The clock and geometry are based on 60 because Babylonians (from Sumerians) used it (60 has a lot of factors).

Hopefully you don't teach such guff. Your "information" about A being 440 is from a website that promotes homeopathy whilst attacking vaccination and pharmacology. Why would anybody look there for the truth? lol "Musical cult control" - seriously?

 

Equal temperament has nothing to do with a base frequency. It is a system of always the same intervals regardless of the base frequency. You can have ET at any base frequency. You would know this from hardware synths, that you can set to a base frequency of your choice without leaving equal temperament. Here's a page showing frequencies of equal temperament in various base frequencies: http://www.phy.mtu.edu/~suits/notefreqs.html

If you want to play around with scales, try to grab an old Korg M1 (the hardware, I loved it). It supported several predefined tunings as well as a completely free user tuning. You can't get it any easier. Look at the manual (scroll to page 114): http://www.synthfool.com/docs/Korg/Korg_M1_Owners_Manual.pdf

 

Welcome back @superliquidsunshine

 

Tuning to lower A than 440 is perfect for ambient, chill-out or soulful beats. Tuning higher than 440 is an option, if you are producing euro-house or bubblegum pop.

 

12 tone equal temperament means that you have 12 divisions in an octave each the same exact spacing( 100 cents.) 7 natural notes, 7 sharps and 7 flats
F C G D A E B
F# C# G# D# A# E#=F) B#=C)
F- =E) C- =B ) G- D- A- E- B-



think of a round clock on the wall.


where as pythagorean tuning is a spiral (makes no sense to me)




as you can see 12 tone equal temperament is the only one that gives you 12 legit major-minors keys all the symmetrical scales(augmented and diminished etc) and alterations deviations harmic minor major 8 and 9 tones 5 tonmes scales etc.etc.

 

Last edited: Jun 2, 2017

I don't get it with this thread;12 tone tempered system is the starting point for the ability to modulate in a piece of music and so the start for all western music from Bach to now.There are different ways to deal with the way of tuning a piano, I think the modern one is the best so far, 4th/5th/8th are perfectly tuned, the others are not perfectly tuned and it's the tuner's art to do it the best possible listening to second harmonic while tuning, not to mention that a 440 piano is around 442 in the high and 338 in the low; depending on the piano a good tuner will adapt his tuning.Synths are more abrupt on the tuning: the scale is really divided in 12 equal intervals from bottom to end.Eastern tunings are very interesting but only to play eastern stuff, anyway you can't modulate very far with these.

 

I think everything comes back to the ratio 3/2. This ratio is the golden one that forms our circle of fifths. Indexes are the octave numbers:
G0/C0 = 3/2
D1/G0 = 3/2 ---> D0/C0 = 9/8
A1/D1 = 3/2 ---> A0/C0 = 5/3
.
.
.



Nobody has yet proven a physical basis for why simple-ratio combinations sound pleasant to us.

 

Last edited by a moderator: Jun 2, 2017

You have much to learn about the nature of this world. Also, keep in mind, that no human source has 100% correct information, or all of the information.

 

Well, definately 12 equal tones is NOT the starting point for the ability to modulate. You aren't modulating.
C Major is something completely different from G major and you need to retune to modulate. When played by vocalists, string, woodwind players or other instruments capable of dynamic retuning, you will hear pitch drifts.
12 equal tones is ideal for chromatic COMPOSITIONS in 5-limit scales that will explore different tonalities and let the players INTERPRET the music in the adaptive tuning of the ensemble of musicians. For PERFORMANCE: It's not okay to play in 12et all the extended chords (Wagner etc) sounds like trash, because of the beating of frequencies. When you go to the concert hall, you DON"T hear 12et. even if the composer used 12et system to compose the notes as long as there isn't some kind of keyboard and the rest of the players try to play in tune with it. That's why orchestral sample libraries will NEVER sound like the real thing. The developers record real string players, then retune the notes to 12et (at least most of the time - it's annoying when RR sample from 8dio or Spitfire product triggers a note that clashes with the rest of the harmony), so you can play with the rest of sounds in your DAW. If you to make a realistic midi mockup, you need to retune closer to JI, but not totally JI, because noone actually plays perfectly in tune.

Foster911: "Nobody has yet proven a physical basis for why simple-ratio combinations sound pleasant to us."
Simple ratio combinations don't sound more pleasant than the more complex ratios. What sounds pleasant is the difference between the different steps.

In 12 et the steps are all at 100 cents and sound like lacking life. In JI, meantone or the other historical temperaments, the steps sound more musical, because of the differences between them.
It's like the difference between quantized metronome pulse and nice funky swing.
Before the invention of autotune, we could hear tons of non-12et pop vocal music composed using 12et.
Western music theory works in the other tuning systems, we are only lacking theory about the neutral intervals between the notes (you are generally not going to mix different intervals for the same musical note in a certain scale like 182 c. or 203 c. tone in a passage), so you are generally going to hear 5-7 notes scales even if using different system, but the notes will be slightly different and the harmony tones will also be different.
Equal 24 (step is 50) and 36 (step -33) are perfect for composing for the notes we are lacking in the western tuning, but they will also sound ugly just as equal 12 as long as the performers stick to the equal versions.
I think that in the future we will see more western music in non-12 ET.

 

A few matters of fact.

Western classical music is based on highly developed harmonic conventions. Whether this makes it superior when compared with other musical cultures/traditions is debatable. And the pretended harmonic freedom that is supposed to be gained using the tempered 12 tone scales isn't the only form of freedom one can appreciate in music. Think about the polytheisms that are usual in African music, and that the western musicians rarely use and most of the time can't even notate on a score, or the melodic freedom of a santur player that retunes his instrument for any piece he plays. Different musical cultures simply trade the freedom on one side with the restrictions on the others.

One point for those who suggested that it's mainly a matter of cultural imprinting.

Early music specialist actually tune their instruments using tempered scales because using pre-tempered scales sound harsh to their audience. They tried to adopt those ones, but their philological approach failed to be appreciated, since the ear of their listeners is prone to the tempered harmony rules.

Two points for the cultural imprinting.

Among the western musical traditions, there is a lot of variety. A number of key instruments – and among them may bagpipes – don't conform to the tempered intervals. To play with different instruments, that's a peculiar folk revival practice, a Scottish Highland bagpipe player orders a “pitched chanter”, that obviously sounds out of tune played in unison with a proper traditional instrument.

Also, the music remain mainly diatonic, because a number of traditional instrument
s are not chromatic, or anyway not fully chromatic. And there are a number of tunes that are modal in nature, and that avoid the tonic vs dominant cliche of the western art music. Not to tell about the hundreds of chordal tunes (i.e. The melody spans a fourth or a fifth), that can eventually be correctly notated using two different key signatures without the need to transpose – yes, they are mainly found in the traditional music of Brittany, but there examples of chordal tunes all over Europe.

Yet, for those who love such musical traditions, and eventually play them with real respect, this doesn't seem to be a problem.

A third point for the cultural imprinting.

Just scratching the surface... but let's not forget: as Shaw said, the golden rule is that there is no golden rule!

 

The quote from SuperLiquidSunshine is from February. But why sweat the details?

I didn't mention 100% correct information.

Are you trying to say there is value in total bullshit? Does total bullshit add to our attempt to reach 100% correct information? Or is it an impediment? All the answers to the universe in my toe-jam. Oh wow.

Man, am I sick of folk telling me bullshit is golden.

Oh, and I have a lot to learn? You say. Well, OK. And which of us is going around telling people they have a lot to learn? la dee dah.

It's beyond me that anybody can seriously countenance that A=440 is a standard "imposed by elite manipulation". Even more crazy is to believe it based on some crappy website which has no "about us" information whatsoever. The website is (obviously) unethical bullshit. It's a load of fanciful shit posted without attribution. Oh yeah, real serious stuff. Forget history and physics, listen to total bullshit instead.

yet again, a musical forum is surreptitiously overtaken by total (political) bullshit.





:D

 

Last edited: Jun 3, 2017

That's easy. Simple ratios make the sounds closer to each other because they'll "sync" faster. That sounds better for the brain as it can identify the sound faster. The octave (2:1 ratio) is the simplest sync. It syncs at every other cycle. Perfect fifth is the next best sounding because it syncs at every 3rd cycle.

Now, mind you, 12-tone equal temperament is not perfectly synced, except for the octave. I'm talking about why just intonation sounds good (simple ratios), not equal temperament.

Just in case you're still confused about the "sync". Just play two waveforms with one frequency at specific ratios. See when they sync up (they both repeat exactly as at the start) in an audio editor. A 3:2 ratio (perfect fifth) means you need the higher waveform to cycle 3 times before they "sync" and restart their shape from the beginning. The lower waveform will cycle twice.

Because after one cycle of the lower waveform, they will be shifted by half a period. You need another cycle of the lower waveform to get them back in sync. Contrast this with the simpler ratio of 2:1 (octave), where after one cycle of the lower waveform, they will be in sync (the upper one will simply do two cycles in that time).


Faster sync = sounds better. No magic, just math.

 

Last edited: Jun 4, 2017

A = 440, because of equal temperament.
440 literally means 900 cents = 168179283051/100000000000 ratio.
If you want to use scientific tuning with C4 = 256 hz (1,2,4,8,16,32,64,128,256,512 etc) for C (instead of
261.6255653006), A will be 432, if your A is Pythagorean 27/16 = 905 hz. If it's purer M6 like 5/3, it will be 426.666666667 hz. 9/8 to 27/16 is a perfect fifth, but 27/16 is not that harmonic to the root of scale as 5/3, but 5/3 creates a wolf with 9/8, so I guess you won't be playing II-V-I in JI without adding too many keys, if you want pure fifths.
So, there is no point in tuning to 432, if you are not gonna use Pythagorean M6s.
I guess that, if everything is in harmony in your track, it will sound a little clearer and louder, so it's a plus for all the hassle. Sounding better and louder without using compression, eq and stuff.

 

Last edited: Jun 4, 2017

equal temperament gives you the most options , you can make it sound good ( say you dont like the sound of major third, easy solution raise it by octave while keeping the notes in the chord the same location, now because it is far away it sounds great.

 

I know everyone has given a lot of detailed responses but I thought I'd throw in a simple Cliff's notes version of the answer.

Note ratios are based upon very simple mathematics ratios -- nothing mystical or superstitious about it. Take the frequency of any note, double it, and you've got your octave. That's an obviously clean ratio as each higher note "matches up" with the lower note every two repeats. Simple for the brain to process and ear to detect. Extrapolate this for everything else like perfect fifths and so on. It's a very simple mathematical principle that's apparent everywhere in nature.

Dividing the octave (the most simple ratio) into other simple ratios starts breaking down when you get more than 12 notes per octave because the distance between the individual notes created starts to become hard to discern. In other words, if you divide an octave into 24 then the smallest interval between any two notes becomes what we'd consider a 50 cent difference. Can people hear that? Yes, but it's harder for untrained people to pick up on and sing, and starts to become hard to separate an intentional note change from vibrato and such.

Plus it's a matter of diminishing returns -- more and more complexity (harder to build some instruments, etc.) with less musical payoff as the simplest ratios (more musically useful) are already accounted for. Do we really need a musical scale which gives note names to one note that's 10 cents above another? Where do you draw the line? Well, 12 is pretty good.

Why is it even-tempered? Well, do you want to have 12 pianos on hand so you can play in every key? Anything fretted or with an individual string/key/etc per note becomes impossible to manage. Sure voices, violins, drums and such are easy to throw into any musical setup, but some stuff has tuning that is really difficult to change on the fly. Even-tempered is just a really good compromise for an annoying problem. Pure practicality, and it works damn well.

 

EQUAL TEMPERAMENT AT ITS FINEST

if you dont care for the way the sounds are, try to just listen for the melody,harmony rhyth etc.

 

Last edited: Jun 12, 2017

Actually the more you divide the octave, the payoff becomes bigger with more options for expressions and harmony: I dare you to try playing some authentic blues (pretty popular style in USA) on the keyboard. You will need not only to detune some of the notes, you will have to insert notes that aren't there and bend them while playing...
The neutral intervals were used thousands of years before the western system was invented. Check some historical scales especially the enharmonic, chromatic and the mixture between them.
Music doesn't start and end with the Western piano tuning and the Major/Minor system

 

Yes, more "power" in capabilities, but that always seems to come at a price, doesn't it? How many notes per octave can you put into a keyboard style instrument before it becomes too unwieldy to play?

In a certain sense, having more notes is more desirable because you're not artificially limited, but is it generally worth it? Western theory says no. Other people and cultures think otherwise -- just different schools of thought.

 

Last edited: Jun 21, 2017

People are already playing with bazillion keys.

It's not like traditional piano keyboard makes any sense outside of the C major, chromatic and whole tone patterns.
There are way better designs out there where each scale pattern is the same for each keys.

 

Fine, you win. Beethoven and Mozart were idiots for not embracing the horrendous racket that is that video.

Nah, but I do agree that the traditional piano is laid out poorly in the sense you speak, but that isn't really a good basis for a critique of Western music theory. Sure, the implementation is poor due to tradition and lack of foresight, but that doesn't mean the concept doesn't stand.

 

Last edited: Jun 22, 2017