Tuning

[snailed]

From original thread: Poll: If you play an instrument, can you read music?
Located HERE

I'm another Nay that never voted, actually i have no interest in being able to read music, but I would truly love to understand tuning theory. Is it possible to learn the one without the other?

Absolutely. As I said in that other thread, I'm a horrible reader as far as being able to pick up and play something at first glance. While these two subjects are intertwined in their nature of representing sound, in a lot of ways they have very little to do with one another besides some vocabulary terms. Writing and reading music is closer to language, and tuning theory is closer to math and science. In the process you might be closer to understanding written music as a result, but in my opinion they are separate subjects. I'll do my best to get some sort of general starting point down in the plainest language I can, others please add more; it'd be much appreciated as I'm no authority on the subject and am somewhat new to it.

OK, first I'm going to say that any historical things I mention are going to be from the perspective of the west, putting it in the context of 'classical' music. At least, from the Greeks to early vocal monophony and polyphony (single voice melodies, and many melodies at once) onward to where things started to cross over more between east and west. These ideas are universal, and no one invented them, only ways to explain them. Feel free to skip the historical stuff if you want for now, but I provided it for a bit of context.

Also, this is just a tool - anytime I've ever seen anyone completely and unconditionally devoted to a system, I've seen ugly results (to my personal taste). We have Feldman to thank for pointing that out. That being said, some of this stuff can be useful in certain contexts. Other contexts, completely useless.

OK, here are a few resources to start with:

First, and most importantly, is to familiarize yourself with the overtone series. In plain english, if you excite a string or any other source of a musical sound, there are other notes inherent in main, fundamental note. For example, if you excite a string tuned to 600hz, or vibrating at 600 cycles per second, there is an octave at 1200hz, a fifth at 1800hz, etc, etc. These can be expressed as ratios, which is referred to as just intonation (the simple numerical relationships are the definition JI, not just because you are expressing it in a fraction/ratio). Octave would be 2/1 or 2:1, and fifth would be 3/2 or 3:2. If you or someone else isn't familiar with terms like octave or fifth, don't worry too much. They're just ways of identifying the distance between the pitch of two sounds. Little more on that later.

The wikipedia entry is a nice guide to start with: Here. Some of this might be a little tough and verbose for now, but just glance it over, and google some other sites to read more and more about it. Just intonation is tuning that is derived from (usually) simple numerical relationships related to the overtone series. It's expressed as a ratio or fraction. 2:1 or 2/1 is an octave. In frequency per second, 100 hertz to 200 hertz is an octave. Theoretically, you can make it as complicated a numerical relationship as you want (97/53 or something), but really, in practice and in real life, the simpler the relationship the closer it is intrinsically related to the overtone series.

Sometimes it's good to start out with a general historical overview. I'd recommend this book for that:
Tuning and Temperament: A Historical Survey, by J. Murray Barbour

In case you or someone else does not know, temperament is the (usually slight) deviation from the intervals inherent in the overtone series to intervals that facilitate a greater range of potential key centers (being able to play in more keys on the same instrument).. By intervals, I mean, the distance between two notes. In many just intonation tunings, as you play in different keys, some sound better than others, and some sound terribly dissonant. Some of these very dissonant intervals are called "wolf" tones, which are referred to occasionally. Some are less dissonant than others. Temperament is an attempt to alter the pure/simple tunings slightly to allow for more tonal centers, more keys, and to eliminate very dissonant intervals.

From Pythagoras and the early vocal music of in the west onward, things became increasingly tempered to allow access to more remote keys in the context of a single instrument. In a very general way, as things progress through the Baroque, into the Classical and finally the Romantic / Modern era, there is more and more of a desire to have access to every one of the keys, as modulations (key changes to different tonal centers) became more and more complex/remote. There are hundreds of years in between here with a rich history of many different temperaments and tuning systems.

All this ultimately leads up to a temperament that would sound equally good (or bad) in each key, equal temperament, the standard tuning any regular piano tuner would use today. In this, every half step between every note is equal. Between C and C#, C# and D, Gb and G, etc. All equal. This was also used in fretted instruments for a very long time, but as a general tuning practice was not adopted until the mid-late 19th century or so (edit: oops, at least according to Gann's article "Not until 1917 was a method devised for tuning exact equal temperament." Not sure what the Barbour book says as it's not on me), and even then was the subject to much controversy.

As a side note, this equal-ing out of consonance and dissonance, from my perspective, seems to have something to do with the development of the atonal and 12-tone / serial styles of composition.

The Barbour book provides a good history of how Western music went from the pure Greek tunings of Pythagoras up until equal temperament. Good for historical context, some meat and potatoes stuff too describing the methods of tuning and theory behind it, describes many different types of temperaments. It will clue you in on a lot of the vocabulary (sometimes the most difficult part to break through).

The most important thing from a regular Western music theory perspective is to familiarize yourself with the names of the basic intervals as they tend to be talked about quite a bit. I'm not sure if you're familiar with the terminology, but I'll just type it here for reference in case anyone else is not. It's really pretty easy. I will just express them in the simplest way possible for now (there are lots of ways to "respell" things, complicate them, and call them different names). These tell the distance between two notes. Let's start from C to ...

C (same note): Perfect Unison
Db: Minor Second
D: Major Second
Eb: Minor Third
E: Major Third
F: Perfect Fourth
F#/Gb: Augmented Fourth / Diminished Fifth (tritone, the octave split in half)
G: Perfect Fifth
Ab: Minor Sixth
A: Major Sixth
Bb: Minor Seventh
B: Major Seventh
C: Perfect Octave

Play these regular equal tempered notes at the piano and get them in your ear. At first, it's easy to just relate them to a melody. For example, the first two notes of "Star Wars" make a perfect fifth. The first two notes of the NBC theme is a major sixth. Get that stuff down and then move on.

There are some REALLY great websites out there, you can probably teach yourself the vast majority just from following your nose with that.

Kyle Gann: Just Intonation Explained is a remarkably clear and easy explanation of some of these principles for the beginner, and he has a ok (but quite flawed and centered to his allegiance to the American just-intonation composers) overview of historical tunings as well. Remember that this stuff has been around since the time of Pythagoras. La Monte Young didn't invent it.

Very little math knowledge is needed. The only thing that is tricky, is that you always represent a ratio (that is, one string vibrating at X cycles per second to another at N per second). The note higher in pitch will be X, and the other N. You express it, X:N or X/N. The simplest ratio is an octave: 2:1. That would be the high note vibrating at 880hz to 440hz, for example, an A. Next on up is a perfect fifth: 3:2. The important thing to remember is that it is ALWAYS expressed as a whole number between 1 and 2.

Now, let's say you wanted to go up two perfect fifths from C and express it as a just ratio.

First, let's say C is 200 hz (I know it isn't, but just an arbitrary number for the sake of clarity). Up a perfect fifth (3:2) from C is G. Up a perfect fifth (3:2) from G is D. So, what is the ratio between C and the high D?

You have to multiply - and then express it as a ratio/fraction that is a whole number between 1 and 2.

3x3 is 9. 2x2 is 4. But 9:4 is between 2 and 3, not 1 and 2. So we express it as 9:8. The ratio between the first C and the high D is really 9:4, but we express it as 9:8 for the sake of consistency. If C is 200hz, G is 300hz, and the high D is 450hz. Remember, 225hz is literally 9:8 from the 200hz C, but we simplified it down an octave to express it in the standard way.

Harry Partch: Genesis of a Music can be a rough read at times, but it also can be entertaining and opinionated. Some of his ideas are completely useless for my purposes personally (Otonality, Utonality), but it is a very good book to have around. One of the criticisms of that concept is that it makes logical sense, but not much musical sense. Once you've got some of the basics down, definitely pick it up and you can get into some of those areas.

OK, I think that's enough to start with. Please feel free to call out any inaccuracies here or further points that may help, but I think that's a good start. Also tell me if anything needs better clarification.

-s

edit: edited some for clarity

[hatta]

There's an incredible book out there called "Tuning the Historical Temperaments by Ear" by Owen Jorgensen which will teach you how to tune non equal temprered tunings by ear. A lot of this can be applied to other tuning systems plus a lot of the historical temperaments are plenty cool in and of themselves. The book is super rare and expensive to own but libraries and inter-library loan is a viable option.

[snailed]

There's an incredible book out there called "Tuning the Historical Temperaments by Ear" by Owen Jorgensen which will teach you how to tune non equal temprered tunings by ear. A lot of this can be applied to other tuning systems plus a lot of the historical temperaments are plenty cool in and of themselves. The book is super rare and expensive to own but libraries and inter-library loan is a viable option.

Oh man, if someone could find a .pdf of this I'd be forever grateful.

[7/4]

There's an incredible book out there called "Tuning the Historical Temperaments by Ear" by Owen Jorgensen which will teach you how to tune non equal temprered tunings by ear. A lot of this can be applied to other tuning systems plus a lot of the historical temperaments are plenty cool in and of themselves. The book is super rare and expensive to own but libraries and inter-library loan is a viable option.

Oh man, if someone could find a .pdf of this I'd be forever grateful.

Hardcover, only $675.00 from Amazon.

[Dohol]

There's an incredible book out there called "Tuning the Historical Temperaments by Ear" by Owen Jorgensen which will teach you how to tune non equal temprered tunings by ear. A lot of this can be applied to other tuning systems plus a lot of the historical temperaments are plenty cool in and of themselves. The book is super rare and expensive to own but libraries and inter-library loan is a viable option.

Oh man, if someone could find a .pdf of this I'd be forever grateful.

Hardcover, only $675.00 from Amazon.

Oh the pain...


It did sound like an interesting book..

[7/4]

For JI, I learned from the JI Primer by Doty. Just get the book, the membership to the JI Network isn't worth the trouble in this age of the Internet.

[7/4]

Kyle Gann: Just Intonation Explained is a remarkably clear and easy explanation of some of these principles for the beginner, and he has a ok (but quite flawed and centered to his allegiance to the American just-intonation composers) overview of historical tunings as well. Remember that this stuff has been around since the time of Pythagoras. La Monte Young didn't invent it.

I've heard that Pythagoras learned math and tuning from the Babylonians. Maybe it was ancient when he learned it!

There's nothing new under the Sun - Ecclesiastes

[snailed]

You're right - La Monte didn't invent it and neither did Pythagoras. It's always been here. Anyway, that was a simplification - the number theory is usually attributed to him but likely inherited from elsewhere. I'm really, really not a history buff, especially Greek history or the history of mathematics, so if someone wants to take a crack at that, please do. Might have to send it off to IHE though...

As I said in the first post, this has been around forever and is universal. No one invented it, just ways to explain it or understand it.

[7/4]

You're right - La Monte didn't invent it and neither did Pythagoras. It's always been here. Anyway, that was a simplification - the number theory is usually attributed to him but likely inherited from elsewhere. I'm really, really not a history buff, especially Greek history or the history of mathematics, so if someone wants to take a crack at that, please do. Might have to send it off to IHE though...

As I said in the first post, this has been around forever and is universal. No one invented it, just ways to explain it or understand it.

La Monte Young always gives credit to Tony Conrad for suggesting the use of JI tuning in the Theatre of Eternal Music in many articles and interviews. That's when La Monte first started working with tuning systems.

[7/4]

Kyle Gann: Just Intonation Explained is a remarkably clear and easy explanation of some of these principles for the beginner, and he has a ok (but quite flawed and centered to his allegiance to the American just-intonation composers) overview of historical tunings as well. Remember that this stuff has been around since the time of Pythagoras. La Monte Young didn't invent it.

Please explain how Ganns overview of historical tunings is quite flawed and how American just-intonation composers have anything to do with his article.

[snailed]

My mistake, I put this together pretty quickly and from memory, and was referring to the way he mostly uses that group of composers for modern examples in his just intonation primer and elsewhere, not the historical overview, so I retract that. Anyway, I don't want to start discussing the minutiae of Gann's position here, that is outside the scope of this thread. Big respect to the guy and not to assume anything, I just wanted to get across that these ideas are not limited to a certain group of composers.

Would someone care to give a plain English definition of standing waves, and inharmonicity?

[7/4]

Shrug.



The overtones of some sounds are in whole number ratios - the harmonic series. Strings, horns, wind instruments. These sounds have harmonicity.

The overtones of other sounds have inharmonicity. These overtones are not in whole number ratios. Percussion instruments, bells, gongs, metal bars, gamelan, membrane drums.

When you hear all the beating notes in a bell, you're hearing all the non-harmonic partials beating against each other like crazy because they're out of tune with the harmonic series and each other.

I think a bell that has overtones only from the harmonic series would sound very pure.

[snailed]

OK - that is a good general definition. What I was referring to in particular was the inharmonicity that occurs in strings, I should have been more specific.

However, on stringed instruments the overtones are inharmonic, which is is caused by a "fastening fault in the string endings"; the string endings are fastened at each end, which means that they cannot "vibrate all the way to its ends." As such, the "effective length of a string is shorter than its geometrical length," especially for shorter, stiffer strings.

(cut)

Piano tuners must deal with the inharmonicity of piano strings, which is present in different amounts in all of the ranges of the instrument, but especially in the bass and high treble registers. Piano strings are under enormous tension compared with the strings on a violin or guitar, and as a result, piano strings are much harder and stiffer. Another factor that can cause problems is the presence of rust on the strings or dirt in the windings. [4]These elements can result in inharmonicity, which has the effect of slightly raising in frequency of the higher modes, which means that they cease to be exact integer multiples of the fundamental.

The harmonic series of strings does not fall exactly into whole-number multiples of a fundamental frequency, but rather each harmonic is slightly sharper than a whole-number ratio, and this sharpness increases as higher tones in the harmonic series are reached. This means that an aurally tuned octave will be a "stretched octave" which is slightly wider than the just 2:1 ratio. The amount of stretching depends on the style of piano and is determined mainly by the length of the strings. On a piano, the notes in the higher register will end up being tuned slightly sharper than those in the lower octave. This is less apparent on longer pianos which have proportionally thinner strings, because string inharmonicity is directly related to the ratio of string thickness to length

Seems to do a reasonably good job of explaining it, but if someone can go into more depth that would be nice.

FWIW, the 'out of tune-ness' of a bell is what gives the sound its character and beauty to me, and sometimes a singular, unchanging goal for purity can leave things very cold. (At least in my opinion).

Another fairly good article, on Stretched Tuning (relevant to the inharmonicity of strings): http://en.wikipedia.org/wiki/Stretched_tuning" onclick= "window.open(this.href);return false;

[7/4]

Herman Helmholtz covered harmonicity/inharmonicity and other issues like the inharmonicity of piano strings and stretch tuning more than a hundred years ago in the Sensations of Tone.



Not an expensive book at all...

[7/4]

OK - that is a good general definition. What I was referring to in particular was the inharmonicity that occurs in strings, I should have been more specific.

snip

Seems to do a reasonably good job of explaining it, but if someone can go into more depth that would be nice.

In one post, you want it in plain English:

Would someone care to give a plain English definition of standing waves, and inharmonicity?

Now you want it in more depth.

I prefer simple:

A metal string under high tension doesn't have the overtones of a string (harmonic series, harmonicity), it behaves like a piece of metal (non-harmonic series, inharmonicity). This is why pianos need to be stretch tuned, to compensate for the absence of harmonics in the overtones.

All those percussion instruments that Partch used were completely wrong for someone who was such a big champion of JI.

[snailed]

OK - that is a good general definition. What I was referring to in particular was the inharmonicity that occurs in strings, I should have been more specific.

snip

Seems to do a reasonably good job of explaining it, but if someone can go into more depth that would be nice.

In one post, you want it in plain English:

Would someone care to give a plain English definition of standing waves, and inharmonicity?

Now you want it in more depth.

I prefer simple:

A metal string under high tension doesn't have the overtones of a string (harmonic series, harmonicity), it behaves like a piece of metal (non-harmonic series, inharmonicity). This is why pianos need to be stretch tuned, to compensate for the absence of harmonics in the overtones.

All those percussion instruments that Partch used were completely wrong for someone who was such a big champion of JI.

OK, about to go to sleep, but quickly:

First off, Partch HATED talking about just intonation all the time. He placed his work first and used it only as a tool towards that end. Just intonation was only one aspect of his work. He was about the entire experience, not just one abstracted idea. Partch was a staunch supporter of corporeality in music, not just chopped off, isolated aspects of sound - he often used theatrical elements often as well.

I'm under the impression that when you start, you want a general definition - which you then provided in regards of the makeup of the overtone series of any sound. I then provided some general info about inharmonicity in relation to strings, a different subject, which has more practical implications. After that, I asked to further the conversation and to get into some more practical, detail oriented stuff about that subject in specific.

Your definition here is a refinement of that, that's good - it's called contributing. Let's try and and lose any unnecessary bickering or criticism along with it after this, shall we?

[Stephen]

Wow, excellent! thanks for starting this Steven, not enough time to read it all now, but VERY pleased this is here.
(unuseful enthusiastic post of the week)

[7/4]

Your definition here is a refinement of that, that's good - it's called contributing. Let's try and and lose any unnecessary bickering or criticism along with it after this, shall we?

My contributions come from 14 years experience of working with microtones plus a lifetime of musical experience.

I'm just sharing from my experience, I'm just trying to help.

Over at the Yahoo Tuning groups, the email lists, they also have years of experience and they're not as kind about correcting misinformation.

[faster]

Over at the Yahoo Tuning groups, the email lists, they also have years of experience and they're not as kind about correcting misinformation.

All the more reason to stay over here instead of going over there.

[snailed]

OK, cool David (7/4), I appreciate your effort and experience, just trying to keep things towards the constructive end and keep on topic. FWIW, I have been working with this for about 6 years of consistent study, but still consider myself a beginner. I think it's best to keep that mindset.

BTW, that Helmholtz book is a monster - another must own. Had it for a while but have not studied it to the extent of some other books I have. This makes me want to read it cover to cover.

Yeah, Joe, I have seen those tuning groups, and they are not a very fun place. I am convinced some of those people don't even like music at all but rather, just the theory (well, I should look at the name of this board before I say that...)

- and no prob, Stephen!