SHEFKHED interval names: Difference between revisions

Line 459:

*Perfect, major and augmented intervals may be given the prefix 'super', with shorthand 'S' which infers an augmentation by the septimal comma, 64/63, whereas perfect, minor and diminished intervals are lowered by the same interval when given the prefix 'sub', with short-form 's'.

*Major and augmented intervals may be given the prefix 'classic', with short-form 'cla', inferring a diminution by the syntonic comma, 81/80, whereas minor and diminished may also be given the prefix 'classic' but with short-hand 'Cla', inferring an augmentation by 81/80. This results in the labeling of 10/9, 6/5, 5/4, 8/5, 5/3 and 9/5 as classic major second, classic major third, classic minor third, classic minor sixth, classic major sixth and classic minor seventh, as per Keenan's suggestion when a comparison to Pythagorean is needed.

*81/80 is referred to by Smith and Bosanquet simple as 'comma'. Smith's interval-naming scheme involves prefixes of ''m''/''n''-comma sharp and ''m''/''n''-comma flat. Using 'wide' and 'narrow' instead of 'sharp' and 'flat', we add long-form prefixes that may be used before perfect intervals, 'comma-wide' and 'comma-narrow' to infer movement up or down a syntonic comma, with short form 'Co-~~wde~~' and 'co-~~nrw~~'. These names are chosen because they start with the same letter as the other prefixes that infer alteration by 81/80.

*81/80 is referred to by Smith and Bosanquet simple as 'comma'. Smith's interval-naming scheme involves prefixes of ''m''/''n''-comma sharp and ''m''/''n''-comma flat. Using 'wide' and 'narrow' instead of 'sharp' and 'flat', we add long-form prefixes that may be used before perfect intervals, 'comma-wide' and 'comma-narrow' to infer movement up or down a syntonic comma, with short form 'Co-W' and 'co-n'. These names are chosen because they start with the same letter as the other prefixes that infer alteration by 81/80.

*For seconds, thirds, sixths and sevenths, any interval exactly half-way major and minor is labelled 'neutral', with short-form 'N'.

*Where neutral intervals split the apotome, to pair with neutral when acting on perfect intervals are 'hemi augmented' and 'hemi diminished', with short form 'h-Aug' and 'h-dim'. 'Hemi' is used instead of 'semi' of 'half' because 'half diminished' is a type of chord, and 'semi' begins with the letter 's', which has been associated with alterations of 64/63. In all cases it's presence implies neutral temperament and the tempering out of 243/242. Accordingly it implies a diminution from perfect, major, augmented of 33/32, as well as an augmentation from perfect, minor or diminished of 33/32, but may not be used to imply those alterations in any other cases.

*To extend to the 13-limit, we add that to co-n P, co-n M and co-n A intervals may be added the 'sub' or 's' prefix, in this instance indicating a diminution of [[65/64]], and that to Co-w P, Co-w m and Co-w dim intervals may be added the 'super' or 'S' prefix, indication an augmentation of the same interval. Accordingly the difference between 65/64 and 64/63, 4096/4095, the ''tridecimal schisma'', is tempered out. Accordingly 16/13 is labelled a 'sub classic major third', or scla M3. In tunings where the syntonic comma is tempered out, such that (co-n P, cla M, cla Aug, Co-w P, Cla m, Cla d) = (P, M, Aug, P, m, dim), the 'cla', 'Cla', 'co-n' and 'Co-w' prefixes are dropped in the short-form.

*To extend to the 13-limit, we add that to co-n P, co-n M and co-n A intervals may be added the 'sub' or 's' prefix, in this instance indicating a diminution of [[65/64]], and that to Co-W P, Co-W m and Co-W dim intervals may be added the 'super' or 'S' prefix, indication an augmentation of the same interval. Accordingly the difference between 65/64 and 64/63, 4096/4095, the ''tridecimal schisma'', is tempered out. Accordingly 16/13 is labelled a 'sub classic major third', or scla M3. In tunings where the syntonic comma is tempered out, such that (co-n P, cla M, cla Aug, Co-W P, Cla m, Cla d) = (P, M, Aug, P, m, dim), the 'cla', 'Cla', 'co-n' and 'Co-W' prefixes are dropped in the short-form.

*Where N indicates a splitting of the apotome and of the perfect fifth, interval names indicating the splitting of the limma and of the perfect fourth are included for remaining unnamed intervals, reflecting limited, but existing practice. The interval half-way between P1 and m2 is given the short-form '1-2', and long-form 'unison-second' and mid-form 'unicond'. Similarly the interval half-way between M7 and P8 is given the long-form 'seventh-octave' and short-form '7-8', that may be said 'sevtave'. The interval splitting the fourth, lying half-way between M2 and m3 is given the long-form 'second-third' and short-form '2-3' that may be said 'serd', and it's octave complement, lying half-way between M6 and m7 is given the long-form 'sixth-seventh', with short-form '6-7' that may be said 'sinth'. The interval half-way between M3 and P4 is given the long-form 'third-fourth', with short-form '3-4', that may be said 'thourth', and it's octave-complement, the interval half-way between P5 and m6 is given the long-form 'fifth-sixth', with short-form '5-6', that may be ~~saud~~ 'fixth'. These interval names can be associated with [[The Archipelago|Barbados]] temperament, indicating the tempering out of 676/675, generated by 2-3, half of the fourth, associated with the ratio 15/13. These ''intermediates'' lie 40/39 above major intervals and the perfect unison and fifth, and below minor intervals and the perfect fourth and octave. 3-4, for example, is associated with the ratio 13/10.

*Where N indicates a splitting of the apotome and of the perfect fifth, interval names indicating the splitting of the limma and of the perfect fourth are included for remaining unnamed intervals, reflecting limited, but existing practice. The interval half-way between P1 and m2 is given the short-form '1-2', and long-form 'unison-second' and mid-form 'unicond'. Similarly the interval half-way between M7 and P8 is given the long-form 'seventh-octave' and short-form '7-8', that may be said 'sevtave'. The interval splitting the fourth, lying half-way between M2 and m3 is given the long-form 'second-third' and short-form '2-3' that may be said 'serd', and it's octave complement, lying half-way between M6 and m7 is given the long-form 'sixth-seventh', with short-form '6-7' that may be said 'sinth'. The interval half-way between M3 and P4 is given the long-form 'third-fourth', with short-form '3-4', that may be said 'thourth', and it's octave-complement, the interval half-way between P5 and m6 is given the long-form 'fifth-sixth', with short-form '5-6', that may be said 'fixth'. These interval names can be associated with [[The Archipelago|Barbados]] temperament, indicating the tempering out of 676/675, generated by 2-3, half of the fourth, associated with the ratio 15/13. These ''intermediates'' lie 40/39 above major intervals and the perfect unison and fifth, and below minor intervals and the perfect fourth and octave. 3-4, for example, is associated with the ratio 13/10.

*For completeness, the 'fourth-fifth', with '4-5' that may be said 'firth' is added, though it is separate to the other intermediates, splitting not the limma, but the dieses (between Aug4 and dim5), or the octave. It does not map to any particular ratios and is not needed as a primary interval name, apart from in 16edo, and is included mostly to be used as an optional secondary interval name when there are no others.

*In any prefix is used before 'P' then 'P' is removed in both the short-form and long-form names.

*The prefixes so far take us as far as 53edo, which is considered a 'commatic' scale by many, and as far as extended-diatonic function, which I hope to reflect with this scheme, could be considered to apply. Keenan's functional names take us to 31edo, after which 'narrow' and 'wide' prefixes are added to differentiate different intervals in medium to large sized edos of the same function. Ups and Downs takes function as far as regular diatonic and mids (equivalent to neutrals), which will give us most of a well-ordered interval name set for 17edo (if mids were extended as I have extended neutrals, all the notes would be obtainable) without up or down prefixes, and only functional names, or all of 19edo or 26edo, since these are meantone edos with the apotome subtended by a single degree and may be given a well-ordered interval names set using only regular diatonic interval names. The up and down prefixes are not functional, and specify movement instead by a single step of an edo. If the naming of systems with more than one interval per function is desired, then 'up' and '~~down~~' prefixes, with short form '^' and 'v' respectively are to be employed. This also allows the notation of intervals for which intermediates are the only available functional interval name. Note: For regular diatonic intervals, I consider function only to go as far as singly diminished or augmented intervals, and never use multiply diminished or augmented intervals for my interval names.

*The prefixes so far take us as far as 53edo, which is considered a 'commatic' scale by many, and as far as extended-diatonic function, which I hope to reflect with this scheme, could be considered to apply. Keenan's functional names take us to 31edo, after which 'narrow' and 'wide' prefixes are added to differentiate different intervals in medium to large sized edos of the same function. Ups and Downs takes function as far as regular diatonic and mids (equivalent to neutrals), which will give us most of a well-ordered interval name set for 17edo (if mids were extended as I have extended neutrals, all the notes would be obtainable) without up or down prefixes, and only functional names, or all of 19edo or 26edo, since these are meantone edos with the apotome subtended by a single degree and may be given a well-ordered interval names set using only regular diatonic interval names. The up and down prefixes are not functional, and specify movement instead by a single step of an edo. If the naming of systems with more than one interval per function is desired, then 'wide' and 'narrow' prefixes, with short form 'W' and 'n' respectively are to be employed. This also allows the notation of intervals for which intermediates are the only available functional interval name. Note: For regular diatonic intervals, I consider function only to go as far as singly diminished or augmented intervals, and never use multiply diminished or augmented intervals for my interval names.

{| class="wikitable"

|+Prefixes summary

Line 511:

|-

|comma-wide

|Co-w

|Co-W

|up 81/80

|-

Line 580:

#Major, minor, Aug 4 and dim 5.

#h-Aug 4 and h-dim 5

#'S', 's', 'Cla', 'cla', 'Co-w', 'co-n', 'SCla', 'scla', 'SCo-w' and 'sco-n' prefixes to major, minor, perfect intervals and to Aug 4 and dim 5

#'S', 's', 'Cla', 'cla', 'Co-W', 'co-n', 'SCla', 'scla', 'SCo-W' and 'sco-n' prefixes to major, minor, perfect intervals and to Aug 4 and dim 5

#h-Aug 1 and h-dim 8 (plus any other h-Augs and h-dims if needed)

#Intermediates

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When more than one interval name corresponds to a specific interval, the names are privileged in order of the tiers. By this ordering, the first available name is the ‘primary’ for that interval, the second available ‘secondary’ and third 'tertiary'.

Where the same interval may be named co-n 4 or s4, s4 is preferred and where the same interval may be named Co-w 4 or S4, Co-w 4 is preferred. Similarly, where the same interval may be named Co-w 5 or S5, S5 is preferred and where the same interval may be named co-n 5 or s5, co-n 5 is preferred. This is to ensure the interval is named after the simpler ratio. On top of this, well-ordered interval-name sets are desired, leading to interval names in lower tires being used in preference to higher-tier names in some cases.

Where the same interval may be named co-n 4 or s4, s4 is preferred and where the same interval may be named Co-W 4 or S4, Co-W 4 is preferred. Similarly, where the same interval may be named Co-W 5 or S5, S5 is preferred and where the same interval may be named co-n 5 or s5, co-n 5 is preferred. This is to ensure the interval is named after the simpler ratio. On top of this, well-ordered interval-name sets are desired, leading to interval names in lower tires being used in preference to higher-tier names in some cases.

=== Regular diatonic edos ===

Line 617:

38edo: P1 S1 A1 sm2 m2 N2 M2 SM2 A2/d3 sm3 m3 N3 M3 SM3 d4 s4 P4 hA4 A4 SA4/sd5 d5 hd5 P5 S5 A5 sm6 m6 N6 M6 SM6 A6/d7 sm7 m7 N7 M7 SM7 d8 s8 P8

41edo: P1 C1/S1 ~~hA1~~ m2 Cm2 N2 cM2 M2 SM2 sm3 m3 Cm3 N3 cM3 M3 SM3 s4 P4 C4 hA4 cA4 Cd5 hd5 c5 P5 S5 sm6 m6 Cm6 N6 cM6 M6 SM6 sm7 m7 Cm7 N7 cM7 M7 ~~hd8~~ c8/s8 P8

41edo: P1 C1/S1 sm2 m2 Cm2 N2 cM2 M2 SM2 sm3 m3 Cm3 N3 cM3 M3 SM3 s4 P4 C4 hA4 cA4 Cd5 hd5 c5 P5 S5 sm6 m6 Cm6 N6 cM6 M6 SM6 sm7 m7 Cm7 N7 cM7 M7 SM7 c8/s8 P8

43edo: P1 S1 1-2 sm2 m2 Sm2 sM2 M2 SM2 2-3 sm3 m3 Sm3 sM3 M3 SM3 3-4 s4 P4 S4 sA4 A4 d5 Sd5 s5 P5 S5 5-6 sm6 m6 Sm6 sM6 M6 SM6 6-7 sm7 m7 Sm7 sM7 M7 SM7 7-8 s8 P8

Line 658:

|m2

|comma-sharp unison/super minor second

|Co-w 1 / sm2

|Co-W 1 / sm2

|54.55

|33/32, 34/33, 25/24, 81/80

Line 727:

|-

|10

|comma-~~sharp~~ fourth

|comma-wide fourth

|C4

|Co-W 4

|diminished fifth

|dim 5

Line 746:

|-

|12

|comma-~~flat~~ fifth

|comma-narrow fifth

|c5

|co-n 5

|augmented fourth

|Aug 4

Line 849:

|1

|comma-wide unison/super unison

|Co-w 1 / S1

|Co-W 1 / S1

|29.27

|[[81/80]], 64/63

|-

|2

|hemi-augmented unison~~, subminor second~~

|subminor second, hemi-augmented unison

|h-Aug 1~~, sm2~~

|sm2, h-Aug 1

|58.54

|[[25/24]], [[28/27]], [[33/32]]

Line 951:

|18

|comma-wide fourth, augmented third

|Co-w 4, Aug 3

|Co-W 4, Aug 3

|526.83

|[[15/11]], [[27/20]]

Line 1,076:

|-

|39

|hemi-diminished octave~~, super major seventh~~

|super major seventh, hemi-diminished octave

|h-dim 8~~, SM7~~

|SM7, h-dim 8

|1141.46

|[[48/25]], [[27/14]], 64/33

Line 1,112:

|1

|comma-narrow unison/super unison

|Co-w 1 / S1

|Co-W 1 / S1

|22.64

|81/80, 64/63, 65/64, 50/49

Line 1,244:

|23

|comma-wide fourth, augmented third

|Co-w 4, Aug 3

|Co-W 4, Aug 3

|520.75

|27/20

Line 1,250:

|24

|super comma-wide fourth

|SCo-w 4

|SCo-W 4

|543.40

|11/8, 15/11

@@ Line 459: / Line 459: @@
 *Perfect, major and augmented intervals may be given the prefix 'super', with shorthand 'S' which infers an augmentation by the septimal comma, 64/63, whereas perfect, minor and diminished intervals are lowered by the same interval when given the prefix 'sub', with short-form 's'.
 *Major and augmented intervals may be given the prefix 'classic', with short-form 'cla', inferring a diminution by the syntonic comma, 81/80, whereas minor and diminished may also be given the prefix 'classic' but with short-hand 'Cla', inferring an augmentation by 81/80. This results in the labeling of 10/9, 6/5, 5/4, 8/5, 5/3 and 9/5 as classic major second, classic major third, classic minor third, classic minor sixth, classic major sixth and classic minor seventh, as per Keenan's suggestion when a comparison to Pythagorean is needed.
-*81/80 is referred to by Smith and Bosanquet simple as 'comma'. Smith's interval-naming scheme involves prefixes of ''m''/''n''-comma sharp and ''m''/''n''-comma flat. Using 'wide' and 'narrow' instead of 'sharp' and 'flat', we add long-form prefixes that may be used before perfect intervals, 'comma-wide' and 'comma-narrow' to infer movement up or down a syntonic comma, with short form 'Co-wde' and 'co-nrw'. These names are chosen because they start with the same letter as the other prefixes that infer alteration by 81/80.
+*81/80 is referred to by Smith and Bosanquet simple as 'comma'. Smith's interval-naming scheme involves prefixes of ''m''/''n''-comma sharp and ''m''/''n''-comma flat. Using 'wide' and 'narrow' instead of 'sharp' and 'flat', we add long-form prefixes that may be used before perfect intervals, 'comma-wide' and 'comma-narrow' to infer movement up or down a syntonic comma, with short form 'Co-W' and 'co-n'. These names are chosen because they start with the same letter as the other prefixes that infer alteration by 81/80.
 *For seconds, thirds, sixths and sevenths, any interval exactly half-way major and minor is labelled 'neutral', with short-form 'N'.
 *Where neutral intervals split the apotome, to pair with neutral when acting on perfect intervals are 'hemi augmented' and 'hemi diminished', with short form 'h-Aug' and 'h-dim'. 'Hemi' is used instead of 'semi' of 'half' because 'half diminished' is a type of chord, and 'semi' begins with the letter 's', which has been associated with alterations of 64/63. In all cases it's presence implies neutral temperament and the tempering out of 243/242. Accordingly it implies a diminution from perfect, major, augmented of 33/32, as well as an augmentation from perfect, minor or diminished of 33/32, but may not be used to imply those alterations in any other cases.
-*To extend to the 13-limit, we add that to co-n P, co-n M and co-n A intervals may be added the 'sub' or 's' prefix, in this instance indicating a diminution of [[65/64]], and that to Co-w P, Co-w m and Co-w dim intervals may be added the 'super' or 'S' prefix, indication an augmentation of the same interval. Accordingly the difference between 65/64 and 64/63, 4096/4095, the ''tridecimal schisma'', is tempered out. Accordingly 16/13 is labelled a 'sub classic major third', or scla M3. In tunings where the syntonic comma is tempered out, such that (co-n P, cla M, cla Aug, Co-w P, Cla m, Cla d) = (P, M, Aug, P, m, dim), the 'cla', 'Cla', 'co-n' and 'Co-w' prefixes are dropped in the short-form.
+*To extend to the 13-limit, we add that to co-n P, co-n M and co-n A intervals may be added the 'sub' or 's' prefix, in this instance indicating a diminution of [[65/64]], and that to Co-W P, Co-W m and Co-W dim intervals may be added the 'super' or 'S' prefix, indication an augmentation of the same interval. Accordingly the difference between 65/64 and 64/63, 4096/4095, the ''tridecimal schisma'', is tempered out. Accordingly 16/13 is labelled a 'sub classic major third', or scla M3. In tunings where the syntonic comma is tempered out, such that (co-n P, cla M, cla Aug, Co-W P, Cla m, Cla d) = (P, M, Aug, P, m, dim), the 'cla', 'Cla', 'co-n' and 'Co-W' prefixes are dropped in the short-form.
-*Where N indicates a splitting of the apotome and of the perfect fifth, interval names indicating the splitting of the limma and of the perfect fourth are included for remaining unnamed intervals, reflecting limited, but existing practice. The interval half-way between P1 and m2 is given the short-form '1-2', and long-form 'unison-second' and mid-form 'unicond'. Similarly the interval half-way between M7 and P8 is given the long-form 'seventh-octave'  and short-form '7-8', that may be said 'sevtave'. The interval splitting the fourth, lying half-way between M2 and m3 is given the long-form 'second-third' and short-form '2-3' that may be said 'serd', and it's octave complement, lying half-way between M6 and m7 is given the long-form 'sixth-seventh', with short-form '6-7' that may be said 'sinth'. The interval half-way between M3 and P4 is given the long-form 'third-fourth', with short-form '3-4', that may be said 'thourth', and it's octave-complement, the interval half-way between P5 and m6 is given the  long-form 'fifth-sixth', with short-form '5-6', that may be saud 'fixth'. These interval names can be associated with [[The Archipelago|Barbados]] temperament, indicating the tempering out of 676/675, generated by 2-3, half of the fourth, associated with the ratio 15/13. These ''intermediates'' lie 40/39 above major intervals and the perfect unison and fifth, and below minor intervals and the perfect fourth and octave. 3-4, for example, is associated with the ratio 13/10.
+*Where N indicates a splitting of the apotome and of the perfect fifth, interval names indicating the splitting of the limma and of the perfect fourth are included for remaining unnamed intervals, reflecting limited, but existing practice. The interval half-way between P1 and m2 is given the short-form '1-2', and long-form 'unison-second' and mid-form 'unicond'. Similarly the interval half-way between M7 and P8 is given the long-form 'seventh-octave'  and short-form '7-8', that may be said 'sevtave'. The interval splitting the fourth, lying half-way between M2 and m3 is given the long-form 'second-third' and short-form '2-3' that may be said 'serd', and it's octave complement, lying half-way between M6 and m7 is given the long-form 'sixth-seventh', with short-form '6-7' that may be said 'sinth'. The interval half-way between M3 and P4 is given the long-form 'third-fourth', with short-form '3-4', that may be said 'thourth', and it's octave-complement, the interval half-way between P5 and m6 is given the  long-form 'fifth-sixth', with short-form '5-6', that may be said 'fixth'. These interval names can be associated with [[The Archipelago|Barbados]] temperament, indicating the tempering out of 676/675, generated by 2-3, half of the fourth, associated with the ratio 15/13. These ''intermediates'' lie 40/39 above major intervals and the perfect unison and fifth, and below minor intervals and the perfect fourth and octave. 3-4, for example, is associated with the ratio 13/10.
 *For completeness, the  'fourth-fifth', with '4-5' that may be said 'firth' is added, though it is separate to the other intermediates, splitting not the limma, but the dieses (between Aug4 and dim5), or the octave. It does not map to any particular ratios and is not needed as a primary interval name, apart from in 16edo, and is included mostly to be used as an optional secondary interval name when there are no others.
 *In any prefix is used before 'P' then 'P' is removed in both the short-form and long-form names.
-*The prefixes so far take us as far as 53edo, which is considered a 'commatic' scale by many, and as far as extended-diatonic function, which I hope to reflect with this scheme, could be considered to apply. Keenan's functional names take us to 31edo, after which 'narrow' and 'wide' prefixes are added to differentiate different intervals in medium to large sized edos of the same function. Ups and Downs takes function as far as regular diatonic and mids (equivalent to neutrals), which will give us most of a well-ordered interval name set for 17edo (if mids were extended as I have extended neutrals, all the notes would be obtainable) without up or down prefixes, and only functional names, or all of 19edo or 26edo, since these are meantone edos with the apotome subtended by a single degree and may be given a well-ordered interval names set using only regular diatonic interval names. The up and down prefixes are not functional, and specify movement instead by a single step of an edo. If the naming of systems with more than one interval per function is desired, then 'up' and 'down' prefixes, with short form '^' and 'v' respectively are to be employed. This also allows the notation of intervals for which intermediates are the only available functional interval name. Note: For regular diatonic intervals, I consider function only to go as far as singly diminished or augmented intervals, and never use multiply diminished or augmented intervals for my interval names.
+*The prefixes so far take us as far as 53edo, which is considered a 'commatic' scale by many, and as far as extended-diatonic function, which I hope to reflect with this scheme, could be considered to apply. Keenan's functional names take us to 31edo, after which 'narrow' and 'wide' prefixes are added to differentiate different intervals in medium to large sized edos of the same function. Ups and Downs takes function as far as regular diatonic and mids (equivalent to neutrals), which will give us most of a well-ordered interval name set for 17edo (if mids were extended as I have extended neutrals, all the notes would be obtainable) without up or down prefixes, and only functional names, or all of 19edo or 26edo, since these are meantone edos with the apotome subtended by a single degree and may be given a well-ordered interval names set using only regular diatonic interval names. The up and down prefixes are not functional, and specify movement instead by a single step of an edo. If the naming of systems with more than one interval per function is desired, then 'wide' and 'narrow' prefixes, with short form 'W' and 'n' respectively are to be employed. This also allows the notation of intervals for which intermediates are the only available functional interval name. Note: For regular diatonic intervals, I consider function only to go as far as singly diminished or augmented intervals, and never use multiply diminished or augmented intervals for my interval names.
 {| class="wikitable"
 |+Prefixes summary
@@ Line 511: / Line 511: @@
 |-
 |comma-wide
-|Co-w
+|Co-W
 |up 81/80
 |-
@@ Line 580: / Line 580: @@
 #Major, minor, Aug 4 and dim 5.
 #h-Aug 4 and h-dim 5
-#'S', 's', 'Cla', 'cla', 'Co-w', 'co-n', 'SCla', 'scla', 'SCo-w' and 'sco-n' prefixes to major, minor, perfect intervals and to Aug 4 and dim 5
+#'S', 's', 'Cla', 'cla', 'Co-W', 'co-n', 'SCla', 'scla', 'SCo-W' and 'sco-n' prefixes to major, minor, perfect intervals and to Aug 4 and dim 5
 #h-Aug 1 and h-dim 8 (plus any other h-Augs and h-dims if needed)
 #Intermediates
@@ Line 588: / Line 588: @@
 When more than one interval name corresponds to a specific interval, the names are privileged in order of the tiers. By this ordering, the first available name is the ‘primary’ for that interval, the second available ‘secondary’ and third 'tertiary'.
-Where the same interval may be named co-n 4 or s4, s4 is preferred and where the same interval may be named Co-w 4 or S4, Co-w 4 is preferred. Similarly, where the same interval may be named Co-w 5 or S5, S5 is preferred and where the same interval may be named co-n 5 or s5, co-n 5 is preferred. This is to ensure the interval is named after the simpler ratio. On top of this, well-ordered interval-name sets are desired, leading to interval names in lower tires being used in preference to higher-tier names in some cases.
+Where the same interval may be named co-n 4 or s4, s4 is preferred and where the same interval may be named Co-W 4 or S4, Co-W 4 is preferred. Similarly, where the same interval may be named   Co-W 5 or S5, S5 is preferred and where the same interval may be named co-n 5 or s5, co-n 5 is preferred. This is to ensure the interval is named after the simpler ratio. On top of this, well-ordered interval-name sets are desired, leading to interval names in lower tires being used in preference to higher-tier names in some cases.
 === Regular diatonic edos ===
@@ Line 617: / Line 617: @@
 edo: P1 S1 A1 sm2 m2 N2 M2 SM2 A2/d3 sm3 m3 N3 M3 SM3 d4 s4 P4 hA4 A4 SA4/sd5 d5 hd5 P5 S5 A5 sm6 m6 N6 M6 SM6 A6/d7 sm7 m7 N7 M7 SM7 d8 s8 P8
-edo: P1 C1/S1 hA1 m2 Cm2 N2 cM2 M2 SM2 sm3 m3 Cm3 N3 cM3 M3 SM3 s4 P4 C4 hA4 cA4 Cd5 hd5 c5 P5 S5 sm6 m6 Cm6 N6 cM6 M6 SM6 sm7 m7 Cm7 N7 cM7 M7 hd8 c8/s8 P8
+edo: P1 C1/S1 sm2 m2 Cm2 N2 cM2 M2 SM2 sm3 m3 Cm3 N3 cM3 M3 SM3 s4 P4 C4 hA4 cA4 Cd5 hd5 c5 P5 S5 sm6 m6 Cm6 N6 cM6 M6 SM6 sm7 m7 Cm7 N7 cM7 M7 SM7 c8/s8 P8
 edo: P1 S1 1-2 sm2 m2 Sm2 sM2 M2 SM2 2-3 sm3 m3 Sm3 sM3 M3 SM3 3-4 s4 P4 S4 sA4 A4 d5 Sd5 s5 P5 S5 5-6 sm6 m6 Sm6 sM6 M6 SM6 6-7 sm7 m7 Sm7 sM7 M7 SM7 7-8 s8 P8
@@ Line 658: / Line 658: @@
 |m2
 |comma-sharp unison/super minor second
-|Co-w 1 / sm2
+|Co-W 1 / sm2
 |54.55
 |33/32, 34/33, 25/24, 81/80
@@ Line 727: / Line 727: @@
 |-
 |10
-|comma-sharp fourth
+|comma-wide fourth
-|C4
+|Co-W 4
 |diminished fifth
 |dim 5
@@ Line 746: / Line 746: @@
 |-
 |12
-|comma-flat fifth
+|comma-narrow fifth
-|c5
+|co-n 5
 |augmented fourth
 |Aug 4
@@ Line 849: / Line 849: @@
 |1
 |comma-wide unison/super unison
-|Co-w 1 / S1
+|Co-W 1 / S1
 |29.27
 |[[81/80]], 64/63
 |-
 |2
-|hemi-augmented unison, subminor second
+|subminor second, hemi-augmented unison
-|h-Aug 1, sm2
+|sm2, h-Aug 1
 |58.54
 |[[25/24]], [[28/27]], [[33/32]]
@@ Line 951: / Line 951: @@
 |18
 |comma-wide fourth, augmented third
-|Co-w 4, Aug 3
+|Co-W 4, Aug 3
 |526.83
 |[[15/11]], [[27/20]]
@@ Line 1,076: / Line 1,076: @@
 |-
 |39
-|hemi-diminished octave, super major seventh
+|super major seventh, hemi-diminished octave
-|h-dim 8, SM7
+|SM7, h-dim 8
 |1141.46
 |[[48/25]], [[27/14]], 64/33
@@ Line 1,112: / Line 1,112: @@
 |1
 |comma-narrow unison/super unison
-|Co-w 1 / S1
+|Co-W 1 / S1
 |22.64
 |81/80, 64/63, 65/64, 50/49
@@ Line 1,244: / Line 1,244: @@
 |23
 |comma-wide fourth, augmented third
-|Co-w 4, Aug 3
+|Co-W 4, Aug 3
 |520.75
 |27/20
@@ Line 1,250: / Line 1,250: @@
 |24
 |super comma-wide fourth
-|SCo-w 4
+|SCo-W 4
 |543.40
 |11/8, 15/11