5L 4s: Difference between revisions
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== Tuning ranges == | == Tuning ranges == | ||
=== Hard-of-basic === | === Hard-of-basic === | ||
Hard-of-basic tunings have [[Semifourth|semifourths]] as generators, between 1\5 (240{{c}}) and 3\14 (257.14{{c}}), where two of them create a diatonic 4th. The generator could be viewed as a 15/13, and the resulting "ultramajor" chords and | Hard-of-basic tunings have [[Semifourth|semifourths]] as generators, between 1\5 (240{{c}}) and 3\14 (257.14{{c}}), where two of them create a diatonic 4th. The generator could be viewed as a 15/13, and the resulting "inframinor" and "ultramajor" chords and triads could be viewed as approximating, respectively, 26:30:39 and 10:13:15 (see [[Arto and Tendo theory]]). | ||
==== Hypohard ==== | ==== Hypohard ==== | ||
| Line 55: | Line 55: | ||
| 4\19, 252.63 | | 4\19, 252.63 | ||
|- | |- | ||
| L ({{nowrap|octave | | L ({{nowrap|octave − 4g}}) | ||
| 171.43 | | 171.43 | ||
| 178.72 | | 178.72 | ||
| Line 62: | Line 62: | ||
| 189.47 | | 189.47 | ||
|- | |- | ||
| s ({{nowrap|5g | | s ({{nowrap|5g − octave}}) | ||
| 85.71 | | 85.71 | ||
| 76.60 | | 76.60 | ||
| Line 71: | Line 71: | ||
This range is notable for having many simple tunings that are close to being "eigentunings" (tunings that tune a certain JI interval exactly): | This range is notable for having many simple tunings that are close to being "eigentunings" (tunings that tune a certain JI interval exactly): | ||
* 33edo semiquartal has close 7/5 (error | * 33edo semiquartal has close 7/5 (error −0.69{{c}}), 9/5 (error −0.59{{c}}) and 9/7 (error +1.28{{c}}), thus can be used for the close 5:7:9 in the two Locrian-like modes 1|7 and 0|8 | ||
* 52edo semiquartal has close 22/19 (error +0.04{{c}}) | * 52edo semiquartal has close 22/19 (error +0.04{{c}}) | ||
* 19edo semiquartal has close 6/5 (error +0.15{{c}}) and 28/27 (error +0.20{{c}}) | * 19edo semiquartal has close 6/5 (error +0.15{{c}}) and 28/27 (error +0.20{{c}}) | ||
| Line 92: | Line 92: | ||
| 6\29, 248.28 | | 6\29, 248.28 | ||
|- | |- | ||
| L ({{nowrap|octave | | L ({{nowrap|octave − 4g}}) | ||
| 189.47 | | 189.47 | ||
| 200.00 | | 200.00 | ||
| 206.90 | | 206.90 | ||
|- | |- | ||
| s ({{nowrap|5g | | s ({{nowrap|5g − octave}}) | ||
| 63.16 | | 63.16 | ||
| 50.00 | | 50.00 | ||
| Line 119: | Line 119: | ||
| 8\37, 259.46 | | 8\37, 259.46 | ||
|- | |- | ||
| L ({{nowrap|octave | | L ({{nowrap|octave − 4g}}) | ||
| 156.52 | | 156.52 | ||
| 150.00 | | 150.00 | ||
| 162.16 | | 162.16 | ||
|- | |- | ||
| s ({{nowrap|5g | | s ({{nowrap|5g − octave}}) | ||
| 104.35 | | 104.35 | ||
| 112.50 | | 112.50 | ||
| 97.30 | | 97.30 | ||
|} | |} | ||
=== Tuning examples === | === Tuning examples === | ||
An example in the Diasem Lydian mode LSLSLMLSLM with M and S equated. ([[:File:Diasem Lydian Example Score.pdf|score]]) | An example in the Diasem Lydian mode LSLSLMLSLM with M and S equated. ([[:File:Diasem Lydian Example Score.pdf|score]]) | ||