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{{Infobox MOS
{{Infobox MOS
| Name = Greater dicoid
|Tuning=7L 3s<15/7>}}
| Periods = 1
| nLargeSteps = 7
| nSmallSteps = 3
| Equalized = 7
| Collapsed = 5
| Pattern = LLLsLLsLLs
|Equave=15/7}}


'''7L 3s''' refers to the structure of [[MOSScales|moment of symmetry scales]] built from a 10-tone chain of neutral or major thirds (assuming a period of an octave up to 10/[[9edo]]):
{{MOS intro|Scale Signature=7L 3s<15/7>}}
 
L s L L L s L L s L


Graham Breed has a [http://x31eq.com/7plus3.htm page on his website] dedicated to 7+3 scales. He proposes calling the large step "t" for "tone", lowercase because the large step is a narrow neutral tone, and the small step "q" for "quartertone", because the small step is often close to a quartertone. (Note that the small step is not a quartertone in every instance of 7+3, so do not take that "q" literally.) Thus we have:
Graham Breed has a [http://x31eq.com/7plus3.htm page on his website] dedicated to 7+3 scales. He proposes calling the large step "t" for "tone", lowercase because the large step is a narrow neutral tone, and the small step "q" for "quartertone", because the small step is often close to a quartertone. (Note that the small step is not a quartertone in every instance of 7+3, so do not take that "q" literally.) Thus we have:
Line 20: Line 11:


==Intervals==
==Intervals==
The generator (g) will fall between 343 cents (2\7 - two degrees of [[7edo|7edo]] and 400 cents (3\9 - three degrees of [[10edo|9edo]]), hence a neutral or major third.
The generator (g) will fall between 377 cents (2\7 - two degrees of [[7ed15/7]]) and 396 cents (3\10 - three degrees of [[10ed15/7]]), hence a major third.


2g, then, will fall between 686 cents (4\7) and 800 cents (2\3), the range of [[5L 2s|diatonic]] fifths.
2g, then, will fall between 754 cents (4\7) and 792 cents (3\5), the range of [[5L 2s|diatonic]] subminor sixths.


The "large step" will fall between 171 cents (1\7) and 120 cents (1\10), ranging from a submajor second to a [[sinaic]].
The "large step" will fall between 188.5 cents (1\7) and 131.9 cents (1\10), ranging from a small major second to a [[sinaic]].


The "small step" will fall between 0 cents and 120 cents, sometimes sounding like a minor second, and sometimes sounding like a quartertone or smaller microtone.
The "small step" will fall between 0 cents and 131.9 cents, sometimes sounding like a minor second, and sometimes sounding like a quartertone or smaller microtone.


The most frequent interval, then is the neutral third (and its inversion, the neutral sixth), followed by the perfect fourth and fifth. Thus, 7+3 combines the familiar sound of perfect fifths and fourths with the unfamiliar sounds of neutral intervals. They are compatible with Arabic and Turkish scales, but not with traditional Western ones.
The most frequent interval, then is the major third (and its inversion, the diminished seventh), followed by the superfourth and subminor sixth.  


Note: In TAMNAMS, a k-step interval class in dicoid may be called a "k-step", "k-mosstep", or "k-dicostep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
Note: In TAMNAMS, a k-step interval class in dicoid may be called a "k-step", "k-mosstep", or "k-dicostep". 1-indexed terms such as "mos(k+1)th" are discouraged for non-diatonic mosses.
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|3L+1s
|3L+1s
| -2
| -2
|6
|6v
|minor 6-step
|minor 6-step
|4L+2s
|4L+2s
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|-
|-
|8
|8
|6^
|6
|major 6-step
|major 6-step
|5L+1s
|5L+1s
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|1L+2s
|1L+2s
|-
|-
| colspan="8" style="text-align:center" |The chromatic 17-note MOS (either [[7L 10s]], [[10L 7s]], or [[17edIX]]) also has the following intervals (from some root):
| colspan="8" style="text-align:center" |The chromatic 17-note MOS (either [[7L 10s (15/7-equivalent)|7L 10s]], [[10L 7s (15/7-equivalent)|10L 7s]], or [[17ed15/7]]) also has the following intervals (from some root):
|-
|-
|12
|12
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|}
|}
==Scale tree==
==Scale tree==
The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edIX would be (3+2)\(10+7) = 5\17 – five degrees of [[17edIX]]:


{| class="wikitable center-all"
! colspan="9" rowspan="2" |Generator
! colspan="2" |Normalized Cents
! colspan="2" |Śata
! rowspan="2" |L
! rowspan="2" |s
! rowspan="2" |L/s
! rowspan="2" |Comments
|-
!Chroma-positive
!Chroma-negative
!Chroma-positive
!Chroma-negative
|-
|7\10|| || || || ||
|
|
| ||933.333||400.000
|1190.000
|510.000||1||1||1.000||
|-
| || || || || ||40\57
|
|
| ||923.077||392.307
|1192.982
|507.018||6||5||1.200||Restles↑
|-
|
|
|
|
|
|
|73\104
|
|
|922.105
|391.579
|1193.269
|506.731
|11
|9
|1.222
|
|-
| || || || ||33\47||
|
|
| ||920.930||390.698
|1193.617
|506.383||5||4||1.250||
|-
| || || || || ||59\84
|
|
| ||919.481||389.610
|1194.048
|505.952||9||7||1.286||
|-
|
|
|
|
|
|
|85\121
|
|
|918.919
|389.189
|1194.215
|505.785
|13
|10
|1.000
|
|-
| || || ||26\37|| ||
|
|
| ||917.647||388.235
|1194.595
|505.405||4||3||1.333||
|-
| || || || || ||71\101
|
|
| ||916.129||387.097
|1195.050
|504.950||11||8||1.375||
|-
| || || || ||45\64||
|
|
| ||915.254||386.441
|1195.3125
|504.6875||7||5||1.400||Beatles
|-
| || || || || ||64\91
|
|
| ||914.286||385.714
|1195.604
|504.396||10||7||1.428||
|-
| || ||19\27|| || ||
|
|
| ||912.000||384.000
|1196.296
|503.704||3||2||1.500||L/s = 3/2, suhajira/ringo
|-
|
|
|
|
|
|
|
|
|126\179
|910.843
|383.133
|1196.648
|503.352
|20
|13
|1.538
|
|-
|
|
|
|
|
|
|
|107\152
|
|910.638
|382.988
|1196.711
|503.289
|17
|11
|1.545
|
|-
|
|
|
|
|
|
|88\125
|
|
|910.345
|382.759
|1196.800
|503.200
|14
|9
|1.556
|
|-
| || || || || ||69\98
|
|
| ||909.890||382.418
|1196.938
|503.062||11||7||1.571||
|-
| || || || ||50\71||
|
|
| ||909.091||381.818
|1197.183
|502.817||8||5||1.600||
|-
| || || || || ||81\115
|
|
| ||908.411||381.308
|1197.391
|502.609||13||8||1.625||Golden suhajira
|-
| || || ||31\44|| ||
|
|
| ||907.317||380.489
|1197.727
|502.273||5||3||1.667||
|-
| || || || || ||74\105
|
|
| ||906.122||379.592
|1198.095
|501.905||12||7||1.714||
|-
| || || || ||43\61||
|
|
| ||905.263||378.947
|1198.361
|501.639||7||4||1.750||
|-
| || || || || ||55\78
|
|
| ||904.110||378.082
|1198.561
|501.439||9||5||1.800||
|-
|
|
|
|
|
|
|67\95
|
|
|903.371
|377.528
|1198.947
|501.053
|11
|6
|1.833
|
|-
|
|
|
|
|
|
|
|79\112
|
|902.857
|377.143
|1199.107
|500.803
|13
|7
|1.857
|
|-
|
|
|
|
|
|
|
|
|91\129
|902.479
|376.860
|1199.224
|500.776
|15
|8
|1.875
|
|-
| ||12\17|| || || ||
|
|
| ||900.000||375.000
|1200.000
|500.000||2||1||2.000||Basic Greater dicoid<br>(Generators smaller than this are proper)
|-
|
|
|
|
|
|
|
|
|
|898.013
|373.510
|1200.625
|499.375
|19
|9
|2.111
|
|-
|
|
|
|
|
|
|
|
|
|897.778
|373.333
|1200.699
|499.301
|17
|8
|2.125
|
|-
|
|
|
|
|
|
|
|
|89\126
|897.479
|373.109
|1200.793
|499.207
|15
|7
|2.143
|
|-
|
|
|
|
|
|
|
|77\109
|
|897.087
|372.816
|1200.917
|499.083
|13
|6
|2.167
|
|-
|
|
|
|
|
|
|65\92
|
|
|896.552
|372.414
|1201.087
|498.913
|11
|5
|2.200
|
|-
| || || || || ||53\75
|
|
| ||895.775||371.831
|1201.333
|498.667||9||4||2.250||
|-
| || || || ||41\58||
|
|
| ||894.545||370.909
|1201.724
|498.276||7||3||2.333||
|-
| || || || || ||70\99
|
|
| ||893.617||370.213
|1202.020
|497.979||12||5||2.400||Hemif/hemififths
|-
| || || ||29\41|| ||
|
|
| ||892.307||369.231
|1202.439
|497.561||5||2||2.500||Mohaha/neutrominant
|-
| || || || || ||75\106
|
|
| ||891.089||368.317
|1202.830
|497.170||13||5||2.600||Hemif/salsa/karadeniz
|-
| || || || ||46\65||
|
|
| ||890.322||367.742
|1203.077
|496.923||8||3||2.667||Mohaha/mohamaq
|-
| || || || || ||63\89
|
|
| ||889.412||367.059
|1203.371
|496.629||11||4||2.750||
|-
|
|
|
|
|
|
|80\113
|
|
|888.889
|366.667
|1203.540
|496.460
|14
|5
|2.800
|
|-
| || ||17\24|| || ||
|
|
| ||886.957||365.213
|1204.167
|495.833||3||1||3.000||L/s = 3/1
|-
|
|
|
|
|
|
|
|90\127
|
|885.246
|363.934
|1204.724
|495.276
|16
|5
|3.200
|
|-
|
|
|
|
|
|
|73\103
|
|
|884.848
|363.636
|1204.854
|495.146
|13
|4
|3.250
|
|-
| || || || || ||56\79
|
|
| ||884.210||363.158
|1205.063
|494.937||10||3||3.333||
|-
| || || || ||39\55||
|
|
| ||883.018||362.264
|1205.455
|494.545||7||2||3.500||
|-
| || || || || ||61\86
|
|
| ||881.928||361.446
|1205.814
|494.186||11||3||3.667||
|-
| || || ||22\31|| ||
|
|
| ||880.000||360.000
|1206.452
|493.548||4||1||4.000||Mohaha/migration/mohajira
|-
|
|
|
|
|
|
|
|93\131
|
|878.740
|359.055
|1206.870
|493.130
|17
|4
|4.250
|
|-
|
|
|
|
|
|
|71\100
|
|
|878.351
|358.762
|1207.000
|493.000
|13
|3
|4.333
|
|-
| || || || || ||49\69
|
|
| ||877.612||358.209
|1207.246
|492.754||9||2||4.500||
|-
|
|
|
|
|
|
|76\107
|
|
|876.923
|357.692
|1207.477
|492.523
|14
|3
|4.667
|
|-
| || || || ||27\38||
|
|
| ||875.676||356.757
|1207.895
|492.105||5||1||5.000||
|-
|
|
|
|
|
|
|59\83
|
|
|874.074
|355.556
|1208.434
|491.566
|11
|2
|5.500
|
|-
| || || || || ||32\45
|
|
| ||872.727||354.545
|1208.889
|491.111||6||1||6.000||Mohaha/ptolemy
|-
|5\7|| || || || ||
|
|
| ||857.143||342.857
|1214.286
|485.714||1||0||→ inf||
|}


The scale produced by stacks of 5\17 is the [[17edIX neutral scale]]. Between 11/38 and 16/55, with 9/31 in between, is the mohajira/mohaha/mohoho range, where mohaha and mohoho use the MOS as the chromatic scale of a [[Chromatic pairs|chromatic pair]].
The generator range reflects two extremes: one where L = s (3\10), and another where s = 0 (2\7). Between these extremes, there is an infinite continuum of possible generator sizes. By taking freshman sums of the two edges (adding the numerators, then adding the denominators), we can fill in this continuum with compatible edos, increasing in number of tones as we continue filling in the in-betweens. Thus, the smallest in-between edIX would be (3+2)\(10+7) = 5\17 – five degrees of [[17ed15/7]]:
 
{{MOS tuning spectrum|Scale Signature=7L 3s <15/7>}}
 
The scale produced by stacks of 5\17 is the [[17ed15/7 neutral scale]]. Between 11/38 and 16/55, with 9/31 in between, is the mohajira/mohaha/mohoho range, where mohaha and mohoho use the MOS as the chromatic scale of a [[Chromatic pairs|chromatic pair]].


Other compatible edIXs include: [[37edIX]], [[27edIX]], [[44edIX]], [[41edIX]], [[24edIX]], [[31edIX]].
Other compatible ed15/7s include: [[37ed15/7]], [[27ed15/7]], [[44ed15/7]], [[41ed15/7]], [[24ed15/7]], [[31ed15/7]].


You can also build this scale by stacking neutral thirds that are not members of edIXs – for instance, frequency ratios 11:9, 5:4, 21:17, 16:13 – or the square root of 3:2 or 11:7 (a bisected just perfect fifth or undecimal subminor sixth).
You can also build this scale by stacking neutral thirds that are not members of ed15/7s – for instance, the frequency ratio 5:4 – or the square root of 11:7 (a bisected undecimal subminor sixth).


==Rank-2 temperaments==
==Rank-2 temperaments==
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