30edt: Difference between revisions
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== Theory == | |||
30edt is related to [[19edo]], but with the [[3/1]] rather than the [[2/1]] being [[just]], which results in octaves being is [[stretched and compressed tuning|stretched]] by about 4.5715{{cent}} and the step size is about. It is [[consistent]] to the 10-[[integer-limit]]. | 30edt is related to [[19edo]], but with the [[3/1]] rather than the [[2/1]] being [[just]], which results in octaves being is [[stretched and compressed tuning|stretched]] by about 4.5715{{cent}} and the step size is about. It is [[consistent]] to the 10-[[integer-limit]]. | ||
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30edt is a [[Phoenix]] tuning and exhibits all the benefits of such tunings. | 30edt is a [[Phoenix]] tuning and exhibits all the benefits of such tunings. | ||
== Harmonics == | === Harmonics === | ||
{{Harmonics in equal | {{Harmonics in equal|30|3|1|intervals=integer}} | ||
| | {{Harmonics in equal|30|3|1|intervals=integer|columns=12|start=12|collapsed=1|Approximation of harmonics in 30edt (continued)}} | ||
| | |||
| | |||
| intervals = integer | |||
}} | |||
{{Harmonics in equal | |||
| | |||
| | |||
| | |||
| start = 12 | |||
| collapsed = 1 | |||
| | |||
}} | |||
== Intervals of 30edt == | == Intervals of 30edt == | ||
{| class="wikitable center-all" | {| class="wikitable center-all right-2 right-3 left-4" | ||
|- | |- | ||
! rowspan="2" | | ! rowspan="2" | # | ||
! rowspan="2" | Cents | ! rowspan="2" | Cents | ||
! rowspan="2" | Hekts | ! rowspan="2" | Hekts | ||
! rowspan="2" | Approximate | ! rowspan="2" | Approximate ratios | ||
! colspan="2" | Scale name | ! colspan="2" | Scale name | ||
|- | |- | ||
| Line 41: | Line 30: | ||
| 0 | | 0 | ||
| 0 | | 0 | ||
| | | [[1/1]] | ||
| colspan="2" | C | | colspan="2" | C | ||
|- | |- | ||
| Line 47: | Line 36: | ||
| 63.3985 | | 63.3985 | ||
| 43.333 | | 43.333 | ||
| 28/27 | | 27/26, 28/27 | ||
| C^/Dbv | | C^/Dbv | ||
| C#/Dbb | | C#/Dbb | ||
| Line 54: | Line 43: | ||
| 126.797 | | 126.797 | ||
| 86.667 | | 86.667 | ||
| [[14/13]], [[15/14]], [[16/15]], 29/27 | | [[14/13]], [[15/14]], [[16/15]], [[29/27]] | ||
| Db | | Db | ||
| Cx/Db | | Cx/Db | ||
| Line 61: | Line 50: | ||
| 190.1955 | | 190.1955 | ||
| 130 | | 130 | ||
| 10/9 | | 9/8, 10/9 | ||
| C# | | C# | ||
| D | | D | ||
| Line 82: | Line 71: | ||
| 380.391 | | 380.391 | ||
| 260 | | 260 | ||
| | | [[5/4]] | ||
| D^/Ev | | D^/Ev | ||
| E | | E | ||
| Line 124: | Line 113: | ||
| 760.782 | | 760.782 | ||
| 520 | | 520 | ||
| | | [[14/9]] | ||
| F | | F | ||
| G#/Hbb | | G#/Hbb | ||
| Line 166: | Line 155: | ||
| 1141.173 | | 1141.173 | ||
| 780 | | 780 | ||
| | | [[27/14]] | ||
| G#^/Hv | | G#^/Hv | ||
| J#/Kbb | | J#/Kbb | ||
| Line 194: | Line 183: | ||
| 1394.767 | | 1394.767 | ||
| 953.333 | | 953.333 | ||
| [[9/4]] | | [[9/4]] | ||
| J^/Av | | J^/Av | ||
| L | | L | ||
| Line 208: | Line 197: | ||
| 1521.564 | | 1521.564 | ||
| 1040 | | 1040 | ||
| [[12/5]] | | [[12/5]] | ||
| A^/Bbv | | A^/Bbv | ||
| Lx/Ab | | Lx/Ab | ||
| Line 222: | Line 211: | ||
| 1648.361 | | 1648.361 | ||
| 1126.667 | | 1126.667 | ||
| [[13/5]] | | [[13/5]] | ||
| A# | | A# | ||
| A#/Bbb | | A#/Bbb | ||
| Line 236: | Line 225: | ||
| 1775.158 | | 1775.158 | ||
| 1213.333 | | 1213.333 | ||
| [[14/5]] | | [[14/5]] | ||
| B | | B | ||
|- | |- | ||
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|} | |} | ||
30edt contains all [[19edo]] intervals within 3/1, all | 30edt contains all [[19edo]] intervals within 3/1, all tempered progressively sharper. The accumulation of the 0.241{{c}} sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615{{c}} flatter than that in 6edo. | ||
30edt also contains all the | 30edt also contains all the mos contained in [[15edt]], being the double of this equal division. Being even, 30edt introduces mos with an even number of periods per tritave such as a {{sl|6L 6s}} similar to Hexe Dodecatonic. This mos has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an [[unfair]] [[Sigma]] scale of {{sl|8L 3s}} and the major scale is LLLsLLLsLLs. The sharp 9/7 of 7 degrees, in addition to generating a Lambda mos will generate a {{sl|4L 9s}} unfair "Superlambda" mos which does not border on being atonal as the 17edt rendition does. | ||
== Music == | == Music == | ||
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* [https://www.youtube.com/watch?v=fEQ13hzs3fY ''Fugue for Piano in 30EDT Bohlen-Pierce-Stearns{{lbrack}}9{{rbrack}} sLsLssLsL "Dur I"''] (2024) | * [https://www.youtube.com/watch?v=fEQ13hzs3fY ''Fugue for Piano in 30EDT Bohlen-Pierce-Stearns{{lbrack}}9{{rbrack}} sLsLssLsL "Dur I"''] (2024) | ||
[[Category:Listen]] | [[Category:Listen]] | ||