7L 1s: Difference between revisions

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== Name ==

[[TAMNAMS~~]] suggests the temperament-agnostic~~ name ~~'''pine''', in reference to porcupine temperament.~~

== ~~Theory~~ ==

== Scale properties ==

~~=== 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.)

== ~~Modes ==~~

==== Proposed names ====

~~{{MOS mode degrees}}~~

===~~Proposed Names~~===

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.

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== Scale tree ==

== 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.)

@@ Line 2: / Line 2: @@
 {{MOS intro}}
 == Name ==
-[[TAMNAMS]] suggests the temperament-agnostic name '''pine''', in reference to porcupine temperament.
+{{TAMNAMS name}}
-== Theory ==
+== Scale properties ==
+{{MOS scale properties}}
-=== 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.)
-== Modes ==
+==== Proposed names ====
-{{MOS mode degrees}}
-===Proposed Names===
 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.
 {| class="wikitable"
@@ Line 60: / Line 56: @@
 |}
-== Scale tree ==
+== 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.)
+==Scale tree==
 {{Scale tree|Comments=5/2: General range of porcupine;
 /1: Optimum rank range for porcupine;