3241		4SUS4 & ♭3+	4SUS4	♭3+
3249		3MI & 4SUS4	3MI	4SUS4
3251		1∆7 & ♭7MI	1∆7	♭7MI
		4SUS4 & ♭2∅7	4SUS4	♭2∅7
3253		1∆7 & ♭7MA	1∆7	♭7MA
		17 & 7◦	17	7◦
3257		1∆7 & ♭7SUS4	1∆7	♭7SUS4
3277		1∅7 & 5MA	1∅7	5MA
		5SUS4 & 7∆7	5SUS4	7∆7
3283		1∆7 & ♭5MA	1∆7	♭5MA
		17 & ♭5SUS4	17	♭5SUS4
3285		1∆7 & 2+	1∆7	2+
		17 & 7MI	17	7MI
3289		1MA & 7∆7	1MA	7∆7
		1∆7 & ♭3MI	1∆7	♭3MI
		1∅7 & 3MI	1∅7	3MI
		17 & 7MA	17	7MA
3291		1∅7 & ♭2∅7	1∅7	♭2∅7
3301		4SUS4 & 5∆7	4SUS4	5∆7
3305		1SUS4 & 7∆7	1SUS4	7∆7
3309		1∅7 & 57	1∅7	57
3315		1∆7 & ♭5∆7	1∆7	♭5∆7
3365		4SUS4 & ♭6◦	4SUS4	♭6◦
3369		4SUS4 & ♭6MI	4SUS4	♭6MI
3377		3MA & 4SUS4	3MA	4SUS4
3381		37 & 4SUS4	37	4SUS4
3385		3∆7 & 4SUS4	3∆7	4SUS4
3405		1∅7 & ♭6◦	1∅7	♭6◦
3417		1+ & 7∆7	1+	7∆7
		1∅7 & 3MA	1∅7	3MA
3421		1∅7 & 37	1∅7	37
3429		4SUS4 & ♭6∅7	4SUS4	♭6∅7
3433		1∅7 & 4◦	1∅7	4◦
		4MI & 7∆7	4MI	7∆7
3435		1∅7 & ♭27	1∅7	♭27
		7∆7 & ♭2∆7	7∆7	♭2∆7
3437		1∅7 & 2◦7	1∅7	2◦7
		2∅7 & 7∆7	2∅7	7∆7
3477		17 & ♭6◦	17	♭6◦
3481		1∆7 & ♭3SUS4	1∆7	♭3SUS4
		17 & ♭6MI	17	♭6MI
3505		17 & 4◦	17	4◦
3507		17 & ♭27	17	♭27
3509		1∆7 & ♭77	1∆7	♭77
		17 & 2◦7	17	2◦7
3513		17 & 4∅7	17	4∅7
3541		17 & ♭6∅7	17	♭6∅7
3633		3SUS4 & 4SUS4	3SUS4	4SUS4
3673		1∅7 & 3SUS4	1∅7	3SUS4
		6MI & 7∆7	6MI	7∆7
3689		4MA & 7∆7	4MA	7∆7
		4SUS4 & 77	4SUS4	77
3693		1∅7 & 7∅7	1∅7	7∅7
3705		4∆7 & 7∆7	4∆7	7∆7
3765		1∆7 & ♭7∆7	1∆7	♭7∆7
		17 & 7∅7	17	7∅7
3801		17 & 77	17	77