This is the first chapter of the book "Just Intonation Premier" (for free) that shows the congenital defects and imperfect essence of 12TET.

After reading this 7 pages, you would try to think about the tunings more consciously.

 

Very interesting.

 

But who cares?

For most people the least important entity is the note. They are quite content with sounds mixing and don't pay any attention that music is mostly about notes and less about other things.

 

the horse has bolted and dragged the barn away into the far paddock.......water logged and sadly forgotten

 

17TET FTW!

 

I think the whole thing about tubes is so overblown.

 

The book is called "primer", not premier.

If you knew more about JI, you would have known that Western art music is not based on just intonation and doesn't work in it.

It is good for 5 chords pop songs. The 6th chord needs enharmonic modulation by a syntonic comma or will have a wolf interval. First case is a pain in the ass, the second case - won't be noticed by the mass of listeners, but musicians won't like it. Some Non-Western cultures actually use wolf intervals, but their music is not really chord based (see Turkish music, traditional Japanese/Chinese etc).

To make 5-limit just intonation to work with standard Western music theory and practice, you need tempering of the syntonic comma, this leads us to 31, 43 or 55 as smallest smallest equal temperaments that sound good (50 also works, but is only slightly better than 19).
12 and 19 are passable.

Btw, there are compositional sequences, chords and scales that only exist in small equal temperaments and most of the times you don't need too complex relations - example: for microtonal Afro/blues/jazz the only passable ETs are 22 and 27, because there the dominant and septimal harmonic 7th chords are equalized (15 edo also does the job, but it's out of tune).

12 equal supports not only 5-limit circle of fifths based music, but also diminished, augmented and other more dissonant harmonies. Basically, you wouldn't have Stravinsky, Debussy etc in 19 equal or whatever (or they would have done things differently).

It is possible to tune a 12 tone keyboard to play like 6 to 8 good triads in just intonation. That's good enough for most simple music. It's not like anyone on this forum is composing symphonies.

 

Last edited: Aug 24, 2019

Thanks for this great info.

Please let me ask these simple questions:

1. Why are there dissonant combinations of notes in tunings? What are their purposes from your perspective?
2. What are their beauty (dissonancy) when the natural human auditory system doesn't tend to tolerate them and want to hear the consonances most of the time?
3. What would happen if all the music to be in the consonance territory?
4. Who has said there must be tensions in the music?

I would be so pleased to know the answers to these questions.

 

Some resources that might be of interest.

HEX - A MIDI sequencer that widens access to the compositional possibilities of novel tunings.
A technical paper describing the HEX Midi Sequencer http://oro.open.ac.uk/30157/

Extract from the paper...
Dynamic Tonality is an audio synthesis and control framework that helps musicians to explore novel tunings using a small number of intuitive parameters. It provides several new musical opportunities: First, it enables users to morph between many well known tunings, and demonstrates both their structure and their relation to a broad continuum of tunings. For example, a single parameter moves the tuning of tones in a repeating scale through a continuum containing a variety of notable tunings such as seven-tone equal temperament (7-TET), 19-TET, various meantones, 12-TET, Pythagorean, 17-TET, 22-TET, and 5-TET (Milne, Sethares and Plamondon 2007).

Software (free) available from http://www.dynamictonality.com/about.htm
Quote from the site...
On this site, you can download a number of free music apps designed to facilitate the composition and performance of microtonal music. The Dynamic Tonality apps include a full-featured microtonal MIDI sequencer (Hex), three microtonal synths that can match their timbre and tuning (The Viking, 2032, and Transformer), and Relayer, which turns your computer's QWERTY keyboard into an isomorphic musical controller and provides a large number of isomorphic note layouts for the AXiS-49 and other MIDI controllers.


My Comments:
My interest in this area is 'very' limited, but in an attempt to make my exploration practical rather than just theoretical, a while ago I found the stuff shown above. It was NOT an easy exploration - and ultimately (for me personally) it was not very satisfying musically, but I still really enjoyed the exploration as an aspect of music theory. I thought the above resources were very helpful.

Good luck!

 

How does this help me tune my guitar?

 

As you know most available physical instruments are not capable of re-tuning by simple instructions.

Without flexible re-tunable physical instruments, there won't be great chances of experimentations with various tunings and accordingly not much music accessible to be heard and therefore no progress.

All advancements in 12TET have taken place because of the availability of different instruments to perform 12TET music but what about other tunings?

 

Last edited by a moderator: Aug 23, 2019

Refretting or new neck.

http://www.guyguitars.com/truetemperament/ttimages/curved1.jpg
https://strandbergguitars.com/true-temperament/
http://www.truetemperament.com/
etc...

 

1. You need to read way more on dissonance and psychoacoustics to understand how human ear and mind supposedly work in analysing what is consonant and dissonant. For musical systems:the more intervals - the more dissonance. I've seen plots of complexity of ratios to scale size and 12 equal is probably the best. (18 equal is the worst.)
2. If you didn't enjoy complex relations (dissonance), you would be only listening to human whistling, flutes and organs... Pianos (even modelled like Pianoteq are even detuned to make them sound better).
3. That's not possible. It would be very boring. Maybe try playing the black keys pentatonic - it is very unambigious and has few dissonant combinations. Try meantone tuning or just intonation variant of it.
4. As long as you play more than 1 note, there would be some kind of tensions.

There are two Kontakt libraries by Soniccouture (and cut down version by NI) that offer original gamelan tunings alongside 12 equal versions. You can probably find them floating online or buy them, if you are interested in microtonality. Despite having nothing to do with just intonation (vibrational models of metal bars are very complex compared to strings, pipes etc), gamelan tunings sound good with these specific instruments.

Someone created a piano that sounds better with the whole tone scale. Notice it sounds like a bell or something not piano-like.

With sawtooth or square waves (basically commercial electronic music or real strings etc) - something that is close to just intonation or slightly tempered version of it (like historical meantone etc) will sound the best.

In Scala go to > New> Periodicity block> (type): 81/80 128/125 or 81/80 2048/2025 or 81/80 648/625 > apply. Then "show" (F6).
It will in general show you the most distorted mode of the scale, but all these are good 12 note just intonation scales with lots of major and minor triads. You can map them to a keyboard using the "map" button and export as a scale for retuning your vst.

If you want to temper them, go to modify->temper-> (on don't temper type: 2 - this is octaves), then type 81/80 (or 2048/2025 in the scale that uses it). Different algorithms will give different results closer to 31, 43, 50, 55 equal. If you temper two commas, you get 12 equal. Think of tunings as distortions of 12 equal that add more chromas.

 

I guess that I'm maybe 8 years behind the times. I had no idea.

I was wrestling with my D-18 a little while ago trying to get it to sound as in tune as it could be in multiple chords in different keys and it was giving me agitada and frustrating the hell outta me. Of my "better" guitars this one has been funky since I installed the Baggs Anthem as a pickup system. I wish Martin would condider it an option.

After your post I took a look at look around and found this fellow and asked him to make me one similar.