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{{Infobox MOS
{{Infobox MOS}}
| Name = pine
{{MOS intro}}
| Periods = 1
== Name ==
| nLargeSteps = 7
{{TAMNAMS name}}
| nSmallSteps = 1
 
| Equalized = 1
== Scale properties ==
| Paucitonic = 1
 
| Pattern = LLLLLLLs
=== Intervals ===
{{MOS intervals}}
 
=== Generator chain ===
{{MOS genchain}}
 
=== Modes ===
{{MOS mode degrees}}
 
=== Proposed names ===
Mode names are from [[Porcupine Temperament Modal Harmony|Porcupine temperament modal harmony]]. Descriptive mode names are based on using {{dash|1, 4, 7}}, i.e. 3+3 triads as a basis for harmony.
{{MOS modes
| Mode names =
octopus $
mantis $
dolphin $
crab $
tuna $
salmon $
starfish $
whale $
| Table Headers=Name Origin
| Table Entries=
Bright quartal $
Dark quartal $
Bright major $
Middle major $
Dark major $
Bright minor $
Middle minor $
Dark minor $
}}
}}


There are two notable [[Harmonic_Entropy|harmonic entropy]] minima with this [[MOSScales|MOS]] pattern. The first is [[Porcupine_family|porcupine]], in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is [[Chromatic_pairs#Greeley|greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc.
== Theory ==
=== Low harmonic entropy scales ===
There are three notable [[harmonic entropy]] minima with this [[mos]] pattern.


Scales of this form are always [[Rothenberg_propriety|proper]], because there is only one small step.
* The lowest accuracy one is [[porcupine]], in which two generators make a [[6/5]] and three make a [[4/3]]. The range of porcupine tunings is about 2\15 to 3\22.
* Less well-known and more accurate is [[greeley]], in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like [[10/7]], [[11/7]], etc.
* Thirdly and finally, [[tempering out]] [[4000/3993|S10/S11]] so that ([[4/3]])/([[11/10]])<sup>3</sup> is tempered out results in an unusually high accuracy and efficient rank-2 temperament in the 2.3.11/5 subgroup for which interpretation as a rank-3 temperament in 2.3.5.11 (the no-7's [[11-limit]]) is natural, making [[10/9]] and [[12/11]] [[square superparticular|equidistant from 11/10]] and offering many fruitful tempering opportunities. Note therefore that [[porkypine]] can be seen as a trivial tuning of [[4000/3993|pine]] tempering out {{nowrap|[[100/99]] {{=}} S10}} and {{nowrap|[[121/120]] {{=}} S11}}.


{| class="wikitable"
== Scale tree ==
|-
{{MOS tuning spectrum
! colspan="6" | [[generator|Generator]]
| 5/2 = General range of porcupine
! | [[cent|Cent]]s
| 2/1 = Optimum rank range for porcupine
! | Scale in [[EDO|EDO]] steps
| 13/8 = Golden porcupine/hemikleismic
! | Comments
| 10/7 = General range of greeley
|-
}}
| | 1\7
| |
| |
| |
| |
| |
| | 171.43
| style="text-align:center;" | 1 1 1 1 1 1 1 0
| style="text-align:center;" |
|-
|
|
|
|
|
|6\43
|167.44
|6 6 6 6 6 6 6 1
|
|-
|
|
|
|
|5\36
|
|166.67
|5 5 5 5 5 5 5 1
|
|-
| |
| |
| |
| | 4\29
| |
| |
| | 165.52
| style="text-align:center;" | 4 4 4 4 4 4 4 1
| style="text-align:center;" | L/s = 4
|-
| |
| |
| |
| |
| |
| |
| | 163.97
| style="text-align:center;" | pi pi pi pi pi pi pi 1
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = pi</span>
|-
| |
| |
| | 3\22
| |
| |
| |
| | 163.64
| style="text-align:center;" | 3 3 3 3 3 3 3 1
| style="text-align:center;" | L/s = 3
|-
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" |
| style="text-align:center;" | 162.87
| style="text-align:center;" | e e e e e e e e 1
| style="text-align:center;" | <span style="display: block; text-align: center;">L/s = e</span>
|-
| |
| |
| |
| |
| | 8\59
| |
| | 162,71
| style="text-align:center;" | <span style="display: block; text-align: center;">8 8 8 8 8 8 8 3</span>
| |
|-
| |
| |
| |
| |
| |
| | 13\96
| | 162.5
| style="text-align:center;" | <span style="display: block; text-align: center;">13 13 13 13 13 13 13 5</span>
| |
|-
| |
| |
| |
| | 5\37
| |
| |
| | 162.16
| style="text-align:center;" | 5 5 5 5 5 5 5 2
| style="text-align:center;" | Porcupine is in this general region
|-
| |
| |
| |
| |
| | 7\52
| |
| | 161.54
| style="text-align:center;" | 7 7 7 7 7 7 7 3
| style="text-align:center;" |
|-
| |
| | 2\15
| |
| |
| |
| |
| | 160
| style="text-align:center;" | 2 2 2 2 2 2 2 1
| style="text-align:center;" | Optimum rank range (L/s=2/1) porcupine
|-
| |
| |
| |
| |
| |
| |
| | 158.37
| style="text-align:center;" | <span style="background-color: #ffffff;">√3 √3 √3 √3 √3 √3 √3 1</span>
| |
|-
| |
| |
| |
| | 5\38
| |
| |
| | 157.89
| style="text-align:center;" | 5 5 5 5 5 5 5 3
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 13\99
| | 157.58
| style="text-align:center;" | 13 13 13 13 13 13 13 8
| style="text-align:center;" | Golden porcupine / golden hemikleismic
|-
| |
| |
| |
| |
| | 8\61
| |
| | 157.38
| style="text-align:center;" | 8 8 8 8 8 8 8 5
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | (11\84)
| | 157.14
| style="text-align:center;" | <span style="display: block; text-align: center;">11 11 11 11 11 11 11 7 </span><span style="display: block; text-align: center;">pi pi pi pi pi pi pi 2</span>
| |
|-
| |
| |
| | 3\23
| |
| |
| |
| | 156.52
| style="text-align:center;" | 3 3 3 3 3 3 3 2
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 10\77
| | 155.84
| style="text-align:center;" | 10 10 10 10 10 10 10 7
| style="text-align:center;" | Greeley is around here
|-
| |
| |
| |
| |
| | 7\54
| |
| | 155.56
| style="text-align:center;" | 7 7 7 7 7 7 7 5
| style="text-align:center;" |
|-
| |
| |
| |
| | 4\31
| |
| |
| | 154.84
| style="text-align:center;" | 4 4 4 4 4 4 4 3
| style="text-align:center;" |
|-
|
|
|
|
|5\39
|
|153.85
|5 5 5 5 5 5 5 4
|
|-
|
|
|
|
|
|6\47
|153.19
|6 6 6 6 6 6 6 5
|
|-
| | 1\8
| |
| |
| |
| |
| |
| | 150
| style="text-align:center;" | 1 1 1 1 1 1 1 1
| style="text-align:center;" |
|}


[[Category:Abstract MOS patterns]]
[[Category:8-tone scales]]
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