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Friendly chromatics

Xenharmonic Guitarist

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Author Topic: Friendly chromatics  (Read 79719 times)

Easy Listening

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Friendly chromatics
« on: January 08, 2012, 08:21:18 AM »

I wouldn't have guessed that 19-edo contains (so to speak, by the ears) 12-edo ... when I try to explain it to musicians the response is at best confusion, usually simple disbelief. Playing 19-edo is the only way I could have imagined it.

So anyway ...

5 - _
6 - _
7 - _
8 - _
9 - _
10 - _
11 - _
12 - 19 - (- 24? or?)
13 - _
14 - _
15 - _
16 - 25
17 - _
18 - _
19 - _
20 - _
21 - _
22 - _
23 - _
24 - _

etc.

If anyone (Ron?) can help fill in the blanks I'd be very grateful!
Is there is a way to understand it as predictable?

I found this http://xenharmonic.wikispaces.com/Chromatic+pairs while looking - seems very related but different, and I don't understand most of it. However, drifting around since then I can't believe I haven't gotten into this wiki yet. Good gosh.
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EricJacksonArts

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Re: Friendly chromatics
« Reply #1 on: January 09, 2012, 07:05:06 PM »

Hmm...I'm not terribly sure I understand this.

Are you saying that 19TET sounds like/similar to 12TET--or that it can produce similar sounding music? I could see that.
I don't dwell in ETs too often (aside from 12, which is primarily when I'm teaching--I don't write in it anymore), but the way I see it, 12, 19, 31, are all capable of producing similar sounding music. With those higher than 12 incorporating greater harmonic representation the higher you go (though the 3rd harmonic becomes flaky in 19 and 31, it renders 5, 7, 11, and 13 better than 12).

But I'm no expert in ETs. I don't find them too tempting a resource for my music.

and for the xenharmonic wiki--I find a good distance from math and more focus on music is a healthy way to explore these subjects. Have the sounds being you to the math that is necessary.
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Easy Listening

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Re: Friendly chromatics
« Reply #2 on: January 09, 2012, 07:31:14 PM »

Are you saying that 19TET sounds like/similar to 12TET--or that it can produce similar sounding music? I could see that.
I don't dwell in ETs too often (aside from 12, which is primarily when I'm teaching--I don't write in it anymore), but the way I see it, 12, 19, 31, are all capable of producing similar sounding music. With those higher than 12 incorporating greater harmonic representation the higher you go (though the 3rd harmonic becomes flaky in 19 and 31, it renders 5, 7, 11, and 13 better than 12).

:) yeah totally, in that you can play familiar scales in 19. and yes you're right, at least from what I understand (not experience yet) the same does apply to 31.

But I'm no expert in ETs. I don't find them too tempting a resource for my music.

and for the xenharmonic wiki--I find a good distance from math and more focus on music is a healthy way to explore these subjects. Have the sounds being you to the math that is necessary.

Totally agree in a sense, but I'm limited to the edos that I've played ... and I am totally tempted by them and want to play all of them.

So, alongside the sound experience and intuitive approach, I have become more interested in the corresponding theory than ever - I never felt like I wanted or needed it when the world was all in 12-edo ... same with scales, I generally play chromatic music in 12 and always try to play the wrong note, only wanted a cursory understanding of modes and scales, and find it impossible to play anything truly wrong - to my ears any note works, any time.

My main motivation for wanting a completed list really has to do with choosing guitars ... if funds were zero issue I'd order 40 guitars today, but I have to take it 1 or 2 at a time, and as they are all temping, I think it might be helpful to understand - at least from a distance and word - how the various edos fit together, or fold into one another, a categorization for sound-worlds.
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Mark Allan Barnes

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Re: Friendly chromatics
« Reply #3 on: January 13, 2012, 06:02:29 AM »

If you can only afford 1 or 2 guitars @ a time &want to try out lots of different equal temperaments, I suggest you get a fretless guitar &use cable ties as temporary frets like Chris Vaisvil does. There are details in the instruments section of this site
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Easy Listening

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Re: Friendly chromatics
« Reply #4 on: January 13, 2012, 06:07:09 AM »

If you can only afford 1 or 2 guitars @ a time &want to try out lots of different equal temperaments, I suggest you get a fretless guitar &use cable ties as temporary frets like Chris Vaisvil does. There are details in the instruments section of this site
Yeah, it's a great idea - I already have one guitar devoted to this and picked up some fret pullers, but haven't started on the mod yet ;-)
Reminds me, I should add another picture :)
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Mat

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Re: Friendly chromatics
« Reply #5 on: January 13, 2012, 06:52:33 PM »

Keep an eye on http://ubertar.com/, Paul Rubenstein is a member here and is working on a guitar with full-width movable frets, i believe he may be patenting so we have to wait for details ... might be worth contacting him to discuss?
I'm not sure i could choose one EDO over another, i'm such an experimenter i know i would need movable frets as i would change my mind the next day ...
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Mark Allan Barnes

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Re: Friendly chromatics
« Reply #6 on: January 14, 2012, 06:50:54 PM »

Thanks for the link to Paul Rubenstein's website, Mat. I am interested in the ideas there.
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Mark Allan Barnes

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Re: Friendly chromatics
« Reply #7 on: January 14, 2012, 07:05:50 PM »

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Mat

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Re: Friendly chromatics
« Reply #8 on: January 14, 2012, 08:04:31 PM »

Amazing guitar, just realised how thin the neck is ... an advantage of the lyre frame supporting the tension.



Venus by Auerswald
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Gedankenwelt

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Re: Friendly chromatics
« Reply #9 on: January 15, 2012, 05:21:24 PM »

Hi,

If anyone (Ron?) can help fill in the blanks I'd be very grateful!
Is there is a way to understand it as predictable?
If you have different tuning systems with a meantone character (like 12-, 19- or 31-edo), then intervals generated by the same number of fifths (and reduced by the same number of octaves) sound similar, as long as the number of fifths isn't too large, and the approximations of the fifth don't differ too much. For example, 4 fifths minus 2 octaves approximates a major third 5:4, no matter which of these tunings you use:

In 12-edo, it's 4 x 7 - 2 x 12 = 28 - 24 = 4 steps (= half tones).
In 19-edo, it's 4 x 11 - 2 x 19 = 44 - 38 = 6 steps.
In 31-edo, it's 4 x 18 - 2 x 31 = 72 - 62 = 10 steps.

Our classical notation system provides a mean to define notes and intervals based on their fifth / octave relationship. Tones on an axis of fifths (an infinite non-closed version of the circle of fifths) can be noted as following (adjacent notes differ by a fifth, octaves are ignored):

... Fbb Cbb Gbb Dbb Abb Ebb Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# Fx Cx Gx Dx Ax Ex Bx ...

So it's basically the 7 notes F C G D A E B, with a # or b added if the number of fifths is increased or decreased by 7, respectively (it's similar to our decimal numeral system, just based on the number 7 and a few other minor differences). Similarly, intervals can be noted on an axis of fifths:

... bb4 bb1 bb5 bb2 bb6 bb3 bb7 b4 b1 b5 b2 b6 b3 b7 4 1 5 2 6 3 maj7 #4 #1 #5 #2 #6 #3 #7 x4 x1 x5 x2 x6 x3 x7 ...

...with b2 to maj7 being major, minor or perfect versions of the intervals, and all other intervals being (1x, 2x, ...) augmented or diminished.

Now to the whole point: If you want to compare intervals in these tunings, just start at 0 fifths (the perfect prime) and generate the intervals in each tuning by adding or subtracting perfect fifths:

Code: [Select]
Intervals: ... b5 b2 b6 b3 b7  4  1  5  2  6  3 maj7 #4 ...
12-edo:    ...  6  1  8  3 10  5  0  7  2  9  4  11   6 ...
19-edo:    ... 10  2 13  5 16  8  0 11  3 14  6  17   9 ...
31-edo:    ... 16  3 21  8 26 13  0 18  5 23 10  28  15 ...

I think a good way to practically apply this is to remember the number of steps for the intervals #1 (augm. prime), b2 (min. 2nd), 2 (maj. 2nd), 4 (perf. 4th) and 5 (perf. 5th) in each tuning, so you can derive other intervals easily:

- A b3 (minor 3rd) is a 2 plus a b2, so in 12-edo it's 2 + 1 = 3, in 19-edo it's 3 + 2 = 5, and in 31-edo it's 5 + 3 = 8.
- A #6 (augmented 6th) is a 6 (= 5 plus 2) plus a #1, so in 12-edo it's 7 + 2 + 1 = 10, in 19-edo it's 11 + 3 + 1 = 15, and in 31-edo it's 18 + 5 + 2 = 25.
- An Fbb is an F plus two diminished primes, or minus two augmented primes, so if you know where an F is, just subtract two #1.

Now, finally the intervals from 12-edo "contained" in 19-edo:

 0   0 (1)
 1   1 (#1)
 2   1 (b2)
 3   2 (2)
 4   3 (#2) / 2 (bb3)
 5   3 (b3)
 6   4 (3)
 7   4 (b4) / 5 (#3)
 8   5 (4)
 9   6 (#4)
10  6 (b5)
11  7 (5)
12  8 (#5) / 7 (bb6)
13  8 (b6)
14  9 (6)
15 10 (#6) / 9 (bb7)
16 10 (b7)
17 11 (maj7)
18 11 (b8)
19 12 (8)

Note that there's no clear mapping, in theory each interval from 12-edo could be mapped to each interval from 19-edo (just apply a bb2 multiple times, which is 0 in 12-edo, but 1 in 19-edo). Also note that this is just one of many possible notations, for example the #6 could be noted as b7L (a minor 7th (b7) diminished by a septimal comma (L) 64:63, which is a harmonic seventh 7:4), if the #6 is a good approximation for the harmonic seventh in that tuning (which is often the case in meantone tunings, especially in 1/4mt, or 31-edo).

Hope this helped more than it confused. ;)

P.S.: I hope the numbers are correct, please notify me if you find any errors.
« Last Edit: January 15, 2012, 05:57:15 PM by Gedankenwelt »
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Ron

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Re: Friendly chromatics
« Reply #10 on: January 16, 2012, 12:55:05 AM »

i think if im not mistaken- what youre interested in is recurrent sequences / musical identities and Rothenberg propriety (full chromatic notations like 19-edo does for 12 but for others)?


so heres an example of a recurrent sequence for
mavila:        7 9 16 25 41
and heres
meantone:  5 7 12 19 31
father:        5 8 13 21 34

I have a giant list of these...
it generally moves from the pentatonic or diatonic to the enharmonic version of the scale.

you'll notice something after awhile.....
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Ron

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Re: Friendly chromatics
« Reply #11 on: January 16, 2012, 12:58:49 AM »

" Is there is a way to understand it as predictable? "

recurrent sequences

2+3=5 
3+5 =8
5+8=13
8+13=21
13+21=34

so 5 8 13 21 34 = father temperament and contains the distributionally even / MOS (2 step sizes L and s)
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Easy Listening

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Re: Friendly chromatics
« Reply #12 on: January 16, 2012, 07:53:23 AM »

A friend recently noticed that 12+19=31 and we wondered if that had something to do with it.

but I did not expect the relationships to follow the Fibonacci sequence!!!

That's super groovy. Thanks for the mental food!
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Ron

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Re: Friendly chromatics
« Reply #13 on: January 16, 2012, 01:52:43 PM »

but I did not expect the relationships to follow the Fibonacci sequence!!!

I know..... definitely cosmic stuff ....

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Easy Listening

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Re: Friendly chromatics
« Reply #14 on: January 17, 2012, 02:42:37 PM »

Alphabetically listed from the link in the original post, which I started to grok after some of the replies.
Posting here mainly so I know where to look at it again! Thanks!!!

Antikythera 4, 6, 10, 16, 22, 28
Augment 3, 6, 9, 15, 21
Baldy 6, 11, 17, 23, 29, 35, 41, 47, 100, 147
Bleu 17, 43, 60c
Bossier 17, 20, 37, 57, 94, 225
Bridgetown 5, 9, 14, 19, 24, 29
Cata 7, 11, 15, 19, 34, 53, 140, 193, 246, 1177cd
Deutone 6, 7, 13, 19, 25, 44, 69
Father 5 8 13 21 34
Garibaldi 7, 12, 17, 29, 41, 53, 94
Gariberttet 29, 33, 37, 41, 78
Guanyintet 9, 31, 40, 49, 89, 227bc, 316bcd
Greeley 8, 15, 23, 77, 100
Hemif 7, 10, 17, 24, 41, 58
Huntington 7, 10, 17, 27, 37, 84, 121, 400
Indium 33, 41, 49, 57, 106, 204, 253
Leantone 6, 7, 13, 19, 25, 31, 56, 81
Lovecraft 13, 30, 43, 73, 116b
Mavila 7, 9, 16, 25, 41, 66
Machine 5, 6, 11, 17, 28
Magic 19, 22, 41, 104, 145
Magicaltet 11, 15, 79cd, 94cd, 109cd, 124cd, 139cd
Marveltri 12, 13, 16, 19, 22, 47, 69
Marveltwintri 11, 15, 19, 34, 185, 219, 253, 287b, 321b
Meantone 5, 7, 12, 19, 31, 81, 112, 143
Mohaha 24, 31, 69d, 100d, 131bd
Mohoho 17c, 24, 31, 55, 86de, 141cde
Mothwelltri 9, 40, 49c, 58c, 67c, 76c
Myna 4, 27, 31, 58, 89
Nestoria 7, 12, 17, 29, 41, 53, 118, 171
Neutraltet 7, 17, 24, 65, 89, 202, 291, 380
Orgone 4, 7, 11, 15, 26, 89, 115, 141, 167, 308
Orwell 9, 22, 31, 53, 84
Penta 8, 11, 30, 41, 52
Pepperoni 5, 7, 12, 17, 29, 46, 75, 196, 271
Petrtri 21, 29, 211, 240, 269, 298, 327, 356, 385, 741c, 1126c
Photia 7, 12, 17, 29, 41, 53, 65
Radon 5, 36, 41, 87, 128
Roulette 6, 7, 13, 19, 25, 31, 37
Score 5, 7, 9, 11, 20
Semidim 5, 8, 13, 21, 29, 37, 45
Semiphore 5, 9, 14, 19, 24
Sensi 5, 8, 11, 19, 27, 46
Sentry 8, 11, 30, 41, 52, 145b, 197bc
Silver 7, 10, 17, 27, 37, 47, 84, 131, 487
Shoe 16, 21, 37
Skwares 5, 8, 11, 14, 17, 31, 48, 79, 127, 206
Slendric 5, 6, 11, 16, 21, 26, 31, 36, 41, 77, 113, 190
Starlingtet 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b
Stacks 11, 30, 41
Supra 5, 7, 12, 17, 22, 34c, 39c, 56c
Supraphon 5, 7, 12, 17
Terrain 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558
Tridec 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c
Tutone 25, 31, 68b, 99b

11
Baldy 6, 11, 17, 23, 29, 35, 41, 47, 100, 147
Cata 7, 11, 15, 19, 34, 53, 140, 193, 246, 1177cd
Machine 5, 6, 11, 17, 28
Magicaltet 11, 15, 79cd, 94cd, 109cd, 124cd, 139cd
Marveltwintri 11, 15, 19, 34, 185, 219, 253, 287b, 321b
Orgone 4, 7, 11, 15, 26, 89, 115, 141, 167, 308
Penta 8, 11, 30, 41, 52
Score 5, 7, 9, 11, 20
Sensi 5, 8, 11, 19, 27, 46
Sentry 8, 11, 30, 41, 52, 145b, 197bc
Skwares 5, 8, 11, 14, 17, 31, 48, 79, 127, 206
Slendric 5, 6, 11, 16, 21, 26, 31, 36, 41, 77, 113, 190
Stacks 11, 30, 41

13
Leantone 6, 7, 13, 19, 25, 31, 56, 81
Marveltri 12, 13, 16, 19, 22, 47, 69
Roulette 6, 7, 13, 19, 25, 31, 37
Semidim 5, 8, 13, 21, 29, 37, 45

14
Bridgetown 5, 9, 14, 19, 24, 29
Semiphore 5, 9, 14, 19, 24
Skwares 5, 8, 11, 14, 17, 31, 48, 79, 127, 206

15
Cata 7, 11, 15, 19, 34, 53, 140, 193, 246, 1177cd
Greeley 8, 15, 23, 77, 100
Magicaltet 11, 15, 79cd, 94cd, 109cd, 124cd, 139cd
Marveltwintri 11, 15, 19, 34, 185, 219, 253, 287b, 321b
Orgone 4, 7, 11, 15, 26, 89, 115, 141, 167, 308
Starlingtet 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b

16
Antikythera 4, 6, 10, 16, 22, 28
Mavila 7, 9, 16, 25, 41, 66
Marveltri 12, 13, 16, 19, 22, 47, 69
Shoe 16, 21, 37
Slendric 5, 6, 11, 16, 21, 26, 31, 36, 41, 77, 113, 190

17
Baldy 6, 11, 17, 23, 29, 35, 41, 47, 100, 147
Bleu 17, 43, 60c
Bossier 17, 20, 37, 57, 94, 225
Garibaldi 7, 12, 17, 29, 41, 53, 94
Hemif 7, 10, 17, 24, 41, 58
Huntington 7, 10, 17, 27, 37, 84, 121, 400
Machine 5, 6, 11, 17, 28
Mohoho 17c, 24, 31, 55, 86de, 141cde
Nestoria 7, 12, 17, 29, 41, 53, 118, 171
Neutraltet 7, 17, 24, 65, 89, 202, 291, 380
Pepperoni 5, 7, 12, 17, 29, 46, 75, 196, 271
Photia 7, 12, 17, 29, 41, 53, 65
Silver 7, 10, 17, 27, 37, 47, 84, 131, 487
Skwares 5, 8, 11, 14, 17, 31, 48, 79, 127, 206
Supra 5, 7, 12, 17, 22, 34c, 39c, 56c
Supraphon 5, 7, 12, 17

18
None!

19
Bridgetown 5, 9, 14, 19, 24, 29
Cata 7, 11, 15, 19, 34, 53, 140, 193, 246, 1177cd
Deutone 6, 7, 13, 19, 25, 44, 69
Leantone 6, 7, 13, 19, 25, 31, 56, 81
Magic 19, 22, 41, 104, 145
Marveltri 12, 13, 16, 19, 22, 47, 69
Marveltwintri 11, 15, 19, 34, 185, 219, 253, 287b, 321b
Meantone 5, 7, 12, 19, 31, 81, 112, 143
Roulette 6, 7, 13, 19, 25, 31, 37
Semiphore 5, 9, 14, 19, 24
Sensi 5, 8, 11, 19, 27, 46
Starlingtet 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b

20
Bossier 17, 20, 37, 57, 94, 225
Score 5, 7, 9, 11, 20

21
Father 5 8 13 21 34
Petrtri 21, 29, 211, 240, 269, 298, 327, 356, 385, 741c, 1126c
Semidim 5, 8, 13, 21, 29, 37, 45
Shoe 16, 21, 37
Slendric 5, 6, 11, 16, 21, 26, 31, 36, 41, 77, 113, 190
Terrain 6, 21, 27, 33, 105, 138, 171, 1848, 2019, 2190, 2361, 2532, 2703, 2874, 3045, 3216, 3387, 3558
Tridec 5, 8, 21, 29, 37, 66, 169, 235, 404c, 639c

22
Antikythera 4, 6, 10, 16, 22, 28
Magic 19, 22, 41, 104, 145
Marveltri 12, 13, 16, 19, 22, 47, 69
Orwell 9, 22, 31, 53, 84
Supra 5, 7, 12, 17, 22, 34c, 39c, 56c

23
Baldy 6, 11, 17, 23, 29, 35, 41, 47, 100, 147
Greeley 8, 15, 23, 77, 100
Starlingtet 15, 19, 23, 27, 239b, 266b, 293b, 320b, 347b, 374b, 401b

24
Bridgetown 5, 9, 14, 19, 24, 29
Hemif 7, 10, 17, 24, 41, 58
Mohaha 24, 31, 69d, 100d, 131bd
Mohoho 17c, 24, 31, 55, 86de, 141cde
Neutraltet 7, 17, 24, 65, 89, 202, 291, 380
Semiphore 5, 9, 14, 19, 24


edited to add another not in source list; to link "the link"; to list inclusion of 17; to list inclusion of 16; etc.
« Last Edit: February 03, 2012, 09:06:58 PM by Easy Listening »
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