User:Eufalesio/PLIN: Difference between revisions

Line 14:

=== Compromise notations ===

The only notation I have knowledge of that can be sensibly called a "compromise notation" is [[Sagittal]]. It can be used to notate almost every tuning imaginable, combining mapping with JI-ish accidentals at high enough complexity. They share the versatility of tempered notations combining it with the exactitude of JI, converging ~~towards~~ a JI interval that is represented through accidentals that represent both a mapping and a precise comma.

The only notation I have knowledge of that can be sensibly called a "compromise notation" is [[Sagittal]]. It can be used to notate almost every tuning imaginable, combining mapping with JI-ish accidentals at high enough complexity. They share the versatility of tempered notations combining it with the exactitude of JI, converging toweeds a JI interval that is represented through accidentals that represent both a mapping and a precise comma.

'''PLIN''', the focus of this article, aims to be such another notation[https://xkcd.com/927/ .]

Line 32:

Any single region has infinite intervals represented in it, and thus it is important to distinguish the breadth of the buckets any JI interval can fall into. So, while there are an infinite amount of minor thirds, and of superminor thirds, and of qu superminorthirds, and of twomins qu superminor thirds, all of them will 6/5; with 12-PLIN being quite rough, 53-PLIN being very accurate, and 665-PLIN and 7315-PLIN further refining the accuracy to extreme levels to the point where all of those will sound indistinguishable from 6/5, since the difference will be only of 0.16 c per region in 7315-PLIN.

12-PLIN, 53-PLIN and 665-PLIN are MOSses, more concretely, 5L 7s 6|5 1.260, 41L 12s 26|26 H=1.1822, and 306L 359s H=1.0427, but 159-PLIN and 7315 are not, as they modify the two last MOSses respectively with fractions of the telic commas. As such, to make things easier, '''EPLIN'''s may be used to have exactly equal regions, which will make things easier to work with. by default, PLINs are not equal, so it needs to be specified when an equalized PLIN is being used, because it can change the region an interval falls into. For example, 31/16 is a rough octave, but in 12-EPLIN, a '''eq'''rough major seventh. 7/4 is a fixsubminor seventh, but in 159-EPLIN, an '''~~equarto~~'''subminor seventh.

12-PLIN, 53-PLIN and 665-PLIN are MOSses, more concretely, 5L 7s 6|5 1.260, 41L 12s 26|26 H=1.1822, and 306L 359s H=1.0427, but 159-PLIN and 7315 are not, as they modify the two last MOSses respectively with fractions of the telic commas. As such, to make things easier, '''EPLIN'''s may be used to have exactly equal regions, which will make things easier to work with. by default, PLINs are not equal, so it needs to be specified when an equalized PLIN is being used, because it can change the region an interval falls into. For example, 31/16 is a rough octave, but in 12-EPLIN, a '''eq'''rough major seventh. 7/4 is a fixsubminor seventh, but in 159-EPLIN, an '''equwee'''subminor seventh.

One glaring design feature about PLINs is the lack of ''neutral'' categories, and of ''augmented'', ''diminished'' and ''perfect''. The reason to avoid those is that for one, true neutral intervals do not exist in integer pythagorean, but even if they did, using this term is unnecessary. 11/9 is commonly called a neutral interval, but it is closer to a minor third. So it is roughly a minor third. More precisely a hyperminor third, at the extreme of minor thirds. Same thing applies to the interordinals like chthonics, naiadics, cocytics and ouranics. You can do fine with using hyper/hypo to refer to them at the edges of the nominals. All of this ''sonically speaking''.

Line 40:

Also, no words for other primes. So no ptolemaic/pental/classical, septimal, undecimal... etc. Everything stays in the 3-limit. Minimum complexity, reducing the amount of classes and descriptors to worry about to the absolute minimum.

Regarding the choice of words to refer to the descriptors; you might not agree about the use of hypo/hyper, or ~~arto~~/~~tendo~~, or qi/qu, or mi/mu, or n-plus/n-minus; but that's only a semantics problem. I chose those names because they kind of make sense to me, but the rigor is in the system, because you have these commas in the k-strong 3-2 telic sequence:

Regarding the choice of words to refer to the descriptors; you might not agree about the use of hypo/hyper, or wee/wide, or qi/qu, or mi/mu, or n-plus/n-minus; but that's only a semantics problem. I chose those names because they kind of make sense to me, but the rigor is in the system, because you have these commas in the k-strong 3-2 telic sequence:

* Limmas and apotomes (1 m2 M2 m3 M3 4 T 5 m6 M6 m7 M7 8) Available in 12-PLIN [rough]

* Pythagorean commas ('''s'''ub/'''S'''uper, '''h'''ypo/'''H'''yper) Available in 53-PLIN [∅], functionally only in 12-PLIN

* ''Pythagorean comma thirds (~~'''a'''rto~~/~~'''t'''endo~~) Available '''only''' in 159-PLIN [fix]''

* ''Pythagorean comma thirds (wee/wide) Available '''only''' in 159-PLIN [fix]''

* Mercator commas ([π]mu/[Π]mi) Available in 665-PLIN [sat], functionally only in 53/159-PLIN

* Sasktel commas (qu/'''Q'''i) Available in 665-PLIN [sat]

Line 57:

* 12-PLIN : rough + diatonic nominal

* 53-PLIN: hypo/sub/∅/super/hyper + diatonic nominal

* 159-PLIN ~~arto~~/fix/~~tendo~~ + hypo/sub/∅/super/hyper + diatonic nominal

* 159-PLIN wee/fix/wide + hypo/sub/∅/super/hyper + diatonic nominal

* 665-PLIN [∅/qi/qu + [∅/two/three][mi/mu]]/sat + hypo/sub/∅/super/hyper + diatonic nominal

* 7315-PLIN [[∅/two/three/four/five][plus/min(u)s]]/spot+[∅/qi/qu+[∅/two/three][mi/mu]]+hypo/sub/∅/super/hyper+diatonic nominal

Line 648:

|729/728

|-

|~~tendounison~~

|wideunison

|t1

|Dt

|DW

|7.8200

|225/224

|-

|~~artosuperunison~~

|weesuperunison

|aS1

|~~DaS~~

|DwS

|15.6400

|121/120

Line 666:

|64/63

|-

|~~tendosuperunison~~

|widesuperunison

|tS1

|DtS

Line 672:

|56/55

|-

|~~artohyperunison~~ / ~~artohypominor~~ second

|weehyperunison / weehypominor second

|aH1

|~~DaH~~ /~~Ebah~~

|DwH /Ebwh

|39.1000

|45/44

Line 684:

|40/39

|-

|~~tendohyperunison~~ / ~~tendohypominor~~ second

|widehyperunison / widehypominor second

|th2

|~~Ebth~~

|EbWh

|54.740021

|33/32

|-

|~~artosubminor~~ second

|weesubminor second

|asm2

|~~Ebas~~

|Ebws

|58.9449

|91/88

Line 702:

|80/77

|-

|~~tendosubminorsecond~~

|widesubminorsecond

|tsm2

|~~Ebts~~

|EbWs

|74.5840

|448/429

|-

|~~artominor~~ second

|weeminor second

|am2

|~~Eba~~

|Ebw

|82.405

|22/21

Line 720:

|96/91

|-

|~~tendominor~~ second

|wideminor second

|tm2

|~~Ebt~~

|EbW

|98.045

|128/121

|-

|~~artosuperminor~~ second

|weesuperminor second

|aSm2

|~~EbaSa~~

|EbwS

|105.865

|1225/1152

Line 738:

|16/15

|-

|~~tendosuperminor~~ second

|widesuperminor second

|tSm2

|~~EbtS~~

|EbWS

|121.505

|15/14

|-

|~~artohyperminor~~ second

|weehyperminor second

|aHm2

|~~EbaH~~

|EbwH

|129.325

|14/13

Line 756:

|13/12

|-

|~~tendohyperminor~~ second

|widehyperminor second

|tHm2

|~~EbtH~~

|EbWH

|144.965

|160/147

|-

|~~artohypomajor~~ second

|weehypomajor second

|ahM2

|~~Eah~~

|Ewh

|149.17

|12/11

Line 774:

|35/32

|-

|~~tendohypomajor~~ second

|widehypomajor second

|thM2

|~~Eth~~

|EWh

|164.809

|11/10

|-

|~~artosubmajor~~ second

|weesubmajor second

|asM2

|~~Eas~~

|Ews

|172.629

|182/165

Line 792:

|231/208

|-

|~~tendosubmajor~~ second

|widesubmajor second

|tsM2

|Ets

Line 798:

|39/35

|-

|~~artomajor~~ second

|weemajor second

|aM2

|Ea

|Ew

|196.09

|160/143

Line 814:

If 53-PLIN is not enough for you, this will be surely be enough. If not... then prepare for what's to come.

As you know, two is a pair, three is a crowd, and each new PLIN continues adding more classes to worry about. So far, it has been only 3 classes at most: ~~tendo~~/~~arto~~, hypo/sub/fix/super/hyper, nominal. But, 665 has now qi/qu (small qian commas) and mi/mu (mercator commas), apart from the hypo/sub/fix/super/hyper, nominal. 7315-PLIN has all those, and five-fold plus/min(u)s.

As you know, two is a pair, three is a crowd, and each new PLIN continues adding more classes to worry about. So far, it has been only 3 classes at most: wide/wee, hypo/sub/fix/super/hyper, nominal. But, 665 has now qi/qu (small qian commas) and mi/mu (mercator commas), apart from the hypo/sub/fix/super/hyper, nominal. 7315-PLIN has all those, and five-fold plus/min(u)s.

{| class="wikitable"

|+665-PLIN until the first pythagorean comma

Line 1,376:

I think the mappings are correct, but I'm too lazy to check my work. Mappings ''may'' change for EPLINs.

== ~~Notes on~~ EPLINs ==

== EPLINs ==

Since EPLINs are essentially edos, I think that allowing more EPLINs than PLINs to exist could be advantageous. Case in point: 41-EPLIN, 94-EPLIN, 118-EPLIN, ~~65/~~130-EPLIN, 171-EPLIN, 217-EPLIN, 311-EPLIN, 1600-EPLIN, 2460-EPLIN, 8539-EPLIN. ~~Any edo with~~ a ~~mapped fifth no wider than 41edo~~'s, ~~no narrower than 65edo's would be good~~.

Since EPLINs are essentially edos, I think that allowing more EPLINs than PLINs to exist could be advantageous. Case in point: 41-EPLIN, 94-EPLIN, 118-EPLIN, 130-EPLIN, 171-EPLIN, 217-EPLIN, 270-EPLIN, 311-EPLIN, 1600-EPLIN, 2460-EPLIN, 8539-EPLIN. '''No others'''. This is to prevent bloat of the system and the mapped comma to fall beyond the size of a syntonic or septimal comma. The reason to use these edos is because they're either zeta peaks, or very very consistent.

~~WIP~~

The jump from 311 to 1600 is due to the fact that for its size, there is no better edo for consistency than 311. The next best thing is 1600edo, which has around the same absolute error as 270edo, if a bit less. Just in case, and because I think they're SS-tier edos, I'm putting the behemoths 2460 and 6079 for ultra-mega-hyper accuracy.

=~~= Conclusion ==~~

Here are the prefixes for pythagorean comma fractions in these EPLINs:

~~WIP~~

{| class="wikitable"

|+

!Edosteps

added

!41-EPLIN

!94-EPLIN

!118-EPLIN

!130-EPLIN

!171-EPLIN

!217-EPLIN

!270-EPLIN

!311-EPLIN

!1600-EPLIN

!2460-EPLIN

!6079-EPLIN

|-

| +1

|–

|glus

|hus

|slus

|nus

|clus

|xus

|vlus

|kwus

|krus

|prus

|-

|0

|kite

|gar

|hel

|spen

|nea

|cot

|nex

|vu

|kwa

|kirn

|pir

|-

| -1

|–

|gins

|hins

|spins

|nins

|kins

|xins

|vins

|kwins

|krins

|prins

|-

!Size and

edosteps

|29.268c

[1]

|25.532c

[2]

|20.339c

[2]

|18.4615c

[2]

|21.0526c

[3]

|27.6497c

[5]

|26.<u>6</u>c

[6]

|27.001c

[7]

|24c

[32]

|23.4146c

[48]

|23.4688c

[167]

|}

These prefixes are based on the a temperament they represent, or on Sagittal:

* gar- for Garibaldi

* hel- for Helmholtz

* spen- for Sensipent

* nea- for Ennealimmal

* cot- for Cotoneum

* nex- for Nexus

* vu- for Vavoom

* kwa- for Kwazy

* kirn- for Atomic (Kirnberger's atom)

* pir- for Pirate

@@ Line 14: / Line 14: @@
 === Compromise notations ===
-The only notation I have knowledge of that can be sensibly called a "compromise notation" is [[Sagittal]]. It can be used to notate almost every tuning imaginable, combining mapping with JI-ish accidentals at high enough complexity. They share the versatility of tempered notations combining it with the exactitude of JI, converging towards a JI interval that is represented through accidentals that represent both a mapping and a precise comma.
+The only notation I have knowledge of that can be sensibly called a "compromise notation" is [[Sagittal]]. It can be used to notate almost every tuning imaginable, combining mapping with JI-ish accidentals at high enough complexity. They share the versatility of tempered notations combining it with the exactitude of JI, converging toweeds a JI interval that is represented through accidentals that represent both a mapping and a precise comma.
 '''PLIN''', the focus of this article, aims to be such another notation[https://xkcd.com/927/ .]
@@ Line 32: / Line 32: @@
 Any single region has infinite intervals represented in it, and thus it is important to distinguish the breadth of the buckets any JI interval can fall into. So, while there are an infinite amount of minor thirds, and of superminor thirds, and of qu superminorthirds, and of twomins qu superminor thirds, all of them will 6/5; with 12-PLIN being quite rough, 53-PLIN being very accurate, and 665-PLIN and 7315-PLIN further refining the accuracy to extreme levels to the point where all of those will sound indistinguishable from 6/5, since the difference will be only of 0.16 c per region in 7315-PLIN.
--PLIN, 53-PLIN and 665-PLIN are MOSses, more concretely, 5L 7s 6|5 1.260, 41L 12s 26|26 H=1.1822, and 306L 359s H=1.0427, but 159-PLIN and 7315 are not, as they modify the two last MOSses respectively with fractions of the telic commas. As such, to make things easier, '''EPLIN'''s may be used to have exactly equal regions, which will make things easier to work with. by default, PLINs are not equal, so it needs to be specified when an equalized PLIN is being used, because it can change the region an interval falls into. For example, 31/16 is a rough octave, but in 12-EPLIN, a '''eq'''rough major seventh. 7/4 is a fixsubminor seventh, but in 159-EPLIN, an '''equarto'''subminor seventh.
+-PLIN, 53-PLIN and 665-PLIN are MOSses, more concretely, 5L 7s 6|5 1.260, 41L 12s 26|26 H=1.1822, and 306L 359s H=1.0427, but 159-PLIN and 7315 are not, as they modify the two last MOSses respectively with fractions of the telic commas. As such, to make things easier, '''EPLIN'''s may be used to have exactly equal regions, which will make things easier to work with. by default, PLINs are not equal, so it needs to be specified when an equalized PLIN is being used, because it can change the region an interval falls into. For example, 31/16 is a rough octave, but in 12-EPLIN, a '''eq'''rough major seventh. 7/4 is a fixsubminor seventh, but in 159-EPLIN, an '''equwee'''subminor seventh.
 One glaring design feature about PLINs is the lack of ''neutral'' categories, and of ''augmented'', ''diminished'' and ''perfect''. The reason to avoid those is that for one, true neutral intervals do not exist in integer pythagorean, but even if they did, using this term is unnecessary. 11/9 is commonly called a neutral interval, but it is closer to a minor third. So it is roughly a minor third. More precisely a hyperminor third, at the extreme of minor thirds. Same thing applies to the interordinals like chthonics, naiadics, cocytics and ouranics. You can do fine with using hyper/hypo to refer to them at the edges of the nominals. All of this ''sonically speaking''.
@@ Line 40: / Line 40: @@
 Also, no words for other primes. So no ptolemaic/pental/classical, septimal, undecimal... etc. Everything stays in the 3-limit. Minimum complexity, reducing the amount of classes and descriptors to worry about to the absolute minimum.
-Regarding the choice of words to refer to the descriptors; you might not agree about the use of hypo/hyper, or arto/tendo, or qi/qu, or mi/mu, or n-plus/n-minus; but that's only a semantics problem. I chose those names because they kind of make sense to me, but the rigor is in the system, because you have these commas in the k-strong 3-2 telic sequence:
+Regarding the choice of words to refer to the descriptors; you might not agree about the use of hypo/hyper, or wee/wide, or qi/qu, or mi/mu, or n-plus/n-minus; but that's only a semantics problem. I chose those names because they kind of make sense to me, but the rigor is in the system, because you have these commas in the k-strong 3-2 telic sequence:
 * Limmas and apotomes (1 m2 M2 m3 M3 4 T 5 m6 M6 m7 M7 8) Available in 12-PLIN [rough]
 * Pythagorean commas ('''s'''ub/'''S'''uper, '''h'''ypo/'''H'''yper) Available in 53-PLIN [∅], functionally only in 12-PLIN
-* ''Pythagorean comma thirds ('''a'''rto/'''t'''endo) Available '''only''' in 159-PLIN [fix]''
+* ''Pythagorean comma thirds (wee/wide) Available '''only''' in 159-PLIN [fix]''
 * Mercator commas ([π]mu/[Π]mi) Available in 665-PLIN [sat], functionally only in 53/159-PLIN
 * Sasktel commas (qu/'''Q'''i) Available in 665-PLIN [sat]
@@ Line 57: / Line 57: @@
 * 12-PLIN : rough + diatonic nominal
 * 53-PLIN: hypo/sub/∅/super/hyper + diatonic nominal
-* 159-PLIN arto/fix/tendo + hypo/sub/∅/super/hyper + diatonic nominal
+* 159-PLIN wee/fix/wide + hypo/sub/∅/super/hyper + diatonic nominal
 * 665-PLIN [∅/qi/qu + [∅/two/three][mi/mu]]/sat + hypo/sub/∅/super/hyper + diatonic nominal
 * 7315-PLIN [[∅/two/three/four/five][plus/min(u)s]]/spot+[∅/qi/qu+[∅/two/three][mi/mu]]+hypo/sub/∅/super/hyper+diatonic nominal
@@ Line 648: / Line 648: @@
 |729/728
 |-
-|tendounison
+|wideunison
 |t1
-|Dt
+|DW
 |7.8200
 |225/224
 |-
-|artosuperunison
+|weesuperunison
 |aS1
-|DaS
+|DwS
 |15.6400
 |121/120
@@ Line 666: / Line 666: @@
 |64/63
 |-
-|tendosuperunison
+|widesuperunison
 |tS1
 |DtS
@@ Line 672: / Line 672: @@
 |56/55
 |-
-|artohyperunison / artohypominor second
+|weehyperunison / weehypominor second
 |aH1
-|DaH /Ebah
+|DwH /Ebwh
 |39.1000
 |45/44
@@ Line 684: / Line 684: @@
 |40/39
 |-
-|tendohyperunison / tendohypominor second
+|widehyperunison / widehypominor second
 |th2
-|Ebth
+|EbWh
 |54.740021
 |33/32
 |-
-|artosubminor second
+|weesubminor second
 |asm2
-|Ebas
+|Ebws
 |58.9449
 |91/88
@@ Line 702: / Line 702: @@
 |80/77
 |-
-|tendosubminorsecond
+|widesubminorsecond
 |tsm2
-|Ebts
+|EbWs
 |74.5840
 |448/429
 |-
-|artominor second
+|weeminor second
 |am2
-|Eba
+|Ebw
 |82.405
 |22/21
@@ Line 720: / Line 720: @@
 |96/91
 |-
-|tendominor second
+|wideminor second
 |tm2
-|Ebt
+|EbW
 |98.045
 |128/121
 |-
-|artosuperminor second
+|weesuperminor second
 |aSm2
-|EbaSa
+|EbwS
 |105.865
 |1225/1152
@@ Line 738: / Line 738: @@
 |16/15
 |-
-|tendosuperminor second
+|widesuperminor second
 |tSm2
-|EbtS
+|EbWS
 |121.505
 |15/14
 |-
-|artohyperminor second
+|weehyperminor second
 |aHm2
-|EbaH
+|EbwH
 |129.325
 |14/13
@@ Line 756: / Line 756: @@
 |13/12
 |-
-|tendohyperminor second
+|widehyperminor second
 |tHm2
-|EbtH
+|EbWH
 |144.965
 |160/147
 |-
-|artohypomajor second
+|weehypomajor second
 |ahM2
-|Eah
+|Ewh
 |149.17
 |12/11
@@ Line 774: / Line 774: @@
 |35/32
 |-
-|tendohypomajor second
+|widehypomajor second
 |thM2
-|Eth
+|EWh
 |164.809
 |11/10
 |-
-|artosubmajor second
+|weesubmajor second
 |asM2
-|Eas
+|Ews
 |172.629
 |182/165
@@ Line 792: / Line 792: @@
 |231/208
 |-
-|tendosubmajor second
+|widesubmajor second
 |tsM2
 |Ets
@@ Line 798: / Line 798: @@
 |39/35
 |-
-|artomajor second
+|weemajor second
 |aM2
-|Ea
+|Ew
 |196.09
 |160/143
@@ Line 814: / Line 814: @@
 If 53-PLIN is not enough for you, this will be surely be enough. If not... then prepare for what's to come.
-As you know, two is a pair, three is a crowd, and each new PLIN continues adding more classes to worry about. So far, it has been only 3 classes at most: tendo/arto, hypo/sub/fix/super/hyper, nominal. But, 665 has now qi/qu (small qian commas) and mi/mu (mercator commas), apart from the hypo/sub/fix/super/hyper, nominal. 7315-PLIN has all those, and five-fold plus/min(u)s.
+As you know, two is a pair, three is a crowd, and each new PLIN continues adding more classes to worry about. So far, it has been only 3 classes at most: wide/wee, hypo/sub/fix/super/hyper, nominal. But, 665 has now qi/qu (small qian commas) and mi/mu (mercator commas), apart from the hypo/sub/fix/super/hyper, nominal. 7315-PLIN has all those, and five-fold plus/min(u)s.
 {| class="wikitable"
 |+665-PLIN until the first pythagorean comma
@@ Line 1,376: / Line 1,376: @@
 I think the mappings are correct, but I'm too lazy to check my work. Mappings ''may'' change for EPLINs.
-== Notes on EPLINs ==
+== EPLINs ==
-Since EPLINs are essentially edos, I think that allowing more EPLINs than PLINs to exist could be advantageous. Case in point: 41-EPLIN, 94-EPLIN, 118-EPLIN, 65/130-EPLIN, 171-EPLIN, 217-EPLIN, 311-EPLIN, 1600-EPLIN, 2460-EPLIN, 8539-EPLIN. Any edo with a mapped fifth no wider than 41edo's, no narrower than 65edo's would be good.
+Since EPLINs are essentially edos, I think that allowing more EPLINs than PLINs to exist could be advantageous. Case in point: 41-EPLIN, 94-EPLIN, 118-EPLIN, 130-EPLIN, 171-EPLIN, 217-EPLIN, 270-EPLIN, 311-EPLIN, 1600-EPLIN, 2460-EPLIN, 8539-EPLIN. '''No others'''. This is to prevent bloat of the system and the mapped comma to fall beyond the size of a syntonic or septimal comma. The reason to use these edos is because they're either zeta peaks, or very very consistent.
-WIP
+The jump from 311 to 1600 is due to the fact that for its size, there is no better edo for consistency than 311. The next best thing is 1600edo, which has around the same absolute error as 270edo, if a bit less. Just in case, and because I think they're SS-tier edos, I'm putting the behemoths 2460 and 6079 for ultra-mega-hyper accuracy.
-== Conclusion ==
+Here are the prefixes for pythagorean comma fractions in these EPLINs:
-WIP
+{| class="wikitable"
+|+
+!Edosteps
+added
+!41-EPLIN
+!94-EPLIN
+!118-EPLIN
+!130-EPLIN
+!171-EPLIN
+!217-EPLIN
+!270-EPLIN
+!311-EPLIN
+!1600-EPLIN
+!2460-EPLIN
+!6079-EPLIN
+|-
+| +1
+|–
+|glus
+|hus
+|slus
+|nus
+|clus
+|xus
+|vlus
+|kwus
+|krus
+|prus
+|-
+|0
+|kite
+|gar
+|hel
+|spen
+|nea
+|cot
+|nex
+|vu
+|kwa
+|kirn
+|pir
+|-
+| -1
+|–
+|gins
+|hins
+|spins
+|nins
+|kins
+|xins
+|vins
+|kwins
+|krins
+|prins
+|-
+!Size and
+edosteps
+|29.268c
+[1]
+|25.532c
+[2]
+|20.339c
+[2]
+|18.4615c
+[2]
+|21.0526c
+[3]
+|27.6497c
+[5]
+|26.<u>6</u>c
+[6]
+|27.001c
+[7]
+|24c
+[32]
+|23.4146c
+[48]
+|23.4688c
+[167]
+|}
+These prefixes are based on the a temperament they represent, or on Sagittal:
+* gar- for Garibaldi
+* hel- for Helmholtz
+* spen- for Sensipent
+* nea- for Ennealimmal
+* cot- for Cotoneum
+* nex- for Nexus
+* vu- for Vavoom
+* kwa- for Kwazy
+* kirn- for Atomic (Kirnberger's atom)
+* pir- for Pirate