14edo: Difference between revisions

Yourmusic Productions (talk | contribs)
m Titanium[9]: fix paragraphing error.
Xenwolf (talk | contribs)
Notation: simplified tables, fixes footnotes, I moved the dots in the degree column (seemingly guitar fret marks(?)) to left for better right-aligned look
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=Notation=
=Notation=


{| class="wikitable"
{| class="wikitable center-all right-1 right-2"
|-
|-
| | '''Degree'''
! Degree
| style="text-align:center;" | '''Cents'''
! Cents
| style="text-align:center;" | Nearest<br />Harmonic
! Nearest <br> [[Harmonic]]
| style="text-align:center;" | '''Approximate'''<br />'''Ratios 1''' *
! Approximate <br> Ratios 1 <ref>based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup]]; other approaches are possible.</ref>
| style="text-align:center;" | '''Approximate'''<br />'''Ratios 2''' **
! Approximate <br> Ratios 2 <ref>based on treating 14edo as an 11-limit temperament</ref>
| colspan="3" style="text-align:center;" | [[Ups_and_Downs_Notation|up/down]]<br />[[Ups_and_Downs_Notation| notation]]
! colspan="3" | [[Ups and Downs Notation|up/down <b> notation]]
| style="text-align:center;" | Interval Type
! Interval Type
|-
|-
| 0
| 0
| style="text-align:center;" | 0.000
| 0.000
| style="text-align:center;" | 1
| 1
| colspan="2" style="text-align:center;" | 1/1
| colspan="2" | 1/1
| style="text-align:center;" | unison
| unison
| style="text-align:center;" | 1
| 1
| style="text-align:center;" | D
| D
| style="text-align:center;" | Unison
| Unison
|-
|-
| | 1
| 1
| style="text-align:center;" | 85.714
| 85.714
| style="text-align:center;" | 67
| 67
| style="text-align:center;" | 20/19, 19/18, 18/17
| 20/19, 19/18, 18/17
| style="text-align:center;" | 22/21, 28/27, 21/20
| 22/21, 28/27, 21/20
| style="text-align:center;" | up-unison,<br />down-2nd
| up-unison,<br />down-2nd
| style="text-align:center;" | ^1, v2
| ^1, v2
| style="text-align:center;" | ^D, vE
| ^D, vE
| style="text-align:center;" | Narrow Minor 2nd
| Narrow Minor 2nd
|-
|-
| | 2
| 2
| style="text-align:center;" | 171.429
| 171.429
| style="text-align:center;" | 71
| 71
| style="text-align:center;" | 11/10, 10/9,<br />19/17
| 11/10, 10/9,<br />19/17
| style="text-align:center;" | 9/8, 10/9,<br />11/10, 12/11
| 9/8, 10/9,<br />11/10, 12/11
| style="text-align:center;" | 2nd
| 2nd
| style="text-align:center;" | 2
| 2
| style="text-align:center;" | E
| E
| style="text-align:center;" | Neutral 2nd, or<br />Narrow Major 2nd
| Neutral 2nd, or<br />Narrow Major 2nd
|-
|-
| | 3·
| ·3
| style="text-align:center;" | 257.143
| 257.143
| style="text-align:center;" | 37
| 37
| style="text-align:center;" | 22/19, 20/17
| 22/19, 20/17
| style="text-align:center;" | 7/6, 8/7
| 7/6, 8/7
| style="text-align:center;" | up-2nd,<br />down-3rd
| up-2nd,<br />down-3rd
| style="text-align:center;" | ^2, v3
| ^2, v3
| style="text-align:center;" | ^E, vF
| ^E, vF
| style="text-align:center;" | Subminor 3rd
| Subminor 3rd
|-
|-
| | 4
| 4
| style="text-align:center;" | 342.857
| 342.857
| style="text-align:center;" | 39
| 39
| style="text-align:center;" | 11/9, 17/14
| 11/9, 17/14
| style="text-align:center;" | 11/9, 5/4, 6/5
| 11/9, 5/4, 6/5
| style="text-align:center;" | 3rd
| 3rd
| style="text-align:center;" | 3
| 3
| style="text-align:center;" | F
| F
| style="text-align:center;" | Neutral 3rd
| Neutral 3rd
|-
|-
| | 5·
| ·5
| style="text-align:center;" | 428.571
| 428.571
| style="text-align:center;" | 41
| 41
| style="text-align:center;" | 9/7, 14/11,<br />22/17
| 9/7, 14/11,<br />22/17
| style="text-align:center;" | 9/7, 14/11
| 9/7, 14/11
| style="text-align:center;" | up-3rd,<br />down-4th
| up-3rd,<br />down-4th
| style="text-align:center;" | ^3, v4
| ^3, v4
| style="text-align:center;" | ^F, vG
| ^F, vG
| style="text-align:center;" | Supermajor 3rd
| Supermajor 3rd
|-
|-
| | 6
| 6
| style="text-align:center;" | 51<span style="line-height: 1.5;">4.286</span>
| 51<span style="line-height: 1.5;">4.286</span>
| style="text-align:center;" | 43
| 43
| style="text-align:center;" | 19/14
| 19/14
| style="text-align:center;" | 4/3, 11/8
| 4/3, 11/8
| style="text-align:center;" | 4th
| 4th
| style="text-align:center;" | 4
| 4
| style="text-align:center;" | G
| G
| style="text-align:center;" | Wide 4th
| Wide 4th
|-
|-
| | 7·
| ·7
| style="text-align:center;" | 600
| 600.000
| style="text-align:center;" | 91
| 91
| style="text-align:center;" | 7/5, 10/7
| 7/5, 10/7
| style="text-align:center;" | 7/5, 10/7
| 7/5, 10/7
| style="text-align:center;" | up-4th,<br />down-5th
| up-4th,<br />down-5th
| style="text-align:center;" | ^4, v5
| ^4, v5
| style="text-align:center;" | ^G, vA
| ^G, vA
| style="text-align:center;" | Tritone
| Tritone
|-
|-
| | 8
| 8
| style="text-align:center;" | 685.714
| 685.714
| style="text-align:center;" | 95
| 95
| style="text-align:center;" | 28/19
| 28/19
| style="text-align:center;" | 3/2, 16/11
| 3/2, 16/11
| style="text-align:center;" | 5th
| 5th
| style="text-align:center;" | 5
| 5
| style="text-align:center;" | A
| A
| style="text-align:center;" | Narrow 5th
| Narrow 5th
|-
|-
| | 9·
| ·9
| style="text-align:center;" | 771.429
| 771.429
| style="text-align:center;" | 25
| 25
| style="text-align:center;" | 14/9, 11/7,<br />17/11
| 14/9, 11/7,<br />17/11
| style="text-align:center;" |  
|  
| style="text-align:center;" | up-5th,<br />down-6th
| up-5th,<br />down-6th
| style="text-align:center;" | ^5, v6
| ^5, v6
| style="text-align:center;" | ^A, vB
| ^A, vB
| style="text-align:center;" | Subminor 6th
| Subminor 6th
|-
|-
| | 10
| 10
| style="text-align:center;" | 857.143
| 857.143
| style="text-align:center;" | 105
| 105
| style="text-align:center;" | 18/11
| 18/11
| style="text-align:center;" | 18/11, 8/5, 5/3
| 18/11, 8/5, 5/3
| style="text-align:center;" | 6th
| 6th
| style="text-align:center;" | 6
| 6
| style="text-align:center;" | B
| B
| style="text-align:center;" | Neutral 6th
| Neutral 6th
|-
|-
| | 11·
| ·11
| style="text-align:center;" | 942.857
| 942.857
| style="text-align:center;" | 55
| 55
| style="text-align:center;" | 19/11, 17/10
| 19/11, 17/10
| style="text-align:center;" | 12/7, 7/4
| 12/7, 7/4
| style="text-align:center;" | up-6th,<br />down-7th
| up-6th,<br />down-7th
| style="text-align:center;" | ^6, v7
| ^6, v7
| style="text-align:center;" | ^B, vC
| ^B, vC
| style="text-align:center;" | Supermajor 6th
| Supermajor 6th
|-
|-
| | 12
| 12
| style="text-align:center;" | 1028.571
| 1028.571
| style="text-align:center;" | 29
| 29
| style="text-align:center;" | 20/11, 9/5,<br />34/19
| 20/11, 9/5,<br />34/19
| style="text-align:center;" | 16/9, 9/5,<br />20/11, 11/6
| 16/9, 9/5,<br />20/11, 11/6
| style="text-align:center;" | 7th
| 7th
| style="text-align:center;" | 7
| 7
| style="text-align:center;" | C
| C
| style="text-align:center;" | Neutral 7th, or<br />Wide Minor 7th
| Neutral 7th, or<br />Wide Minor 7th
|-
|-
| | 13
| 13
| style="text-align:center;" | 1114.286
| 1114.286
| style="text-align:center;" | 61
| 61
| style="text-align:center;" | 19/10, 36/19,<br />17/9
| 19/10, 36/19,<br />17/9
| style="text-align:center;" | 21/11, 27/14, 40/21
| 21/11, 27/14, 40/21
| style="text-align:center;" | up-7th,<br />down-8ve
| up-7th,<br />down-8ve
| style="text-align:center;" | ^7, v8
| ^7, v8
| style="text-align:center;" | ^C, vD
| ^C, vD
| style="text-align:center;" | Wide Major 7th
| Wide Major 7th
|-
|-
| | 14··
| ··14
| style="text-align:center;" | 1200
| 1200
| style="text-align:center;" | 2
| 2
| style="text-align:center;" | 2/1
| colspan="2" | 2/1
| style="text-align:center;" | 2/1
| 8ve
| style="text-align:center;" | 8ve
| 8
| style="text-align:center;" | 8
| D
| style="text-align:center;" | D
| Octave
| style="text-align:center;" | Octave
|}
|}
<ul><li>based on treating 14-EDO as a 2.7/5.9/5.11/5.17/5.19/5 [[subgroup|subgroup]]; other approaches are possible.</li></ul><span style="display: block; text-align: left;">** based on treating 14edo as an 11-limit temperament</span>
 
<references/>


[[Ivor_Darreg|Ivor Darreg]] wrote in [http://sonic-arts.org/darreg/dar15.htm this article]:
[[Ivor_Darreg|Ivor Darreg]] wrote in [http://sonic-arts.org/darreg/dar15.htm this article]:
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{| class="wikitable"
{| class="wikitable"
|-
|-
| | [[File:Ciclo_Tetradecafonía.png|alt=Ciclo_Tetradecafonía.png|456x468px|Ciclo_Tetradecafonía.png]]
| [[File:Ciclo_Tetradecafonía.png|alt=Ciclo_Tetradecafonía.png|456x468px|Ciclo_Tetradecafonía.png]]
|-
|-
| | Intervallic Cycle of 14 steps Equal per Octave
| Intervallic Cycle of 14 steps Equal per Octave
|}
|}