3ed4/3

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← 2ed4/33ed4/34ed4/3 →
Prime factorization 3 (prime)
Step size 166.015¢ 
Octave 7\3ed4/3 (1162.1¢)
(semiconvergent)
Twelfth 11\3ed4/3 (1826.16¢)
(semiconvergent)
Consistency limit 3
Distinct consistency limit 2

3ed4/3 is a nonoctave scale which divides the just perfect fourth (frequency ratio 4:3) into three steps of approximately 166.015¢ each.

Intervals

degrees cents value corresponding
JI intervals
0 0.000 exact 1/1
1 166.015 11/10
2 332.030
3 498.045 exact 4/3
4 664.060 22/15
5 830.075 13/8
6 996.090 exact 16/9
7 1162.105 88/45
8 1328.120 13/6
9 1494.135 exact 64/27
10 1660.150
11 1826.165 13/9
12 1992.180
13 2158.195
14 2324.210
15 2490.225 135/32
16 2656.240
17 2822.255
18 2988.270 45/8
19 3154.285
20 3320.300 17/5
21 3486.315 15/2
22 3652.330
23 3818.345 68/15
24 3984.360 10/1

Harmonics

Approximation of harmonics in 3ed4/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -37.9 -75.8 -75.8 +35.9 +52.3 -48.5 +52.3 +14.4 -2.0 -0.9 +14.4
Relative (%) -22.8 -45.7 -45.7 +21.6 +31.5 -29.2 +31.5 +8.7 -1.2 -0.6 +8.7
Steps
(reduced)
7
(1)
11
(2)
14
(2)
17
(2)
19
(1)
20
(2)
22
(1)
23
(2)
24
(0)
25
(1)
26
(2)
Approximation of harmonics in 3ed4/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +41.9 +79.6 -39.8 +14.4 +75.5 -23.5 +49.0 -39.8 +41.7 -38.8 +50.2
Relative (%) +25.2 +47.9 -24.0 +8.7 +45.5 -14.1 +29.5 -24.0 +25.1 -23.4 +30.3
Steps
(reduced)
27
(0)
28
(1)
28
(1)
29
(2)
30
(0)
30
(0)
31
(1)
31
(1)
32
(2)
32
(2)
33
(0)

Regular temperaments

CRP4 tuning is related to temperaments which temper out 4000/3993 (wizardharry temperament). The unit step of CRP4 is approximately a cent sharp of 11/10. Tempering out 4000/3993 leads equating three 11/10s with 4/3, hence wizardharry temperaments split the fourth in three.

Tempering out both 55/54 and 100/99 (equating 10/9 with 11/10 and 12/11) leads porkypine (2.3.5.11 subgroup) or sonic (full 11-limit). Sonic temperaments include porcupine, hystrix, porky, coendou, hedgehog, nautilus, ammonite, ceratitid, and opossum.

Other wizardharry temperaments include octoid, harry, tritikleismic, wizard, septisuperfourth, unthirds, supers, alphaquarter, quincy, stearnscape, pogo, marvolo, cotritone, echidna, marvo, mystery, zarvo, escaped, thuja, and escapade.