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 a natural extension of the [[jubilismic clan]] and a member of the [[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''' is a [[regular temperament]] which is a natural extension of the [[jubilismic clan]] and a member of the [[gamelismic clan]]. This means that the perfect fifth of [[~]][[3/2]] is split into three equal parts, each approximating [[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. Its 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 [[mos scale]]s 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.

The name is from [[Herman Miller]]'s conlang name for the temperament.

See [[Jubilismic clan #Lemba]] for more technical data.

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Gencom: [7/5 8/7; 45/44 50/49 65/64 78/77]

Gencom mapping: [{{val| 2 2 5 6 5 7 }},[{{val| 0 3 -1 -1 5 1 }}]

Gencom mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}]

{| class="wikitable center-all"

{| class="wikitable center-all left-4"

|-

! ET ~~generator~~

! Edo Generator

! [[~~eigenmonzo~~|~~eigenmonzo~~ (~~unchanged interval~~]])

! [[Eigenmonzo|Eigenmonzo (Unchanged Interval)]]

! ~~supermajor second~~ (¢)

! Generator (¢)

! ~~comments~~

! Comments

|-

|

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| 229.179

| Golden Lemba<ref>L/s ratios are always precisely Φ, and ~~MOS~~ scales are always precisely 2Φ</ref>

| Golden Lemba<ref>L/s ratios are always precisely Φ, and mos scales are always precisely 2Φ</ref>

|-

|

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| 234.485

| 2.3.7.17 subgroup least squares {{clarify}}

| 2.3.7.17 subgroup least squares{{clarify}}

|-

| 9\46

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== Music ==

By Claudi Meneghin

; [[Claudi Meneghin]]

* [https://www.youtube.com/watch?v=2ziAZx03KF8 Lemba Suite, for Two Organs] (Prelude, Aria & Fugue)

* [https://www.youtube.com/watch?v=2ziAZx03KF8 ''Lemba Suite, for Two Organs''] (Prelude, Aria & Fugue) in 8/7 eigenmonzo tuning

: in 8/7 eigenmonzo tuning

; [[Herman Miller]]

* [https://sites.google.com/site/teamouse/LembaGalatsia.mp3 ''Lemba Galatsia'']

* [https://sites.google.com/site/teamouse/lemba-gpo-test.mp3 ''GPO Lemb''a]

~~By [[Herman Miller]]~~

== Notes ==

* [https:/~~/sites.google.com/site/teamouse/LembaGalatsia.mp3 Lemba Galatsia]~~

* [https://sites.google.com/site/teamouse/lemba-gpo-test.mp3 GPO Lemba]

[[Category:Temperaments]]

@@ Line 1: / Line 1: @@
-'''Lemba''' (the name is from [[Herman Miller]]'s conlang name for the temperament) as a regular temperament is a natural extension of the [[jubilismic clan]] and a member of the [[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''' is a [[regular temperament]] which is a natural extension of the [[jubilismic clan]] and a member of the [[gamelismic clan]]. This means that the perfect fifth of [[~]][[3/2]] is split into three equal parts, each approximating [[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. Its 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 [[mos scale]]s 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.
+The name is from [[Herman Miller]]'s conlang name for the temperament.
 See [[Jubilismic clan #Lemba]] for more technical data.
@@ Line 76: / Line 78: @@
 Gencom: [7/5 8/7; 45/44 50/49 65/64 78/77]
-Gencom mapping: [{{val| 2 2 5 6 5 7 }},[{{val| 0 3 -1 -1 5 1 }}]
+Gencom mapping: [{{val| 2 2 5 6 5 7 }}, {{val| 0 3 -1 -1 5 1 }}]
-{| class="wikitable center-all"
+{| class="wikitable center-all left-4"
 |-
-! ET<br>generator
+! Edo<br>Generator
-! [[eigenmonzo|eigenmonzo<br>(unchanged interval]])
+! [[Eigenmonzo|Eigenmonzo<br>(Unchanged Interval)]]
-! supermajor<br>second (¢)
+! Generator (¢)
-! comments
+! Comments
 |-
 |
@@ Line 133: / Line 135: @@
 |
 | 229.179
-| Golden Lemba<ref>L/s ratios are always precisely Φ, and MOS scales are always precisely 2Φ</ref>
+| Golden Lemba<ref>L/s ratios are always precisely Φ, and mos scales are always precisely 2Φ</ref>
 |-
 |
@@ Line 243: / Line 245: @@
 |
 | 234.485
-| 2.3.7.17 subgroup least squares {{clarify}}
+| 2.3.7.17 subgroup least squares{{clarify}}
 |-
 | 9\46
@@ Line 297: / Line 299: @@
 == Music ==
-By Claudi Meneghin
+; [[Claudi Meneghin]]
-* [https://www.youtube.com/watch?v=2ziAZx03KF8 Lemba Suite, for Two Organs] (Prelude, Aria &amp; Fugue)
+* [https://www.youtube.com/watch?v=2ziAZx03KF8 ''Lemba Suite, for Two Organs''] (Prelude, Aria &amp; Fugue) in 8/7 eigenmonzo tuning
-: in 8/7 eigenmonzo tuning
+; [[Herman Miller]]
+* [https://sites.google.com/site/teamouse/LembaGalatsia.mp3 ''Lemba Galatsia'']
+* [https://sites.google.com/site/teamouse/lemba-gpo-test.mp3 ''GPO Lemb''a]
-By [[Herman Miller]]
+== Notes ==
-* [https://sites.google.com/site/teamouse/LembaGalatsia.mp3 Lemba Galatsia]
+<references/>
-* [https://sites.google.com/site/teamouse/lemba-gpo-test.mp3 GPO Lemba]
 [[Category:Temperaments]]