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→William Lynch's notation: simplified wiki markup
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For a more complete list of chords, see [[Ups and Downs Notation #Chords and Chord Progressions]].
For a more complete list of chords, see [[Ups and Downs Notation #Chords and Chord Progressions]].


==William Lynch's notation==
== William Lynch's notation ==
 
24 EDO breaks intervals into two sets of five cartegories. Infra - Minor - Neutral - Major - Ultra for seconds, thirds, sixths, and sevenths; and diminished - narrow - perfect - wide - augmented for fourths, fifths, unison, and octave. For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth. See the [[24_EDO_Interval_names_and_Harmonies|full article on 24 Edo intervals.]]
24 EDO breaks intervals into two sets of five cartegories. Infra - Minor - Neutral - Major - Ultra for seconds, thirds, sixths, and sevenths; and diminished - narrow - perfect - wide - augmented for fourths, fifths, unison, and octave. For other strange enharmonics, wide and narrow can be used in conjunction with augmented and diminished intervals such as 550 cents being called a narrow diminished fifth and 850 cents being called a wide augmented fifth. See the [[24_EDO_Interval_names_and_Harmonies|full article on 24 Edo intervals.]]


These are the intervals of 24 EDO that do not exist in 12 EDO:
These are the intervals of 24 EDO that do not exist in 12 EDO:


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
! colspan="4" | The twelve new intervals in 24edo
! colspan="4" | The twelve new intervals in 24edo
! colspan="3" | some nearby JI intervals
! colspan="3" | some nearby JI intervals
|-
|-
! | cents
! cents
!pions
! pions
!7mus
! 7mus
! | common names
! common names
! | frequency ratio
! frequency ratio
! | cents
! cents
! | common name
! common name
|-
|-
| style="text-align:center;" | 50
| 50
|53
| 53
|64 (40<sub>16</sub>)
| 64 (40<sub>16</sub>)
| style="text-align:center;" | quartertone
| quartertone <br> infra second, wide unison
 
| [[36/35]] <br> [[35/34]] <br> [[34/33]] <br> [[33/32]]
infra second, wide unison
| 48.77 <br> 50.184 <br> 51.682 <br> 53.273
| style="text-align:center;" | [[36/35|36/35]]
| large septimal quarter-tone (Archytas) <br> large 17-limit quartertone <br> small 17-limit quartertone <br> 33rd harmonic
 
[[35/34|35/34]]
 
[[34/33|34/33]]
 
[[33/32|33/32]]
| style="text-align:center;" | 48.77
 
50.184
 
51.682
 
53.273
| style="text-align:center;" | large septimal quarter-tone (Archytas)
 
large 17-limit quartertone
 
small 17-limit quartertone
 
33rd harmonic
|-
|-
| style="text-align:center;" | 150
| 150
|159
| 159
|192 (C0<sub>16</sub>)
| 192 (C0<sub>16</sub>)
| style="text-align:center;" | neutral second
| neutral second
| style="text-align:center;" | [[12/11|12/11]]
| [[12/11]]
| style="text-align:center;" | 150.637
| 150.637
| style="text-align:center;" | large undecimal neutral second
| large undecimal neutral second
|-
|-
| style="text-align:center;" | 250
| 250
|265
| 265
|320 (140<sub>16</sub>)
| 320 (140<sub>16</sub>)
| style="text-align:center;" | ultra second
| ultra second <br> infra third
 
| [[144/125]] <br> [[15/13]] <br> [[52/45]]
<span style="line-height: 1.5;">infra third</span>
| 244.969 <br> 247.741 <br> 250.304
| style="text-align:center;" | [[144/125|144/125]]
| diminished third (6/5 x 24/25) <br> .. <br> ..
 
[[15/13|15/13]]
 
[[52/45|52/45]]
| style="text-align:center;" | 244.969
 
247.741
 
250.304
| style="text-align:center;" | diminished third (6/5 x 24/25)
 
..
 
..
|-
|-
| style="text-align:center;" | 350
| 350
|383
| 383
|448 (1C0<sub>16</sub>)
| 448 (1C0<sub>16</sub>)
| style="text-align:center;" | neutral third
| neutral third
| style="text-align:center;" | [[11/9|11/9]]
| [[11/9]] <br> [[27/22]] <br> [[16/13]]
 
| 347.408 <br> 354.547 <br> 359.472
[[27/22|27/22]]
| undecimal neutral third <br> .. <br> tridecimal neutral third
 
[[16/13|16/13]]
| style="text-align:center;" | 347.408
 
354.547
 
359.472
| style="text-align:center;" | undecimal neutral third
 
..
 
tridecimal neutral third
|-
|-
| style="text-align:center;" | 450
| 450
|477
| 477
|576 (240<sub>16</sub>)
| 576 (240<sub>16</sub>)
| style="text-align:center;" | minor fourth, ultra third, narrow fourth
| minor fourth, ultra third, narrow fourth
| style="text-align:center;" | [[22/17|22/17]]
| [[22/17]] <br> [[35/27]] <br> [[13/10]]
 
| 446.363 <br> 449.275 <br> 454.214
[[35/27|35/27]]
| 17-limit supermajor third <br> .. <br> tridecimal subfourth
 
[[13/10|13/10]]
| style="text-align:center;" | 446.363
 
449.275
 
454.214
| style="text-align:center;" | 17-limit supermajor third
 
..
 
tridecimal subfourth
|-
|-
| style="text-align:center;" | 550
| 550
|583
| 583
|704 (2C0<sub>16</sub>)
| 704 (2C0<sub>16</sub>)
| style="text-align:center;" | wide fourth
| wide fourth
| style="text-align:center;" | [[11/8|11/8]]
| [[11/8]]
| style="text-align:center;" | 551.318
| 551.318
| style="text-align:center;" | undecimal superfourth, harmonic 11th
| undecimal superfourth, harmonic 11th
|-
|-
| style="text-align:center;" | 650
| 650
|689
| 689
|832 (340<sub>16</sub>)
| 832 (340<sub>16</sub>)
| style="text-align:center;" | narrow fifth
| narrow fifth
| style="text-align:center;" | [[16/11|16/11]]
| [[16/11]]
| style="text-align:center;" | 648.682
| 648.682
| style="text-align:center;" | undecimal subfifth, 11th subharmonic
| undecimal subfifth, 11th subharmonic
|-
|-
| style="text-align:center;" | 750
| 750
|795
| 795
|960 (3C0<sub>16</sub>)
| 960 (3C0<sub>16</sub>)
| style="text-align:center;" | wide fifth, infra sixth
| wide fifth, infra sixth
| style="text-align:center;" | [[20/13|20/13]]
| [[20/13]] <br> [[54/35]] <br> [[17/11]]
 
| 745.786 <br> 750.725 <br> 753.637
[[54/35|54/35]]
| tridecimal superfifth <br> .. <br> 17-limit subminor sixth
 
[[17/11|17/11]]
| style="text-align:center;" | 745.786
 
750.725
 
753.637
| style="text-align:center;" | tridecimal superfifth
 
..
 
17-limit subminor sixth
|-
|-
| style="text-align:center;" | 850
| 850
|901
| 901
|1088 (340<sub>16</sub>)
| 1088 (340<sub>16</sub>)
| style="text-align:center;" | neutral sixth
| neutral sixth
| style="text-align:center;" | [[13/8|13/8]]
| [[13/8]] <br> [[44/27]] <br> [[18/11]]
 
| 840.528 <br> 845.453 <br> 852.592
[[44/27|44/27]]
| overtone sixth, 13th harmonic <br> .. <br> undecimal neutral sixth
 
[[18/11|18/11]]
| style="text-align:center;" | 840.528
 
845.453
 
852.592
| style="text-align:center;" | overtone sixth, 13th harmonic
 
..
 
undecimal neutral sixth
|-
|-
| style="text-align:center;" | 950
| 950
|1007
| 1007
|1216 (4C0<sub>16</sub>)
| 1216 (4C0<sub>16</sub>)
| style="text-align:center;" | ultra sixth , infra seventh
| ultra sixth , infra seventh
| style="text-align:center;" | [[45/26|45/26]]
| [[45/26]] <br> [[26/15]] <br> [[125/72]]
 
| 949.696 <br> 952.259 <br> 955.031
[[26/15|26/15]]
| .. <br> .. <br> ..
 
[[125/72|125/72]]
| style="text-align:center;" | 949.696
 
952.259
 
955.031
| style="text-align:center;" | ..
 
..
 
..
|-
|-
| style="text-align:center;" | 1050
| 1050
|1113
| 1113
|1344 (540<sub>16</sub>)
| 1344 (540<sub>16</sub>)
| style="text-align:center;" | neutral seventh
| neutral seventh
| style="text-align:center;" | [[11/6|11/6]]
| [[11/6]]
| style="text-align:center;" | 1049.363
| 1049.363
| style="text-align:center;" | undecimal neutral seventh
| undecimal neutral seventh
|-
|-
| style="text-align:center;" | 1150
| 1150
|1219
| 1219
|1472 (5C0<sub>16</sub>)
| 1472 (5C0<sub>16</sub>)
| style="text-align:center;" | ultra seventh, narrow octave
| ultra seventh, narrow octave
| style="text-align:center;" | [[31/16|31/16]]
| [[31/16]] <br> [[33/17]] <br> [[35/18]]
 
| 1145.036 <br> 1148.318 <br> 1151.230
[[33/17|33/17]]
| 31st harmonic <br> .. <br> ..
 
|}
[[35/18|35/18]]
| style="text-align:center;" | 1145.036
 
1148.318


1151.230
=== Interval Alterations ===
| style="text-align:center;" | 31st harmonic


..
..
|}
===Interval Alterations===
The special alterations of the intervals and chords of 12 equal can be notated like this:
The special alterations of the intervals and chords of 12 equal can be notated like this:


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The Latin words "tendo" (meaning "expand") and "arto" (meaning "contract") can be used to replace the words "supermajor" and "subminor" in order to shorten the names of the intervals.
The Latin words "tendo" (meaning "expand") and "arto" (meaning "contract") can be used to replace the words "supermajor" and "subminor" in order to shorten the names of the intervals.


===Chord Names===
=== Chord Names ===
 
Naming chords in 24edo can be achieved by adding a few things to the already [[#|existing]] set of terms that are used to name 12edo chords.
Naming chords in 24edo can be achieved by adding a few things to the already [[#|existing]] set of terms that are used to name 12edo chords.


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