Harmonotonic tuning: Difference between revisions

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irrational

|-

! rowspan="17" |'''tuning'''

! rowspan="15" |'''tuning'''

'''shape'''

! rowspan="7" |'''decreasing'''

! rowspan="6" |'''decreasing'''

'''step size'''

|'''[[Overtone series|overtone series, or harmonic series]]'''||'''shifted overtone series''' (± frequency) ''(equivalent to AFS)''

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|-

|'''(n-)OSp:''' (n pitches of an) otonal sequence adding by p

|'''(n-)AFSp:''' (n pitches of an) arithmetic frequency sequence

|'''(n-)AFSp:''' (n pitches of an) arithmetic frequency sequence adding by p

adding by p

|

|-

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|

|'''[[Logharmonic series|b-logharmonic series]]''' base b

|-

~~|[[ADO|'''n-ADO:''' arithmetic division of octave]] ''(equivalent to n-ODO)''~~

|

|-

! rowspan="3" |'''equal'''

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|'''(n-)APSp:''' (n pitches of an) arithmetic pitch sequence adding by p ''(equivalent to rank-1 temperament with generator p)''

|-

! rowspan="7" |'''increasing'''

! rowspan="6" |'''increasing'''

'''step size'''

| '''[[wikipedia:Undertone_series|undertone series, or subharmonic series]]''' || '''shifted undertone series''' (± frequency) ''(equivalent to ALS)'' || '''stretched/compressed undertone series''' (exponentiated frequency, multiplied pitch) ''(equivalent to subpowharmonic series)''

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|

|'''[[Logharmonic series|b-sublogharmonic series]]''' base b

|-

~~|[[EDL|'''EDL:''' equal division of length]] ''(equivalent to n-UDn)''~~

|

|}

[[Shaahin Mohajeri]] has previously developed some tunings which qualify as monotonic. His [[ADO|n-ADO]] is equivalent to n-ODO, and his [[EDL|n-EDL]] is equivalent to n-UDn.

== Example monotonic tuning charts and graphs for comparison ==

@@ Line 107: / Line 107: @@
 irrational
 |-
-! rowspan="17" |'''tuning'''
+! rowspan="15" |'''tuning'''
 '''shape'''
-! rowspan="7" |'''decreasing'''
+! rowspan="6" |'''decreasing'''
 '''step size'''
 |'''[[Overtone series|overtone series, or harmonic series]]'''||'''shifted overtone series''' (± frequency) ''(equivalent to AFS)''
@@ Line 123: / Line 123: @@
 |-
 |'''(n-)OSp:''' (<u>n</u> pitches of an) <u>o</u>tonal <u>s</u>equence adding by <u>p</u>
-|'''(n-)AFSp:''' (n pitches of an) arithmetic frequency sequence
+|'''(n-)AFSp:''' (n pitches of an) arithmetic frequency sequence adding by p
-adding by p
 |
 |-
@@ Line 134: / Line 133: @@
 |
 |'''[[Logharmonic series|b-logharmonic series]]''' base b
-|-
-|[[ADO|'''n-ADO:''' arithmetic division of octave]] ''(equivalent to n-ODO)''
-|
-|
 |-
 ! rowspan="3" |'''equal'''
@@ Line 150: / Line 145: @@
 |'''(n-)APSp:''' (n pitches of an) arithmetic pitch sequence adding by p ''(equivalent to rank-1 temperament with generator p)''
 |-
-! rowspan="7" |'''increasing'''
+! rowspan="6" |'''increasing'''
 '''step size'''
 | '''[[wikipedia:Undertone_series|undertone series, or subharmonic series]]''' || '''shifted undertone series''' (± frequency) ''(equivalent to ALS)'' || '''stretched/compressed undertone series''' (exponentiated frequency, multiplied pitch)  ''(equivalent to subpowharmonic series)''
@@ Line 173: / Line 168: @@
 |
 |'''[[Logharmonic series|b-sublogharmonic series]]''' base b
-|-
-|[[EDL|'''EDL:''' equal division of length]] ''(equivalent to n-UDn)''
-|
-|
 |}
+[[Shaahin Mohajeri]] has previously developed some tunings which qualify as monotonic. His [[ADO|n-ADO]] is equivalent to n-ODO, and his [[EDL|n-EDL]] is equivalent to n-UDn.
 == Example monotonic tuning charts and graphs for comparison ==