Exactly. It can be divided infinitely. Once you're on that "wavelength" it becomes a case of what are the limits of human perception ? 20 Cents is around the average untrained musician and assuming the pitch is not too high (I think).

12Tet is to music what 22/7 is for mathematics and PI.

FWIW I am thinking of trying to experiment with Lucy tuning in various different forms.

Trouble is even on a QWERTY (In an attempt to emulate isomorphic) keyboard I can only have one octave (Lucy25). What if I want an open voiced (IE chords that span greater than an octave.) harmonic possibilities ?

It's a pain. Certainly would be intriguing experiments.

 

Just Intonation. And obviously it sounds better because it's what 12TET was trying to emulate in the first place.

Some people here think 12TET is "Western" tuning, but it is not the "western tuning". It is a compromise of the real western tuning, which is Just Intonation. What compromise? Because of this instrument called the piano. The piano has a fixed range of pitches so 12TET was used as a compromise to make it "easier" to work in any key or whatever.

In an Orchestra, for example string instruments (violins, violas, cellos, basses) generally harmonize by ear which means Just Intonation (to answer your "what sounds good" part). The only exception is when they accompany or need to blend with a fixed pitch instrument like the Piano. By fixed pitch I mean a fixed amount of keys it can play and not deviate from. Same with Guitar.

To summarize, 12TET is not the western tuning and not the one that sounds the best, and neither the one that makes the most sense harmonically. It is a compromise because of the limitations of certain instruments.


Now, the MIDI standard is based off 12TET, so I assume it's what you meant with limitations. But you can work around it with 1) Pitch-bending "micro-tonal" effects that will work on any synth by sending pitchbend on different channels or 2) Synths that are able to use micro-tonal tuning in the first place.

In this day and age of computing, we can definitely utilize Just Intonation in each and every instrument. Even the piano (because the computer can synthesize it or pitch it slightly up/down). The thing with Just Intonation is that it requires effort to properly change the tuning on every chord. There are many papers on this subject and you need a bit of math to understand it all.

But anyway it's only human lazyness or convenience that makes 12TET so widespread with computers which ARE NOT limited like a piano is. And as you know most people making music don't give a shit and just want it easy!

String instruments can play in Just Intonation (and do all the time!) because they adjust their tuning on every chord, "by ear". Consequently, computers and synths are far more powerful and capable of anything, so it follows everything virtual (instrument) can be done in Just Intonation. Unfortunately lazyness of "producers" follows the simplest progressions to the simplest goal, so it will be a niche for a long time.

But anyway, personally, there's no reason to use 12TET unless you deal with a real instrument with a real limitation on why it cannot be used in Just Intonation. Obviously, if you have one instrument (e.g. a synth) playing alongside a real piano recording you will have to use 12TET, else it will sound out of tune relative to the piano which makes it worse.

Nevermind, I misread you! You're right!

12TET is like trimming the digits of Pi to 5 decimal places! Just Intonation is the real Pi! Not a compromise.

 

Hi there! Thank you! I was just having experimentation with different tunings like below chords' progressions. I really don't have any idea about their usage. Also don't know how an ear-trained person (based on 12tet) could be comfortable with them or not but I had really an enjoyable time hearing them. I also don't know they can be made by our known 12tet tuning or not but I'm sure using these kinds of tunings would give you originality accompanying them because no one can steal your pitches.

 

Try playing with 5et (pentatonic shape ), 7et ( it's dorian scale, but slightly retuned), 8et (octatonic, some of the steps need to to tuned), 10 et (there is a nice blues scale with better harmonic seventh than 12 tet and has the characteristic "blue notes", so this is probably where the jazz, gospel, blues and so on come from).
You are messing with chords, but I think that it's a waste of time (decent edos that can support harmony and melody outside of 12tet contain too many notes per octave - something like 31+, 58 + and similar craziness).

 

Last edited: Feb 12, 2017

Your allegation of wasting time was acceptable for me before my experimentation but now I think they provide uncharted territories for musicians. As you can hear in my posted work, some chords sound so good but I need to put them in a logical order.

12tet is a vast container for the whole life but one of the reasons for people alluding to the tracks sounding the same would be the 12tet itself. Could you please give me a music that has been done by other tunings and sounds astonishing? Something at the level of Bach. I really need to know.

Tunings when the timbre of sounds would be considered is a big project for more than 1000 years. For a person that their goals are just the market and more production, spending time on tuning is worthless but from a musician's perspective the issue is so different.

 

Last edited by a moderator: Feb 12, 2017

this video explains the answer to the threads question in full detail but i can go into it if you like fine sir.

I will cheat and give you the answer.

equal temperament was created so that instruments of all types could play with each other.

 

No.
Many instruments, such as some wind, keyboard, and fretted instruments, in fact have difficulties and often only approximate equal temperament, where technical limitations prevent exact tunings.
Unfretted string ensembles, which can adjust the tuning of all notes except for open strings, and vocal groups, who have no mechanical tuning limitations, many times use a tuning much closer to just intonation (JI) - acoustic reasons.
Some wind instruments that can easily and spontaneously bend their tone, most notably trombones, use tuning similar to string ensembles and vocal groups. So they practically follow the JI.

It's main purpose is harmonic freedom at the expense of a little impurities in every interval - mainly use to have the possibility to play in all keys and to modulate into distant keys (almost without the listeners noticing it.)

Edit: sorry, an old thread.. don't know why it was reopened

 

Last edited: Jun 1, 2017

interesting, so you disagree with history

 

Equal temperament



The emerging technology of the 1800's had a profound impact on keyboard tuning. The issue was forced by advances in piano design. In the search for more power, high-tension, cast-iron-framed pianos, using newly-developed, much stronger wire, came into use. As the tension increased, so did the number of audible overtones. Dissonances that could be tolerated on the much more lightly strung harpsichords and fortepianos became unbearable on the new high-tension instruments. Musicians and composers - the Romantics in particular - wanted a temperament that would let them modulate freely without encountering the wolf. The first pianos to be tuned to equal temperament were produced by Broadwoods in the middle of the 19th century.

The 19th century was a time of tremendous advances in materials technology and engineering. Science was becoming synonymous with progress in all walks of life, and musical instrument design was not immune to its inroads. The "mathematically correct" equal temperament held great appeal in this atmosphere of trust in science, particularly since vast improvements in the accuracy and sophistication of machine tools were making it possible to mass-produce musical instruments to a degree of precision undreamed of a few generations earlier.

Equal temperament is the ultimate compromise. Tonal purity is sacrificed for freedom of modulation. Depending on your viewpoint, equal temperament either a) makes every key equally in tune, or b) makes every key equally out of tune... The idea is to make it possible to play all intervals and chords, in all keys, with the same relative accuracy. Although every key is very slightly out of tune, every key is also useable. No key sounds worse than any other key. The same applies to all chords.

The final countdown The key to the equal tempered scale is the number 1.0594631, the twelfth root of two. This number has a bunch of tricks up its sleeve! If you multiply one by it twelve times you get two (and if you divide two by it twelve times you get one...).
1 x 1.0594631 = 1.0594631
1.0594631 x 1.0594631 = 1.1224621
1.1224621 x 1.0594631 = 1.1892071
1.1892071 x 1.0594631 = 1.2599211
1.2599211 x 1.0594631 = 1.3348399
1.3348399 x 1.0594631 = 1.4142136
1.4142136 x 1.0594631 = 1.4983071
1.4983071 x 1.0594631 = 1.5874011
1.5874011 x 1.0594631 = 1.6817929
1.6817929 x 1.0594631 = 1.7817975
1.7817975 x 1.0594631 = 1.8877487
1.8877487 x 1.0594631 = 2.0000001

The right-hand column of figures defines the semitones of the equal tempered scale, which gives us 12 semitones of 100 cents each and thus an octave of exactly 1200 cents. The old Rule of 18 was not so far off - extrapolation of the twelfth root of two ratio gives us a divisor of 17.817152.
The equal-tempered fifth is fairly "sweet" at 700 cents compared to the just fifth at 702 cents, and the equal-tempered fourth works well at 500 cents compared to 498 cents for the just fourth - but thirds, sixths and sevenths fare less well. Thirds are especially troublesome, as the equal-tempered minor third is 16 cents flat to the just minor third, and the equal-tempered major third is 14 cents sharp of just. The equal-tempered major sixth is 16 cents sharp of just, and the equal tempered major seventh is 12 cents sharp of just. The only interval which is identical in the two scales is the octave.

 

1st - I can not disagree /w "history" - it is an abstract connotation. I can only disagree with people who interpret history.
2nd - I copy/ pasted 75% of what I've written from a source that most people regard as "the history"
3rd - If I disagree /w what you call "history", so do you because you wrote the same thing that I did

Now read my last sentence.

PLEASE DO NOT REPLY HERE! THERE IS ALREADY A RECENT THREAD ABOUT MUSIC THEORY (THIS IS AN OLD ONE)!

 

you said no to 12et being created so that instruments could play together, that was the intention and it did accomplish that.

 

Last edited: Jun 1, 2017

i love 12et and i am comfortable with your progressions sir.

 

why dont we have trouble dividing a wall clock into 12 pieces to tell time? you know 12 pm 1pm 2pm and so on? think about it.

 

12 is a good number, the only one better than it 19, then 31.
17 equal is the closest to the arabic/turkish scales, but still needs tempering for them, because of how distorted are the intervals.
Most people need years to learn to play 12 keys. What about 19 or 31?

He is one Indian shruti system. This is basically the western 12 tone system, but in JI, so you need 22 tones. You can see that most intervals are represented by 2 slightly different keys.
It's cool, because it sounds more harmonic, but good luck learning to play 22 keys. You also need to retune, if you want to modulate, but the different keys sound different unlike the modern western system.
Indian shruti scale
0: 1/1 0.000000 unison, perfect prime
1: 256/243 90.224996 limma, Pythagorean minor second
2: 16/15 111.731285 minor diatonic semitone
3: 10/9 182.403712 minor whole tone
4: 9/8 203.910002 major whole tone
5: 32/27 294.134997 Pythagorean minor third
6: 6/5 315.641287 minor third
7: 5/4 386.313714 major third
8: 81/64 407.820003 Pythagorean major third
9: 4/3 498.044999 perfect fourth
10: 27/20 519.551289 acute fourth
11: 45/32 590.223716 diatonic tritone
12: 729/512 611.730005 Pythagorean tritone
13: 3/2 701.955001 perfect fifth
14: 128/81 792.179997 Pythagorean minor sixth
15: 8/5 813.686286 minor sixth
16: 5/3 884.358713 major sixth, BP sixth
17: 27/16 905.865003 Pythagorean major sixth
18: 16/9 996.089998 Pythagorean minor seventh
19: 9/5 1017.596288 just minor seventh, BP seventh
20: 15/8 1088.268715 classic major seventh
21: 243/128 1109.775004 Pythagorean major seventh
22: 2/1 1200.000000 octave

You can continue extending this 5-limit scale to over 30, 50, 70 etc notes, while getting new microtonal notes that are in the same 5-limit gamut.
If you want 7-limit gamut (for authentic african, blues and jazz music ) with with intervals like 7/4 and so on, you will get more than 12 notes just for the basic scales.
There is a reason why non-western cultures didn't develop harmony - many of their scales were too complex and hard to play.
Let's say that 20 cents is the difference between the notes that the normal non-musician can recognise, this gives us 60 notes per octave.
There are qanuns (turkish zither) with more than 70 notes per octave.

 

Oh fly (me, foster911) , the phoenix's haunt is no place for you to flaunt. TBH, sounds resulted from chords are similar to other sounds for me. I don't see anything special in them. Their quality and use have been greatly exaggerated by pure instrumentalists. Also music is not an absolute term. Everyone can have their own interpretation and explanation of it.

 

It's not an issue with the synthesizers, the problem is when you want to add anything live like piano or guitar, you're screwed

 

And the western musicians have been cocky and self-righteous about their note-stackings and calling them harmony for centuries.

 

Harmony is "note stacking". You can harmonize any pitch by adding a 5th, 3rd, 7th and so on. The problem with the ethnic instruments is that it's easy to play the wrong note, if there are too many and the fingering is awkward or impossible.

 

Because major/minor pentatonic scales sound good to 99.9% of the world. That's why.

 

I shed a little tear when I saw all your commas and full-stops (btw, I am a licenced and qualified English Teacher in addition to my work as producer/broadcaster).

Back to this topic. Just to throw something in that might or might not be useful to the OP's question which, expresses a feeling that Western music is somehow limited. This article explains the true history of how Western 'tuning' was changed by the Elite from A=444Hz to A=440Hz (and much, much more true history about the Elite's manipulations of our society). I admit that I don't know whether A=444Hz was not equal temperament. It's a truly fabulous eye-opening read anyway. Apologies in advance if it's not relevant to this topic.