3ed4/3: Difference between revisions
m Added harmonics |
m Removing from Category:Edonoi using Cat-a-lot |
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Other wizardharry temperaments include [[octoid]], [[harry]], [[tritikleismic]], [[wizard]], [[Porwell temperaments #Septisuperfourth|septisuperfourth]], [[unthirds]], [[supers]], [[alphaquarter]], [[quincy]], [[Stearnsmic clan #Stearnscape|stearnscape]], [[pogo]], [[marvolo]], [[Breedsmic temperaments #Cotritone|cotritone]], [[echidna]], [[marvo]], [[mystery]], [[zarvo]], [[Escapade family #Escaped|escaped]], [[thuja]], and [[escapade]]. | Other wizardharry temperaments include [[octoid]], [[harry]], [[tritikleismic]], [[wizard]], [[Porwell temperaments #Septisuperfourth|septisuperfourth]], [[unthirds]], [[supers]], [[alphaquarter]], [[quincy]], [[Stearnsmic clan #Stearnscape|stearnscape]], [[pogo]], [[marvolo]], [[Breedsmic temperaments #Cotritone|cotritone]], [[echidna]], [[marvo]], [[mystery]], [[zarvo]], [[Escapade family #Escaped|escaped]], [[thuja]], and [[escapade]]. | ||
[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||
[[Category:Perfect fourth]] | [[Category:Perfect fourth]] | ||
Revision as of 19:22, 1 August 2025
| ← 2ed4/3 | 3ed4/3 | 4ed4/3 → |
(semiconvergent)
(semiconvergent)
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
| 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) | |
| 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.