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8L 3s (3/1-equivalent): Difference between revisions

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| Paucitonic = 3
| Paucitonic = 3
| Pattern = LLLsLLLsLLs
| Pattern = LLLsLLLsLLs
}}
}}  
==Relationship to the Obikhod==
The '''Obikhod''' (Обиход церковного пения) is a collection of polyphonic Russian Orthodox liturgical chants forming a major tradition of Russian liturgical music; it includes both liturgical texts and psalm settings.
 
The original ''Obikhod,'' the book of rites of the monastery of Volokolamsk, was composed about 1575. Among its subjects were traditional liturgical chants. The Obikhod was originally monodic but later developed polyphony. In 1772 the Obikhod was the first compilation of music printed in Russia, in Moscow. The common version was extensively revised and standardized by composer Nikolai Rimsky-Korsakov; this version was published as the 1909 edition of the Obikhod, the last before the Russian Revolution.
 
The Obikhod style, and the 1909 edition, was predominately used by the Russian Orthodox Church during the decades of Soviet Union rule in the 20th century, displacing both traditional Russian styles, such as the Ruthenian Prostopinije style, and also the chant traditions of Georgia, Armenia, and Carpatho-Russia.<ref>John Anthony McGuckin, ''The Encyclopedia of Eastern Orthodox Christianity'', 2010, p406. Quote: "During the Soviet period, Russian obikhod-style choral polyphony all but eradicated the received chant traditions of Georgia, Armenia, and Carpatho-Russia, but currently there is a trend to revive the Znamenny, Iberian, and Ruthenian chant ..."</ref>
 
Pyotr Ilyich Tchaikovsky drew from the Obikhod style for his ''1812 Overture'', as did Nikolai Rimsky-Korsakov in his ''Russian Easter Festival Overture.'' Anatoly Lyadov also drew from them in his ''Ten Arrangements from Obikhod'' Op.61, as did Alexander Raskatov in his  ''Obikhod'' (2002).
 
The pitch set used in these chants traditionally consists of four three-note groups. Each note within a group is separated by a whole tone, and each group is separated by a semitone. If starting from G, the result is: G, A, B / C, D, E / F, G, A / B♭, C, D. Theoretically, more groups can be added either above or below, which has been done by some 20th-century Russian composers. This pitch set also influenced Russian folk music: for example, the Livenka accordion contains the pitch set on its melody side. On a common Livenka accordion, the pitch set will not span a pure tritave.<ref>[https://en.wikipedia.org/wiki/Obikhod Obikhod - Wikipedia]. ''en.wikipedia.org''. Retrieved July 28, 2021.</ref>
==Standing assumptions==
==Standing assumptions==
The tempered generalized Livenka accordion is used in this article to refer to tunings of the pitch set.
The tempered generalized Livenka accordion is used in this article to refer to tunings of the pitch set.
Line 43: Line 53:
|0
|0
|G
|G
|perfect unison
| perfect unison
|0
|0
|0
|0
Line 70: Line 80:
|3
|3
|H
|H
|major 2nd
| major 2nd
|1L
|1L
| -3
| -3
|Ff
|Ff
|natural 11th
|natural 11th
Line 106: Line 116:
|7
|7
|B
|B
|major 7th
| major 7th
|5L+1s
|5L+1s
| -7
| -7
|Af
|Af
|minor 6th
|minor 6th
Line 124: Line 134:
|9
|9
|K#
|K#
|augmented 4th
| augmented 4th
|3L
|3L
| -9
| -9
Line 176: Line 186:
|Fff
|Fff
|diminished 11th
|diminished 11th
|6L+4s
| 6L+4s
|-
|-
|15
|15
Line 200: Line 210:
|augmented 3rd
|augmented 3rd
|3L-1s
|3L-1s
| -17
| -17
|Eff
|Eff
|diminished 10th
|diminished 10th
Line 206: Line 216:
|-
|-
|18
|18
|B#
| B#
|augmented 7th
|augmented 7th
|6L
|6L
Line 215: Line 225:
|}
|}
==Tuning ranges==
==Tuning ranges==
===Simple tunings===
===Simple tunings ===
Table of intervals in the simplest Obikhodic tunings:
Table of intervals in the simplest Obikhodic tunings:
{| class="wikitable right-2 right-3 right-4 sortable"
{| class="wikitable right-2 right-3 right-4 sortable"
Line 243: Line 253:
|2\19, 200.00
|2\19, 200.00
|3\27, 211.765 (211.11)
|3\27, 211.765 (211.11)
|3\30, 189.47 (190.00)
| 3\30, 189.47 (190.00)
|H
|H
|3
|3
Line 256: Line 266:
|major 3rd
|major 3rd
|4\19, 400.00
|4\19, 400.00
|6\27, 423.53 (422.22)
| 6\27, 423.53 (422.22)
|6\30, 378.95 (380.00)
|6\30, 378.95 (380.00)
|J
|J
Line 277: Line 287:
|diminished 5th
|diminished 5th
|8\27, 564.71 (562.96)
|8\27, 564.71 (562.96)
|10\30, 631.58 (633.33)
| 10\30, 631.58 (633.33)
|Lf
|Lf
| -10
| -10
Line 285: Line 295:
|10\27, 705.88 (703.70)
|10\27, 705.88 (703.70)
|11\30, 694.74 (696.67)
|11\30, 694.74 (696.67)
|L
| L
|1
|1
|-
|-
Line 343: Line 353:
|2
|2
|-
|-
|minor 10th
| minor 10th
|15\19, 1500.00
|15\19, 1500.00
|21\27, 1482.35 (1477.78)
|21\27, 1482.35 (1477.78)
|24\30, 1515.79 (1520.00)
|24\30, 1515.79 (1520.00)
|Ef
|Ef
| -6
| -6
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 10th
|major 10th
Line 371: Line 381:
|8
|8
|}
|}
===Hypohard===
===Hypohard ===
[[Hypohard]] Obikhodic tunings (with generator between 7\19 and 10\27) have step ratios between 2/1 and 3/1.  
[[Hypohard]] Obikhodic tunings (with generator between 7\19 and 10\27) have step ratios between 2/1 and 3/1.  


Line 395: Line 405:
|2\19, 200.00
|2\19, 200.00
|3\27, 211.765 (211.11)
|3\27, 211.765 (211.11)
|5\46, 206.90 (206.52)
| 5\46, 206.90 (206.52)
|-
|-
|s (-8g + 3 ~tritaves)
|s (-8g + 3 ~tritaves)
Line 410: Line 420:
!Size in [[27edt|~27edt]] (hard)
!Size in [[27edt|~27edt]] (hard)
!Size in ~[[46edt]] (semihard)
!Size in ~[[46edt]] (semihard)
!Note name on G
! Note name on G
!#Gens up
!#Gens up
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|unison
|unison
|0\19, 0.00
| 0\19, 0.00
|0\27, 0.00
|0\27, 0.00
|0\46, 0.00
|0\46, 0.00
Line 427: Line 437:
| -8
| -8
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 2nd
| major 2nd
|2\19, 200.00
|2\19, 200.00
|3\27, 211.765 (211.11)
|3\27, 211.765 (211.11)
|5\46, 206.90 (206.52)
|5\46, 206.90 (206.52)
|H
|H
|3
| 3
|-
|-
|minor 3rd
|minor 3rd
Line 438: Line 448:
|4\27, 282.35 (281.48)
|4\27, 282.35 (281.48)
|7\46, 289.655 (289.13)
|7\46, 289.655 (289.13)
|Jf
| Jf
| -5
| -5
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 445: Line 455:
|6\27, 423.53 (422.22)
|6\27, 423.53 (422.22)
|10\46, 413.79 (413.04)
|10\46, 413.79 (413.04)
|J
| J
|6
|6
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
Line 451: Line 461:
|5\19, 500.00
|5\19, 500.00
|7\27, 494.12 (493.59)
|7\27, 494.12 (493.59)
|12\46, 496.55 (495.65)
| 12\46, 496.55 (495.65)
|K
|K
| -2
| -2
Line 471: Line 481:
|7\19, 700.00
|7\19, 700.00
|10\27, 705.88 (703.70)
|10\27, 705.88 (703.70)
|17\46, 703.45 (702.17)
| 17\46, 703.45 (702.17)
|L
|L
|1
|1
Line 485: Line 495:
|9\19, 900.00
|9\19, 900.00
|13\27, 917.65 (914.81)
|13\27, 917.65 (914.81)
|22\46, 910.345 (908.70)
| 22\46, 910.345 (908.70)
|A
|A
|4
|4
Line 504: Line 514:
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|perfect octave
|perfect octave
|12\19, 1200.00
| 12\19, 1200.00
|17\27, 1200.00 (1196.30)
|17\27, 1200.00 (1196.30)
|29\46, 1200.00 (1197.83)
| 29\46, 1200.00 (1197.83)
|C
|C
| -1
| -1
Line 518: Line 528:
|-
|-
|minor 9th
|minor 9th
|18\27, 1270.59 (1266.67)
| 18\27, 1270.59 (1266.67)
|31\46, 1282.76 (1280.435)
|31\46, 1282.76 (1280.435)
|Df
|Df
Line 581: Line 591:
|3\49, 116.13 (116.33)
|3\49, 116.13 (116.33)
|}
|}
====Intervals====
==== Intervals ====
Sortable table of major and minor intervals in hyposoft Obikhod tunings (~19edt not shown):
Sortable table of major and minor intervals in hyposoft Obikhod tunings (~19edt not shown):
{| class="wikitable"
{| class="wikitable"
|+
|+
!Degree
! Degree
!Size in ~[[30edt]] (soft)
!Size in ~[[30edt]] (soft)
!~[[49edt]] (semisoft)
!~[[49edt]] (semisoft)
Line 613: Line 623:
|3
|3
|-
|-
|minor 3rd
| minor 3rd
|5\30, 315.79 (316.67)
|5\30, 315.79 (316.67)
|8\49, 309.68 (310.20)
|8\49, 309.68 (310.20)
Line 627: Line 637:
|6
|6
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|natural 4th
| natural 4th
|8\30, 505,26 (506.67)
|8\30, 505,26 (506.67)
|13\49, 503.23 (504.08)
|13\49, 503.23 (504.08)
Line 698: Line 708:
|-
|-
|minor 9th
|minor 9th
|21\30, 1326.32 (1330.00)
| 21\30, 1326.32 (1330.00)
|34\49, 1316.13 (1318.37)
|34\49, 1316.13 (1318.37)
|Df
|Df
|15/7
|15/7
| -9
| -9
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 9th
|major 9th
|22\30, 1389.47 (1393.33)
| 22\30, 1389.47 (1393.33)
|36\49, 1393.55 (1395.92)
|36\49, 1393.55 (1395.92)
|D
|D
Line 711: Line 721:
|2
|2
|-
|-
|minor 10th
| minor 10th
|24\30, 1515.79 (1520.00)
|24\30, 1515.79 (1520.00)
|39\49, 1508.68 (1512.245)
|39\49, 1508.68 (1512.245)
Line 721: Line 731:
|25\30, 1578.95 (1583.33)
|25\30, 1578.95 (1583.33)
|41\49, 1587.10 (1590.80)
|41\49, 1587.10 (1590.80)
|E
| E
|5/2
|5/2
|5
|5
Line 735: Line 745:
|28\30, 1768.42 (1773.33)
|28\30, 1768.42 (1773.33)
|46\49, 1780.645 (1783.67)
|46\49, 1780.645 (1783.67)
|F
| F
|14/5
|14/5
|8
|8
Line 846: Line 856:
|augmented 4th
|augmented 4th
|12\41, 553.85 (556.10)
|12\41, 553.85 (556.10)
|K
| K
|[[11/8]], [[18/13]]
|[[11/8]], [[18/13]]
|9
|9
Line 854: Line 864:
|K#, Lff
|K#, Lff
|[[7/5]], [[10/7]]
|[[7/5]], [[10/7]]
|20,-21
| 20,-21
|-
|-
|diminished 5th
|diminished 5th
|14\41, 646.15 (648.78)
|14\41, 646.15 (648.78)
|Lf
| Lf
|[[16/11]], [[13/9]]
|[[16/11]], [[13/9]]
| -10
| -10
Line 868: Line 878:
|1
|1
|-
|-
|augmented 5th
| augmented 5th
|16\41, 738.46 (741.46)
|16\41, 738.46 (741.46)
|L#
|L#
Line 880: Line 890:
| -18
| -18
|-
|-
|minor 6th
| minor 6th
|18\41, 830.77 (834.15)
|18\41, 830.77 (834.15)
|Af
|Af
Line 923: Line 933:
|-
|-
|diminished octave
|diminished octave
|25\41, 1153.85 (1158.54)
| 25\41, 1153.85 (1158.54)
|Cf
|Cf
|[[64/33]], [[96/49]], [[35/18]], [[48/25]]
|[[64/33]], [[96/49]], [[35/18]], [[48/25]]
Line 938: Line 948:
|C#
|C#
|33/16, 49/24, 72/35, 25/12
|33/16, 49/24, 72/35, 25/12
|10
| 10
|-
|-
|doubly augmented octave, diminished 9th
|doubly augmented octave, diminished 9th
Line 960: Line 970:
|augmented 9th
|augmented 9th
|31\41, 1430.77 (1436.595)
|31\41, 1430.77 (1436.595)
|D#
| D#
|16/7, 30/13
|16/7, 30/13
|13
|13
Line 976: Line 986:
| -6
| -6
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 10th
| major 10th
|34\41, 1569.23 (1575.61)
|34\41, 1569.23 (1575.61)
|E
|E
Line 985: Line 995:
|35\41, 1615.385 (1621.95)
|35\41, 1615.385 (1621.95)
|E#
|E#
|18/7, 28/11, 33/13
| 18/7, 28/11, 33/13
|16
|16
|-
|-
Line 1,002: Line 1,012:
|augmented 11th
|augmented 11th
|38\41, 1753.85 (1760.98)
|38\41, 1753.85 (1760.98)
|F#
| F#
|11/4, 36/13
|11/4, 36/13
|8
|8
Line 1,028: Line 1,038:
!Note name on G
!Note name on G
!Approximate Ratios*
!Approximate Ratios*
!#Gens up
! #Gens up
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|unison
|unison
Line 1,061: Line 1,071:
|-
|-
|diminished 3rd
|diminished 3rd
|2\35, 109.09 (108.57)
| 2\35, 109.09 (108.57)
|Jff
|Jff
|[[18/17]], [[17/16]], [[16/15]], [[15/14]]
|[[18/17]], [[17/16]], [[16/15]], [[15/14]]
Line 1,084: Line 1,094:
|17
|17
|-
|-
|diminished 4th
| diminished 4th
|6\35, 327.27 (325.71)
|6\35, 327.27 (325.71)
|Kff
|Kff
Line 1,110: Line 1,120:
|perfect 5th
|perfect 5th
|13\35, 709.09 (705.71)
|13\35, 709.09 (705.71)
|L
| L
|[[3/2]]
|[[3/2]]
|1
|1
|-
|-
|augmented 5th
| augmented 5th
|16\35, 872.73 (868.57)
|16\35, 872.73 (868.57)
|L#
|L#
Line 1,120: Line 1,130:
|12
|12
|-
|-
|diminished 6th
| diminished 6th
|11\35, 600.00 (597.14)
|11\35, 600.00 (597.14)
|Aff
|Aff
Line 1,158: Line 1,168:
|major 7th
|major 7th
|21\35, 1145.455 (1140.00)
|21\35, 1145.455 (1140.00)
|B
| B
|[[31/16]], [[64/33]], [[33/17]], [[35/18]]
|[[31/16]], [[64/33]], [[33/17]], [[35/18]]
|7
|7
Line 1,168: Line 1,178:
|18
|18
|-
|-
|diminished octave
| diminished octave
|19\22, 1036.36 (1031.43)
|19\22, 1036.36 (1031.43)
|Cf
| Cf
|[[9/5]], [[11/6]], [[20/11]]
|[[9/5]], [[11/6]], [[20/11]]
| -12
| -12
Line 1,194: Line 1,204:
|major 9th
|major 9th
|26\35, 1418.18 (1411.43)
|26\35, 1418.18 (1411.43)
|D
| D
|9/4, 34/15, 16/7
|9/4, 34/15, 16/7
|2
|2
Line 1,214: Line 1,224:
|Ef
|Ef
|40/17, 7/3
|40/17, 7/3
| -6
| -6
|- bgcolor="#eaeaff"
|- bgcolor="#eaeaff"
|major 10th
|major 10th
|30\35, 1636.36 (1628.57)
|30\35, 1636.36 (1628.57)
|E
|E
|28/11, 18/7, 44/17
| 28/11, 18/7, 44/17
|5
|5
|-
|-
Line 1,229: Line 1,239:
|-
|-
|diminished 11th
|diminished 11th
|28\35, 1527.27 (1520.00)
| 28\35, 1527.27 (1520.00)
|Ff
|Ff
|12/5, 17/7, 22/9
|12/5, 17/7, 22/9
Line 1,253: Line 1,263:
|}
|}
===Ultrahard===
===Ultrahard===
[[Archytas cla|Ultrapythagorean]] Obikhodic is a rank-2 temperament in the [[Step ratio|pseudopaucitonic]] range. It represents the only [[harmonic entropy]]<nowiki/>minimum of the oneirotonic spectrum.
[[Archytas clan#Ultrapyth|Ultrapythagorean]] Obikhodic is a rank-2 temperament in the [[Step ratio|pseudopaucitonic]] range. It represents the [[harmonic entropy]] minimum of the Obikhodic spectrum where [[7/4]] is the minor seventh.


In the broad sense, Buzzard can be viewed as any tuning that divides the 3rd harmonic into 4 equal parts. [[23edo]], [[28edo]]<nowiki/>and [[33edo]] can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between 18edo and true Buzzard in terms of harmonies. [[38edo]] & [[43edo]] are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but [[48edo]] is where it really comes into its own in terms of harmonies, providing not only an excellent [[3/2]], but also [[7/4]] and [[The_Archipelago|archipelago]] harmonies, as by dividing the 5th in 4 it obviously also divides it in two as well.  
In the broad sense, Ultrapyth can be viewed as any tuning that divides a 16/7 into 2 equal parts. ~[[35edt]] and ~[[43edt]] can nominally be viewed as supporting it, but are still very flat and in an ambiguous zone between ~[[27edt]] and true Ultrapyth in terms of harmonies. ~[[51edt]] & ~[[59edt]] are good compromises between melodic utility and harmonic accuracy, as the small step is still large enough to be obvious to the untrained ear, but ~[[67edt]] is where it really comes into its own in terms of harmonies, providing not only an excellent [[6/5]], but also 7:8:9 melodies, as by shifting one whole tone done a comma, it shifts from [[The Archipelago|archipelago]] to septimal harmonies.  


Beyond that, it's a question of which intervals you want to favor. [[53edo]] has an essentially perfect [[3/2]], [[58edo]] gives the lowest overall error for the Barbados triads 10:13:15 and 26:30:39, while [[63edo]] does the same for the basic 4:6:7 triad. You could in theory go up to [[83edo]] if you want to favor the [[7/4]] above everything else, but beyond that, general accuracy drops off rapidly and you might as well be playing equal pentatonic.
Beyond that, it's a question of which intervals you want to favor. ~[[75edt]] has an essentially perfect [[9/8]], either ~[[83edt]] or ~[[91edt]] has an essentially perfect [[7/4]] and multiple chains of essentially perfect [[meantone]], and while ~[[99edt]] does not have an essentially perfect [[7/4]], it has a double chain of essentially perfect quarter-comma meantone. You could in theory go up to ~[[131edt]] if you want to favor the [[3/2]] above everything else, but beyond that, general accuracy drops off rapidly and you might as well be playing equal pentatonic.


The sizes of the generator, large step and small step of oneirotonic are as follows in various buzzard tunings.
The sizes of the generator, large step and small step of Obikhodic are as follows in various ultrapyth tunings.
{| class="wikitable right-2 right-3 right-4 right-5"
{| class="wikitable right-2 right-3 right-4 right-5"
|-
|-
!
!
![[38edo]]
![[38edo|~]][[59edt]]
![[53edo]]
!~[[83edt]]
![[63edo]]
!~[[91edt]]
!Optimal ([[POTE]]) Buzzard tuning
!~[[99edt]]
!Optimal ([[POTE|PHTE]]) Ultrapyth tuning
!JI intervals represented (2.3.5.7.13 subgroup)
!JI intervals represented (2.3.5.7.13 subgroup)
|-
|-
|generator (g)
| generator (g)
|15\38, 473.68
|22\59, 713.51
|21\53, 475.47
|31\83, 715.385
|25\63, 476.19
|34\91, 715.79
|475.69
| 37\99, 716.13
|4/3 21/16
|712.61
| 3/2
|-
|-
|L (3g - octave)
|L (3g - ~tritave)
|7/38, 221.04
| 7\39, 227.03
|10/53, 226.41
|10\83, 230.77
|12/63, 228.57
|11\91, 231.58
|227.07
|12\99, 232.26
| 230.55
|8/7
|8/7
|-
|-
|s (-5g + 2 octaves)
|s (-8g + 3 ~tritaves)
|1/38, 31.57
| 1\59, 32.43
|1/53 22.64
|1\83, 23.08
|1/63 19.05
|1\91, 21.05
|21.55
|1/99, 19.355
|50/49 81/80 91/90
|20.96
| 50/49 81/80 91/90
|}
|}
====Intervals====
====Intervals====
Sortable table of intervals in the Dylathian mode and their Buzzard interpretations:
Sortable table of intervals in the Great Mixolydian mode and their Buzzard interpretations:
{| class="wikitable right-2 right-3 right-4 right-5 sortable"
{| class="wikitable right-2 right-3 right-4 right-5 sortable"
|-
|-
!Degree
!Degree
!Size in 38edo
!Size in [[38edo|~]][[59edt]]
!Size in 53edo
!Size in ~[[83edt]]
!Size in 63edo
!Size in ~[[91edt]]
!Size in ~[[99edt]]
!Size in POTE tuning
!Size in POTE tuning
!Note name on Q
!Note name on D
! class="unsortable" |Approximate ratios
! class="unsortable" |Approximate ratios
!#Gens up
!#Gens up
|-
|-
|1
|1
|0\38, 0.00
|0\59, 0.00
|0\53, 0.00
|0\83, 0.00
|0\63, 0.00
|0\91, 0.00
|0\99, 0.00
|0.00
|0.00
|Q
|D
|1/1
|1/1
|0
|0
|-
|-
|2
|2
|7\38, 221.05
| 7\59, 227.03
|10\53, 226.42
| 10\83, 230.77
|12\63, 228.57
|11\91, 231.58
|227.07
|12\99, 232.26
|J
|230.55
|E
|8/7
|8/7
| +3
| +3
|-
|-
|3
|3
|14\38, 442.10
|14\59, 454.05
|20\53, 452.83
| 20\83, 461.54
|24\63, 457.14
|22\91, 463.16
|453.81
|24\99, 464.52
|K
|461.10
|F
|13/10, 9/7
|13/10, 9/7
| +6
| +6
|-
|-
|4
| 4
|15\38, 473.68
|15\59, 486.49
|21\53, 475.47
|21\83, 484.615
|25\63, 476.19
|23\91, 484.21
|475.63
|25\99, 483.87
|L
|482.06
|21/16
| G
| +1
|4/3
| -2
|-
|-
|5
|5
|22\38, 694.73
| 22\59, 713.51
|31\53, 701.89
| 31\83, 715.385
|37\63, 704.76
|34\91, 715.79
|702.54
|37\99, 716.13
|M
| 712.61
|H
|3/2
|3/2
| +4
| +1
|-
|-
|6
|6
|29\38, 915.78
|29\59, 940.54
|41\53, 928.30
| 41\83, 946.15
|49\63, 933.33
|45\91, 947.36
|929.45
|49\99, 948.39
|N
|943.16
|12/7, 22/13
|J
| +7
| 12/7, 26/15
| +4
|-
|-
|7
|7
|30\38, 947.36
|30\38, 972.97
|42\53, 950.94
|42\83, 969.23
|50\63, 952.38
|46\91, 968.42
|951.27
|50\99, 967.74
|O
|964.12
|26/15
|K
| 7/4
| -4
|-
|8
|37\59, 1200.00
|52\83, 1200.00
|57\91, 1200.00
|62\99, 1200.00
|1194.67
|L
|2/1
| -1
|-
|9
|44\59, 1427.03
|62\83, 1430.77
|68\91, 1430.58
|74\99, 1432.26
|1425.22
|A
|16/7
| +2
| +2
|-
|-
|8
|10
|37\38, 1168.42
|51\59, 1654.05
|52\53, 1177.36
|72\83, 1661.54
|62\63, 1180.95
|79\91, 1663.16
|1178.18
|86\99, 1664.52
|P
|1655.77
|98/50, 160/81
|B
|13/5, 18/7
| +5
| +5
|-
|11
|52\59, 1686.49
|73\83,
1684.615
|80\91,
1684.21
|87\99, 1683.87
|1676.32
|C
|4/3
| -3
|}
|}
==Modes==
==Modes==
Line 1,397: Line 1,452:
| |LsLLsLsL
| |LsLLsLsL
| style="text-align:center;" |<nowiki>4|3</nowiki>
| style="text-align:center;" |<nowiki>4|3</nowiki>
| |Ultharian (ul-THA(I)R-iən)
| | Ultharian (ul-THA(I)R-iən)
|-
|-
| |LsLsLLsL
| |LsLsLLsL
Line 1,405: Line 1,460:
| |sLLsLLsL
| |sLLsLLsL
| style="text-align:center;" |<nowiki>2|5</nowiki>
| style="text-align:center;" |<nowiki>2|5</nowiki>
| |Kadathian (kə-DA(H)TH-iən)
| | Kadathian (kə-DA(H)TH-iən)
|-
|-
| |sLLsLsLL
| |sLLsLsLL
Line 1,416: Line 1,471:
|}<references />
|}<references />


== Relationship to the Obikhod ==
The '''Obikhod''' (Обиход церковного пения) is a collection of polyphonic Russian Orthodox liturgical chants forming a major tradition of Russian liturgical music; it includes both liturgical texts and psalm settings.
The original ''Obikhod,'' the book of rites of the monastery of Volokolamsk, was composed about 1575. Among its subjects were traditional liturgical chants. The Obikhod was originally monodic but later developed polyphony. In 1772 the Obikhod was the first compilation of music printed in Russia, in Moscow. The common version was extensively revised and standardized by composer Nikolai Rimsky-Korsakov; this version was published as the 1909 edition of the Obikhod, the last before the Russian Revolution.
The Obikhod style, and the 1909 edition, was predominately used by the Russian Orthodox Church during the decades of Soviet Union rule in the 20th century, displacing both traditional Russian styles, such as the Ruthenian Prostopinije style, and also the chant traditions of Georgia, Armenia, and Carpatho-Russia.<ref>John Anthony McGuckin, ''The Encyclopedia of Eastern Orthodox Christianity'', 2010, p406. Quote: "During the Soviet period, Russian obikhod-style choral polyphony all but eradicated the received chant traditions of Georgia, Armenia, and Carpatho-Russia, but currently there is a trend to revive the Znamenny, Iberian, and Ruthenian chant ..."</ref>
Pyotr Ilyich Tchaikovsky drew from the Obikhod style for his ''1812 Overture'', as did Nikolai Rimsky-Korsakov in his ''Russian Easter Festival Overture.'' Anatoly Lyadov also drew from them in his ''Ten Arrangements from Obikhod'' Op.61, as did Alexander Raskatov in his  ''Obikhod'' (2002).
The pitch set used in these chants traditionally consists of four three-note groups. Each note within a group is separated by a whole tone, and each group is separated by a semitone. If starting from G, the result is: G, A, B / C, D, E / F, G, A / B♭, C, D. Theoretically, more groups can be added either above or below, which has been done by some 20th-century Russian composers. This pitch set also influenced Russian folk music: for example, the Livenka accordion contains the pitch set on its melody side. On a common Livenka accordion, the pitch set will not span a pure tritave.<ref>[https://en.wikipedia.org/wiki/Obikhod Obikhod - Wikipedia]. ''en.wikipedia.org''. Retrieved July 28, 2021.</ref>
== References ==
<references />
<references />


[[Category:Nonoctave]]
[[Category:Nonoctave]]
[[Category:Abstract MOS patterns]]
[[Category:Abstract MOS patterns]]
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