16ed5/2

16ED5/2 is the equal division of the 5/2 interval into 16 parts of 99.1446 cents each. This is the scale which occurs as the dominant reformed Mixolydian mode tuned as an equal division of a just interval.

← 15ed5/2

16ed5/2

17ed5/2 →

Prime factorization	24
Step size	99.1446 ¢
Octave	12\16ed5/2 (1189.74 ¢) (→ 3\4ed5/2)
Twelfth	19\16ed5/2 (1883.75 ¢) (semiconvergent)
Consistency limit	11
Distinct consistency limit	6

Intervals

Degrees	Enneatonic			Cents
1	1#/2b	F#/Gb		99.145
2	2	G		198.289
3	2#/3b	G#/Jb	G#/Ab	297.433
4	3	J	A	396.578
5	3#/4b	J#/Ab	A#/Bb	495.723
6	4	A	B	594.868
7	5	B	H	694.012
8	5#/6b	B#/Hb	H#/Cb	793.157
9	6	H	C	892.3015
10	6#/7b	H#/Cb	C#/Db	991.446
11	7	C	D	1090.591
12	7#/8b	C#/Db	D#/Sb	1189.735
13	8	D	S	1288.88
14	8#/9b	D#/Eb	S#/Eb	1388.0245
15	9	E		1487.169
16	1	F		1586.314

Coincidentally, 133 steps of the pyrite EDX of this size exceed 11 octaves by only 2.978¢.

Regular temperaments

Main article: Quintaleap family

16ed5/2 can also be thought of as a generator of the 2.3.5.17.19 subgroup temperament which tempers out 256/255, 361/360, and 4624/4617, which is a cluster temperament with 12 clusters of notes in an octave (quintaleap temperament). This temperament is supported by 12-, 109-, 121-, 133-, 145-, and 157edo.

Tempering out 400/399 (equating 20/19 and 21/20) leads to quintupole (12&121), and tempering out 476/475 (equating 19/17 with 28/25) leads to quinticosiennic (12&145).

Another temperament related to 16ed5/2 is quintapole (12&85). It is practically identical to the Galilei tuning, which is generated by the ratios 2/1 and 18/17.

Scale tree

Ed5/2 scales can be approximated in EDOs by subdividing their approximations of 5/2.

Major tenths				Period	Notes
6\5				90	Intense Aeolian-Subpental Dorian mode begins
	17\14			91.071
11\9				91.6	Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
	16\13			92.308
5\4				93.75	Subpental Dorian mode ends, Pental Dorian mode begins
		24\19		94.737
	19\15			95
14\11				95.45	Pental Dorian mode ends, Superpental Dorian mode begins
	23\18			95.83
9\7				96.429	Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
	31\24			96.875
22\17				97.059	Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
	35\27			97.2
13\10				97.5	Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
17\13				98.077
21\16				98.4375	Subpental Mixolydian mode ends, Pental Mixolydian mode begins
	25\19			98.684
		29\22		98.863
			33\25	99
4\3				100	Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
	19\14			101.786
15\11				102.27	Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
	26\19			102.632
11\8				103.125	Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
	18\13			103.846
		25\18		104.16
7\5				105	Mixolydian-Ionian mode ends

Relative cents

Degrees	Enneatonic			Intense Aeolian-Subpental Dorian	Dorian
1	1#/2b	G#/Jb	G#/Ab	90.625	93.75
2	2	J	A	181.25	187.5
3	2#/3b	J#/Ab	A#/Bb	271.875	281.25
4	3	J	B	362.5	375
5	3#/4b	J#/Ab	B#/Cb	453.125	468.75
6	4	A	C	543.75	562.5
7	5	A#/Bb	C#/Qb	633.375	656.25
8	5#/6b	B	Q	725	750
9	6	C	D	815.625	843.75
10	6#/7b	C#/Db	D#/Sb	906.25	937.5
11	7	D	S	996.875	1031.25
12	7#/8b	D#/Eb	S#/Eb	1087.5	1125
13	8	E		1178.125	1218.75
14	8#/9b	E#/Fb		1268.75	1312.5
15	9	F		1359.375	1406.25
16	1	G		1450	1500

Degrees	Enneatonic			Subpental-Soft Superpental Mixolydian	Intense Superpental Mixolydian ~ Mixolydian-Ionian
1	1#/2b	F#/Gb		100	103.125
2	2	G		200	206.25
3	2#/3b	G#/Jb	G#/Ab	300	309.375
4	3	J	A	400	412.5
5	3#/4b	J#/Ab	A#/Bb	500	515.625
6	4	A	B	600	618.75
7	5	B	H	700	721.875
8	5#/6b	B#/Hb	H#/Cb	800	825
9	6	H	C	900	928.125
10	6#/7b	H#/Cb	C#/Db	1000	1031.25
11	7	C	D	1100	1134.375
12	7#/8b	C#/Db	D#/Sb	1200	1237.5
13	8	D	S	1300	1340.625
14	8#/9b	D#/Eb	S#/Eb	1400	1443.75
15	9	E		1500	1546.875
16	1	F		1600	1650	See also 16EDX 12EDO - relative EDO 28ED5 - relative ED5 34ED7 - relative ED7 40ED10 - relative ED10 42ED11 - relative ED11 AS18/17 - relative ambitonal sequence