Lemba: Difference between revisions
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'''Lemba''' (the name is from [[Herman Miller]]'s conlang name for the temperament) as a regular temperament is the intersection of the [[Jubilismic clan #Lemba|Jubilismic clan]] and the [[Gamelismic clan #Lemba|Gamelismic clan]]. This means that the perfect fifth is split into three equal parts, each approximately an [[8/7]]. It also means the period is half an octave, and repeats precisely a tritone apart, tempering out [[50/49]]. A generator plus a period comes very close to the [[golden ratio]] phi, which means ratios in the sequence 8:13:21:34:55 etc are also well approximated, and any one of these can be made just by choosing the right [[eigenmonzo]]. The combination of these factors means many composite ratios in the 2.3.5.7.13.17 subgroup are both well approximated and accessible with a relatively small gamut, giving you a strong selection of chords to choose from. It's main weaknesses are that ratios of 5 and 13 are conflated by the tempering out of [[65/64]], favoring 13 in the better tunings, so traditional major and minor chords are strongly neutral flavoured, and ratios involving 11 are not approximated at all until you have a large gamut. However, ignoring the 5 and 13, and focusing purely on the 2.3.7.17 subgroup, it can be highly accurate, with a total error of less than 7 cents in the tonality diamond in the least squares tuning. It forms mode of symmetry scales that are always double a fibonacci sequence number, at 4, 6, 10, 16, 26, etc, which means L/s ratios remain well mixed and clearly distinct many iterations down. | '''Lemba''' (the name is from [[Herman Miller]]'s conlang name for the temperament) as a regular temperament is the intersection of the [[Jubilismic clan #Lemba|Jubilismic clan]] and the [[Gamelismic clan #Lemba|Gamelismic clan]]. This means that the perfect fifth is split into three equal parts, each approximately an [[8/7]]. It also means the period is half an octave, and repeats precisely a tritone apart, tempering out [[50/49]]. A generator plus a period comes very close to the [[golden ratio]] phi, which means ratios in the sequence 8:13:21:34:55 etc are also well approximated, and any one of these can be made just by choosing the right [[eigenmonzo]]. The combination of these factors means many composite ratios in the 2.3.5.7.13.17 subgroup are both well approximated and accessible with a relatively small gamut, giving you a strong selection of chords to choose from. It's main weaknesses are that ratios of 5 and 13 are conflated by the tempering out of [[65/64]], favoring 13 in the better tunings, so traditional major and minor chords are strongly neutral flavoured, and ratios involving 11 are not approximated at all until you have a large gamut. However, ignoring the 5 and 13, and focusing purely on the 2.3.7.17 subgroup, it can be highly accurate, with a total error of less than 7 cents in the tonality diamond in the least squares tuning. It forms mode of symmetry scales that are always double a fibonacci sequence number, at 4, 6, 10, 16, 26, etc, which means L/s ratios remain well mixed and clearly distinct many iterations down. | ||
== Spectrum of | == Spectrum of lemba tunings by eigenmonzos == | ||
Gencom: [7/5 8/7; 45/44 50/49 65/64 78/77] | Gencom: [7/5 8/7; 45/44 50/49 65/64 78/77] | ||
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| | | | ||
|- | |- | ||
| (2 - Φ) | | (2 - Φ)\2 | ||
| 229.179 | | 229.179 | ||
| Golden Lemba. L/s ratios are always precisely Φ, and MOS scales are always precisely 2Φ | | Golden Lemba. L/s ratios are always precisely Φ, and MOS scales are always precisely 2Φ | ||
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* [http://soonlabel.com/xenharmonic/archives/1232 Lemba Suite] (Prelude, Aria & Fugue) by Claudi Meneghin | * [http://soonlabel.com/xenharmonic/archives/1232 Lemba Suite] (Prelude, Aria & Fugue) by Claudi Meneghin | ||
: in 8/7 eigenmonzo tuning | |||
[[Category:Lemba]] | [[Category:Lemba]] | ||