3ed4/3: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
== Theory == | |||
=== Harmonics === | |||
{{Harmonics in equal|3|4|3|intervals=integer|columns=11}} | |||
{{Harmonics in equal|3|4|3|intervals=integer|columns=11|start=12|collapsed=true|title=Approximation of harmonics in 3ed4/3 (continued)}} | |||
== Intervals == | == Intervals == | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
| | | ! # | ||
| | ! Cents | ||
| | ! Approximate ratios | ||
|- | |||
| 0 | |||
| 0.000 | |||
| [[1/1]] | |||
|- | |- | ||
| | | 1 | ||
| | | 166.015 | ||
| | | [[11/10]] | ||
|- | |- | ||
| | | 2 | ||
| | | 332.030 | ||
| | |||
|- | |- | ||
| | | 3 | ||
| | | 498.045 | ||
| | | [[4/3]] | ||
|- | |- | ||
| | | 4 | ||
| | | 664.060 | ||
| | | [[22/15]] | ||
|- | |- | ||
| | | 5 | ||
| | | 830.075 | ||
| | | [[13/8]] | ||
|- | |- | ||
| | | 6 | ||
| | | 996.090 | ||
| | | [[16/9]] | ||
|- | |- | ||
| | | 7 | ||
| | | 1162.105 | ||
| | | 88/45 | ||
|- | |- | ||
| | | 8 | ||
| | | 1328.120 | ||
| | | [[13/6]] | ||
|- | |- | ||
| | | 9 | ||
| | | 1494.135 | ||
| | | [[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]] | ||
|} | |} | ||
== Regular temperaments == | == Regular temperaments == | ||
3ed4/3 tuning is related to temperaments which temper out [[4000/3993]] (wizardharry temperament). The unit step of 3ed4/3 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 [[ | Tempering out both [[55/54]] and [[100/99]] (equating 10/9 with 11/10 and 12/11) leads to [[porcupine]] (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]], [[Porwell temperaments #Septisuperfourth|septisuperfourth]], [[unthirds]], [[supers]], [[alphaquarter]], [[quincy]], [[ | Other wizardharry temperaments include [[octoid]], [[harry]], [[tritikleismic]], [[wizard]], [[Porwell temperaments #Septisuperfourth|septisuperfourth]], [[unthirds]], [[supers]], [[alphaquarter]], [[quincy]], [[stearnscape]], [[pogo]], [[marvolo]], [[cotritone]], [[echidna]], [[marvo]], [[mystery]], [[zarvo]], [[escaped]], [[thuja]], and [[escapade]]. | ||
[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||
[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||
[[Category:Perfect fourth]] | [[Category:Perfect fourth]] | ||