7L 1s: Difference between revisions

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== Scale properties ==

~~{{MOS scale properties}}~~

==== Proposed names ====

=== Intervals ===

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"~~

~~!Mode~~

=== Generator chain ===

~~!UDP~~

~~!Mode name~~

~~!Descriptive mode name~~

=== Modes ===

|-

~~|LLLLLLLs~~

|~~<nowiki>7|0</nowiki>~~

=== Proposed names ===

|~~octopus~~

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.

|Bright quartal

{{MOS modes

|-

| Mode names =

~~|LLLLLLsL~~

octopus $

~~|<nowiki>6|1</nowiki>~~

mantis $

~~|mantis~~

dolphin $

|Dark quartal

crab $

|-

tuna $

~~|LLLLLsLL~~

salmon $

~~|<nowiki>5|2</nowiki>~~

starfish $

~~|dolphin~~

whale $

|Bright major

| Table Headers=Name Origin

|-

| Table Entries=

~~|LLLLsLLL~~

Bright quartal $

~~|<nowiki>4|3</nowiki>~~

Dark quartal $

~~|crab~~

Bright major $

|Middle major

Middle major $

|-

Dark major $

~~|LLLsLLLL~~

Bright minor $

~~|<nowiki>3|4</nowiki>~~

Middle minor $

~~|tuna~~

Dark minor $

|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~~

|}

== 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.

==Scale tree==

{{~~Scale tree~~|~~Comments=~~5/2: General range of porcupine;

* 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.

2/1: Optimum rank range for porcupine;

* 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.

13/8: Golden porcupine/hemikleismic

* 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}}.

10/7: General range of greeley}}

== 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

}}

[[Category:8-tone scales]]

@@ Line 5: / Line 5: @@
 == Scale properties ==
-{{MOS scale properties}}
-==== Proposed names ====
+=== Intervals ===
-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.
+{{MOS intervals}}
-{| class="wikitable"
-!Mode
+=== Generator chain ===
-!UDP
+{{MOS genchain}}
-!Mode name
-!Descriptive mode name
+=== Modes ===
-|-
+{{MOS mode degrees}}
-|LLLLLLLs
-|<nowiki>7|0</nowiki>
+=== Proposed names ===
-|octopus
+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.
-|Bright quartal
+{{MOS modes
-|-
+| Mode names =
-|LLLLLLsL
+octopus $
-|<nowiki>6|1</nowiki>
+mantis $
-|mantis
+dolphin $
-|Dark quartal
+crab $
-|-
+tuna $
-|LLLLLsLL
+salmon $
-|<nowiki>5|2</nowiki>
+starfish $
-|dolphin
+whale $
-|Bright major
+| Table Headers=Name Origin
-|-
+| Table Entries=
-|LLLLsLLL
+Bright quartal $
-|<nowiki>4|3</nowiki>
+Dark quartal $
-|crab
+Bright major $
-|Middle major
+Middle major $
-|-
+Dark major $
-|LLLsLLLL
+Bright minor $
-|<nowiki>3|4</nowiki>
+Middle minor $
-|tuna
+Dark minor $
-|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
-|}
 == 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.
-==Scale tree==
-{{Scale tree|Comments=5/2: General range of porcupine;
+* 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.
-/1: Optimum rank range for porcupine;
+* 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.
-/8: Golden porcupine/hemikleismic
+* 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}}.
-/7: General range of greeley}}
+== 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
+}}
 [[Category:8-tone scales]]