User:Eufalesio/Good scales

Here's a data dump of scales I use. Some of them with funny names because they are in conlangs. I will provide the scales and all their modes, apart from other properties. Note however that for chiral scales I am NOT pairing them up. The first mode of a scale is one that I deem the most useful to me. This is why chiral scales are all messed up in order.

Notice, NONE of them are tempered scales, det scales, whatever. If I happen to be using one (like for instance minthmic scales), it's pure coincidence. My mind thinks only in JI, and the det scale pops up not because I want to use det scales, but because I want to reach the primes with the least amount of commas.

Right next to the name, you will see the following descriptors on each scale:

• SV3: Strict variety 3.
• HSA5: Harmonic Segments Along Fifths: Made up concept; a mix of diatonoid structures and harmonic segments, where a given harmonic segment that spans a fourth or a fifth is repeated along a fifth to end up at the octave.
• SP: Strictly proper. Because I'm cataloging JI scales, they can only be strictly proper or not proper.
• SYM: Symmetric. That is, not chiral.
• MOS: MOS scale, which implies SYM, SV2 and CS.

One pattern you'll see in all my scale prime modes is that they always have 3/2, and extremely frequently, 9/8 too. This is one hill I will die on, the perfect fifth 3/2 is obligatory! I need not have 4/3 (and in many cases I use other types of fourths such as 21/16, 27/20, 65/48, 11/8).

Also, all the scales I use seem to be constant structures, coincidentally. I don't require them to be though, I constantly alternate between modes of scales of different lengths or pull up commas out of thin air so the concept of 3/2 being the fifth, sixth or seventh step of the scale is not surprising to me.

5-form

Zontatonic [HSA5, SV3, CS, SP]

A clipping of "zo pentatonic". RH is based on the 6::9 tetrachord. RH is often simpler and has a more otonal flavor specially with the mode on 4/3, but I'd say I use both with some gusto.

LH					RH
Scale degrees					Scale degrees
7/6	21/16	3/2	7/4	2	7/6	4/3	3/2	7/4	2
9/8	9/7	3/2	12/7		8/7	9/7	3/2	12/7
8/7	4/3	32/21	16/9		9/8	21/16	3/2	7/4
7/6	4/3	14/9	7/4		7/6	4/3	14/9	16/9
8/7	4/3	3/2	12/7		8/7	4/3	32/21	12/7

The Tridecimal Skirmish [SV3, CS]

It's called a Skirmish because I like to arpeggiate it. Either the RH prime or the mode on 4/3 is good. I shy away from the utonal versions. It's a subset of the scale I call Ghyef.

LH					RH
Scale degrees					Scale degrees
13/12	4/3	3/2	13/8	2	13/12	39/32	3/2	13/8	2
16/13	18/13	3/2	24/13		9/8	18/13	3/2	24/13
9/8	39/32	3/2	13/8		16/13	4/3	64/39	16/9
13/12	4/3	13/9	16/9		13/12	4/3	13/9	13/8
16/13	4/3	64/39	24/13		16/13	4/3	3/2	24/13

A general Skirmish [SV3, CS, SP]

Any scale of this form for any cent value 0 < C < 4/3. I declare to be a Skirmish. RH Skirmish have sqrt(4/3) < C < 4/3, and LH 1 < C < sqrt(4/3). This also means that the above scales, Nicepent, Pyth pentic modes, and semiquartal scales are Skirmishes, though... the term is better for C ≈ 13/12, you know, "minor second-ish" intervals. The choice of prime mode is entirely arbitrary.

Scale degrees
C	4/3	3/2	3/2C	2
4/(3C)	3/(2C)	3/2	2/C
9/8	9/8C	3/2	3/2C
C	4/3	4/3C	16/9
4/(3C)	4/3	16/(9C)	2/C

7-form

Zarlino [SV3, CS, SP]

Best Zarlino. I interchange often between the minor of LH and the major of the RH. I suppose, this includes Nicepent but I don't use the Nicepent as much.

LH							RH
Scale degrees							Scale degrees
9/8	6/5	4/3	3/2	8/5	9/5	2	9/8	5/4	4/3	3/2	5/3	15/8	2
16/15	32/27	4/3	64/45	8/5	16/9		10/9	32/27	4/3	40/27	5/3	16/9
10/9	5/4	4/3	3/2	5/3	15/8		16/15	6/5	4/3	3/2	8/5	9/5
9/8	6/5	27/20	3/2	27/16	9/5		9/8	5/4	45/32	3/2	27/16	15/8
16/15	6/5	4/3	3/2	8/5	16/9		10/9	5/4	4/3	3/2	5/3	16/9
9/8	5/4	45/32	3/2	5/3	15/8		9/8	6/5	27/20	3/2	8/5	9/5
10/9	5/4	4/3	40/27	5/3	16/9		16/15	6/5	4/3	64/45	8/5	16/9

Didymus [CS, SP]

A scale that Aura really likes to use. It's good in some places, but Zarlino is better generally. The LH version is good basically only for its minor scale, because the major is kind of harsh with 10/9 and 40/27.

LH							RH
Scale degrees							Scale degrees
9/8	6/5	4/3	3/2	8/5	16/9	2	9/8	5/4	4/3	3/2	27/16	15/8	2
16/15	32/27	4/3	64/45	128/81	16/9		10/9	32/27	4/3	3/2	5/3	16/9
10/9	5/4	4/3	40/27	5/3	15/8		16/15	6/5	27/20	3/2	8/5	9/5
9/8	6/5	4/3	3/2	27/16	9/5		9/8	81/64	45/32	3/2	27/16	15/8
16/15	32/27	4/3	3/2	8/5	16/9		9/8	5/4	4/3	3/2	5/3	16/9
10/9	5/4	45/32	3/2	5/3	15/8		10/9	32/27	4/3	40/27	128/81	16/9
9/8	81/64	27/20	3/2	27/16	9/5		16/15	6/5	4/3	64/45	8/5	9/5

Haáshi - Qhöqsh [SV3, CS, SP, SYM]

I use modal interchange of this scale a lot, specially because it is softer than Zarlino and has more xen qualities to it. It also is symmetric, which is cool.

Scale degrees
9/8	5/4	27/20	3/2	5/3	9/5	2
10/9	6/5	4/3	40/27	8/5	16/9
27/25	6/5	4/3	36/25	8/5	9/5
10/9	100/81	4/3	40/27	5/3	50/27
10/9	6/5	4/3	3/2	5/3	9/5
27/25	6/5	27/20	3/2	81/50	9/5
10/9	5/4	25/18	3/2	5/3	50/27

Archylino [SV3, CS]

An interesting scale in its own right. Both LH and RH are solid options, with LH having a more marked otonal flavor on the prime. It's also the scale with the smallest step I am certain to use melodically, 28/27. I tend to use the pentatonic version more.

LH							RH
Scale degrees							Scale degrees
9/8	7/6	21/16	3/2	14/9	7/4	2	9/8	7/6	4/3	3/2	14/9	7/4	2
28/27	7/6	4/3	112/81	14/9	16/9		28/27	32/27	4/3	112/81	14/9	16/9
9/8	9/7	4/3	3/2	12/7	27/14		8/7	9/7	4/3	3/2	12/7	27/14
8/7	32/27	4/3	32/21	12/7	16/9		9/8	7/6	21/16	3/2	27/16	7/4
28/27	7/6	4/3	3/2	14/9	7/4		28/27	7/6	4/3	3/2	14/9	16/9
9/8	9/7	81/56	3/2	27/16	27/14		9/8	9/7	81/56	3/2	12/7	27/14
8/7	9/7	4/3	3/2	12/7	16/9		8/7	9/7	4/3	32/21	12/7	16/9

Úuñmulu - Íegmul [HSA5, CS, SP]

The simples 7et detempers that are easy to use and have delectable sonorities, based on the 10::12 trichord and 9::12 tetrachord respectively. I prefer LH but RH has its uses.

LH							RH
Scale degrees							Scale degrees
11/10	6/5	4/3	3/2	33/20	9/5	2	10/9	11/9	4/3	3/2	5/3	11/6	2
12/11	40/33	15/11	3/2	18/11	20/11		11/10	6/5	27/20	3/2	33/20	9/5
10/9	5/4	11/8	3/2	5/3	11/6		12/11	27/22	15/11	3/2	18/11	20/11
9/8	99/80	27/20	3/2	33/20	9/5		9/8	5/4	11/8	3/2	5/3	11/6
11/10	6/5	4/3	22/15	8/5	16/9		10/9	11/9	4/3	40/27	44/27	16/9
12/11	40/33	4/3	16/11	160/99	20/11		11/10	6/5	4/3	22/15	8/5	9/5
10/9	11/9	4/3	40/27	5/3	11/6		12/11	40/33	4/3	16/11	18/11	20/11

Jyüüp'hi - Ghyef - Tridecimal Diatonoid [SV3, CS, SP]

One of my favorite non-harmonic-segmental scales. It's so cold. This time, it's my favorite rendition of a mosh-like scale. This is a generator-stacking scale. Combining this with minor Zarlinos yields incredibly powerful results. It contains the Skirmish. I sometimes swap the tridecimal intervals with undecimal ones in a fudged-like fashion, sweeping 352/351 under the rug.

LH							RH
Scale degrees							Scale degrees
9/8	39/32	4/3	3/2	13/8	117/64	2	13/12	39/32	4/3	3/2	13/8	117/64	2
13/12	32/27	4/3	13/9	13/8	16/9		9/8	16/13	18/13	3/2	27/16	24/13
128/117	16/13	4/3	3/2	64/39	24/13		128/117	16/13	4/3	3/2	64/39	16/9
9/8	39/32	351/256	3/2	27/16	117/64		9/8	39/32	351/256	3/2	13/8	117/64
13/12	39/32	4/3	3/2	13/8	16/9		13/12	39/32	4/3	13/9	13/8	16/9
9/8	16/13	18/13	3/2	64/39	24/13		9/8	16/13	4/3	3/2	64/39	24/13
128/117	16/13	4/3	512/351	64/39	16/9		128/117	32/27	4/3	512/351	64/39	16/9

A general Diatonoid [SV3, CS, SP]

A generalization of the general 2.3.p thing that makes all of the scales I've shown before so great, baked into a general scale. This means that Zarlino is a Diatonoid, Ghyef is a Diatonoid, Archylino is a Diatonoid, etc... Just like with Skirmishes, apply 9/8 < C < sqrt(3/2) beget L modes, sqrt(3/2) < C < 4/3 beget R modes.

Scale degrees
9/8	C	4/3	3/2	4/3*C	3/2*C	2
8/9*C	32/27	4/3	32/27*C	4/3*C	16/9
4/(3C)	3/(2C)	4/3	3/2	2/C	9/(4C)
9/8	C	9/8*C	3/2	27/16	3/2*C
8/9*C	C	4/3	3/2	4/3*C	16/9
9/8	3/(2C)	27/(16C)	3/2	2/C	9/(4C)
4/(3C)	3/(2C)	4/3	16/(9C)	2/C	16/9

10-form

Ngwóoghe - Góqäi [HSA5, CS, SP]

24:26:28:30:32:34:36:39:42:45:48. 12::18 repeated and cut at the octave, or alternatively, two 12::16 pentachords, with another a fifth up and with the addition of 17/12 to fill out the scale into a proper 10-form. I personally don't use the 17/ intervals as much, instead I change between the modes to pick what I need, but 17 is undoubtedly the most natural rendition of the 5-step of the scale.

One of my favorite scales, and it is notably no-11s. Its subsets also include archylino, a xen interpretation of the double harmonic scale and zontatonic.

Scale degrees
13/12	7/6	5/4	4/3	17/12	3/2	13/8	7/4	15/8	2
14/13	15/13	16/13	17/13	18/13	3/2	21/13	45/26	24/13
15/14	8/7	17/14	9/7	39/28	3/2	45/28	12/7	13/7
16/15	17/15	6/5	13/10	7/5	3/2	8/5	26/15	28/15
17/16	9/8	39/32	21/16	45/32	3/2	13/8	7/4	15/8
18/17	39/34	21/17	45/34	24/17	26/17	28/17	30/17	32/17
13/12	7/6	5/4	4/3	13/9	14/9	5/3	16/9	17/9
14/13	15/13	16/13	4/3	56/39	20/13	64/39	68/39	24/13
15/14	8/7	26/21	4/3	10/7	32/21	34/21	12/7	13/7
16/15	52/45	56/45	4/3	64/45	68/45	8/5	26/15	28/15

12-form

The Spine [MOS, SP]

Pyth 5L 7s 6|5. This is an extremely important scale, not because I use this directly in my music, but because it serves as the fundamental scale to build the chain of fifths. Unlike the rest of scales, I only use this mode, and no others. No modal interchange, no alterations outside the modal framework... no.

The reason to use this mode and no others is that it provides an easy set of dodecatonic nominals to alter outwards from, also the numerically simplest mode of p-chromatic. Despite how bad it may seem to have a spine that is not symmetric across the octave, working with a MOS is wayyy better than whatever amalgamation I'd end up with were I to have √2 stuck in the middle.

Besides, this is the only scale for which I have proper, fully standardized names. You know them well: Unison, Minor second (or Limma), Major second (or Tone), Minor third, Major third, Perfect fourth, Tritone, Perfect Fifth, Minor sixth, Major Sixth, Minor seventh, Major seventh, Octave. Which Tritone? 729/512. The one that's three stacked tones one on top of each other, for real.

Scale degrees
256/243 m2	9/8 M2	32/27 m3	81/64 M3	4/3 P4	729/512 TT	3/2 P5	128/81 m6	27/16 M6	16/9 m7	15/8 M7	2 P8

Duodene [CS, SP, SYM]

The best realization of the 12 notes of the piano, when played in a 5-limit fashion. Doing modal interchanges with these, you're pretty much set when it comes to 5-limit JI, with the benefit of being achiral, so you can set this on your MTS-ESP and just use the 12 modes of this without needing to contend with LH or RH.

Scale degrees
16/15	9/8	6/5	5/4	4/3	45/32	3/2	8/5	5/3	9/5	15/8	2
135/128	9/8	75/64	5/4	675/512	45/32	3/2	25/16	27/16	225/128	15/8
16/15	10/9	32/27	5/4	4/3	64/45	40/27	8/5	5/3	16/9	256/135
25/24	10/9	75/64	5/4	4/3	25/18	3/2	25/16	5/3	16/9	15/8
16/15	9/8	6/5	32/25	4/3	36/25	3/2	8/5	128/75	9/5	48/25
135/128	9/8	6/5	5/4	27/20	45/32	3/2	8/5	27/16	9/5	15/8
16/15	256/225	32/27	32/25	4/3	64/45	1024/675	8/5	128/75	16/9	256/135
16/15	10/9	6/5	5/4	4/3	64/45	3/2	8/5	5/3	16/9	15/8
25/24	9/8	75/64	5/4	4/3	45/32	3/2	25/16	5/3	225/128	15/8
27/25	9/8	6/5	32/25	27/20	36/25	3/2	8/5	27/16	9/5	48/25
25/24	10/9	32/27	5/4	4/3	25/18	40/27	25/16	5/3	16/9	50/27
16/15	256/225	6/5	32/25	4/3	64/45	3/2	8/5	128/75	16/9	48/25

Nelaá - Jälg [CS, SP]

A closely related scale to Duodene that is almost the same, but this one IS chiral. I use RH more.

LH
Scale degrees
16/15	9/8	6/5	5/4	4/3	45/32	3/2	8/5	5/3	16/9	15/8	2
135/128	9/8	75/64	5/4	675/512	45/32	3/2	25/16	5/3	225/128	15/8
16/15	10/9	32/27	5/4	4/3	64/45	40/27	128/81	5/3	16/9	256/135
25/24	10/9	75/64	5/4	4/3	25/18	40/27	25/16	5/3	16/9	15/8
16/15	9/8	6/5	32/25	4/3	64/45	3/2	8/5	128/75	9/5	48/25
135/128	9/8	6/5	5/4	4/3	45/32	3/2	8/5	27/16	9/5	15/8
16/15	256/225	32/27	512/405	4/3	64/45	1024/675	8/5	128/75	16/9	256/135
16/15	10/9	32/27	5/4	4/3	64/45	3/2	8/5	5/3	16/9	15/8
25/24	10/9	75/64	5/4	4/3	45/32	3/2	25/16	5/3	225/128	15/8
16/15	9/8	6/5	32/25	27/20	36/25	3/2	8/5	27/16	9/5	48/25
135/128	9/8	6/5	81/64	27/20	45/32	3/2	405/256	27/16	9/5	15/8
16/15	256/225	6/5	32/25	4/3	64/45	3/2	8/5	128/75	16/9	256/135
RH
Scale degrees
16/15	9/8	6/5	5/4	4/3	45/32	3/2	8/5	27/16	9/5	15/8	2
135/128	9/8	75/64	5/4	675/512	45/32	3/2	405/256	27/16	225/128	15/8
16/15	10/9	32/27	5/4	4/3	64/45	3/2	8/5	5/3	16/9	256/135
25/24	10/9	75/64	5/4	4/3	45/32	3/2	25/16	5/3	16/9	15/8
16/15	9/8	6/5	32/25	27/20	36/25	3/2	8/5	128/75	9/5	48/25
135/128	9/8	6/5	81/64	27/20	45/32	3/2	8/5	27/16	9/5	15/8
16/15	256/225	6/5	32/25	4/3	64/45	1024/675	8/5	128/75	16/9	256/135
16/15	9/8	6/5	5/4	4/3	64/45	3/2	8/5	5/3	16/9	15/8
135/128	9/8	75/64	5/4	4/3	45/32	3/2	25/16	5/3	225/128	15/8
16/15	10/9	32/27	512/405	4/3	64/45	40/27	128/81	5/3	16/9	256/135
25/24	10/9	32/27	5/4	4/3	25/18	40/27	25/16	5/3	16/9	15/8
16/15	256/225	6/5	32/25	4/3	64/45	3/2	8/5	128/75	9/5	48/25

Carlos Harmonic [CS]

19-limit realized into an easy 12-note scale, and a very easy way to approach the 19-limit, in only one key. With modal interchange, you can basically play in 19-limit JI with big wide steps, so no quartertones or things like that. Most you'll get is 27/16!

This is still the base scale of what I call the "fudge workflow", when you want and can do JI stuff but you must play within the limitations of 12 keys per octave. I found that moving the fundamental of the scale along 48edo is good enough. Why move the fundamental of the scale along 48edo? Because that way you have the harmonic scale along all 48edo notes, which includes the 12edo chain of fifths, 25c steps close to 81/80 and 64/63, and 50c steps close to 33/32 and 1053/1024.

The otonal version (LH) is the only one worth using. The utonal version (RH) really only has one use, to go down the subharmonic series in a progression, and for that a fudge workflow makes it useless. RH is horrible, so bad that I won't even write it.

Scale degrees
17/16	9/8	19/16	5/4	21/16	11/8	3/2	13/8	27/16	7/4	15/8	2
18/17	19/17	20/17	21/17	22/17	24/17	26/17	27/17	28/17	30/17	32/17
19/18	10/9	7/6	11/9	4/3	13/9	3/2	14/9	5/3	16/9	17/9
20/19	21/19	22/19	24/19	26/19	27/19	28/19	30/19	32/19	34/19	36/19
21/20	11/10	6/5	13/10	27/20	7/5	3/2	8/5	17/10	9/5	19/10
22/21	8/7	26/21	9/7	4/3	10/7	32/21	34/21	12/7	38/21	40/21
12/11	13/11	27/22	14/11	15/11	16/11	17/11	18/11	19/11	20/11	21/11
13/12	9/8	7/6	5/4	4/3	17/12	3/2	19/12	5/3	7/4	11/6
27/26	14/13	15/13	16/13	17/13	18/13	19/13	20/13	21/13	22/13	24/13
28/27	10/9	32/27	34/27	4/3	38/27	40/27	14/9	44/27	16/9	52/27
15/14	8/7	17/14	9/7	19/14	10/7	3/2	11/7	12/7	13/7	27/14
16/15	17/15	6/5	19/15	4/3	7/5	22/15	8/5	26/15	9/5	28/15

Tritave-periodic scales

Pats'huu - Püch [SV3, CS, SYM]

The 1 9/8 5/4 4/3 3/2 pentachord, stacked until it reaches 3. How to use this is that you DON'T octave reduce... no, you simply take one mode and stick with it, doing modal interchange in here isn't as useful because it's hard to work without octaves as your period.

9/8	5/4	4/3	3/2	5/3	15/8	2	9/4	5/2	45/16	3
10/9	32/27	4/3	40/27	5/3	16/9	2	20/9	5/2	8/3
16/15	6/5	4/3	3/2	8/5	9/5	2	9/4	12/5	27/10
9/8	5/4	45/32	3/2	27/16	15/8	135/64	9/4	81/32	45/16
10/9	5/4	4/3	3/2	5/3	15/8	2	9/4	5/2	8/3
9/8	6/5	27/20	3/2	27/16	9/5	81/40	9/4	12/5	27/10
16/15	6/5	4/3	3/2	8/5	9/5	2	32/15	12/5	8/3
9/8	5/4	45/32	3/2	27/16	15/8	2	9/4	5/2	45/16
10/9	5/4	4/3	3/2	5/3	16/9	2	20/9	5/2	8/3
9/8	6/5	27/20	3/2	8/5	9/5	2	9/4	12/5	27/10
16/15	6/5	4/3	64/45	8/5	16/9	2	32/15	12/5	8/3