Musical terms in Gjarrda
skiz2or Jardae
 (For best results, install the Gjarrda TrueType font, Lhoerr, to read examples written in Gjarrda.)

Scales

Traditional names for musical notes are based on a 7-note diatonic scale, extended (with sharps and flats) to fill in the gaps for the 12-note equally tempered scale. This naming system is also suitable for many other scales, such as meantone, well-tempered, and 19-note equally tempered scales, but runs into problems with just intonation. Gjarrda uses a two-dimensional grid, with perfect fifths (3/2) along one axis and major thirds (5/4) on the other axis, to allow naming the notes in just intonation and many other kinds of tuning systems. (An optional third axis represents a frequency ratio of 7/4.) Going up the circle of fifths from Ga gha (1/1), the Gjarrda names for notes and their equivalents in just intonation are ta ta (3/2), sa sa (9/8), mi mi (27/16), li li (81/64), ki ki (243/128), fW feu (729/512), and going down from Ga, they are ne nei (4/3), ve vei (16/9), Re rei (32/27), lW leu (128/81), jW yeu (256/243), $W thleu (1024/729). The difference between fW feu and $W thleu is the Pythagorean comma, kE ke (531441/524288). All of these intervals are powers of three, scaled by a power of two to fit within the range 1/1 to 2/1. The Gjarrda names for intervals that include powers of five are sy sue (5/4), jy yue (25/16), my mue (125/64), b8 beo (8/5), g8 geo (32/25), and m8 meo (128/125). A factor of seven is represented by z0 zoe (7/4) and ru rru (8/7). Names for higher prime factors such as 11/8 are listed in the Gjarrda dictionary. More complex ratios are indicated by multiplying two or more of the basic ratios, starting with powers of three, then five, then seven and so on: tab8 tabeo (6/5), vez0 vezoe (7/9), sasy sasue (45/32), tasyru tasuerru (15/14).

In addition to just intonation, the Gjarrda system can be applied to many other kinds of scales. One note (such as the tonic of a diatonic scale) is chosen to represent Ga. The note closest to a 3/2 ratio above Ga is called ta, and the note closest to a 4/3 ratio above Ga is called ne. Similarly, the note closest to a 5/4 ratio above Ga is called sy, and the note closest to an 8/5 ratio above Ga is called b8. The grid is expanded in all directions by naming the note closest to each of those four basic ratios around each note that has already been named.

Here is an example of the Gjarrda system applied to a 12-note equally tempered scale (and a chance to practice your knowledge of the L0r alphabet, if you have the Lhoerr font installed):

nesy A (9)

sy E (4)

tasy B (11)

sasy F# (6)

ne F (5)

Ga C (0)

ta G (7)

sa D (2)

neb8 D-flat (1)

b8 A-flat (8)

tab8 E-flat (3)

sab8 B-flat (10)

For meantone scales, and other scales that work in a similar manner, this 12-note table can be extended vertically in both directions as far as necessary. Here is an example of a 19-note equal scale, such as the one used by the Marsupial Jazz Ensemble:

nejy C# (1)

jy G# (12)

tajy D# (4)

sajy A# (15)

nesy A (14)

sy E (6)

tasy B (17)

sasy F# (9)

ne F (8)

Ga C (0)

ta G (11)

sa D (3)

neb8 D-flat (2)

b8 A-flat (13)

tab8 E-flat (5)

sab8 B-flat (16)

 

g8 F-flat (7)

tag8 C-flat (18)

sag8 G-flat (10)

The 15-note equal scale of Mizarian Porcupine Opera (for example, this two-minute selection from Têka î së rrakî) is difficult to handle in traditional musical notation, but this Gjarrda version of the scale (one of several possible versions) is as easy to use as the 12-note scale.

nesy H (11)

sy Z (5)

tasy O (14)

sasy T (8)

misy I (2)

ne S (6)

Ga A (0)

ta C (9)

sa U (3)

mi M (12)

neb8 E (1)

b8 K (10)

tab8 R (4)

sab8 N (13)

mib8 P (7)

The 17-note equal scale, used in music of the Mizarian rat-people (such as this 20-second sample of a triek chirikit), is unusual in that there is only one kind of third, intermediate between major and minor. The note sy sue could also be identified as tab8 tabeo, b8 beo as nesy nesue, and so on. This table shows one possible assignment of note names to notes.

 

 

sy 5

tasy 15

sasy 8

misy 1

lisy 11

kisy 4

ve 14

ne 7

Ga 0

ta 10

sa 3

mi 13

li 6

ki 16

veb8 9

neb8 2

b8 12

 

 

 

 

 

Enharmonic equivalents

The familiar sequence I - vi - ii - V - I (gha - nesue - sa - ta - gha) in the traditional diatonic major scale relies on the fact that the notes sa and vesue are equivalent in the 12-note scale (or the 19-note scale, or any sort of meantone tuning). However, a similar sequence in the Mizarian 15-note scale turns out as gha - nesue - misue - sasue - tasue, ending a step lower than it starts! In the 15-note scale, vesue is a step lower than sa, but it is equivalent to misue. On the other hand, the 15-note scale has a circle of fifths A - S - M - U - C - A (gha - ne - mi - sa - ta - gha), which relies on the fact that ve is equivalent to mi. This enharmonic equivalence can be indicated with the verb-preposition s8 seo (gha - ne - ve seo mi - sa - ta - gha), clarifying the relationship between the otherwise distant ne and mi.

Unusual scales

Well-tempered scales were used in Bach's time as a compromise that allowed music to be played in different keys without retuning the instrument. Such scales are also used in Kolagian music, but Nikta music is unusual in having 19-note and even 31-note well-tempered scales! !Tkasni-tli!c is a typical 19-note well tempered scale that works well for Elvish music such as this excerpt from Rriladéni Tharnien. Unlike the equal 19-note scale, !tkasni-tli!c also has a few close approximations to a 7/4 interval (z0 zoe). The numbers in parentheses are the frequencies in Hz of one octave of the scale that starts at 469 Hz.

my #18 (912)

 

 

nejy #1 (489)

jy #12 (731)

 

 

nesy #14 (782)

sy #6 (586)

tasy #17 (875)

sasy #9 (654)

ne #8 (627)

Ga #0 (469)

ta #11 (702)

sa #3 (524)

neb8 #2 (507)

b8 #13 (757)

tab8 #5 (565)

sab8 #16 (842)

 

nesyz0 #10 (681)

 

 

 

nez0 #4 (547)

z0 #15 (819)

taz0 #7 (612)

 

Owen Jorgensen's "Five and Seven Temperament" (hear the example) is an unusual scale that has many different kinds of intervals: a combination of a five note equal scale on the black notes of a piano keyboard and a seven note equal scale on the white notes. G# is exactly halfway between G and A. This kind of scale with many unconventional intervals is not one that is well suited to the Gjarrda nomenclature, but it does have enough intervals that are close enough to perfect fifths and major thirds to fit (though uncomfortably) into a typical 4x3 grid.

sy E

tasy B

sasy F#

misy C#

Ga C

ta G

sa D

mi A

b8 A-flat

tab8 E-flat

sab8 B-flat

mib8 F

The Gjarrda system for identifying musical notes assumes that the scale repeats from one octave to the next (there is no explicit name for factors of two). This is not always the case, but exceptions are few, and they can generally be made to correspond with scales that do fit the Gjarrda system. Wendy Carlos' Alpha and Beta scales, for instance (heard on the album Beauty In the Beast), are very similar to the 15 and 19-note equal scales. (In fact, it's even possible to play Mizarian Porcupine Opera in the Alpha scale! Here is a sample.) Carlos' Gamma scale, with 34.188 equal steps per octave, is similar to the 34-note equal scale, which can be named in the same way as just intonation.

A more unusual approach is to repeat the scale at an interval greater than an octave. Here is an example of music using a scale, discovered by John R. Pierce and Heinz Bohlen, that divides the interval of an octave and a fifth (3/2) into 13 equal steps of 146.3 cents each! The Gjarrda notation isn't designed well for scales of this nature, but I'll cheat and pretend that it is a scale with 8.2 notes per octave, which is almost the same as 8. The 8-note equal scale has the unusual characteristic that ta ta is the enharmonic equivalent of b8 beo, and ne nei is the equivalent of sy sue, so there is no point in using factors of 3.

Re 1, 9

ve 6

ne 3, 11

Ga 0, 8

ta 5

sa 2, 10

mi 7

li 4, 12

The notes in the "upper octave" of the 13-note scale are distinguished by adding si si (high-pitched), so the complete scale reads: gha rei sa nei li ta vei mi sigha sirei sisa sinei sili. The example music uses a 9-note mode based on this scale: gha rei nei li vei mi sirei sisa sili. (Remember that the note following sili is not sita but gha! This usage is really a questionable stretch of the Gjarrda musical nomenclature to fit a scale that it is not well suited to represent, but scales of this nature are fortunately rare in Kolagian music.)

Return

Back to the main Gjarrda page.