14edo: Difference between revisions

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__FORCETOC__

=~~'''Intervals'''~~=

=Notation=

{| class="wikitable"

Line 35:

| style="text-align:center;" | up-unison, down-2nd

| style="text-align:center;" | ^1, v2

| style="text-align:center;" | D^, Ev

| style="text-align:center;" | ^D, vE

| style="text-align:center;" | Narrow Minor 2nd

|-

Line 55:

| style="text-align:center;" | up-2nd, down-3rd

| style="text-align:center;" | ^2, v3

| style="text-align:center;" | E^, Fv

| style="text-align:center;" | ^E, vF

| style="text-align:center;" | Subminor 3rd

|-

Line 75:

| style="text-align:center;" | up-3rd, down-4th

| style="text-align:center;" | ^3, v4

| style="text-align:center;" | F^, Gv

| style="text-align:center;" | ^F, vG

| style="text-align:center;" | Supermajor 3rd

|-

Line 95:

| style="text-align:center;" | up-4th, down-5th

| style="text-align:center;" | ^4, v5

| style="text-align:center;" | G^, Av

| style="text-align:center;" | ^G, vA

| style="text-align:center;" | Tritone

|-

Line 115:

| style="text-align:center;" | up-5th, down-6th

| style="text-align:center;" | ^5, v6

| style="text-align:center;" | A^, Bv

| style="text-align:center;" | ^A, vB

| style="text-align:center;" | Subminor 6th

|-

Line 135:

| style="text-align:center;" | up-6th, down-7th

| style="text-align:center;" | ^6, v7

| style="text-align:center;" | B^, Cv

| style="text-align:center;" | ^B, vC

| style="text-align:center;" | Supermajor 6th

|-

Line 155:

| style="text-align:center;" | up-7th, down-8ve

| style="text-align:center;" | ^7, v8

| style="text-align:center;" | C^, Dv

| style="text-align:center;" | ^C, vD

| style="text-align:center;" | Wide Major 7th

|-

Line 169:

|}

<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>** based on treating 14edo as an 11-limit temperament

[[Ivor_Darreg|Ivor Darreg]] wrote in [http://sonic-arts.org/darreg/dar15.htm this article]:

''The 14-tone scale presents a new situation: while one might use ordinary sharps and flats in addition to conventional naturals for the notes of the 7-tone-equal temperament, it would be misleading and confusing to do so, because there is a 7-tone circle of fifths (admittedly quite distorted) already notatable and nameable as F C G D A E B in the usual manner. But there is no 14-tone circle of fifths. There is simply a second set of 7 fifths in a circle which does not intersect the with the first set. Thus is we think of B-flat and B, or B-natural and F-sharp, the 14-tone-system interval would NOT be a fifth of that system and would not sound like one, since B F would be the very same kind of distorted fifth that C G or A E happens to be in 7 or 14. Our suggestion is to call the new notes of 14, the second set of 7, F* C* G* D* A* E* B*, and use asterisks or arrows or whatever you please on the staff. Or just number the tones as for 13.''

The following chart (made by [[Tútim_Dennsuul_Wafiil|TDW]]) shows this recommendation as "standard notation" as well as a proposed alternative.

{| class="wikitable"

|-

|-

| | Intervallic Cycle of 14 steps Equal per Octave

|}

=Chord Names=

Line 175:

Line 188:

0-4-8 = C E G = C = C or C perfect

0-3-8 = C Ev G = C(v3) = C down-three

0-3-8 = C vE G = C(v3) = C down-three

0-5-8 = C E^ G = C(^3) = C up-three

0-5-8 = C ^E G = C(^3) = C up-three

0-4-7 = C E Gv = C(v5) = C down-five

0-4-7 = C E vG = C(v5) = C down-five

0-5-9 = C E^ G^ = C(^3,^5) = C up-three up-five

0-5-9 = C ^E ^G = C(^3,^5) = C up-three up-five

0-4-8-12 = C E G B = C7 = C seven

0-4-8-11 = C E G Bv = C(v7) = C down-seven

0-4-8-11 = C E G vB = C(v7) = C down-seven

0-3-8-12 = C Ev G B = C7(v3) = C seven down-three

0-3-8-12 = C vE G B = C7(v3) = C seven down-three

0-3-8-11 = C Ev G Bv = ~~C.v7~~ = C ~~dot~~ down seven

0-3-8-11 = C vE G vB = Cv7 = C down-seven

For a more complete list, see [[Ups_and_Downs_Notation#~~Chord names in other EDOs|Ups~~ and ~~Downs Notation -~~ Chord ~~names in other EDOs~~]].

For a more complete list, see [[Ups_and_Downs_Notation#Chords and Chord Progressions]].

= Intervals =

[[File:14ed2-001.svg|alt=alt : Your browser has no SVG support.]]

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13\14: Major 9th9: A high, incisive leading tone.

14\14: The 10th9 or "enneatonic decave", (i. e., the octave, 2:1).

~~=Notation=~~

~~[[Ivor_Darreg|Ivor Darreg]] wrote in [http://sonic-arts.org/darreg/dar15.htm this article]:~~

''The 14-tone scale presents a new situation: while one might use ordinary sharps and flats in addition to conventional naturals for the notes of the 7-tone-equal temperament, it would be misleading and confusing to do so, because there is a 7-tone circle of fifths (admittedly quite distorted) already notatable and nameable as F C G D A E B in the usual manner. But there is no 14-tone circle of fifths. There is simply a second set of 7 fifths in a circle which does not intersect the with the first set. Thus is we think of B-flat and B, or B-natural and F-sharp, the 14-tone-system interval would NOT be a fifth of that system and would not sound like one, since B F would be the very same kind of distorted fifth that C G or A E happens to be in 7 or 14. Our suggestion is to call the new notes of 14, the second set of 7, F* C* G* D* A* E* B*, and use asterisks or arrows or whatever you please on the staff. Or just number the tones as for 13.''

~~The following chart (made by [[Tútim_Dennsuul_Wafiil|TDW]]) shows this recommendation as "standard notation" as well as a proposed alternative.~~

~~{| class="wikitable"~~

|-

|-

~~| | Intervallic Cycle of 14 steps Equal per Octave~~

|}

~~=Images=~~

~~[[File:14edo_wheel.png|alt=14edo wheel.png|343x343px|14edo wheel.png]]~~

=Commas=

Line 244:

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! | Comma

! | Monzo

! | ~~Value (~~Cents)

! | Cents

![[Color notation/Temperament Names|Color Names]]

! | Name 1

! | Name 2

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Line 248:

| |<nowiki> | -11 7 </nowiki>>

| style="text-align:right;" | 113.69

| style="text-align:center;" |Lawa

| style="text-align:center;" | Apotome

| style="text-align:center;" |

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| |<nowiki> | 11 -4 -2 </nowiki>>

| style="text-align:right;" | 19.55

| style="text-align:center;" |Sagugu

| style="text-align:center;" | Diaschisma

| style="text-align:center;" |

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| |<nowiki> | 2 2 -1 -1 </nowiki>>

| style="text-align:right;" | 48.77

| style="text-align:center;" |Rugu

| style="text-align:center;" | Septimal Quarter Tone

| style="text-align:center;" |

Line 269:

| |<nowiki> | -4 -1 0 2 </nowiki>>

| style="text-align:right;" | 35.70

| style="text-align:center;" |Zozo

| style="text-align:center;" | Slendro Diesis

| style="text-align:center;" |

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| |<nowiki> | 6 3 -1 -3 </nowiki>>

| style="text-align:right;" | 13.07

| style="text-align:center;" |Triru-agu

| style="text-align:center;" | Orwellisma

| style="text-align:center;" | Orwell Comma

Line 281:

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| |<nowiki> | 5 -7 -1 3 </nowiki>>

| style="text-align:right;" | 6.48

| style="text-align:center;" |Satrizo-agu

| style="text-align:center;" | Hemimage

| style="text-align:center;" |

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| |<nowiki> | 47 -7 -7 -7 </nowiki>>

| style="text-align:right;" | 0.34

| style="text-align:center;" |Trisa-seprugu

| style="text-align:center;" | Akjaysma

| style="text-align:center;" | 5\7 Octave Comma

Line 293:

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| |<nowiki> | -1 2 0 -2 1 </nowiki>>

| style="text-align:right;" | 17.58

| style="text-align:center;" |Loruru

| style="text-align:center;" | Mothwellsma

| style="text-align:center;" |

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Line 304:

| |<nowiki> | -1 5 0 0 -2 </nowiki>>

| style="text-align:right;" | 7.14

| style="text-align:center;" |Lulu

| style="text-align:center;" | Rastma

| style="text-align:center;" |

Line 305:

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| |<nowiki> | -7 -1 1 1 1 </nowiki>>

| style="text-align:right;" | 4.50

| style="text-align:center;" |Lozoyo

| style="text-align:center;" | Keenanisma

| style="text-align:center;" |

Line 311:

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| |<nowiki> | -1 -2 -1 1 0 1 </nowiki>>

| style="text-align:right;" | 19.13

| style="text-align:center;" |Thozogu

| style="text-align:center;" | Superleap

| style="text-align:center;" |

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| |<nowiki> | 2 -3 -2 0 0 2 </nowiki>>

| style="text-align:right;" | 2.56

| style="text-align:center;" |Bithogu

| style="text-align:center;" | Parizeksma

| style="text-align:center;" |

|}

=Images=

[[File:14edo_wheel.png|alt=14edo wheel.png|343x343px|14edo wheel.png]]

=[[modes|Modes]]=

5 5 4 - [[MOSScales|MOS]] of [[2L_1s|2L1s]]

5 4 5 - [[MOSScales|MOS]] of [[2L_1s|2L1s]]

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''Sword, Ron. "Tetradecaphonic Scales for Guitar" IAAA Press. First Ed: June 2009.''

=~~'''~~Compositions~~'''~~=

=Compositions=

[https://soundcloud.com/overtoneshock/our-pixel-perfect-telephone-discussion-14-edo?in=overtoneshock/sets/xenharmonic-microtonal Our Pixel Perfect Telephone Conversation] by Stephen Weigel

@@ Line 7: / Line 7: @@
 __FORCETOC__
-='''Intervals'''=
+=Notation=
 {| class="wikitable"
@@ Line 35: / Line 35: @@
 | style="text-align:center;" | up-unison,<br />down-2nd
 | style="text-align:center;" | ^1, v2
-| style="text-align:center;" | D^, Ev
+| style="text-align:center;" | ^D, vE
 | style="text-align:center;" | Narrow Minor 2nd
 |-
@@ Line 55: / Line 55: @@
 | style="text-align:center;" | up-2nd,<br />down-3rd
 | style="text-align:center;" | ^2, v3
-| style="text-align:center;" | E^, Fv
+| style="text-align:center;" | ^E, vF
 | style="text-align:center;" | Subminor 3rd
 |-
@@ Line 75: / Line 75: @@
 | style="text-align:center;" | up-3rd,<br />down-4th
 | style="text-align:center;" | ^3, v4
-| style="text-align:center;" | F^, Gv
+| style="text-align:center;" | ^F, vG
 | style="text-align:center;" | Supermajor 3rd
 |-
@@ Line 95: / Line 95: @@
 | style="text-align:center;" | up-4th,<br />down-5th
 | style="text-align:center;" | ^4, v5
-| style="text-align:center;" | G^, Av
+| style="text-align:center;" | ^G, vA
 | style="text-align:center;" | Tritone
 |-
@@ Line 115: / Line 115: @@
 | style="text-align:center;" | up-5th,<br />down-6th
 | style="text-align:center;" | ^5, v6
-| style="text-align:center;" | A^, Bv
+| style="text-align:center;" | ^A, vB
 | style="text-align:center;" | Subminor 6th
 |-
@@ Line 135: / Line 135: @@
 | style="text-align:center;" | up-6th,<br />down-7th
 | style="text-align:center;" | ^6, v7
-| style="text-align:center;" | B^, Cv
+| style="text-align:center;" | ^B, vC
 | style="text-align:center;" | Supermajor 6th
 |-
@@ Line 155: / Line 155: @@
 | style="text-align:center;" | up-7th,<br />down-8ve
 | style="text-align:center;" | ^7, v8
-| style="text-align:center;" | C^, Dv
+| style="text-align:center;" | ^C, vD
 | style="text-align:center;" | Wide Major 7th
 |-
@@ Line 169: / Line 169: @@
 |}
 <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>
+[[Ivor_Darreg|Ivor Darreg]] wrote in [http://sonic-arts.org/darreg/dar15.htm this article]:
+''The 14-tone scale presents a new situation: while one might use ordinary sharps and flats in addition to conventional naturals for the notes of the 7-tone-equal temperament, it would be misleading and confusing to do so, because there is a 7-tone circle of fifths (admittedly quite distorted) already notatable and nameable as F C G D A E B in the usual manner. But there is no 14-tone circle of fifths. There is simply a second set of 7 fifths in a circle which does not intersect the with the first set. Thus is we think of B-flat and B, or B-natural and F-sharp, the 14-tone-system interval would NOT be a fifth of that system and would not sound like one, since B F would be the very same kind of distorted fifth that C G or A E happens to be in 7 or 14. Our suggestion is to call the new notes of 14, the second set of 7, F* C* G* D* A* E* B*, and use asterisks or arrows or whatever you please on the staff. Or just number the tones as for 13.''
+The following chart (made by [[Tútim_Dennsuul_Wafiil|TDW]]) shows this recommendation as "standard notation" as well as a proposed alternative.
+{| class="wikitable"
+|-
+| | [[File:Ciclo_Tetradecafonía.png|alt=Ciclo_Tetradecafonía.png|456x468px|Ciclo_Tetradecafonía.png]]
+|-
+| | Intervallic Cycle of 14 steps Equal per Octave
+|}
 =Chord Names=
@@ Line 175: / Line 188: @@
 -4-8 = C E G = C = C or C perfect<br />
--3-8 = C Ev G = C(v3) = C down-three<br />
+-3-8 = C vE G = C(v3) = C down-three<br />
--5-8 = C E^ G = C(^3) = C up-three<br />
+-5-8 = C ^E G = C(^3) = C up-three<br />
--4-7 = C E Gv = C(v5) = C down-five<br />
+-4-7 = C E vG = C(v5) = C down-five<br />
--5-9 = C E^ G^ = C(^3,^5) = C up-three up-five<br />
+-5-9 = C ^E ^G = C(^3,^5) = C up-three up-five<br />
 -4-8-12 = C E G B = C7 = C seven<br />
--4-8-11 = C E G Bv = C(v7) = C down-seven<br />
+-4-8-11 = C E G vB = C(v7) = C down-seven<br />
--3-8-12 = C Ev G B = C7(v3) = C seven down-three<br />
+-3-8-12 = C vE G B = C7(v3) = C seven down-three<br />
--3-8-11 = C Ev G Bv = C.v7 = C dot down seven<br />
+-3-8-11 = C vE G vB = Cv7 = C down-seven<br />
-For a more complete list, see [[Ups_and_Downs_Notation#Chord names in other EDOs|Ups and Downs Notation - Chord names in other EDOs]].
+For a more complete list, see [[Ups_and_Downs_Notation#Chords and Chord Progressions]].
+= Intervals =
 [[File:14ed2-001.svg|alt=alt : Your browser has no SVG support.]]
@@ Line 218: / Line 232: @@
 \14: Major 9th<span style="vertical-align: sub;">9</span>: A high, incisive leading tone.<br />
 \14: The 10th<span style="vertical-align: sub;">9 </span>or "enneatonic decave", (i. e., the octave, 2:1).
-=Notation=
-[[Ivor_Darreg|Ivor Darreg]] wrote in [http://sonic-arts.org/darreg/dar15.htm this article]:
-''The 14-tone scale presents a new situation: while one might use ordinary sharps and flats in addition to conventional naturals for the notes of the 7-tone-equal temperament, it would be misleading and confusing to do so, because there is a 7-tone circle of fifths (admittedly quite distorted) already notatable and nameable as F C G D A E B in the usual manner. But there is no 14-tone circle of fifths. There is simply a second set of 7 fifths in a circle which does not intersect the with the first set. Thus is we think of B-flat and B, or B-natural and F-sharp, the 14-tone-system interval would NOT be a fifth of that system and would not sound like one, since B F would be the very same kind of distorted fifth that C G or A E happens to be in 7 or 14. Our suggestion is to call the new notes of 14, the second set of 7, F* C* G* D* A* E* B*, and use asterisks or arrows or whatever you please on the staff. Or just number the tones as for 13.''
-The following chart (made by [[Tútim_Dennsuul_Wafiil|TDW]]) shows this recommendation as "standard notation" as well as a proposed alternative.
-{| class="wikitable"
-|-
-| | [[File:Ciclo_Tetradecafonía.png|alt=Ciclo_Tetradecafonía.png|456x468px|Ciclo_Tetradecafonía.png]]
-|-
-| | Intervallic Cycle of 14 steps Equal per Octave
-|}
-=Images=
-[[File:14edo_wheel.png|alt=14edo wheel.png|343x343px|14edo wheel.png]]
 =Commas=
@@ Line 244: / Line 240: @@
 ! | Comma
 ! | Monzo
-! | Value (Cents)
+! | Cents
+![[Color notation/Temperament Names|Color Names]]
 ! | Name 1
 ! | Name 2
@@ Line 251: / Line 248: @@
 | |<nowiki> | -11 7 </nowiki>&gt;
 | style="text-align:right;" | 113.69
+| style="text-align:center;" |Lawa
 | style="text-align:center;" | Apotome
 | style="text-align:center;" |
@@ Line 257: / Line 255: @@
 | |<nowiki> | 11 -4 -2 </nowiki>&gt;
 | style="text-align:right;" | 19.55
+| style="text-align:center;" |Sagugu
 | style="text-align:center;" | Diaschisma
 | style="text-align:center;" |
@@ Line 263: / Line 262: @@
 | |<nowiki> | 2 2 -1 -1 </nowiki>&gt;
 | style="text-align:right;" | 48.77
+| style="text-align:center;" |Rugu
 | style="text-align:center;" | Septimal Quarter Tone
 | style="text-align:center;" |
@@ Line 269: / Line 269: @@
 | |<nowiki> | -4 -1 0 2 </nowiki>&gt;
 | style="text-align:right;" | 35.70
+| style="text-align:center;" |Zozo
 | style="text-align:center;" | Slendro Diesis
 | style="text-align:center;" |
@@ Line 275: / Line 276: @@
 | |<nowiki> | 6 3 -1 -3 </nowiki>&gt;
 | style="text-align:right;" | 13.07
+| style="text-align:center;" |Triru-agu
 | style="text-align:center;" | Orwellisma
 | style="text-align:center;" | Orwell Comma
@@ Line 281: / Line 283: @@
 | |<nowiki> | 5 -7 -1 3 </nowiki>&gt;
 | style="text-align:right;" | 6.48
+| style="text-align:center;" |Satrizo-agu
 | style="text-align:center;" | Hemimage
 | style="text-align:center;" |
@@ Line 287: / Line 290: @@
 | |<nowiki> | 47 -7 -7 -7 </nowiki>&gt;
 | style="text-align:right;" | 0.34
+| style="text-align:center;" |Trisa-seprugu
 | style="text-align:center;" | Akjaysma
 | style="text-align:center;" | 5\7 Octave Comma
@@ Line 293: / Line 297: @@
 | |<nowiki> | -1 2 0 -2 1 </nowiki>&gt;
 | style="text-align:right;" | 17.58
+| style="text-align:center;" |Loruru
 | style="text-align:center;" | Mothwellsma
 | style="text-align:center;" |
@@ Line 299: / Line 304: @@
 | |<nowiki> | -1 5 0 0 -2 </nowiki>&gt;
 | style="text-align:right;" | 7.14
+| style="text-align:center;" |Lulu
 | style="text-align:center;" | Rastma
 | style="text-align:center;" |
@@ Line 305: / Line 311: @@
 | |<nowiki> | -7 -1 1 1 1 </nowiki>&gt;
 | style="text-align:right;" | 4.50
+| style="text-align:center;" |Lozoyo
 | style="text-align:center;" | Keenanisma
 | style="text-align:center;" |
@@ Line 311: / Line 318: @@
 | |<nowiki> | -1 -2 -1 1 0 1 </nowiki>&gt;
 | style="text-align:right;" | 19.13
+| style="text-align:center;" |Thozogu
 | style="text-align:center;" | Superleap
 | style="text-align:center;" |
@@ Line 317: / Line 325: @@
 | |<nowiki> | 2 -3 -2 0 0 2 </nowiki>&gt;
 | style="text-align:right;" | 2.56
+| style="text-align:center;" |Bithogu
 | style="text-align:center;" | Parizeksma
 | style="text-align:center;" |
 |}
+=Images=
+[[File:14edo_wheel.png|alt=14edo wheel.png|343x343px|14edo wheel.png]]
 =[[modes|Modes]]=
 5 4 - [[MOSScales|MOS]] of [[2L_1s|2L1s]]<br />
 4 5 - [[MOSScales|MOS]] of [[2L_1s|2L1s]]<br />
@@ Line 350: / Line 362: @@
 ''Sword, Ron. "Tetradecaphonic Scales for Guitar" IAAA Press. First Ed: June 2009.''
-='''Compositions'''=
+=Compositions=
 [https://soundcloud.com/overtoneshock/our-pixel-perfect-telephone-discussion-14-edo?in=overtoneshock/sets/xenharmonic-microtonal Our Pixel Perfect Telephone Conversation] by Stephen Weigel