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The equally tempered scale is dirty

Chords, scales, harmony, melody, etc.

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jancivil
KVRAF
 
9490 posts since 20 Oct, 2007

Postby jancivil; Wed Apr 09, 2014 2:32 pm Re: The equally tempered scale is dirty

JumpingJackFlash wrote:
jancivil wrote:You are arguing with yourself through a misconstruction of what I have said... I'm growing weary of you trying to hammer me with something really basic I've known for decades.


I think you'll find that you started it.
No, you made statements that I showed to be mistakes and now you have to stick with being right. All of this comes out of that and you figuring you don't need to read what I wrote. Anyone can read this, I did some work to show specifically how it [harmonically pure intervals at all times] isn't true, as a matter of fact. "at all times" meaning 'harmonies are all pure'. Right, doesn't happen.

JumpingJackFlash wrote:Just Intonation, that is a system that calls for harmonically pure intervals at all times, requires that notes have the flexibility to vary in pitch according to the needs of the harmony at any given moment, and thus is only possible with voices or on instruments with the capacity to make real-time adjustments as the music is being performed.

Fact.
That's some moving the goalposts. "Just intonation is a system that calls for harmonically pure intervals at all times" Is your problem. I don't know where that comes from, it's a whopping error. There is no such thing as that in a 12 note JI, this is a known thing.

"Wow, I didn't realise that you were psychic!" Save your sarcasm, there is no mind reading. FFS.
You have said it twice and now a third sort of revision. It's there, I quoted you, you said only singers and certain string instruments could work in JI because of these adjustments. I happen to know that is just not true. You have to define a certain situation - which I have done! This is why I went into my experience, to found this IN PRACTICE - for it to be conditionally true. It is not true in and of itself. One can define an intonation and stick with it. It is more typical to have a fretless stringed inst OR A WIND inst to make adjustments, within a tonal context, but there is nothing about JI that means you have to be sliding around redefining pitch to harmony. If you did the work, you would disabuse yourself of this notion.
When you modulate, there are obvious issues. You said you have to retune for every new chord. No, that is just mistaken. I actually have to wonder if you're proceeding thinking people simply must adjust to conform with 12tET. There things that are imperfect to both. People adjust to better thirds doing ET; it doesn't mean that ET doesn't do what it does. You need to retune to get the change of 'key' or new tonic.

One can do this working with triadic harmony, totally, and not deviate. I showed how triads work; if you're going to require an E major triad within twelve tones in that JI with C = 1:1, we have a M3 in that particular JI that's flatter VIS A VIS C than 12tET's G#/Ab. BUT, it's a good result for E! I wonder if the respondents to your straw test will notice a C/Ab that's bad.

I have to disengage now, too much bullshit, and you won't bother to read what I actually am saying.
Last edited by jancivil on Wed Apr 09, 2014 6:13 pm, edited 2 times in total.
JumpingJackFlash
KVRian
 
1146 posts since 10 Oct, 2004

Postby JumpingJackFlash; Wed Apr 09, 2014 2:49 pm Re: The equally tempered scale is dirty

jancivil wrote:you won't bother to read what I actually am saying.


Have you ever thought it's you that isn't reading what I'm saying?

You're the one that's introduced all kinds of things which were not relevant to the original point. I was talking about pure intervals only. You're talking about having some intervals pure and others less so.

I have shown above what I meant, you were talking about something entirely different
Unfamiliar words can be looked up in my Glossary of musical terms.
Also check out my Introduction to Music Theory.
jancivil
KVRAF
 
9490 posts since 20 Oct, 2007

Postby jancivil; Wed Apr 09, 2014 2:59 pm Re: The equally tempered scale is dirty

I wouldn't think that here because I know I did read, and have dealt with it in writing.

You said 'For JI you need to retune for every new chord' and I have shown how that isn't a workable statement. That statement was NOT restricted to this new revised statement. You meant that people, purely through the fact of using JI, have to adjust all the time to form useful concords; to the extent you believed that fixed note instruments aren't at all suitable to it. I think that had to be sorted. It doesn't work.
jancivil
KVRAF
 
9490 posts since 20 Oct, 2007

Postby jancivil; Wed Apr 09, 2014 3:26 pm Re: The equally tempered scale is dirty

Frantz wrote:
jancivil wrote:No shit Sherlock. My first reply to JJF said that bit. He said that you have to retune it for every new chord.


Sorry, I'm at work and don't have time to follow the discussion in detail. The limited reading I have done mostly agreed with what you are saying. On the other hand, I had a book by Yehudi Menuhin that spoke about a Russian choir which sang in JI and how they could make adjustments as needed. I don't know whether they were supposed to be adjusting per chord or per key change.

I never said you don't ever adjust, just that this 'fixed instruments are impractical for JI per se' is baseless. I have shown a theory that accounts for pure triads by applying syntonic comma. But that JI and 12tEt are not wildly different as applies to making triads work, there is nothing about it that makes it exotic like that. If you stay in key, there is no substantive difference in 'you have to adjust' via a JI fixed vs a ET fixed. You live with the tuning, or not. Reason I showed Hansford Rowe is here is a bass guitar set up to give you the best of both worlds, it isn't a fretless bass. Proof of concept. It requires more than 12 to an 'octave', and I showed some of why that is. He works in jazz fusion, there are key changes I'm pretty sure.

As per that JI choir, it has to be noted that people that get into JI do it because they're interested specifically in what works to make the thing better intoned; the things I went into are as applicable to classical repertoire as to anything. VSL is pretty much concert hall-oriented and they show you what can be done in their marketing.
JumpingJackFlash
KVRian
 
1146 posts since 10 Oct, 2004

Postby JumpingJackFlash; Wed Apr 09, 2014 4:07 pm Re: The equally tempered scale is dirty

jancivil wrote:You said 'For JI you need to retune for every new chord' and I have shown how that isn't a workable statement.


My point was that it's very difficult with Western instrumental music with more than one note sounding at once to use nothing but harmonically pure ratios without having to make adjustments as you go. If the music was really simple it might just be possible, but there are bound to be problems because our 12-note octave does not divide equally into either all pure fifths or all pure thirds.

There is clearly some breakdown in communication here. I don't know whether it's the "pure" or the "adjustments" that's causing problems or something else, but surely you must agree that stacking twelve pure 3:2 fifths or three pure 5:4 major thirds do not equate to one pure 2:1 octave. The mathematics don't lie - with 12-notes to an octave, every interval cannot be pure.
Unfamiliar words can be looked up in my Glossary of musical terms.
Also check out my Introduction to Music Theory.
jancivil
KVRAF
 
9490 posts since 20 Oct, 2007

Postby jancivil; Wed Apr 09, 2014 6:28 pm Re: The equally tempered scale is dirty

JumpingJackFlash wrote:
jancivil wrote:You said 'For JI you need to retune for every new chord' and I have shown how that isn't a workable statement.


My point was that it's very difficult with Western instrumental music with more than one note sounding at once to use nothing but harmonically pure ratios without having to make adjustments as you go. If the music was really simple it might just be possible, but there are bound to be problems because our 12-note octave does not divide equally into either all pure fifths or all pure thirds.

There is clearly some breakdown in communication here. I don't know whether it's the "pure" or the "adjustments" that's causing problems or something else, but surely you must agree that stacking twelve pure 3:2 fifths or three pure 5:4 major thirds do not equate to one pure 2:1 octave. The mathematics don't lie - with 12-notes to an octave, every interval cannot be pure.
If you did actually read what I have you would not be putting this to me a third or fourth time. I have said this (exactly what you're saying, I guess I have to state it more obviously) countless times and done some work to show it in detail.
From the very beginning of tempering intervals, we know that 3:2 out to twelve places does not agree with 2:1.
I have said, additionally, more than once before now that I NEVER SAID THERE WOULD BE PURE INTERVALS AT ALL TIMES.
Not only have I stated these things I have amplified them and shown how the triads result actually.

C = unity. Let's go out to a major triad on E within a JI that gives 5:4, 8:5, 15:8. The fifth happily turns up as 3:2. But 5:4 x 5:4 = 25:16, which is @ variance from our given 'G#/Ab'. So it's 27¢ smaller than ET gives. It is appx the difference of two syntonic commas, I discovered in the meantime, in relationship to 8:5. I had a 25:16 I adjusted to 8:5 last night (8:5 is 13.69¢ sharper than in ET, just like 5:4 is that much flatter). I know from these choices. You believe these details amount to a virtual unworkability but I say you will want to work with them before forming such conclusive and overarching statements. I wonder how many people are even going to know this thing is that flat in a harmony? If I had to I could produce something like that in a violin solo I bet. I chose 25:16 as an expressive device. People do this in harmony, not just melody. In raga, a founding principle in thought is the beauty of a pure fifth. The rules of raga so often reflect this. Melody is harmony, then, this is not a true dichotomy to begin with.

You have said unambiguously that JI, through itself is too problematic to make concords on a fixed type of instrument. Which is unworkable as a true statement. I went into examples and the arithmetic. I am sure I have not gone off topic in the slightest. Hansford's Warwick bass is all about harmony, it is a fretted instrument. Proof of concept, but nooooooooo.

It isn't my fault you said that and now revise it. You actually did say that thing. Now you want it to be a more reasonable statement. Now it is: "it's very difficult with Western instrumental music with more than one note sounding at once to use nothing but harmonically pure ratios without having to make adjustments as you go". Well, once you compare the intervals in my JI, which is probably the most typical, you find problems such as the one I showed twice. Two violations of a perfect triad within a ditone, I showed. It's beyond difficult, I'm pretty sure there is no such thing.
So I think 'it's impossible per se, regardless of instrument, to keep to 5:4, 3:2 relationships within a 12 note [JI] set.' clarifies this.* Western instrumental music doesn't enter into it. Unless you have to modulate, your problem is not that different than the problems of 12tET. So, I went into more practical application: VSL gives you scala support, and teaches you the concept of applying JI in orchestral music. You probably want the better intervals at some point, but should you modulate, here is JI on the new tonic; through a keyswitch once you set it up. You're being kind of obtuse trying to make this into something else. (*: however, one more again, a rational system with more than twelve makes these 'perfect concords' more and more available, through syntonic comma for instance)

My understanding is not the problem. You wouldn't act like it is if you read what I provided you.

EDITED TO MAXIMIZE CLARITY
JumpingJackFlash wrote:I don't know whether it's the "pure" or the "adjustments" that's causing problems or something else...
I'll tell you exactly what caused the problems: you have concluded that I or someone I agree with has stated that JI totally gives up pure concords at all times, and that the reason a person would even bother to use it is that it does that thing.

So you stated that we need a type of unfixed instrument of fluid pitche production, "a singer or..." to be constantly adjusting live to solve this terrible problem of even two notes at one time. No, that is just you and your problem of understanding, compounded by constantly skipping most of what I wrote, and even saying proof of concept is irrelevant. Take a moment.
Last edited by jancivil on Wed Apr 09, 2014 8:02 pm, edited 8 times in total.
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aciddose
KVRAF
 
9056 posts since 7 Dec, 2004, from Vancouver, Canada

Postby aciddose; Wed Apr 09, 2014 7:05 pm Re: The equally tempered scale is dirty

vurt wrote:so is your mom! :party:


I think vurt said it. Sums up this whole thread.

I can sum up your arguments for you so you both understand each other, is that cool?

JumpingJackFlash says: You can't get absolutely perfect harmonics from your scale and expect to play absolutely perfect chords. When I read this, I read-between-the-lines that he means "as we do with equal temperament, without significant limitations".

jancivil says: Sure you can, they're just a bit out of tune. What problem, bro?

My opinion is that both points of view are entirely correct, and entirely irrelevant to anyone actually wanting to compose anything. Now go compose something other than a pointless argument in a web forum.
KoolFartWind
KVRist
 
63 posts since 17 Jul, 2010, from Beerlin

Postby KoolFartWind; Thu Apr 10, 2014 2:33 am Re: The equally tempered scale is dirty

It's not pointless. It just got a bit out of hand :hihi: A lot of good points were made.

"Without significant limitations" lies basically in the ear of the beholder. :hyper:
JumpingJackFlash
KVRian
 
1146 posts since 10 Oct, 2004

Postby JumpingJackFlash; Thu Apr 10, 2014 6:48 am Re: The equally tempered scale is dirty

jancivil wrote:I have said this... we know that 3:2 out to twelve places does not agree with 2:1. ...I NEVER SAID THERE WOULD BE PURE INTERVALS AT ALL TIMES.


Ok, so we agree then.
I'm just going to leave it there because I don't think this is helping anyone.
Unfamiliar words can be looked up in my Glossary of musical terms.
Also check out my Introduction to Music Theory.
jancivil
KVRAF
 
9490 posts since 20 Oct, 2007

Postby jancivil; Thu Apr 10, 2014 8:51 am Re: The equally tempered scale is dirty

That statement there I had already made, very clearly and it's evident in all of the work I showed. I stated it in my first post here. The last time intonation came up I showed these type of things and have stated that as a fundament. I think it's best to read the things before replying, I do. We agree on this fundamental arithmetical truth, but apparently you still believe that JI means people need to slide around trying to find normal vertical concords, which is just a total confusion on your part, and if you look at my examples you'll see it.

I think there is a ton of knowledge to be had out of this argument. I don't think saying that JI is so problematic as to make even two notes vertically very dodgy is helpful, but the opposite, so I argued it.
Last edited by jancivil on Thu Apr 10, 2014 9:28 am, edited 1 time in total.
jancivil
KVRAF
 
9490 posts since 20 Oct, 2007

Postby jancivil; Thu Apr 10, 2014 9:05 am Re: The equally tempered scale is dirty

I think in music that moves around a lot, in terms of a center that does not enjoy long duration, 12tET might be the best system. The logical outcome of making 12 equidistant steps inside the 2:1 is dodecaphony. That said there are microtonal atonal serialists. Depends on what you want to hear. I have things where the larger environment is the overtone series and the lines within that are various things, incl. 12tET and microtonal harmony. I'm not a 'music theorist', let alone an ideologue, I use knowledge towards results and play by ear. These are materials.
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IncarnateX
KVRAF
 
1790 posts since 25 Jan, 2009

Postby IncarnateX; Thu Apr 10, 2014 10:10 am Re: The equally tempered scale is dirty

Frantz wrote:
Sendy wrote:There is a solution - dynamic tuning.


Yes, the Waldorf Q synth, for example, attempts to do this if you use setting HMT tonal:



This is brilliant IMO. If anyone has complaints about the equally tempered scale, Waldorf Q is the answer. Almost makes me want to buy one, just to experiment with that kind of tuning. Might be a challenge for a highly habituated brain to adjust to but could be exciting to try.
jancivil
KVRAF
 
9490 posts since 20 Oct, 2007

Postby jancivil; Thu Apr 10, 2014 11:20 am Re: The equally tempered scale is dirty

Frantz wrote:
Sendy wrote:There is a solution - dynamic tuning.


Yes, the Waldorf Q synth, for example, attempts to do this if you use setting HMT tonal:

Image
What it does essentially is form the third and fifth of the 'I' chord into 5:4 and 3:2 having detected through emphasis via duration a chord is now 'I' chord. There are 3 modes. I don't know what to do with this exactly:

- HMT 3/5 creates thirds and fifths with a high scaled tuning affect. In extreme cases (for example when two or more notes have to be retuned inversely) the scaled tuning effect will be reduced resulting in nearly inaudible tuning changes.

- HMT 3/5ref works like HMT 3/5 but does not reduce the scaled tuning effect in extreme cases like HMT 3/5 does. Using this Mode only makes sense with a scaled tuning value of 100%.

So I reckon it tweaks other chords based in what is the tonic chord. These sentences look to me like a maths person made them, and I don't know what the musical context is at all.

The 3rd mode gives some kind of natural seventh, saying "This effect is most pleasing in music that is based primarily around this chord structure." (a major triad with a minor seventh)
I don't know what that means. I don't know what music does a barbershop quartet seventh in music that's <based in M/m7 chord>, at all. It's a dissonant statement to me.
So I don't trust this musically after that. It may be that it provides a richer thing in general through these if your music agrees with these ideas, but I would do something else that specifically is determined by musical thought.
Last edited by jancivil on Thu Apr 10, 2014 11:30 am, edited 1 time in total.
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aciddose
KVRAF
 
9056 posts since 7 Dec, 2004, from Vancouver, Canada

Postby aciddose; Thu Apr 10, 2014 11:30 am Re: The equally tempered scale is dirty

I find the harmonic frequencies to sound horrible when applied dynamically. Sure, it's subjective of course.

The difference though is the fact that there is no "gentle" phasing effect (seconds) when you use integer fractions. Instead you get the LCM, which in some cases can be "very small" (10 cycles...)

While the elimination of phasing might be desirable in some cases, it needs to be kept in mind that this is actually not always going to produce a positive effect. Instead, it can be extremely distracting as the initial phase of notes in a chord can radically influence the timbre of the chord while given ET the phasing is equal and steady in all cases, dependent only upon the distance between notes rather than the particular notes or starting phase.

What makes it really jarring is when you use one of these dynamic tuning systems and the effect is more ET-like in some chords and suddenly more JT-like in others.

jancivil; You get a comb-filtered timbre applied to chords that are locked into harmonic ratios where the timbre doesn't change over time. The timbre is "brighter" then but static rather than fluid. Like the difference between a ET fifth of two saws vs. a hard-sync of the same.
jancivil
KVRAF
 
9490 posts since 20 Oct, 2007

Postby jancivil; Thu Apr 10, 2014 11:44 am Re: The equally tempered scale is dirty

IE: it proceeds from a first principle, the 5:4 3:2 parts of a major chord are superior, noting that orchestral musicians do this in practice. Then there is scaling by percentage of how much tuning adjustment happens toward that kind of end, following 'what is the I chord'.

Maybe that page http://www.hermode.com/html/hermode-tuning_en.html
is just not conveying the idea so well to me.

The creator of this comes out of chamber orch and symphonic orch practice. His first principle is a sound one, I think.

http://sethares.engr.wisc.edu/paperspdf/hermode.pdf

He does go into a lot of musical context, so I think my allergy to the other presentation should be placed specifically. I know from that barbershop 'natural 7th' and I wouldn't want it for Foxy Lady.
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