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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 ==
| Collapsed = 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}}.
 
== Scale tree ==
{{MOS tuning spectrum
| 5/2 = General range of porcupine
| 2/1 = Optimum rank range for porcupine
| 13/8 = Golden porcupine/hemikleismic
| 10/7 = General range of greeley
}}


{| class="wikitable"
[[Category:8-tone scales]]
|-
! colspan="6" | [[generator|Generator]]
! |[[Cent]]s
!Remainder
! |Scale in [[EDO|EDO]] steps
! |Comments
|-
| |1\7
| |
| |
| |
| |
| |
| | 171.43
|0.00
| style="text-align:center;" |1 1 1 1 1 1 1 0
| style="text-align:center;" |
|-
|
|
|
|
|
|6\43
|167.44
|27.91
| style="text-align:center;" |6 6 6 6 6 6 6 1
|
|-
|
|
|
|
| 5\36
|
|166.67
|33.32
| style="text-align:center;" |5 5 5 5 5 5 5 1
|
|-
| |
| |
| |
| | 4\29
| |
| |
| |165.52
|41.38
| style="text-align:center;" |4 4 4 4 4 4 4 1
| style="text-align:center;" |L/s = 4
|-
| |
| |
| |
| |
| |
| |
| |163.97
|52.19
| style="text-align:center;" |π π π π π π π 1
| style="text-align:center;" |<span style="display: block; text-align: center;">L/s = π</span>
|-
| |
| |
| |3\22
| |
| |
| |
| |163.64
|54.55
| 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
|59.92
| 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
|61.02
| style="text-align:center;" |<span style="display: block; text-align: center;">8 8 8 8 8 8 8 3</span>
| |
|-
| |
| |
| |
| |
| |
| |13\96
| |162.5
|62.5
| style="text-align:center;" |<span style="display: block; text-align: center;">[[Tel:13 13 13 13 13 13 13|13 13 13 13 13 13 13]] 5</span>
| |
|-
| |
| |
| |
| |5\37
| |
| |
| |162.16
|64.86
| 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
|69.23
| style="text-align:center;" | 7 7 7 7 7 7 7 3
| style="text-align:center;" |
|-
| |
| |2\15
| |
| |
| |
| |
| |160
|80
| 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
|91.43
| style="text-align:center;" |<span style="background-color: #ffffff;">√3 √3 √3 √3 √3 √3 √3 1</span>
| |
|-
| |
| |
| |
| |5\38
| |
| |
| |157.89
|94.73
| style="text-align:center;" |5 5 5 5 5 5 5 3
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |13\99
| |157.58
|96.97
| style="text-align:center;" |[[Tel:13 13 13 13 13 13 13|13 13 13 13 13 13 13]] 8
| style="text-align:center;" |Golden porcupine / golden hemikleismic
|-
| |
| |
| |
| |
| |8\61
| |
| | 157.38
|98.36
| style="text-align:center;" |8 8 8 8 8 8 8 5
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| |(11\84)
| |(157.14)
|(100)
| style="text-align:center;" |<span style="display: block; text-align: center;">[[Tel:11 11 11 11 11 11 11|11 11 11 11 11 11 11]] 7 </span><span style="display: block; text-align: center;">π π π π π π π 2</span>
| |
|-
| |
| |
| | 3\23
| |
| |
| |
| |156.52
|104.348
| style="text-align:center;" |3 3 3 3 3 3 3 2
| style="text-align:center;" |
|-
| |
| |
| |
| |
| |
| | 10\77
| | 155.84
|109.09
| style="text-align:center;" |[[Tel:10 10 10 10 10 10 10|10 10 10 10 10 10 10]] 7
| style="text-align:center;" |Greeley is around here
|-
| |
| |
| |
| |
| |7\54
| |
| | 155.56
|111.11
| style="text-align:center;" |7 7 7 7 7 7 7 5
| style="text-align:center;" |
|-
| |
| |
| |
| |4\31
| |
| |
| |154.84
|116.13
| style="text-align:center;" |4 4 4 4 4 4 4 3
| style="text-align:center;" |
|-
|
|
|
|
|5\39
|
|153.85
|123.08
| style="text-align:center;" |5 5 5 5 5 5 5 4
|
|-
|
|
|
|
|
|6\47
|153.19
|127.66
| style="text-align:center;" |6 6 6 6 6 6 6 5
|
|-
| |1\8
| |
| |
| |
| |
| |
| |150
|150
| style="text-align:center;" |1 1 1 1 1 1 1 1
| style="text-align:center;" |
|}
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