Chromatic pairs: Difference between revisions

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A '''chromatic pair''' is a pair of [[~~MOS~~ scale]]s in some [[rank-2 temperament]] (either a full [[Harmonic limit|''p''-limit]] temperament or a [[subgroup temperament]]) that are analogous to the familiar [[5L 2s|diatonic]] and [[chromatic]] scales of standard tuning. The smaller scale is an '''albitonic scale''' (from Latin ''albus'', "white"), named such since the diatonic scale can be played using the white keys of a piano, and the larger of the two is a '''chromatic scale''', analogous to the chromatic scale of standard tuning. Other related scales can be associated to chromatic pairs, namely a '''haplotonic scale''' (from Greek ''haplóos'', "single, simple"), analogous to the pentatonic scale of standard tuning and played using the black keys of a piano.

A '''chromatic pair''' is a pair of [[mos scale]]s in some [[rank-2 temperament]] (either a full [[Harmonic limit|''p''-limit]] temperament or a [[subgroup temperament]]) that are analogous to the familiar [[5L 2s|diatonic]] and [[chromatic]] scales of standard tuning. The smaller scale is an '''albitonic scale''' (from Latin ''albus'', "white"), named such since the diatonic scale can be played using the white keys of a piano, and the larger of the two is a '''chromatic scale''', analogous to the chromatic scale of standard tuning. Other related scales can be associated to chromatic pairs, namely a '''haplotonic scale''' (from Greek ''haplóos'', "single, simple"), analogous to the pentatonic scale of standard tuning and played using the black keys of a piano.

In the sections below, the pair temperaments are listed in order of increasing [[~~Tp_tuning~~#T2 tuning|RMS error]], which is an appropriate error measure for subgroups as well as full ''p''-limit groups.

In the sections below, the pair temperaments are listed in order of increasing [[Tp tuning#T2 tuning|RMS error]], which is an appropriate error measure for subgroups as well as full ''p''-limit groups.

== Terrain ==

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== Neutral ==

~~Subgroup: 2.3.11~~

~~Commas: 243/242~~

~~Svalname: 7&17~~

~~[[Tp_tuning|POT2 generator]]: ~11/9 = 350.525~~

~~[[Gencom|Gencom]]: [2 11/9; 243/242]~~

~~Gencom mapping: [<1 1 0 0 2|, <0 2 0 0 5|]~~

~~Mapping: [<1 1 2|, <0 2 5|]~~

~~EDOs:~~ {{~~EDOs~~|~~7, 17, 24, 65, 89, 202, 291, 380~~}}

~~[[Tp_tuning#T2 tuning|RMS error]]: 0.3021 cents~~

[[File:neutral_380edo.png|alt=neutral_380edo.png|neutral_380edo.png]]

[[neutral7~~|Seven note~~ albitonic scale]]

* [[neutral7]] – 7-tone [[albitonic scale]]

* [[neutral10]] – 10-tone [[chromatic scale]]

[[neutral10~~|Ten note~~ chromatic scale]]

* [[neutral17]] – 17-tone [[mega-chromatic scale]]

[[neutral17~~|Seventeen note~~ mega chromatic scale]]

=== Music ===

[https://soundcloud.com/jdfreivald/mo-happy-happy Mo - Happy - Happy] [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3 play] by Jake Freivald in Neutral[7], 24et tuning

[https://soundcloud.com/jdfreivald/mo-happy-happy Mo - Happy - Happy] [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3 play] by [[Jake Freivald]] in Neutral[7], 24et tuning

== Slendric ==

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== Namo ==

~~Subgroup: 2.3.11.13~~

~~Commas~~: ~~144/143, 243/242~~

Scales:

* [[namo7]]| – 7-tone [[haplotonic scale]]

~~Related temperament:~~ [[~~Valinorismic_temperaments#Mandos|mandos~~]]~~, mohajira, hemif~~

* [[namo10]] – 10-tone [[albitonic scale]]

* [[namo17]] – 17-tone [[chromatic scale]]

[[~~Tp_tuning|POT2 generator~~]]~~: ~11/9 = 351.488~~

[[~~Gencom|Gencom~~]]~~: [2 11/9; 144/143 243/242]~~

~~Gencom mapping: [<1 1 0 0 2 4|, <0 2 0 0 5~~ -~~1|]~~

~~Mapping: [<1 1 2 4|, <0 2 5 -1|]~~

~~EDOs: {{EDOs|7, 10, 17, 41, 58, 99cd}}~~

[[~~Tp_tuning#T2 tuning|RMS error]]: 0.7038 cents~~

~~[[namo7|Seven note haplotonic~~ scale]]

[[~~namo10|Ten note albitonic scale~~]]

[[~~namo17|Seventeen note~~ chromatic scale]]

== Sentry ==

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== Mohaha ==

[[File:mohaha_131edo.png|right|alt=mohaha_131edo.png|Mohaha in 131edo]]

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=== Mohoho ===

== Joan ==

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-A '''chromatic pair''' is a pair of [[MOS scale]]s in some [[rank-2 temperament]] (either a full [[Harmonic limit|''p''-limit]] temperament or a [[subgroup temperament]]) that are analogous to the familiar [[5L 2s|diatonic]] and [[chromatic]] scales of standard tuning. The smaller scale is an '''albitonic scale''' (from Latin ''albus'', "white"), named such since the diatonic scale can be played using the white keys of a piano, and the larger of the two is a '''chromatic scale''', analogous to the chromatic scale of standard tuning. Other related scales can be associated to chromatic pairs, namely a '''haplotonic scale''' (from Greek ''haplóos'', "single, simple"), analogous to the pentatonic scale of standard tuning and played using the black keys of a piano.
+A '''chromatic pair''' is a pair of [[mos scale]]s in some [[rank-2 temperament]] (either a full [[Harmonic limit|''p''-limit]] temperament or a [[subgroup temperament]]) that are analogous to the familiar [[5L 2s|diatonic]] and [[chromatic]] scales of standard tuning. The smaller scale is an '''albitonic scale''' (from Latin ''albus'', "white"), named such since the diatonic scale can be played using the white keys of a piano, and the larger of the two is a '''chromatic scale''', analogous to the chromatic scale of standard tuning. Other related scales can be associated to chromatic pairs, namely a '''haplotonic scale''' (from Greek ''haplóos'', "single, simple"), analogous to the pentatonic scale of standard tuning and played using the black keys of a piano.
-In the sections below, the pair temperaments are listed in order of increasing [[Tp_tuning#T2 tuning|RMS error]], which is an appropriate error measure for subgroups as well as full ''p''-limit groups.
+In the sections below, the pair temperaments are listed in order of increasing [[Tp tuning#T2 tuning|RMS error]], which is an appropriate error measure for subgroups as well as full ''p''-limit groups.
 == Terrain ==
@@ Line 293: / Line 293: @@
 == Neutral ==
-Subgroup: 2.3.11
+{{See also| Rastmic clan #Neutral }}
-Commas: 243/242
-Svalname: 7&amp;17
-[[Tp_tuning|POT2 generator]]: ~11/9 = 350.525
-[[Gencom|Gencom]]: [2 11/9; 243/242]
-Gencom mapping: [&lt;1 1 0 0 2|, &lt;0 2 0 0 5|]
-Mapping: [&lt;1 1 2|, &lt;0 2 5|]
-EDOs: {{EDOs|7, 17, 24, 65, 89, 202, 291, 380}}
-[[Tp_tuning#T2 tuning|RMS error]]: 0.3021 cents
 [[File:neutral_380edo.png|alt=neutral_380edo.png|neutral_380edo.png]]
-[[neutral7|Seven note albitonic scale]]
+* [[neutral7]] – 7-tone [[albitonic scale]]
+* [[neutral10]] – 10-tone [[chromatic scale]]
-[[neutral10|Ten note chromatic scale]]
+* [[neutral17]] – 17-tone [[mega-chromatic scale]]
-[[neutral17|Seventeen note mega chromatic scale]]
 === Music ===
-[https://soundcloud.com/jdfreivald/mo-happy-happy Mo - Happy - Happy] [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3 play] by Jake Freivald in Neutral[7], 24et tuning
+[https://soundcloud.com/jdfreivald/mo-happy-happy Mo - Happy - Happy] [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/mo-happy-happy.mp3 play] by [[Jake Freivald]] in Neutral[7], 24et tuning
 == Slendric ==
@@ Line 780: / Line 762: @@
 == Namo ==
-Subgroup: 2.3.11.13
+{{See also| Rastmic clan #Namo }}
-Commas: 144/143, 243/242
+Scales:
+* [[namo7]]| – 7-tone [[haplotonic scale]]
-Related temperament: [[Valinorismic_temperaments#Mandos|mandos]], mohajira, hemif
+* [[namo10]] – 10-tone [[albitonic scale]]
+* [[namo17]] – 17-tone [[chromatic scale]]
-[[Tp_tuning|POT2 generator]]: ~11/9 = 351.488
-[[Gencom|Gencom]]: [2 11/9; 144/143 243/242]
-Gencom mapping: [&lt;1 1 0 0 2 4|, &lt;0 2 0 0 5 -1|]
-Mapping: [&lt;1 1 2 4|, &lt;0 2 5 -1|]
-EDOs: {{EDOs|7, 10, 17, 41, 58, 99cd}}
-[[Tp_tuning#T2 tuning|RMS error]]: 0.7038 cents
-[[namo7|Seven note haplotonic scale]]
-[[namo10|Ten note albitonic scale]]
-[[namo17|Seventeen note chromatic scale]]
 == Sentry ==
@@ Line 1,300: / Line 1,265: @@
 == Mohaha ==
-{{See also| Meantone family #Mohaha }}
+{{See also| Rastmic clan #Mohaha }}
 [[File:mohaha_131edo.png|right|alt=mohaha_131edo.png|Mohaha in 131edo]]
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 === Mohoho ===
-{{See also| Meantone family #Mohoho }}
+{{See also| Rastmic clan #Mohoho }}
 == Joan ==