Tuning systems and composition?

@AntiA:

The second harmonic (or first overtone), twice the frequency of the fundamental, sounds an octave higher; the third harmonic, three times the frequency of the fundamental, sounds a perfect fifth above the second. The fourth harmonic vibrates at four times the frequency of the fundamental and sounds a perfect fourth above the third (two octaves above the fundamental). Double the harmonic number means double the frequency (which sounds an octave higher).

But we can continue: The seventh harmonic vibrates at seven times the frequency of the fundamental, and so on. In this regard, we can say that the conventional 12-tone scale, which is essentially build around the 5 limit, isn't the best approximation to the overtone series, since it ignores the overtones above the fifth. True, the seventh harmonic is farther in the series than the third and the fifth, its amplitude is normally lower (unless manipulated electronically, for example), so one could say it isn't -that- significant, but at the same time it isn't -that- far as to be ignored. I fail to see a good enough reason to do that. Even acousticians have debates how up in the overtone series they should go when making different assestments (such as in psychoacoustics) and how to assign weights to the overtones. So, I wouldn't say that the 12-tone scale is the best option - it is (again) a compromise. And in 12-ET the only pure / natural interval is the octave.

As for the 'against the overtones' part: Having in mind the above-mentioned, it could also be said that the current system is 'against' the overtones, since it 'cuts' the series above the fifth harmonic. Similarly, the 'classical' Pythagorean tuning (which is fundamentally 3-limit Just Intonation) doesn't "care" much about the thirds. However, it served its purpose in Medieval times (when thirds were considered unstable / dissonant) and still does for the enthusiasts. So, it has been 'against' the overtones. What is going on is simply considering more of the upper partials of the overtone series. Not only do systems with more tones in the octave (if we decide to stay within the limits of octave tunings in this discussion) give you richer palettes of intervals, but also allow you to temper out more commas (when it comes to temperaments). I don't know by heart about the characteristics of many ETs - which intervals they approximate better and which commas they temper out - I should either read this up or make calculations myself - but perhaps Charlie could list some examples. For example, 19-ET deviates more from the just fifth than 12-ET does, but it gives you better thirds. Also, it utilizes the 7th harmonic (though doesn't approximate 7-limit tuning accurately), which gives you the expressive opportunity to build septimal triads.

Timbre is related to tuning and consonance and nobody denied that. Gamelan scales are more or less influenced by the inharmonicity of their instruments, too. And as I mentioned in another topic a few days ago, it is possible to change / manipulate the timbre as you wish - with synthesizers and computers all this is easily accessible.

And, harmonics -are- overtones, but harmonic ones, since you can also have inharmonic overtones.

Notice I was never arguing with you about why you find other tuning systems appealing or not, or whether anyone should use them or not. I don't care in the least whether you like them or use them.

I was merely arguing the technical errors in your posts. So if you're not interested in "hyper-technicalities being thrown in your face" then simply stop bringing up incorrect information.

I think your interest in these "technical errors" largely deals with how you interpret what I'm saying.

I see now that it's futile. You seem to read neither the links you are putting up to prove your point, nor what other people such as charliep and I are posting. And what you -do- seem to read in our posts really has nothing to do with what we said at all. Where the hell did I ever say the overtone series was a hurdle to overcome?

You imply this when you say, "Adding valves to the trumpet and horn to give them a 12-tone chromaticism is nothing but working against the limits their inherent focus on the harmonic series places upon them." I'm referring to your comment that the harmonic series imposes an inherent focus. It doesn't. Our arrival at understandings of sound mechanics led us to the use of 12tET. We arrived at conclusions about sound, as opposed to making decisions based wholly on aesthetics (not to say aesthetics had nothing to do with it - surely it did).

I will cease correcting your points. If you want to insist on your strange and often wrong ideas, be my guest. (I just hope other people reading this thread will take it with a grain of salt and not "learn" too much from it.)

Right. What you're correcting is your interpretation, not what I said.

Nobody is asking you to write music you don't want to write, quite the opposite. Quit acting like a victim.

I'm taking issue with these claims of my views being erroneous, where they aren't errors at all.

-------------------------

Let's go over it again.

http://en.wikipedia....Psychoacoustics

Frequency resolution of the ear is 3.6 Hz within the octave of 1,000–2,000 Hz. That is, changes in pitch larger than 3.6 Hz can be perceived in a clinical setting. However, even smaller pitch differences can be perceived through other means. For example, the interference of two pitches can often be heard as a (low-)frequency difference pitch.

This refers to what the human ear has been proven to be able to hear as a difference in pitch. So, the fundamental pitch A must fall between 436.4 and 443.6 to sound as an A in our 12tET tuning system. That pitch produces overtones:

http://en.wikipedia....ies_%28music%29

Because of the typical spacing of the resonances, these frequencies are mostly limited to integer multiples, or harmonics, of the lowest frequency, and such multiples form the harmonic series.

The distinction we make between Partials and Harmonics is important... (I misstated partials as harmonics and harmonics as overtones by mistake, nothing more than a memory error - let me adjust the terminology for accuracy)

A partial is any of the sine waves by which a complex tone is described.

Partials refer to all frequencies produced by a single instrument or source of sound - all of which affect the timbre of an instrument.

A harmonic (or a harmonic partial) is any of a set of partials that are whole number multiples of a common fundamental frequency.^[2] This set includes the fundamental, which is a whole number multiple of itself (1 times itself).

Harmonics are those specific frequencies that occur above the fundamental in whole number multiples of the fundamental frequency.

The second harmonic (or first overtone), twice the frequency of the fundamental, sounds an octave higher; the third harmonic, three times the frequency of the fundamental, sounds a perfect fifth above the second. The fourth harmonic vibrates at four times the frequency of the fundamental and sounds a perfect fourth above the third (two octaves above the fundamental). Double the harmonic number means double the frequency (which sounds an octave higher).

If this is not accurate, if the harmonics produced above a fundamental don't produce these intervals, then I can see the case being made that 12tET is merely a compromise. I happen to find that claim laughable. There's no "compromise" taking place if the fundamental is producing harmonics above the fundamental that are very closely approximated (within 3.6 Hz of the overtone frequency) by the 12t tuning system. Does anyone have evidence of this?

If this isn't the case, if the harmonic series deviates enough from the 12t system that we can aurally perceive the difference, then let's hear where that occurs in the series so we're all aware of it. I'm happy to learn more about it at this point, but if I'm correct, other tuning systems need to account for these mechanics. Additionally, the partials that produce the timbre of the instrument should be accounted for as well in the instruments we use with different tuning systems because of the inharmonic qualities of those instruments.

For example, if I want to blend a group of orchestral instruments in a homophonic musical texture using any of these other tuning systems, without accounting for the harmonic series and the partials produced by these instruments in this new tuning system, I'm going to run into a plethora of difficulties because of the mechanics of sound using these orchestral instruments - nevermind the difficulty of actually getting performers to play it correctly on instruments that have been redisigned, over and over again, with the goal of improving performance in a 12t tuning system.

Let's go over this to see what is erroneous. I'm open to learning what is not accurate in my understanding so I'm better informed.

I was going to respond to all of this, but there have been plenty of more-than-valid responses so far.

So I will just take this:

And I have heard ONE WORK written by a masters student for orchestra that used a different tuning system. The orchestra wasn't perfect, and I can give some wiggle room in that area, but by and large, I was not very impressed with the way the instruments came together. Had I known there would be this much discussion to be had with you about tuning, I would have remembered the name of the composer and the work... it wasn't a memorable work to me.

And the fact that you keep posting Wikipedia articles, as a sign that you have no idea what you're talking about.

And for the record, I'm positive you've heard many more works in different temperaments. An educated person such as yourself has to have heard Medieval music in Pythagorean tuning, Renaissance music in mean-tone tuning, Baroque music in Well-temperament, and Classical music in both Well and mean-tone tunings, as well as works by Xenakis, Ligeti, Grisey, Murail, Partch, etc.

So I guess this:

I dare to say that a full orchestra playing a work written for a completely different tuning system does not appeal to me - the instrument combinations don't blend well enough for my aesthetic when we get into homophonic textures and so forth. Sure, a unison microtone between F# and G might sound just fine, but when we get into larger harmonic structures, we're talking about a plethora of overtones and harmonic issues between the instruments of the orchestra..

Isn't all that true.

Also:

In other words, changing the tuning system doesn't change the overtone series.

No one said it does -- we're not talking about isomorphic BS -- but I appreciate the misinformed lesson on the harmonic series and overtones.

The 12t system didn't come about just because people like it... the 12t system is the closest (I should add - audible) approximation to the series of overtones produced by a fundamental pitch, and the whole tonal system that forms around this also approximates this series. It's pretty difficult to make the case for other tuning systems given how closely this tuning system audibly approximates how sound actually results when a pitch is performed on an instrument. I happen to find this appealing to my aesthetic, so I'm content with it.

The closest approximation of the overtone series would be a Just tuning. After that, Pythagorean gives you pure fifths, 1/4 comma meantone pure major thirds (except for 4 major thirds). 12tET flattens the fifth, raises the major third, flattens the major second, etc.

12tET came about because composers got more and more chromatic and were modulating to more and more distant keys, and -- like with all tunings -- was a way to get as many thirds as possible to be "usable". Like Well-temperaments, it sacrifices the purity of intervals in order to make more available and to make them roughly the same size (or, the exact same size, in the case of 12tET). Not because it is the "closest approximation of the series of overtones", its actually extremely far from it.

Its all a matter of making all keys usable, not approximating the harmonic series.

The closest approximation of the overtone series would be a Just tuning. After that, Pythagorean gives you pure fifths, 1/4 comma meantone pure major thirds (except for 4 major thirds). 12tET flattens the fifth, raises the major third, flattens the major second, etc.

So, when I play an A2 on piano, holding down the A, E, A, and C an octave above it, you're saying those pitches are not close approximations of the whole number multiples of the fundamental pitch, A?

How about a citation or two in your response...?

http://en.wikipedia.org/wiki/Inharmonicity

Since we're so fond of wikipedia...

Yeah, no kidding...

Music harmony and intonation depends strongly on the harmonicity of tones. An ideal, homogeneous, infinitesimally thin or infinitely flexible string or column of air has exactly harmonic modes of vibration.^[1] In any real musical instrument, the resonant body that produces the music tone—typically a string, wire, or column of air—deviates from this ideal and has some small or large amount of inharmonicity.

This refers to those frequencies that affect the timbre of the instrument, like I said. There's even an example in another of these articles that explains how Bells sound like they do because of the prevailing inharmonic partials we here when bells are struck - that's covered here:

http://en.wikipedia.org/wiki/Harmonic

The untrained human ear typically does not perceive harmonics as separate notes. Rather, a musical note composed of many harmonically related frequencies is perceived as one sound , the quality, or timbre of that sound being a result of the relative strengths of the individual harmonic frequencies. Bells have more clearly perceptible inharmonics than most instruments. Antique singing bowls are well known for their unique quality of producing multiple harmonic partials or multiphonics.

So, let's hear it for wikipedia for explaining this for us. How are inharmonics (partials outside the spectrum of harmonics that occur above a fundamental pitch) relevant to the question of the harmonic series? It seems pretty simple to me: in the spectrum of partials we have those that are harmonics (overtones) that make up the tone/pitch and inharmonics that make up the timbre of the instrument. What am I missing?

Please, please read all your wikipedia articles -before- posting. Don't just come up with statements and when people point out your errors you read some more on wikipedia to jump to the next faulty conclusion and post your most recent findings as wikipedia links to whatever your position currently is.

Either we try to educate other people by giving correct well-founded information here (which means informing yourself before you post), or we leave that out entirely and concentrate on stating our aesthetic opinions and such.

I mean, if I say things like "the closest approximation to the harmonic series -is- the harmonic series" I actually mean them. If you simply ignore such obvious facts and insist that 12TET is a better approximation and doesn't stem from making a compromise with some other demands (i.e. wishing to have a -scale-, octave identity, the ability to freely modulate, etc.) then I really can't argue much more...

And the last sentence you posted right up there just goes overboard completely...

Just to clarify this once for all:

"Overtones": Any frequencies higher than the fundamental that are present in a periodic sound. In most western instruments those frequencies are pretty close to the harmonic series, in which case we speak of a harmonic spectrum. In other cases, the frequencies are further away from whole numbered multiples of the fundamental, in which case we speak of inharmonic spectra. It is how strong particular overtones are in an instrument and how their amplitudes evolve over time that determines the timbre of an instrument, next to some other things (such as formants, amplitude envelope, noise components, etc.).

"Harmonic series": The harmonic series is (when talking about music) a series where each frequency is a whole-numbered multiple of a fundamental frequency. It is commonly found, as mentioned, in the overtone spectra of many instruments (approximatively at least), as the notes of natural brass instruments, as divisions of a string in equal distances, etc.

"Partials": Basically the same as overtones, just that the numbering differs, since the fundamental of a sound is already the first partial, whereas the counting for overtones only begins at the first partial -above- the fundamental.

How about a citation or two in your response...?

Sure.

How about The Myth of Equal Temperament by Ll. S. Lloyd from Music & Letters, Vol. 21, No. 4 (Oct. 1940), pp. 347-361?

Or would you prefer more "easily digestible" internet links?

http://www.phy.mtu.edu/~suits/scales.html

http://www.kylegann.com/tuning.html#tune3

Oh know! I posted something other than Wikipedia articles. Uh-oh, I read scholarly writings.

There's plenty more more where that came from, champ.

What am I missing?

Facts.

EDIT:

Just saw this:

I don't know by heart about the characteristics of many ETs - which intervals they approximate better and which commas they temper out - I should either read this up or make calculations myself - but perhaps Charlie could list some examples. For example, 19-ET deviates more from the pure fifth than 12-ET does, but it gives you better thirds. Also, it utilizes the 7th harmonic (though doesn't approximate 7-limit tuning very accurately), which gives you the expressive opportunity to build septimal triads.

31tET, tempers out the syntonic comma (which basically makes it a mean-tone tuning), and it supports pretty great approximations for a few kinds of mean-tone and Just tunings. Which is why, historically speaking, 31tET has been a big topic of discussion.

The major third is .79 cents away from being Just, so it has very close to pure thirds. The fifth is .19 cents different than in 1/4 comma mean-tone.

That's basically why you have Huygens writing about it in the 17th cent. and Fokker picking it up in the early 20th cent., etc.

19tET does give you better major thirds than 12tET, but they're actually about 8 cents flat.

41tET you have a fifth of 702.44 cents, so sharp by .48 cents, but your major third is flat. You have closer to pure major second, it being sharp by .92 cents.

59tET is pretty good. You have a major second of 203.39 cents (.52 cents flat), a major third of 386.44 (.13 cents sharp), your fifth is sharp by about 9 cents. It also approximates some of the higher partials (11th, 13th) better.

65tET has a major second of 203.08, a minor third of 295.38, a major third of 387.69, a fifth of 701.54, a major 7th of 1089.23,

I mean the higher up you go in divisions, the more likely you are to match (or get close to matching) a Just interval.

Hope that helps, Km7.

Yes, it's a very good addition to the topic (and also illustates some of the points I raised). Also, thanks for the link to the Custom Scale Editor - I was looking for software that is alternative to Scala, but didn't find this one while I was searching.

EDIT: Unfortunately, it is not working. I followed the install instructions, but I get a weird error message on open. I think it should work on Windows XP, which is what I use.

Yes, it's a very good addition to the topic (and also illustates some of the points I raised). Also, thanks for the link to the Custom Scale Editor - I was looking for software that is alternative to Scala, but didn't find this one while I was searching.

EDIT: Unfortunately, it is not working. I followed the install instructions, but I get a weird error message on open. I think it should work on Windows XP, which is what I use.

I'm glad I could be of some assistance! :D

I knew I made a chart of ETs from 1tET - 96tET (I'm workin' to 205tET) for a reason. :lol:

Hmm. Its always worked fine for me (though I have a Mac), aside from a crash here or there. It should work with XP...

There are also many other microtonal sources coming from H-Pi Instruments, aside from the Custom Scale Editor, there is also microtonal ear training software, ScalaVista, notation software, etc.

Not to mention the microtonal synth and the Tuning Box (which I use), as well as links to some public domain books and articles on temperament.

It really is a great resource, though I don't necessarily agree with everything on there.

h-pi.com

Sure.

How about The Myth of Equal Temperament by Ll. S. Lloyd from Music & Letters, Vol. 21, No. 4 (Oct. 1940), pp. 347-361?

Or would you prefer more "easily digestible" internet links?

http://www.phy.mtu.e...its/scales.html

http://www.kylegann....ning.html#tune3

Oh know! I posted something other than Wikipedia articles. Uh-oh, I read scholarly writings.

I asked you to post sources. I didn't ask this to be a dick but to compare the information you're looking at with the information I'm looking at.

There's plenty more more where that came from, champ.

Really? Why are you "escalating" this discussion with sarcasm and disrespectful language? This is entirely uncalled for.

If anything, I'm more open to take the time to read more into this. I'm reconsidering how seriously I can take you given this outright rudeness, champ!

Facts.

Okay. You're not directly answering my questions at all. I'm simply asking whether or not the 12tET closely approximates the overtone series. If the crux of the issue is...

"Many recent composers have come to feel that the compromise of equal temperament was a mistake. They feel that the musical logic of moving from any key to any other key became a priority at the expense of music's sonic sensuousness. Harry Partch was the first such composer. He defined his own scale with 43 pitches to the octave, and invented his own instruments to play it. Lou Harrison was the next major figure to abandon equal temperament; he has used many tunings taken from Indonesian gamelans, and also, in his Piano Concerto, returned to an almost-pure tuning called Kirnberger II from the 18th century. Other composers to work in pure tuning (just intonation) include Partch's protege Ben Johnston (my teacher), La Monte Young, Terry Riley, Pauline Oliveros, James Tenney, Rhys Chatham, Glenn Branca (in his middle symphonies, Nos. 3, 4, and 5), Ben Neill, Dean Drummond, and myself (Kyle Gann)."

I'm so very tired of this discussion at this point. I happen to think equal temperament is more "sonically sensuous" than unequal (?) temperament. That's a wholly different, wholly SUBJECTIVE issue that in NO WAY addresses, directly or indirectly, my point about the harmonic series and tuning systems.

I'm done with this discussion because A) you're unjustifiably rude in your responses, B) you're not directly addressing my points, and C) you're wasting my time with subjectivity. Peace out!

I'll just point out that you quoted Kyle Gann to make the point that I'm "wasting your time with subjectivity". Apparently you didn't read anything but the conclusion of that page. (Also, note that he's saying "they feel", not "its a fact that this is better than that")

I'm rude because you're "unjustifiably" shitting on what I do as a composer and bringing in unbelievably incorrect information.

Everyone is addressing your points, its just that once they're addressed you seem to forget you made them.

So, to escalate this and be rude again: DUH.

Oh, and your question about whether or not 12tET closely approximates the harmonic series has been answered a few times here, so why don't you go ahead and actually read what's been posted.

I'll just point out that you quoted Kyle Gann to make the point that I'm "wasting your time with subjectivity". Apparently you didn't read anything but the conclusion of that page. (Also, note that he's saying "they feel", not "its a fact that this is better than that")

I read every last bit of it, actually. The discussion there revolves around tuning systems, not how those tuning systems relate to the harmonic series -the subject of my particular question- as far as I could tell.

I'm rude because you're "unjustifiably" shitting on what I do as a composer and bringing in unbelievably incorrect information.

No, let's be clear. Not once have I spoken about what you do as a composer... I'm genuinely trying to have a rather objective discussion about how the mechanics of sound are being taken into account with these other tuning systems, specifically, the harmonic series.

Initially, I stated what -MY- reasons were for not experimenting with different tuning systems. That was attacked as somehow "inaccurate," so I was then goaded into defending my reasons. Now I'm asking what's wrong with my understandings and you're taking offense?

Are you delusional?!

Oh, and your question about whether or not 12tET closely approximates the harmonic series has been answered a few times here, so why don't you go ahead and actually read what's been posted.

Right, right, the "compromise." Because there MUST be a compromise when a "mistake" has been made (like that doesn't "scraggy" on everything -I- do as a composer - geez!). So, what this all comes down to is whether you believe equal temperament is a mistake. I happen to think it isn't. There we are -subjectively- disagreeing about something I intended to discuss objectively.

Discussion over.

K, enough. Please let's just all stop unless the posts can start being something OTHER than "ur dumb :<" Lets have other people post if they want and not keep bumping the thread out of dumb fighting, thx.

I've recently really gotten into microtonal music and have written some myself:

A piece in the "magic temperament" including 10-, 13-, 23-, 19-, 16-, and 3-equal divisions of the octave:

House MD theme mapped to 7-edo:

5-edo Theme improvisation:

Microtonal (or xentonal) music, I've found, is most accessible using isomorphic keyboards because they have the same fingering in every tuning of a given temperament making them very accessible. They also allow for effects like polyphonic tuning bends where you change from tuning to tuning in real time. You can try it here for yourself in the syntonic temperament where this flash app adapts your QWERTY keyboard to be an isomorphic keyboard:

http://blog.igetitmusic.com/2010/02/exploretuning1.html

This method of using linear temperaments and isomorphic keybaords allows for a perspective to compare tunings, relate them in a perceptually relevant way, and also learn to play them very easily to experience them yourself.

Poor guy couldn't help his name, but What The Fokker: http://www.huygens-fokker.org/instruments/fokkerorgan.html

I don't understand what this topic is about. Is it supposed to ask something or...? Anyway, I think your post is a good addition to the Tuning systems topic.

I've recently really gotten into microtonal music and have written some myself:

A piece in the "magic temperament" including 10-, 13-, 23-, 19-, 16-, and 3-equal divisions of the octave:

House MD theme mapped to 7-edo:

5-edo Theme improvisation:

Microtonal (or xentonal) music, I've found, is most accessible using isomorphic keyboards because they have the same fingering in every tuning of a given temperament making them very accessible. They also allow for effects like polyphonic tuning bends where you change from tuning to tuning in real time. You can try it here for yourself in the syntonic temperament where this flash app adapts your QWERTY keyboard to be an isomorphic keyboard:

http://blog.igetitmusic.com/2010/02/exploretuning1.html

This method of using linear temperaments and isomorphic keybaords allows for a perspective to compare tunings, relate them in a perceptually relevant way, and also learn to play them very easily to experience them yourself.

Still? Get a new interest and please stop invading any conversation that even remotely deals with tuning with your isomorphic bullshit.

I don't understand what this topic is about. Is it supposed to ask something or...? Anyway, I think your post is a good addition to the Tuning systems topic.

Ditto.

All I wanted was to share this nice piece of Dutch craftmanship. I just liked the idea of this organ.

My desciption was maybe a bit cryptic. My initial thought was "WTF"; and the builders name was Fokker, you can do the math...

Woops, Jaap, I think I decline the invitation to play that organ it looks like designed for an Alien player or somebody with a different brain, I think after playing that thing you end totally dizzy ....

The only good thing is that if you make a mistake and play a wrong note, nooooobody will note it

These two topics have been merged. Have a nice day.

http://blog.igetitmusic.com/2010/02/exploretuning1.html

Just play the keyboard that loads in the flash app with your qwerty keyboard? It will take you thirty seconds at the most to try it out. Play "do re mi fa so la ti do", then slide the slider to 19-edo and do the same thing, then slide the slider to 17-edo and do the same thing one more time. You will be playing each tuning's major scale with the same fingering.

Are you an advocate of isomorphic keyboards and are paid to advertise them? Because it gets really annoying that you post about this stuff in every thread that is somehow related to microtonal music and tunings.

http://blog.igetitmusic.com/2010/02/exploretuning1.html

Just play the keyboard that loads in the flash app with your qwerty keyboard? It will take you thirty seconds at the most to try it out. Play "do re mi fa so la ti do", then slide the slider to 19-edo and do the same thing, then slide the slider to 17-edo and do the same thing one more time. You will be playing each tuning's major scale with the same fingering.

I don't really get this, when I choose 31 tet, then I still have only 19 different tones to play, the others are octaves of the first 19...or did I understand something wrong?