Harmonotonic tuning: Difference between revisions

Line 122:

{| class="wikitable"

|+Table of monotonic tunings

! colspan="2" rowspan="2" style="background-color: white; border-left: 1px solid white; border-top: 1px solid white;" |

! colspan="3" rowspan="2" style="background-color: white; border-left: 1px solid white; border-top: 1px solid white;" |

! colspan="3" |tuning type

! colspan="5" |tuning type

|-

! arithmetic

rational

!

! arithmetic

irrational

!

! non-arithmetic

irrational

|-

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

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

'''shape'''

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

'''step size'''

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

!open-ended

|'''[[Overtone series|overtone series, or harmonic series]]'''

!

|[[AFS|'''shifted overtone series''' (± frequency) ''(equivalent to AFS)'']]

!

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

|-

! rowspan="2" |division

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

|

! rowspan="2" |

|

| rowspan="2" |[[EFD|'''n-EFDp:''' n equal frequency divisions of interval p]]

! rowspan="2" |

| rowspan="2" |

|-

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

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

|

|-

!sequence

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

!

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

!

|

|-

|

! rowspan="2" |other open

|

| rowspan="2" |

! rowspan="2" |

| rowspan="2" |

! rowspan="2" |

|'''[[Powharmonic series|c-powharmonic series]]''' exponent c

|-

|

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

|-

! colspan="7" |

|-

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

'''step size'''

!open-ended

|'''1D [[Harmonic Lattice Diagram|JI lattice]]'''

| [[Tour of Regular Temperaments#Equal temperaments .28Rank-1 temperaments.29|'''rank-1 temperament''']] || rowspan="3" style="background-color: white; border-right: 1px solid white;" |

!

|[[Tour of Regular Temperaments#Equal temperaments .28Rank-1 temperaments.29|'''rank-1 temperament''']]

!

| rowspan="3" style="background-color: white; border-right: 1px solid white;" |

|-

!division

|

!

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

!

|-

!sequence

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

!

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

!

|-

! colspan="7" |

|-

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

'''step size'''

| '''[[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)'']]

!open-ended

|'''[[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)'']]

|-

! rowspan="2" |division

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

|

! rowspan="2" |

|

| rowspan="2" |[[ELD|'''n-ELDp:''' n equal length divisions of interval p]]

! rowspan="2" |

| rowspan="2" |

|-

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

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

|

|-

!sequence

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

!

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

!

|

|-

|

! rowspan="2" |other open

|

| rowspan="2" |

! rowspan="2" |

| rowspan="2" |

! rowspan="2" |

|'''[[Powharmonic series|c-subpowharmonic series]]''' exponent c

|-

|

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

|}

@@ Line 122: / Line 122: @@
 {| class="wikitable"
 |+Table of monotonic tunings
-! colspan="2" rowspan="2" style="background-color: white; border-left: 1px solid white; border-top: 1px solid white;" |
+! colspan="3" rowspan="2" style="background-color: white; border-left: 1px solid white; border-top: 1px solid white;" |
-! colspan="3" |tuning type
+! colspan="5" |tuning type
 |-
 ! arithmetic
 rational
+!
 ! arithmetic
 irrational
+!
 ! non-arithmetic
 irrational
 |-
-! rowspan="15" |'''tuning'''
+! rowspan="17" |'''tuning'''
 '''shape'''
 ! rowspan="6" |'''decreasing'''
 '''step size'''
-|'''[[Overtone series|overtone series, or harmonic series]]'''||[[AFS|'''shifted overtone series''' (± frequency) ''(equivalent to AFS)'']]
+!open-ended
+|'''[[Overtone series|overtone series, or harmonic series]]'''
+!
+|[[AFS|'''shifted overtone series''' (± frequency) ''(equivalent to AFS)'']]
+!
 | [[Powharmonic series|'''stretched/compressed overtone series''' (exponentiated frequency, multiplied pitch) ''(equivalent to powharmonic series)'']]
 |-
+! rowspan="2" |division
 |[[Overtone scale#Over-n Scales|'''overtone mode, or over-n scale''' ''(equivalent to n-ODO)'']]
-|
+! rowspan="2" |
-|
+| rowspan="2" |[[EFD|'''n-EFDp:''' <u>n</u> <u>e</u>qual <u>f</u>requency <u>d</u>ivisions of interval <u>p</u>]]
+! rowspan="2" |
+| rowspan="2" |
 |-
 |[[OD|'''n-ODp:''' <u>n</u> <u>o</u>tonal <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>]]
-|
 |-
+!sequence
 |[[OS|'''(n-)OSp:''' (<u>n</u> pitches of an) <u>o</u>tonal <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>]]
+!
 |
 |-
-|
+! rowspan="2" |other open
-|
+| rowspan="2" |
+! rowspan="2" |
+| rowspan="2" |
+! rowspan="2" |
 |'''[[Powharmonic series|c-powharmonic series]]''' exponent c
 |-
-|
-|
 |'''[[Logharmonic series|b-logharmonic series]]''' base b
+|-
+! colspan="7" |
 |-
 ! rowspan="3" |'''equal'''
 '''step size'''
+!open-ended
 |'''1D [[Harmonic Lattice Diagram|JI lattice]]'''
-| [[Tour of Regular Temperaments#Equal temperaments .28Rank-1 temperaments.29|'''rank-1 temperament''']] || rowspan="3" style="background-color: white; border-right: 1px solid white;" |
+!
+|[[Tour of Regular Temperaments#Equal temperaments .28Rank-1 temperaments.29|'''rank-1 temperament''']]
+!
+| rowspan="3" style="background-color: white; border-right: 1px solid white;" |
 |-
+!division
 |
+!
 |[[EPD|'''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)'']]
+!
 |-
+!sequence
 |[[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)'']]
+!
 |[[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)'']]
+!
+|-
+! colspan="7" |
 |-
 ! rowspan="6" |'''increasing'''
 '''step size'''
-| '''[[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)'']]
+!open-ended
+|'''[[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)'']]
 |-
+! rowspan="2" |division
 |[[Overtone scale#Next Steps|'''undertone mode, or under-n scale''' ''(equivalent to n-UDO)'']]
-|
+! rowspan="2" |
-|
+| rowspan="2" |[[ELD|'''n-ELDp:''' <u>n</u> <u>e</u>qual <u>l</u>ength <u>d</u>ivisions of interval <u>p</u>]]
+! rowspan="2" |
+| rowspan="2" |
 |-
 |[[UD|'''n-UDp:''' <u>n</u> <u>u</u>tonal <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>]]
-|
 |-
+!sequence
 |[[US|'''(n-)USp:''' (<u>n</u> pitches of a) <u>u</u>tonal <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>]]
+!
 |
 |-
-|
+! rowspan="2" |other open
-|
+| rowspan="2" |
+! rowspan="2" |
+| rowspan="2" |
+! rowspan="2" |
 |'''[[Powharmonic series|c-subpowharmonic series]]''' exponent c
 |-
-|
-|
 |'''[[Logharmonic series|b-sublogharmonic series]]''' base b
 |}