Tuning: An Introduction

Рет қаралды 3,164

Ай бұрын

🎶 Support the channel: / classicalnerd
📚 Sources/further reading:
Info on quarter-comma meantone and Werkmeister III were sourced from tables on Kyle Gann's web site [www.kylegann.com/histune.html], which in turn comes from "Tuning: Containing the Perfection of Eighteenth-Century Temperament, the Lost Art of Nineteenth-Century Temperament, and the Science of Equal Temperament" by Owen Jorgensen (Michigan State University Press, 1991).
The video featuring split sharps may be found at • Quarter-comma Meantone...
Additionally, I highly recommend the book "How Equal Temperament Ruined Harmony (and Why You Should Care)" by Ross W. Duffin (Norton, 2007).
----------
Music:
- Thomas Little: Dance! #2, performed by Rachel Fellows, Michael King, and Bruce Tippette
----------
Contact Information:
Questions and comments can be directed to:
nerdofclassical [at] gmail.com
Facebook:
/ classicalnerd
Instagram:
/ the_classical_nerd
----------
All images and audio in this video are for educational purposes only and are not intended as copyright infringement. If you have a copyright concern, please contact me using the above information.

Пікірлер: 37

@Dovith Ай бұрын

Seriously this guy has one of the best if not the best music KZfaq channel.

@jbradleymusic Ай бұрын

This is the first clear and concise introduction I’ve seen that doesn’t make me feel like a dodo.

@user-xm2lh5fu3p Ай бұрын

Man these thumbnails are getting wilder and wilder, keep em up.

@laurencefinston7036 Ай бұрын

I forgot to say, thank you for this interesting video with the clear and concise explanations.

@avaonalee Ай бұрын

I love your channel so much !!!!

@nicholasschuman4805 Ай бұрын

My party trick is to display the vast amount of info I learn from you and then happily direct them to your channel.

@AtomizedSound Ай бұрын

“Fun to name things after a guy that had a math cult” love the witty sarcasm. Great video on tuning

@darkstudios001 Ай бұрын

Great video! Love this channel ❤️

@enri_mucca Ай бұрын

This video is the demonstration that youe channel is not only fantastic, but also... just

@ConvincingPeople Ай бұрын

Excellent primer on this subject. My only addition would be to note that, within traditional and colloquial forms such as barbershop quartet and older styles of the blues, 7-limit and even some higher prime-limit intervals are common enough to not be especially alien to the contemporary Western tonal vocabulary through the influence of those styles on, for instance, jazz and gospel; and indeed, long before that, those narrow minor thirds in meantone were very close to 7/6 and were exploited for that darker effect by certain Renaissance composers. But you kind of see that extended vocabulary largely disappear from court and sacred music in Europe during the Baroque and don't really see it come back into classical music really until Cowell, Partch and Carillo, while even in many styles influenced by the blues, the predominance of keyboards and fretted instruments has limited how far that kind of harmony can usually be taken.

@christopherjwillsmusic Ай бұрын

Excellent!

@laurencefinston7036 Ай бұрын

A few months ago stumbled on an idea that I think is pretty good: I wanted a chromatic kalimba so I bought two and tuned one down to B. This worked great and I realized that the kalimba is much easier to retune to any tuning you want, within reason, than any other instrument I know (excluding electronics). I then bought two more and tuned them to quarter tones. This also worked great, except that it's an awful lot of tines to tune; more than I ever feel like doing in one sitting. For this purpose I bought myself a high-end tuner from TLA, which as far as I know is apparently the only one on the market with a preset for microtonal tunings. I used equal temperament (based on the 24th root of 2) but I plan to retune them using the pure intervals of the harmonic series. As a brass player, I'm particularly interested in the harmonic series and I also have some overtone flutes (fujaras and koncovkas), which are sort of like the fipple flute version of the alphorn (but not quite so large). I also have some other ideas involving the harmonic series and quarter-tones, so yesterday, as it happens, I wrote a little program in C++ to calculate the frequencies from a given fundamental. The program also calculates the ratios of whole numbers that arise. I may be wrong, but I don't think these numbers, i.e., the integers in the numerator and the denominator of the ratios, are all primes. For example, my program calculates the ratio for the interval of a maj. 2nd (the ninth partial) as 8/7 and the ratio for a maj. 3rd as 5/4. I think this is correct, however, due to the way computers perform arithmetic with real numbers, there may be rounding error involved. I would also have to review your video to see if you said these integers are always prime; I may have misunderstood you. One thing that became clear to me by doing this is that the Pythagorean comma has nothing to do with this when calculating the intervals of the harmonic series directly, i.e., by multiplying the fundamental frequency by 1, 2, 3, 4 ... and then dividing the result one or more times in order to get a value within a single octave. The commas only arise when using a given interval to find pitches, e.g., the fifth of C is G (got the fifth), the fifth of G is D (got the second), the fifth of D is A (got the sixth), etc. When calculating the frequencies directly, the frequencies of the octaves will always be exactly the frequency of the fundamental multiplied by a power of 2, i.e., 2, 4, 8, 16, 32 ... Incidentally, it wouldn't be possible to create a quarter-tone scale by a series of 12 successive fifths. A fifth is 3 1/2 steps. Edit: The following statement is wrong (see my reply, below.) To get a quarter tone scale in this way, you would need a series of 24 intervals of 1 3/4 steps. A couple of years ago, I wrote another program for calculating the positions of the frets for fretted stringed instruments using equal temperament. That was also interesting.

@laurencefinston7036 Ай бұрын

I wrote: "To get a quarter tone scale in this way, you would need a series of 24 intervals of 1 3/4 steps." This was wrong. You would need the interval, which when doubled, would result in an octave plus a semitone, namely 3.25 steps, i.e., a quarter-tone below G. Let alpha be this interval. Then, one would to find 24 successive alphas to get to a higher-order octave. I think this must be correct, but haven't tested it yet.

@danteferrari8032 Ай бұрын

love ur channel

@stephenweigel Ай бұрын

Great starter video on this! I see my 31-TET circle of fifths made it in :) also, using a six-way symmetrical shape for triple sharp? That’s so much more elegant looking than an X with another sharp next to it. Where did you find that? With the flats you can just keep piling them on so it looks better ofc

@Jinkaza1882 Ай бұрын

The music related topic I know I should know more about.

@sr-kt9ml Ай бұрын

i love this discussion. I bought a microtonal guitar with adjustable fretlets to experiment with different tuning systems :). You'd be amazing how out of tune a guitar is

@RachManJohn Ай бұрын

I listen to far too much Haas to be flustered by anything this video throws at me. Great, if basic, explaination!

@dreadmirror985 24 күн бұрын

Good for you.

@gonzoengineering4894 Ай бұрын

Interesting thing about the 3 limit: that B#, when played over an A is only one measley cent sharp of the 5 limit minor third. 2 cents is often considered the practical limit of tuning precision. This may well be how our composing ancestors began to dip their toes into the 5 limit, but that's pure speculation on my end

@karawethan Ай бұрын

I think the 5-limit emerged quite naturally in the context of (ostensibly 3-limit) vocal polyphony. I also think people were tending toward 5-limit tuning long before it was acknowledged in the literature that informs our narrative about the "evolution" of Western music. The mathematical coincidence that you can closely approximate 5-limit intervals by stacking enough pure 3:2s is integral to the theory (if not always the practice) of Turkish classical music, which divides the octave into 53 commas.

@dansynth8408 Ай бұрын

tuning a piano to ET is pretty interesting....look up 4:2 and a 6:3 octaves, and stretch tuning

@whatever19735 Ай бұрын

What math and other concepts would i need to understand before learning about tuning systems?

@laurencefinston7036 Ай бұрын

Not very much. Basic arithmetic, fractions, roots, exponents and high school algebra should do it. I recommend the book "Horns, Strings and Harmony" by Arthur Benade for starters. It's published by Dover Books and is in print. The basic idea of equal temperament can be explained as follows: Say you have a string of a given length L that has a frequency F and you want to find the lengths of the strings you would need for the next notes in the chromatic scale. The length of the second string would be L divided by the 12th root of 2. The twelfth root of 2 is approximately equal to 1.05946. Let A = the twelfth root of 2 and L_2 be L/A. Then, the length of the third string will be L_3 = L_2/A, i.e., the length of the second string divided by the 12th root of two. If you do this 12 times, you get a length exactly half of the length of the first string and the pitch is the octave. If you want quarter-tones, you have to use the 24th root of two and perform the division 24 times to get to the octave. The resulting values approximate the values of the harmonic series, while the proportion of subsequent values remains constant. That is, the lengths don't decrease linearly, but the ratio of adjacent lengths remains constant. The rest is details. And, of course, equal temperament is just one of many tuning systems. It's important because it's the one in universal use in Western music (though not my favorite).

@TollsterMensch Ай бұрын

02:05 shouldn't that be "B#7" in the top left since B#7 would be the closest to C8? Or am I getting something wrong here?

@ClassicalNerd Ай бұрын

I've always thought the numerical notation assumes enharmonic equivalency (and the software I used to double-check the numbers agreed). But I can see the argument to the contrary, too.

@TollsterMensch Ай бұрын

@@ClassicalNerd Ah I see! As an electronic musician I'm probably just too piano roll brained x) Great video also!

@ThatOneGuyRAR Ай бұрын

No intro 🥺

@KirkWaiblinger Ай бұрын

4 is a funny-looking prime number 😅

@KirkWaiblinger Ай бұрын

Solid video though

@robhogg68 29 күн бұрын

Saying it's impossible to have a keyboard perfectly in tune is privileging a mathematical abstraction over actual musical practice. There are many tuning systems across the world, and a keyboard tuned to 12-tone equal temperament is in tune according to that system. This ideal of "purity" is a flawed goal, IMO. Distilled water is nice and pure, but bland... it's the impurities which give mineral waters (or tea, coffee, beer, ...) their flavours.

@laurencefinston7036 25 күн бұрын

I think if you tested this, you would probably find, like most people, that pure intervals sound better. Pure intervals aren't just a mathematical abstraction, they are a physical phenomenon. The math is used to explain why people prefer certain intervals. Of course, it is an abstraction, because there are complications when using real instruments due to the physical properties of real materials such as wood, wire, brass, etc. The whole point of equal-tempered tuning is to make all of the intervals in a semitone tuning except for the octave a little out of tune in order to make all of the intervals usable in the same piece of music. It's a trade-off.

@robhogg68 25 күн бұрын

@@laurencefinston7036 I'm not so sure. I just searched for "empirical study preference pure intonation vs equal temperament" in Google, and this is from the abstract of the first result: "Results of the study revealed an overall preference for equal temperament in contradiction to coincidence theory. Several additional areas for research are suggested to further investigate the results of this study." That's from a 2008 PhD thesis: "COINCIDENCE THEORY: SEEKING A PERCEPTUAL PREFERENCE FOR JUST INTONATION, EQUAL TEMPERAMENT, AND PYTHAGOREAN INTONATION IN EXCERPTS FOR WIND INSTRUMENTS " by Derle Ray Long. I think, generally, people prefer what they're familiar with, which in much of Europe and the Americas is 12TET.