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19-EDO

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Author Topic: 19-EDO  (Read 5961 times)

bostjan

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19-EDO
« on: July 18, 2011, 08:00:06 AM »

Perhaps it may seem a bit sophomoric of me in the eyes of the microtonal community, but I am very much imfatuated with 19-EDO.

It offers the convenience of any equal divided octave tuning in that fretwork is simple and that you can modulate into any key without complication.  The number of notes is still small so that fret spacing is comfortable and so that it is not so easy to mistake one note for another in performance.  It offers good approximations to many important just intervals.  Also, I don't see why one would not be able to take any strictly classical music theory and apply it directly to  19-EDO...but there are a few things that have tripped me up with this tuning.

With experienced microtonal guitar players on this forum, I don't see why it would be inappropriate to ask my questions here.

First question:
The "Jimi Hendrix Chord" E7aug9 doesn't sound right to me in 19-EDO as long as it is interpretted as a dominant seventh chord with an augmented ninth.  It sounds better to my ears with the augmented ninth replaced by a minor tenth (minor third or x9 - its enharmonic equivalnce in 19-EDO).  I've come up with a little ditty that I call "The Funky Chicken" that plays off of a E7#9 and E7x9 interpretation.  The difference between the two is striking in this context.

So in terms of just intervals, is this chord, which is well known and heavily used by rock guitarists, mistakenly named, or is the clash in sounds strictly due to the nature of the tuning?

I will post more questions here in the next day or so.
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bostjan

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Re: 19-EDO
« Reply #1 on: July 18, 2011, 08:19:39 AM »

Question number two:

A popular interval in blues and metal, the tritone, has a distinct just tuning ratio from the diminished fifth and augmented fourth.  It is easily approximated in even number equal divided octaves as the square root of two times the tonic (in terms of frequency), but which more appropriately approximates the interval in 19-EDO, E to Bb or E to A#?

Theoretically, A# is a closer approximation at 568 cents, but is this practicably more correct?
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Ron

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Re: 19-EDO
« Reply #2 on: July 18, 2011, 01:22:10 PM »

These questions could be answered by yourself if you have the program Scala, which is free on the Huygens-Fokker page. http://www.huygens-fokker.org/scala/
Also in the chord player of Scala you can find more about the Hendrix chord.
http://sonic-arts.org/monzo/hendrix/hendrix.htm  monzo and paul also had a debate about this before on the tuning list.
Anytime you need to know something just search the tuning list or xenharmonic wiki....it'll probably be there.
Playing in 19-edo is actually like taking a step back historically tuning wise- having 1/3 comma meantone and having major and minor thirds that don't add up to a unison.
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bostjan

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Re: 19-EDO
« Reply #3 on: July 18, 2011, 02:04:34 PM »

Ok, so it is neither a #9 nor a b3 / b10, but something else that is still up for debate?  I suppose I will stick with the note that is enharmonic with b10, though.
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Ron

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Re: 19-EDO
« Reply #4 on: July 18, 2011, 02:28:40 PM »

Ok, so it is neither a #9 nor a b3 / b10, but something else that is still up for debate?  I suppose I will stick with the note that is enharmonic with b10, though.


Its still that same chord- just the 19-edo version of it. If you're using meantone notation it should be notated the same - and have the same identity. what part of the chord tone to you sounds out?
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bostjan

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Re: 19-EDO
« Reply #5 on: July 25, 2011, 10:08:46 AM »

Its still that same chord- just the 19-edo version of it. If you're using meantone notation it should be notated the same - and have the same identity. what part of the chord tone to you sounds out?

It's the #9 that sounds out to me.  b10 (min. 3) sounds better to me.  It has a brighter, cheerier but equally funky sound, whereas the #2 has more of an enigmatic/augmented suspenseful sound. - If I can describe in such vague terms.

As far as the diminished fifth and augmented fourth, they sound more correct to my ears than they do in 12-EDO in a modal or classical sense, but I'm still struggling with use of the tritone in a bluesy context.
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All_Your_Bass

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Re: 19-EDO
« Reply #6 on: August 07, 2011, 06:41:15 PM »

It's not surprising that it works great for classical stuff since a good deal of the older classical stuff was written in a meantone tuning which 19EDO approximates very closely.

I think with using the tritone in a bluesy way depends on which note you start on and if it is resolved up or down.
For a blues in A, I'd bend a Eb up to E if the phrase was moving up, but going down I'd do the opposite-playing E D# D C A in a downward phrase.

This is just my opinion, from my meager messing around with bluesy playing in scala. But I'm pretty sure I'm right about it depending on the direction of the phrase.
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bostjan

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Re: 19-EDO
« Reply #7 on: August 11, 2011, 07:35:45 AM »

It's not surprising that it works great for classical stuff since a good deal of the older classical stuff was written in a meantone tuning which 19EDO approximates very closely.

I think with using the tritone in a bluesy way depends on which note you start on and if it is resolved up or down.
For a blues in A, I'd bend a Eb up to E if the phrase was moving up, but going down I'd do the opposite-playing E D# D C A in a downward phrase.

This is just my opinion, from my meager messing around with bluesy playing in scala. But I'm pretty sure I'm right about it depending on the direction of the phrase.

I agree...it sounds better to me when the blue note is closer to the resolving note.  Also E Eb D# D C A sounds good.  I suppose my understanding of the tritone was not clear.

Thanks.
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Easy Listening

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Re: 19-EDO
« Reply #8 on: October 19, 2011, 10:49:10 AM »

Edit - sorry, I don't want to hijack your thread. Will start another ...

I've been playing a 19-edo as well, my first non-12 equal. I enjoy it and find it sonically relieving. But I can't imagine being able to approach these questions ;-)
« Last Edit: October 19, 2011, 11:09:27 AM by Easy Listening »
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All_Your_Bass

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Re: 19-EDO
« Reply #9 on: January 28, 2013, 06:34:40 PM »

I can see why you'd like a b10 rather than a #9

E7#9 in cents in 12edo is
0 400 700 1000 1500 (300 when octave reduced)

In 19edo
0 379 695 1010 1452 (252 when octave reduced)

E7 add b10 in 19 is
0 379 695 1010 1516 (316 when octave reduced)

The 316c b3/b10 is closer to the 12edo 300c b3/b10/#2/#9, than the 252c #2/#9 of 19edo.
For a bluesy 7#9 chord (or 7!3 if you prefer) having the min3/#9 close to ~300c sounds more appropriate (IMO).
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Easy Listening

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Re: 19-EDO
« Reply #10 on: February 04, 2013, 10:04:04 AM »

Easy for me to imagine that you might find a number further from the 12-edo equivalent better fitting than one closer, as those numbers (like the system they refer to) are not "truth" and contain some intervals pretty far from harmonically consonant.
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Gedankenwelt

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Re: 19-EDO
« Reply #11 on: February 10, 2013, 12:04:40 PM »

In 19edo
0 379 695 1010 1452 (252 when octave reduced)

E7 add b10 in 19 is
0 379 695 1010 1516 (316 when octave reduced)

The 316c b3/b10 is closer to the 12edo 300c b3/b10/#2/#9, than the 252c #2/#9 of 19edo.
For a bluesy 7#9 chord (or 7!3 if you prefer) having the min3/#9 close to ~300c sounds more appropriate (IMO).

I think a reason why you prefer the second variant may be because in that case, there's a (consonant) perfect fourth between the 7 and b10, while in the first variant, you have a (dissonant) 442 cent interval between the 7 and #9.

Have you tried using a #9 while swapping the 7 for a #6? In that case, you have a consonant 4:5:6:7 chord with an additional 7:3 on top of the root (7:6 when octave-reduced), and with a perfect fourth between the 6# and #9:

0 379 695 947 1453

This variant works much better in 31-edo though, where 7-limit intervals are better approximated. And which variant sounds better (#6/#9 or 7/b10) also largely depends on the musical context, and on personal taste. ;)
« Last Edit: February 10, 2013, 12:26:15 PM by Gedankenwelt »
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Gedankenwelt

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Re: 19-EDO
« Reply #12 on: March 15, 2013, 05:52:10 AM »

And which variant sounds better (#6/#9 or 7/b10) also largely depends on the musical context, and on personal taste. ;)

About the musical context:

In a meantone / jazz context, simple progressions where the dominant seventh resolves to a chord a fifth below (V7 - I, V7 - i or something with secondary dominants like V7/V - V) usually work well with a minor seventh, so I'd recommend 7/b10 then.

On the other side, progressions that use substitute dominants seem to work better with an augmented sixth. For example, if we have the progression G7 - C and make a tritone substitiution, the G7's tritone B - F (diminished fifth) becomes F - B (augmented fourth). If we add a major third below F, we get the chord Db - F - B. Now add a fifth above Db, and we have Db - F - Ab - B, a dominant seventh chord where the minor seventh is replaced by an augmented sixth. If we add the notes from the C major chord, we get the following scale, which is known as Gypsy if 225/224 is tempered out, which is the case in septimal meantone (12-,19-, 31-edo and others):

C Db E F G Ab B C
0 2 6 8 11 13 17 19 (19-edo steps)

Here, I'd recommend #6/#9, because Db - B is a #6, and Db - E is a #2. Since Gypsy (here) is a simple meantone[7] MODMOS, it is closely related to the diatonic scale. In addition, it is a sub-scale of the tripod scale, which - in 19-edo - tempers to negri[9]:

meantone[7]: 0 3 6 8 11 14 17 19 (major scale)
Gypsy: 0 2 6 8 11 13 17 19 (meantone[7] MODMOS)
negri[9]: 0 2 4 6 8 11 13 15 17 19 (tempered tripod scale)
tripod scale: 1/1 16/15 7/6 5/4 4/3 3/2 8/5 12/7 16/15 2/1

Of course it's all a matter of taste, and there's no "correct way", but this would be my first, "safe" approach before trying other options. Not sure if #6/#9 is always a good idea in the case of substitute dominants though, I'd have to look at more examples...
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