User:CritDeathX/Sam's Musings

This is the page that I will use to just splatter my thoughts on; I think most of it will center around notation & regular temperaments. Some things you may see in specific are a notation for 14EDO around Titanium(9), a theory system for Orwell(22), and microtonal marimba layouts.

Titanium(9) Notation for 14EDO

To quote the Titanium(9) section of the 14EDO page,

"14edo is also the largest edo whose patent val supports titanium temperament, tempering out the chromatic semitone (21:20), and falling toward the "brittle" (fifths wider than in 9edo) end of that spectrum. Titanium is one of the simplest 7-limit temperaments, although rather inaccurate (the 7:5 is mapped onto 6\14, over 70 cents flat). Its otonal/major and utonal/minor tetrads are inversions of one another, which allows a greater variety of chord progressions (since different inversions of the same chord may have very different expressive qualities). Despite being so heavily tempered, the tetrads are still recognizable and aren't unpleasant-sounding as long as one uses the right timbres ("bell-like" or opaque-sounding ones probably work best). Titanium forms enneatonic modes which are melodically strong and are very similar to diatonic modes, only with two mediants and submediants instead of one. Titanium[9] has similarities to mavila, slendro, and pelog scales as well."

This notation places the clefs in the same places as 5 lines do; the treble clef (G clef) is placed on the 2nd line, and the bass clef (F clef) is placed on the 4th. Starting from the 1st ledger line to the 4th space on the treble clef & the 2nd space to the 1st ledger line above for the bass clef, the note names are C-D-E-F-G-H-J-A-B-C'.

Although (i believe) my notation doesn't follow the interval list it speaks of, I believe it still does its job in notating 14EDO in a 6-line staff.

Diatonic Notation

Chromatic Notation

Basic Chords

2 Basic Progressions (and also an example of a time signature)

Christopher Temperament

Christopher temperament is the name I give to the 2.3.7.11.13-limit temperament with a generator of a sharp 7/6 that tempers out 99/98, 44/43, 17496/16807, etc. It would be a generator of Orwell if it wasn't for the fact that its too sharp. Two generators give an 8c sharp 11/8, three of them make a 0.7c flat 13/8, and five make a 4c sharp 9/8.

Using a scale tree, you can find the EDOs that approximate the generator, starting with 13 & 17EDO; you could also find a zigzag series of EDOs that approximate the generator, starting with 13 & 30.

Interval Chain

1000.28	80.22	360.17	640.11	920.06	0.0	279.94	559.89	839.83	1119.78	199.72
16/9	22/21	16/13	16/11	12/7	1/1	7/6	11/8	13/8	21/11	9/8

MOS Scales

(charts inspired from Andrew Heathwaite's MOS Investigations)

4L1s

0	1	2	3	4
0.0
	279.94
		559.89
			839.83
				1119.78

L = 279.94 (1x)

s = 80.22 (-4x)

c = 199.72 (5x)

4L5s

0	1	2	3	4	5	6	7	8
0.0
					199.72
	279.94
						479.67
		559.89
							759.61
			839.83
								1039.56
				1119.78

L = 199.72 (5x)

s = 80.22 (-4x)

c = 119.50 (9x)

4L9s

0	1	2	3	4	5	6	7	8	9	10	11	12
0.0
									119.50
					199.72
	279.94
										399.44
						479.67
		559.89
											679.39
							759.61
			839.83
												959.33
								1039.56
				1119.78

L = 119.50 (9x)

s = 80.22 (-4x)

c = 39.28 (13x)