Topic: latest generalized diatonic review
3 scales
| File | Description | Notes | Period (ยข) |
|---|---|---|---|
| qm2 | Qm(2) 7-note quasi-miracle scale | 7 | 1200.0 |
| qm3a | Qm(3) 10-note quasi-miracle scale, mode A | 10 | 1200.0 |
| qm3b | Qm(3) 10-note quasi-miracle scale, mode B | 10 | 1200.0 |
Thread (14 messages)
From: Carl Lumma (2002-05-20) Subject: latest generalized diatonic review At Graham's suggestion I've tried to make my gd rules more simple and objective. Resulting in the following spec: http://lumma.org/spec.txt I applied it to the usual suspects, and the results are shown in this excel spreadsheet: http://lumma.org/results.xls The scala files I used, a text-file version of the results with notes: http://lumma.org/gd.zip There are 28 scales in all. There are only two scales which are in the top 14 of all four areas: the usual diatonic in 12-tet and Balzano's nonatonic in 20-tet. There are 7 scales common to the top-14 of the 3rd and 4th areas: octatonic blackwood symmaj diatonic balzano hahn-433 pentmaj -Carl
From: genewardsmith (2002-05-20)
Subject: Re: latest generalized diatonic review
--- In tuning-math@y..., Carl Lumma <carl@l...> wrote:
> http://lumma.org/spec.txt
This spec does not pinpoint the features of a scale which make it a good one, IMHO. Part of the problem is that you assume a sort of rough linearity ("higher values are better.") Are they really? For
number of scale steps, you restrict to 5-10, which is reasonable, but claim that in that range lower is better; I don't agree. The numbers given by "modal transposition" reflect scale regularity to some extent, but seem to suggest an equal division is melodically perfect--in fact, like number of scale steps, this is highly nonlinear, and you want to do a Goldilocks and come out somewhere in the sweet spot. The numbers for the Miracle-10 MOS (0.75) and Porcupine-7 (0.73) reflect the bland and pudding-like quality which makes them less interesting than they might be, but the Orwell-9 (0.71), despite its comparitive regularity, is melodically wonderful, like Meantone-7 (ie, diatonic) at 0.61. You need a number to reflect the difference, which is crucial to the sound of these scales!
From: Carl Lumma (2002-05-20)
Subject: Re: [tuning-math] Re: latest generalized diatonic review
>> http://lumma.org/spec.txt
>
>This spec does not pinpoint the features of a scale which make it a good
>one, IMHO.
It isn't supposed to do that -- just the features that make scales like
the diatonic scale, in its application in Western music.
>Part of the problem is that you assume a sort of rough linearity
>("higher values are better.") Are they really?
Sure.
>For number of scale steps, you restrict to 5-10, which is reasonable,
>but claim that in that range lower is better; I don't agree.
Me either. Lower values make pitch tracking easier. I didn't say this
desirable. I do cut it off at 5, which is enough to prevent the scale
from sounding like a chord in most cases.
>The numbers given by "modal transposition" reflect scale regularity to
>some extent, but seem to suggest an equal division is melodically
>perfect--in fact, like number of scale steps, this is highly nonlinear,
>and you want to do a Goldilocks and come out somewhere in the sweet spot.
An equal division is supposedly perfect with respect to modal
transposition, but will be poor with respect to mode autonomy.
>The numbers for the Miracle-10 MOS (0.75) and Porcupine-7 (0.73) reflect
>the bland and pudding-like quality which makes them less interesting than >they might be, but the Orwell-9 (0.71), despite its comparitive
>regularity, is melodically wonderful, like Meantone-7 (ie, diatonic) at
>0.61. You need a number to reflect the difference, which is crucial to
>the sound of these scales!
So what do you think is going on here?
-Carl
From: [email protected] (2002-05-22) Subject: Re: [tuning-math] Re: latest generalized diatonic review Carl, maybe there's an error in 08-star.scl? When you take the 46-tET version of the scale Gene posted you get 5 7 3 9 3 7 5 7 which is different and has a higher stability. 07-graham.scl is a mode of harmonic major in 31-tET. Manuel
From: Carl Lumma (2002-05-22) Subject: Re: [tuning-math] Re: latest generalized diatonic review >Carl, maybe there's an error in 08-star.scl? >When you take the 46-tET version of the scale >Gene posted you get 5 7 3 9 3 7 5 7 which is >different and has a higher stability. Gene? 0 3 12 15 22 27 34 [37] 46 >07-graham.scl is a mode of harmonic major in 31-tET. Yeah, I saw that. Graham asked me to put it in. -Carl
From: genewardsmith (2002-05-23) Subject: Re: latest generalized diatonic review --- In tuning-math@y..., Carl Lumma <carl@l...> wrote: > >Carl, maybe there's an error in 08-star.scl? > >When you take the 46-tET version of the scale > >Gene posted you get 5 7 3 9 3 7 5 7 which is > >different and has a higher stability. > > Gene? I should have written [1,25/24,6/5,5/4,36/25,3/2,5/3,9/5], the 46-et version of which is [0, 3, 12, 15, 24, 27, 34, 39]. However, the alternative with second degree being approximately 27/25 is very much worthy of notice also--like star, it is a 126/125-tempered version of a Fokker block, consisting of two parallel chains of minor thirds, with a lot of nice harmonic properties. Being a new star, maybe it's "nova" :)
From: Carl Lumma (2002-05-25) Subject: Re: [tuning-math] Re: latest generalized diatonic review >I should have written [1,25/24,6/5,5/4,36/25,3/2,5/3,9/5], the 46-et >version of which is [0, 3, 12, 15, 24, 27, 34, 39]. However, the >alternative with second degree being approximately 27/25 is very much >worthy of notice also--like star, it is a 126/125-tempered version of >a Fokker block, consisting of two parallel chains of minor thirds, >with a lot of nice harmonic properties. Being a new star, maybe >it's "nova" :) Just for my sanity, fill in the blanks: star = 0 _ _ _ _ _ _ _ 46 nova = 0 _ _ _ _ _ _ _ 46 Thanks! -Carl
From: genewardsmith (2002-05-25) Subject: Re: latest generalized diatonic review --- In tuning-math@y..., Carl Lumma <carl@l...> wrote: > Just for my sanity, fill in the blanks: > > star = 0 3 12 15 24 27 34 39 46 > nova = 0 5 12 15 24 27 34 39 46
From: Carl Lumma (2002-05-25) Subject: Re: [tuning-math] Re: latest generalized diatonic review >> star = 0 3 12 15 24 27 34 39 46 >> nova = 0 5 12 15 24 27 34 39 46 Thanks, Gene. So what I've been calling star is indeed star. I've added nova to the search. It comes out just above star because its stability is higher while all its other values are the same. It also has one more 3:2 in it (vs. star's extra 8:5). I'll update the search on my site as warranted by the number of new scales. -Carl
From: genewardsmith (2002-05-25) Subject: Re: latest generalized diatonic review --- In tuning-math@y..., Carl Lumma <carl@l...> wrote: > I'll update the search on my site as warranted by the number of new > scales. Did you see my recent posting to the main list? I'd be interested in your assessment of Qm(2) and Qm(3).
From: Carl Lumma (2002-05-25) Subject: Re: [tuning-math] Re: latest generalized diatonic review >>I'll update the search on my site as warranted by the number of new >>scales. > >Did you see my recent posting to the main list? I'd be interested in your >assessment of Qm(2) and Qm(3). I get the main list and Columbia in digest format, so it may be another day until I see your post. -Carl
From: Carl Lumma (2002-05-25) Subject: Re: [tuning-math] Re: latest generalized diatonic review >>I'll update the search on my site as warranted by the number of new >>scales. > >Did you see my recent posting to the main list? I'd be interested in >your assessment of Qm(2) and Qm(3). Oh, I guess Qm(2) is possible. I'll have to make it up. It'd be great if you could post Scala files for these. Qm(3) is a mode of this scale: >10-tone Fokker-Lumma, e=27 c=5, in 72-tET >(0 5 12 19 28 35 42 49 58 65) -> ((32 $ 39 % rms) (20 $ 24 % mad)) Which brings up an important point: who's keeping track of these discoveries? Perhaps we should begin a database, with keys for both interval and rank-order matrices. For example, Qm(3) interval matrix: ((7 14 21 30 37 44 49 56 63 72) (7 14 23 30 37 42 49 56 65 72) (7 16 23 30 35 42 49 58 65 72) (9 16 23 28 35 42 51 58 65 72) (7 14 19 26 33 42 49 56 63 72) (7 12 19 26 35 42 49 56 65 72) (5 12 19 28 35 42 49 58 65 72) (7 14 23 30 37 44 53 60 67 72) (7 16 23 30 37 46 53 60 65 72) (9 16 23 30 39 46 53 58 65 72)) Qm(3) rank-order matrix: ((2 5 8 12 15 18 20 23 26 29) (2 5 9 12 15 17 20 23 27 29) (2 6 9 12 14 17 20 24 27 29) (3 6 9 11 14 17 21 24 27 29) (2 5 7 10 13 17 20 23 26 29) (2 4 7 10 14 17 20 23 27 29) (1 4 7 11 14 17 20 24 27 29) (2 5 9 12 15 18 22 25 28 29) (2 6 9 12 15 19 22 25 27 29) (3 6 9 12 16 19 22 24 27 29)) Manuel, () What's the best way to get Scala to represent scales as degrees of an et? () As far as inputting scales as et subsets, I do "equal n" and then "select". Is that the Official Way? () Think we could get View -> rank-order matrix? (Yes, I'm using 2.05 now). -Carl
From: genewardsmith (2002-05-26) Subject: Re: latest generalized diatonic review --- In tuning-math@y..., Carl Lumma <carl@l...> wrote: > >>I'll update the search on my site as warranted by the number of new > >>scales. > > > >Did you see my recent posting to the main list? I'd be interested in > >your assessment of Qm(2) and Qm(3). > > Oh, I guess Qm(2) is possible. I'll have to make it up. It'd be > great if you could post Scala files for these. Here are my own personal Scala files for them: ! qm2.scl ! [0, 7, 23, 30, 42, 49, 65] Qm(2) 7-note quasi-miracle scale 7 ! 116.6666667 383.3333333 500. 700. 816.6666667 1083.333333 2/1 ! qm3a.scl ! [0, 7, 16, 23, 30, 35, 42, 49, 58, 65] Qm(3) 10-note quasi-miracle scale, mode A 10 ! 116.6666667 266.6666667 383.3333333 500. 583.3333333 700. 816.6666667 966.6666667 1083.333333 2/1 ! qm3b.scl ! [0, 7, 14, 23, 30, 37, 42, 49, 56, 65] Qm(3) 10-note quasi-miracle scale, mode B 10 ! 116.6666667 233.3333333 383.3333333 500. 616.6666667 700. 816.6666667 933.3333333 1083.333333 2/1 > Qm(3) is a mode of this scale: > > >10-tone Fokker-Lumma, e=27 c=5, in 72-tET > >(0 5 12 19 28 35 42 49 58 65) -> ((32 $ 39 % rms) (20 $ 24 % mad)) > > Which brings up an important point: who's keeping track of these > discoveries? Nobody, I think. Where is the Fokker-Lumma 2-parameter family described?
From: Carl Lumma (2002-05-26) Subject: Re: [tuning-math] Re: latest generalized diatonic review >Here are my own personal Scala files for them: Thanks. >> Qm(3) is a mode of this scale: >> >> >10-tone Fokker-Lumma, e=27 c=5, in 72-tET >> >(0 5 12 19 28 35 42 49 58 65) -> ((32 $ 39 % rms) (20 $ 24 % mad)) >> >> Which brings up an important point: who's keeping track of these >> discoveries? > >Nobody, I think. Where is the Fokker-Lumma 2-parameter family described? Don't know what you mean by 2-parameter. AFAIK Fokker-Lumma refers to any scale with a 225:224 in the map. -Carl