Ringer scale: Difference between revisions

(4 intermediate revisions by 3 users not shown)

Line 27:

== Origin of ringer scales ==

The name ''ringer'' was chosen by tuning theorist Scott Dakota (who discovered and raised awareness of the concept) to refer to the property of these scales to [[Harmonic_entropy#Background|"ring"]] extremely and about as much as might be possible for a [[JI]] scale because the [[odd-limit]] complexity of the intervals in such scales is near-minimal meaning they consume as much of the early harmonic series as possible. It is worth noting however that the appearance of a [[virtual fundamental]] depends strongly on which notes of the scale you play - an observation important to [[primodality]]. The concept of ringer scales was additionally further developed by tuning theorists Praveen Venkataramana and later [[user:Godtone]].

The name ''ringer'' was chosen by tuning theorist [[Scott Dakota]] (who discovered and raised awareness of the concept) to refer to the property of these scales to [[Harmonic_entropy#Background|"ring"]] extremely and about as much as might be possible for a [[JI]] scale because the [[odd-limit]] complexity of the intervals in such scales is near-minimal meaning they consume as much of the early harmonic series as possible. It is worth noting however that the appearance of a [[virtual fundamental]] depends strongly on which notes of the scale you play - an observation important to [[primodality]]. The concept of ringer scales was additionally further developed by tuning theorists Praveen Venkataramana and later [[user:Godtone]].

== Example: Ringer 15 ==

Line 87:

9:10:12:14:16:17:18

'''Ringer 8:''' 7:8:'''17/2''':9:10:11:12:13:14

'''Ringer 8d:''' 7:8:'''17/2''':9:10:11:12:13:14

9:10:11:12:13:14:16:17:18

Line 109:

'''Ringer 12:''' 11:12:'''[25/2''':13(f) OR 13:'''27/2]''':14:15:16:17:18:19:20:21:22

14:15:16:17:18:19:20:21:22:24:[25:26 OR 26:27]:28

14:15:16:17:18:19:20:21:22:24:[25:26(f) OR 26:27]:28

'''Ringer 13g:''' 9:10:'''21/2''':11:'''23/2''':12:13:14:'''29/2''':15:16:'''33/2''':17:18

Line 123:

'''Ringer 15:''' 13:14:'''29/2''':15:16:'''[33/2''':17(g) OR 17:'''35/2]''':18:19:20:21:22:23:24:25:26

18:19:20:21:22:23:24:25:26:28:29:30:32:[33:34 OR 34:35]:36

18:19:20:21:22:23:24:25:26:28:29:30:32:[33:34(g) OR 34:35]:36

'''Ringer 16:'''

13:'''55/4''':14:15:'''31/2''':16:17:18:'''[37/2''':19 OR 19:'''39/2(h)]''':20:21:22:23:24:25:26

28:30:31:32:34:36:[37:38 OR 38:39(h)]:40:42:44:46:48:50:52:55:56

'''Ringer 17cffg:''' 13:14:'''29/2''':15:16:'''33/2''':17:18:19:'''[77/4''' OR '''79/4]''':20:21:22:23:24:'''49/2''':25:26

Line 185:

Line 190:

75:76:77:78:79:80:81:82:83:84:85:86:87:88:89:90:91:92:93:94:96:'''97''':98:'''99''':100:102:'''103''':104:106:'''107''':108:'''109''':110:112:'''113''':114:116:'''[117''':118(q=59) OR 118:'''119]''':120:'''[121:122(rr=61)''' OR 122:'''123]''':124:126:128:'''129''':130:132:134:136:'''137''':138:140:142:144:146:148:'''149''':150

=== See also ===

== See also ==

* [[Neji]]

[[Category:Just intonation scales]]

[[Category:Pages with proofs]]

@@ Line 27: / Line 27: @@
 == Origin of ringer scales ==
-The name ''ringer'' was chosen by tuning theorist Scott Dakota (who discovered and raised awareness of the concept) to refer to the property of these scales to [[Harmonic_entropy#Background|"ring"]] extremely and about as much as might be possible for a [[JI]] scale because the [[odd-limit]] complexity of the intervals in such scales is near-minimal meaning they consume as much of the early harmonic series as possible. It is worth noting however that the appearance of a [[virtual fundamental]] depends strongly on which notes of the scale you play - an observation important to [[primodality]]. The concept of ringer scales was additionally further developed by tuning theorists Praveen Venkataramana and later [[user:Godtone]].
+The name ''ringer'' was chosen by tuning theorist [[Scott Dakota]] (who discovered and raised awareness of the concept) to refer to the property of these scales to [[Harmonic_entropy#Background|"ring"]] extremely and about as much as might be possible for a [[JI]] scale because the [[odd-limit]] complexity of the intervals in such scales is near-minimal meaning they consume as much of the early harmonic series as possible. It is worth noting however that the appearance of a [[virtual fundamental]] depends strongly on which notes of the scale you play - an observation important to [[primodality]]. The concept of ringer scales was additionally further developed by tuning theorists Praveen Venkataramana and later [[user:Godtone]].
 == Example: Ringer 15 ==
@@ Line 87: / Line 87: @@
 :10:12:14:16:17:18
-'''Ringer 8:''' 7:8:'''17/2''':9:10:11:12:13:14
+'''Ringer 8d:''' 7:8:'''17/2''':9:10:11:12:13:14
 :10:11:12:13:14:16:17:18
@@ Line 109: / Line 109: @@
 '''Ringer 12:''' 11:12:'''[25/2''':13(f) OR 13:'''27/2]''':14:15:16:17:18:19:20:21:22
-:15:16:17:18:19:20:21:22:24:[25:26 OR 26:27]:28
+:15:16:17:18:19:20:21:22:24:[25:26(f) OR 26:27]:28
 '''Ringer 13g:''' 9:10:'''21/2''':11:'''23/2''':12:13:14:'''29/2''':15:16:'''33/2''':17:18
@@ Line 123: / Line 123: @@
 '''Ringer 15:''' 13:14:'''29/2''':15:16:'''[33/2''':17(g) OR 17:'''35/2]''':18:19:20:21:22:23:24:25:26
-:19:20:21:22:23:24:25:26:28:29:30:32:[33:34 OR 34:35]:36
+:19:20:21:22:23:24:25:26:28:29:30:32:[33:34(g) OR 34:35]:36
+'''Ringer 16:'''
+:'''55/4''':14:15:'''31/2''':16:17:18:'''[37/2''':19 OR 19:'''39/2(h)]''':20:21:22:23:24:25:26
+:30:31:32:34:36:[37:38 OR 38:39(h)]:40:42:44:46:48:50:52:55:56
 '''Ringer 17cffg:''' 13:14:'''29/2''':15:16:'''33/2''':17:18:19:'''[77/4''' OR '''79/4]''':20:21:22:23:24:'''49/2''':25:26
@@ Line 185: / Line 190: @@
 :76:77:78:79:80:81:82:83:84:85:86:87:88:89:90:91:92:93:94:96:'''97''':98:'''99''':100:102:'''103''':104:106:'''107''':108:'''109''':110:112:'''113''':114:116:'''[117''':118(q=59) OR 118:'''119]''':120:'''[121:122(rr=61)''' OR 122:'''123]''':124:126:128:'''129''':130:132:134:136:'''137''':138:140:142:144:146:148:'''149''':150
-=== See also ===
+== See also ==
 * [[Neji]]
+{{navbox scale gallery}}
 [[Category:Just intonation scales]]
 [[Category:Pages with proofs]]