7L 1s: Difference between revisions

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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}}
-{{MOS intro}}
+=== Modes ===
-Scales of this form are always [[Rothenberg_propriety|proper]], because there is only one small step.
+{{MOS mode degrees}}
-== Name ==
+=== Proposed names ===
-[[TAMNAMS]] suggests the temperament-agnostic name '''pine''', in reference to porcupine temperament.
+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 $
+}}
 == Theory ==
 === Low harmonic entropy scales ===
-There are three notable [[Harmonic_Entropy|harmonic entropy]] minima with this [[MOSScales|MOS]] pattern. The lowest accuracy one 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 and more accurate 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. Thirdly and finally, tempering [[4000/3993|S10/S11]] so that ([[4/3]])/([[11/10]])<sup>3</sup> is tempered results in an unusually high accuracy & efficient rank 2 temperament in the 2.3.11/10 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 [[Porcupine family#2.3.5.11 subgroup .28porkypine.29|porkypine]] can be seen as a trivial tuning of [[4000/3993|pine]] tempering [[100/99]] = S10 and [[121/120]] = S11.)
+There are three notable [[harmonic entropy]] minima with this [[mos]] pattern.
-== Modes ==
+* 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.
-Mode names are from [[Porcupine Temperament Modal Harmony|Porcupine temperament modal harmony]]. Descriptive mode names are based on using 1-4-7, i.e. 3+3 triads as a basis for harmony.
+* 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.
-{| class="wikitable"
+* 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}}.
-!Mode
-!UDP
-!Mode name
-!Descriptive mode name
-|-
-|LLLLLLLs
-|<nowiki>7|0</nowiki>
-|octopus
-|Bright quartal
-|-
-|LLLLLLsL
-|<nowiki>6|1</nowiki>
-|mantis
-|Dark quartal
-|-
-|LLLLLsLL
-|<nowiki>5|2</nowiki>
-|dolphin
-|Bright major
-|-
-|LLLLsLLL
-|<nowiki>4|3</nowiki>
-|crab
-|Middle major
-|-
-|LLLsLLLL
-|<nowiki>3|4</nowiki>
-|tuna
-|Dark major
-|-
-|LLsLLLLL
-|<nowiki>2|5</nowiki>
-|salmon
-|Bright minor
-|-
-|LsLLLLLL
-|<nowiki>1|6</nowiki>
-|starfish
-|Middle minor
-|-
-|sLLLLLLL
-|<nowiki>0|7</nowiki>
-|whale
-|Dark major
-|}
 == Scale tree ==
-{{Scale tree|Comments=5/2: General range of porcupine;
+{{MOS tuning spectrum
-/1: Optimum rank range for porcupine;
+| 5/2 = General range of porcupine
-/8: Golden porcupine/hemikleismic
+| 2/1 = Optimum rank range for porcupine
-/7: General range of greeley}}
+| 13/8 = Golden porcupine/hemikleismic
+| 10/7 = General range of greeley
+}}
 [[Category:8-tone scales]]