3ed4/3: Difference between revisions
Wikispaces>FREEZE No edit summary |
No edit summary |
||
| Line 1: | Line 1: | ||
The Cube Root of the | The '''Cube Root of the Perfect fourth''' (3ED4/3, CRP4) is a nonoctave scale which divides the just [[perfect fourth]] (frequency ratio [[4/3|4:3]]) into three steps of approximately 166.015[[cent|¢]] each. | ||
== Intervals == | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| Line 105: | Line 104: | ||
| | 218.34 | | | 218.34 | ||
|} | |} | ||
[[ | |||
[[Category: | == Regular temperaments == | ||
[[Category: | 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. | ||
[[Category: | |||
[[Category: | Tempering out both [[55/54]] and [[100/99]] (equating 10/9 with 11/10 and 12/11) leads [[Subgroup temperaments #No-sevens subgroup|porkypine]] (2.3.5.11 subgroup) or [[Porcupine rank three family|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]], [[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:Edonoi]] | |||
[[Category:Equal-step tuning]] | |||
[[Category:Nonoctave]] | |||
[[Category:Perfect fourth]] | |||
Revision as of 10:35, 12 September 2021
The Cube Root of the Perfect fourth (3ED4/3, CRP4) is a nonoctave scale which divides the just perfect fourth (frequency ratio 4:3) into three steps of approximately 166.015¢ each.
Intervals
| degrees of CRP4 | cents value | cents value octave-reduced |
| 0 | 0.00 | |
| 1 | 166.01 | |
| 2 | 332.03 | |
| 3 | 498.04 | |
| 4 | 664.06 | |
| 5 | 830.07 | |
| 6 | 996.09 | |
| 7 | 1162.10 | |
| 8 | 1328.12 | 128.12 |
| 9 | 1494.13 | 294.13 |
| 10 | 1660.15 | 460.15 |
| 11 | 1826.16 | 626.16 |
| 12 | 1992.18 | 792.18 |
| 13 | 2158.19 | 958.19 |
| 14 | 2324.21 | 1124.21 |
| 15 | 2490.22 | 90.22 |
| 16 | 2656.24 | 256.24 |
| 17 | 2822.25 | 422.25 |
| 18 | 2988.27 | 588.27 |
| 19 | 3154.28 | 754.28 |
| 20 | 3320.30 | 920.30 |
| 21 | 3486.31 | 1086.31 |
| 22 | 3652.33 | 52.33 |
| 23 | 3818.34 | 218.34 |
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.