57

Yes, you're right. As for why the harmonic series doesn't produce notes that work in all keys, the simple answer is that the math just doesn't add up. Let's work out the math for just intonation: Suppose you choose X Hz for the fundamental frequency and go from there. Then the octave above the fundamental should have frequency 2X Hz. Meanwhile, the ...


45

I think this particular phrasing is rather confusing, as it is trying to talk about two concepts at the same time: enharmonic equivalence, and intonation. The concept of intonation (and temperament, which relates to systems of intonation) deals with the fact that even given a certain reference pitch (such as A4=440), there is no one absolutely correct ...


41

The thing is that the "some tunings that define the notes in that way" in the Wikipedia quote include the most common tuning today, 12-tone equal temperament (12-TET). So, E# and F natural do usually sound the same. ...But not always. Change the tuning system and you can easily have an E# and an F natural that sound slightly different. Just intonation will ...


26

I want to make an addition to all these excellent answers. With just intonation, it's not possible to make all the chords just. Not even in a single key. Let's look at the common just major scale based on I, IV and V just major triads: C 1:1 D 9:8 E 5:4 F 4:3 G 3:2 A 5:3 B 15:8 In this scale, I, IV, V major triads (4:5:6) and iii and vi minor triads (10:...


20

Note: For the sake of discussion, I'm limiting myself here to equal temperaments, which is the most common way of tuning keyboards. Other systems exist, of course, but would probably only confuse the matter. Why do B and C and E and F not have a sharp note between them? Simply because, acoustically speaking, there is no room in our current system for ...


17

I strongly suspect that practicing singing (I know, you said you can't, but trust me on this) will be the best possible thing for you. Unlike playing an instrument, singing removes all the extraneous technical baggage that sits between your mental musical intuition and the physical production of a musical sound, so its the most direct way to train your mind ...


13

No worries. Here are some things to help you get a better understanding of where your ears are at and how your brain processes it. DISCLAIMER: I am not a physician or am I qualified to recommend specialists. First thing you should do is visit an audiologist and get some testing done so that you have a base line reference to how you perceive sound vs. what ...


13

You are right, it is because they are using very old horns known as natural horns which had no valves or holes. They had known limitations and were quite difficult to play. You can see and hear a natural horn here: Here is an excerpt from a review of the show which mentions it: However, because they were playing on ...


12

Standard tuning for solo violin in classical music is just intonation. Tune the A string and, from there, tune the other strings with just-intonated perfect fifths. Some times, as a compromise you may need to tune the violin temperate, for example when you need to play many open strings in duo/ensemble with a instrument not capable of just-intonation. ...


12

A trivial answer : yes. When I was quite young I wrote a computer program to spit out a succession of 'beeps' at random frequencies not related to any musical scale; I suspect many people who have a computer and a bit of an interest in music have done the same. In practice how close you could get to infinity (!) would be limited by the resolution at which ...


11

The top string is a little too low, so as you get to the dusty end, it's catching on the fretwire of fret 20. If that's the only problem, raising the saddle on the the string should be enough to get it sounding past fret 17. There's a faint possibility that the fretwire itself is just too high - check using a ruler - not to measure, but as a straight edge. ...


10

As per the app you were asking, Pythagorean is the temperament you're looking for. The perfect fifth is the 2:3 frequency ratio (and small rational number frequency ratios are required for the sympathetic vibrations to work). So if your A string is 440Hz, the tuning is as follows: E - 660 Hz A - 440 Hz D - 293.33 Hz G - 195.56 Hz C - 130.37 Hz If you tune ...


10

A pithy way of saying it is that intonation is the process by which a temperament is achieved. Intonation is what is done in order that the sound is produced at the desired/intended pitch. This can be done as part of instrument setup, e.g. "setting the guitar intonation", or as an integral part of performing the music, e.g. as in expressive intonation. ...


10

I suggest reading this answer first (where I derive the stuff I talk about here with some extra graphics). Western music is derived from diatonic scales, like the one created by all the white keys on piano. Not sharps and flats at all! Such diatonic scales are based on just intonation, i.e. intervals that sound good because of objective physical reasons, ...


10

Intonation in classical music is one of the things where there isn't a single, catch-all rule that you can just apply to get it “right”. Really, it's part of an interpretation. Perhaps the only thing we can say universally is that it should have a purpose. 12-edo is a good starting point. Although I often rant against the dominance of 12-edo, it can't be ...


9

First off, there is no reason to give up music just because you can’t tell pitches apart. It’s a mountain of a problem, but not impossible. Filzilla gave some very good suggestions for where to start. Here’s a few more for after you’ve gotten a baseline from the audiologist. I’ll add the suggestion of voice games. Singing has the advantage that it is very ...


9

The difference is that the nylon strings on the classical are all close to the same diameter, whereas on the steel string the diameter of the smallest string might be about 20% of the size of the diameter of the largest. This matters because the physics you have learned is simplified. Only string that have no thickness and no stiffness exactly fit the model,...


9

There are a few other types of intonation: Ptolemaic sequence - a tuning for the diatonic scale proposed by Ptolemy It is produced through a tetrachord consisting of a greater tone (9:8), lesser tone (10:9), and just diatonic semitone (16:15). C - 1:1 (0 cents) D - 9:8 (204 cents) E - 5:4 (386 cents) F - 4:3 (498 cents) G - 3:2 (702 cents) A - 5:3 (...


8

First, you both will need patience. Learning to distinguish sounds from one another is not a simple process. Imagine if you were color blind and had to reproduce the color blue after only seeing it flash in front of you for a moment. Of course, the obvious difference here is that there is little to be done for color-blind people, and hearing notes / music is ...


8

The earliest use of equal temperament was on fretted instruments with fixed frets. The ratio of 17:18 for the string length for successive frets is a good approximation to equal temperament. The errors were well within the tolerance of other intonation issues such as non-uniform gut strings, and the different amounts of string bending on different frets ...


7

Using a keyed instrument with Just Intonation creates a bunch of puzzles that need to be solved. You are either faced with observing limits on navigating from place to place, or doing "comma pumps" (equating near by intervals, or bend/vibrato between them because they are close enough). The problem isn't really Just Intonation though. It's caused by ...


7

I have often found it helpful to use mental cues to aid pitch when I'm having trouble. I have heard many choral directors, as well as my own college voice professor, talk about 'landing on top of the pitch'. This really has to do with a sort of 'musical momentum,' almost as if our pitch were an object governed by Newton's first law. When a melodic line is ...


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