User:Inthar/4L 3s

11edo smitonic

The intervals of the symmetric LsLsLsL mode (harmonics in bold):

Degree (1 = tonic)	Cents	Note name on C (22edo notation)	Approximate ratios	#Gens up
1	0	C	1/1	0
2	218.18	D	8/7, 9/8, 17/15	-3
3	327.27	Eb^	6/5, 11/9, 17/14	+1
4	545.45	F^	11/8, 15/11	-2
5	654.54	Gv	16/11, 22/15	+2
6	872.72	Av	5/3, 18/11, 28/17	-1
7	981.81	Bb	7/4, 16/9, 30/17	+3

Assuming the symmetric 2121212 mode, the 1-4-7 chord is:

• 8:11:14 on degrees 1 and 6
• 8:11:15 on degrees 3, 5, and 7
• 44:56:77 (approx. 25:32:44) on degrees 2 and 4

Modal harmony

Main article: Smitonic

The seven modes are, from brightest to darkest:

Nerevarine mode	2212121
Vivecan mode	2122121
Lorkhanic mode	2121221
Sothic mode	2121212
Kagrenacan mode	1221212
Almalexian mode	1212212
Dagothic mode	1212122

Modally, the highest to lowest entropy scale degrees (unison = 1) are:

• 2 and 7 (equally): .99 bits
• 4 and 5 (equally): .86 bits
• 3 and 6 (equally): .59 bits

If a scale degree is high entropy it tends to be the most informative on average; the modes that have this interval as major and minor respectively are roughly a 50-50 split. This tells us that unlike in the diatonic scale, thirds and sixths are the least informative in distinguishing smitonic modes. On the other hand, seconds, fourths and sevenths are highly informative.

In orgone, these scale degrees appear in the most consonant triads and tetrads of 11edo orgone, namely 8:9:11:15, 8:9:11:14 and 16:17:22:28. Those chords are therefore crucial for Orgone[7] modal harmony.

18edo smitonic

Degree	18edo (soft)	25edo (supersoft)	43edo	Note name on J	Approximate ratios	#Gens up
unison	0\18, 0.0	0\25, 0.0	0\43, 0.0	J	1/1	0
chroma	1\18, 66.7	1\25, 48.0	2\43, 55.8	J&		-7
dim. mos2nd	1\18, 66.7	2\25, 96.0	3\43, 83.7	K@@		+11
minor mos2nd	2\18, 133.3	3\25, 144.0	5\43, 139.5	K@	13/12	+4
major mos2nd	3\18, 200.0	4\25, 192.0	7\43, 195.3	K	9/8, 10/9	-3
aug. mos2nd	4\18, 266.7	5\25, 240.0	9\43, 251.2	K&		-10
dim. mos3rd	4\18, 266.7	6\25, 288.0	10\43, 279.1	L@		+8
perf. mos3rd	5\18, 333.3	7\25, 336.0	12\43, 334.9	L	17/14, 40/33	+1
aug. mos3rd	6\18, 400.0	8\25, 384.4	14\43, 390.7	L&	5/4	-6
doubly aug. mos3rd	7\18, 466.7	9\25, 432.0	16\43, 446.5	L&&		-13
dim. mos4th	6\18, 400.0	9\25, 432.0	15\43, 418.6	M@@		+12
minor mos4th	7\18, 466.7	10\25, 480.0	17\43, 474.4	M@	21/16	+5
major mos4th	8\18, 533.3	11\25, 528.0	19\43, 530.2	M	19/14, 34/25	-2
aug. mos4th	9\18, 600.0	12\25, 576.0	21\43, 586.0	M&	7/5	-9
dim. mos5th	9\18, 600.0	13\25, 624.0	22\43, 614.0	N@	10/7	+9
minor mos5th	10\18, 666.7	14\25, 672.0	24\43, 669.8	N	28/19, 25/17	+2
major mos5th	11\18, 733.3	15\25, 720.0	26\43, 725.6	N&	32/21	-5
aug. mos5th	12\18, 800.0	16\25, 768.0	28\43, 781.4	N&&		-12
doubly dim. mos6th	11\18, 733.3	16\25, 768.0	27\43, 753.5	O@@		+13
dim. mos6th	12\18, 800.0	17\25, 816.0	29\43, 809.3	O@	8/5	+6
perf. mos6th	13\18, 866.7	18\25, 864.0	31\43, 865.1	O	28/17, 33/20	-1
aug. mos6th	14\18, 933.3	19\25, 912.0	33\43, 920.9	O&		-8
dim. mos7th	14\18, 933.3	20\25, 960.0	34\34, 948.8	P@		+10
minor mos7th	15\18, 1000.0	21\25, 1008.0	36\43, 1004.7	P	16/9, 9/5	+3
major mos7th	16\18, 1066.7	22\25, 1056.0	38\43, 1060.5	P&	24/13	-4
aug. mos7th	17\18, 1133.3	23\25, 1104.0	40\43, 1116.3	P&		-11
dim. mosoctave	17\18, 1133.3	24\25, 1152.0	41\43, 1144.2	J@		+7

Modal harmony

MODMOSes and chroma modification become more important...

Treat it as neutralized mavila?