Harmonotonic tuning: Difference between revisions

Line 129:

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

'''step size'''

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

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

| '''stretched/compressed overtone series''' (exponentiated frequency, multiplied pitch) ''(equivalent to powharmonic series)''

| [[Powharmonic series|'''stretched/compressed overtone series''' (exponentiated frequency, multiplied pitch) ''(equivalent to powharmonic series)'']]

|-

|~~'''~~[[Overtone scale#Over-n Scales|overtone mode, or over-n scale]]''' ''(equivalent to n-ODO)''

|[[Overtone scale#Over-n Scales|'''overtone mode, or over-n scale''' ''(equivalent to n-ODO)'']]

|

|-

|'''n-ODp:''' n otonal divisions of interval p

|[[OD|'''n-ODp:''' n otonal divisions of interval p]]

|'''n-EFDp:''' n equal frequency divisions of interval p

|[[EFD|'''n-EFDp:''' n equal frequency divisions of interval p]]

|

|-

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

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

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

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

|

|-

Line 158:

|-

|

|'''n-EDp:''' n equal (pitch) divisions of interval p (e.g. 12-EDO) ''(equivalent to rank-1 temperament of p/n)''

|[[EDO vs ET|'''n-EDp:''' n equal (pitch) divisions of interval p (e.g. 12-EDO) ''(equivalent to rank-1 temperament of p/n)'']]

|-

|'''(n-)ASp:''' (n pitches of an) ambitonal sequence adding by p ''(equivalent to 1D JI lattice of p)''

|[[AS|'''(n-)ASp:''' (n pitches of an) ambitonal sequence adding by p ''(equivalent to 1D JI lattice of p)'']]

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

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

|-

! 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)''

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

|-

|~~'''~~[[Overtone scale#Next Steps|undertone mode, or under-n scale]]''' ''(equivalent to n-UDO)''

|[[Overtone scale#Next Steps|'''undertone mode, or under-n scale''' ''(equivalent to n-UDO)'']]

|

|-

|'''n-UDp:''' n utonal divisions of interval p

|[[UD|'''n-UDp:''' n utonal divisions of interval p]]

|'''n-ELDp:''' n equal length divisions of interval p

|[[ELD|'''n-ELDp:''' n equal length divisions of interval p]]

|

|-

|'''(n-)USp:''' (n pitches of a) utonal sequence adding by p

|[[US|'''(n-)USp:''' (n pitches of a) utonal sequence adding by p]]

|'''(n-)ALSp:''' (n pitches of an) arithmetic length sequence adding by p

|[[ALS|'''(n-)ALSp:''' (n pitches of an) arithmetic length sequence adding by p]]

|

|-

@@ Line 129: / Line 129: @@
 ! rowspan="6" |'''decreasing'''
 '''step size'''
-|'''[[Overtone series|overtone series, or harmonic series]]'''||'''shifted overtone series''' (± frequency) ''(equivalent to AFS)''
+|'''[[Overtone series|overtone series, or harmonic series]]'''||[[AFS|'''shifted overtone series''' (± frequency) ''(equivalent to AFS)'']]
-| '''stretched/compressed overtone series''' (exponentiated frequency, multiplied pitch) ''(equivalent to powharmonic series)''
+| [[Powharmonic series|'''stretched/compressed overtone series''' (exponentiated frequency, multiplied pitch) ''(equivalent to powharmonic series)'']]
 |-
-|'''[[Overtone scale#Over-n Scales|overtone mode, or over-n scale]]''' ''(equivalent to n-ODO)''
+|[[Overtone scale#Over-n Scales|'''overtone mode, or over-n scale''' ''(equivalent to n-ODO)'']]
 |
 |
 |-
-|'''n-ODp:''' <u>n</u> <u>o</u>tonal <u>d</u>ivisions of interval <u>p</u>
+|[[OD|'''n-ODp:''' <u>n</u> <u>o</u>tonal <u>d</u>ivisions of interval <u>p</u>]]
-|'''n-EFDp:''' <u>n</u> <u>e</u>qual <u>f</u>requency <u>d</u>ivisions of interval <u>p</u>
+|[[EFD|'''n-EFDp:''' <u>n</u> <u>e</u>qual <u>f</u>requency <u>d</u>ivisions of interval <u>p</u>]]
 |
 |-
-|'''(n-)OSp:''' (<u>n</u> pitches of an) <u>o</u>tonal <u>s</u>equence adding by <u>p</u>
+|[[OS|'''(n-)OSp:''' (<u>n</u> pitches of an) <u>o</u>tonal <u>s</u>equence adding by <u>p</u>]]
-|'''(n-)AFSp:''' (<u>n</u> pitches of an) <u>a</u>rithmetic <u>f</u>requency <u>s</u>equence adding by <u>p</u>
+|[[AFS|'''(n-)AFSp:''' (<u>n</u> pitches of an) <u>a</u>rithmetic <u>f</u>requency <u>s</u>equence adding by <u>p</u>]]
 |
 |-
@@ Line 158: / Line 158: @@
 |-
 |
-|'''n-EDp:''' <u>n</u> <u>e</u>qual (pitch) <u>d</u>ivisions of interval <u>p</u> (e.g. 12-EDO) ''(equivalent to rank-1 temperament of p/n)''
+|[[EDO vs ET|'''n-EDp:''' <u>n</u> <u>e</u>qual (pitch) <u>d</u>ivisions of interval <u>p</u> (e.g. 12-EDO) ''(equivalent to rank-1 temperament of p/n)'']]
 |-
-|'''(n-)ASp:''' (<u>n</u> pitches of an) <u>a</u>mbitonal <u>s</u>equence adding by <u>p</u> ''(equivalent to 1D JI lattice of p)''
+|[[AS|'''(n-)ASp:''' (<u>n</u> pitches of an) <u>a</u>mbitonal <u>s</u>equence adding by <u>p</u> ''(equivalent to 1D JI lattice of p)'']]
-|'''(n-)APSp:''' (<u>n</u> pitches of an) <u>a</u>rithmetic <u>p</u>itch <u>s</u>equence adding by <u>p</u> ''(equivalent to rank-1 temperament with generator p)''
+|[[APS|'''(n-)APSp:''' (<u>n</u> pitches of an) <u>a</u>rithmetic <u>p</u>itch <u>s</u>equence adding by <u>p</u> ''(equivalent to rank-1 temperament with generator p)'']]
 |-
 ! 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)''
+| '''[[wikipedia:Undertone_series|undertone series, or subharmonic series]]''' || [[ALS|'''shifted undertone series''' (± frequency) ''(equivalent to ALS)'']] || [[Powharmonic series|'''stretched/compressed undertone series''' (exponentiated frequency, multiplied pitch)  ''(equivalent to subpowharmonic series)'']]
 |-
-|'''[[Overtone scale#Next Steps|undertone mode, or under-n scale]]''' ''(equivalent to n-UDO)''
+|[[Overtone scale#Next Steps|'''undertone mode, or under-n scale''' ''(equivalent to n-UDO)'']]
 |
 |
 |-
-|'''n-UDp:''' <u>n</u> <u>u</u>tonal <u>d</u>ivisions of interval <u>p</u>
+|[[UD|'''n-UDp:''' <u>n</u> <u>u</u>tonal <u>d</u>ivisions of interval <u>p</u>]]
-|'''n-ELDp:''' <u>n</u> <u>e</u>qual <u>l</u>ength <u>d</u>ivisions of interval <u>p</u>
+|[[ELD|'''n-ELDp:''' <u>n</u> <u>e</u>qual <u>l</u>ength <u>d</u>ivisions of interval <u>p</u>]]
 |
 |-
-|'''(n-)USp:''' (<u>n</u> pitches of a) <u>u</u>tonal <u>s</u>equence adding by <u>p</u>
+|[[US|'''(n-)USp:''' (<u>n</u> pitches of a) <u>u</u>tonal <u>s</u>equence adding by <u>p</u>]]
-|'''(n-)ALSp:''' (<u>n</u> pitches of an) <u>a</u>rithmetic <u>l</u>ength <u>s</u>equence adding by <u>p</u>
+|[[ALS|'''(n-)ALSp:''' (<u>n</u> pitches of an) <u>a</u>rithmetic <u>l</u>ength <u>s</u>equence adding by <u>p</u>]]
 |
 |-