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23

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 2 X Hz. Meanwhile, the ...


15

There are at least two things wrong in how your mandolin is calibrated, according to your excellent and helpful photographs. Your wooden bridge saddle needs to be replaced because it is cracked in half, between the first and second pairs of strings. You can clearly see that the bridge saddle has collapsed and caved in, downward toward the top of the ...


14

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

Alex Basson has given you a great introduction to the mathematics. Let me approach the answer from a different perspective, that of the performing musician in a historical context. Setting the mathematics aside, to put it simply, just intonation is what happens when you have a group of singers performing a capella, or a string quartet, or any other ensemble ...


11

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 ...


10

You have asked two questions. First "What is the measurement of the G-string that you should use on your Epiphone Les Paul guitar?" The correct technical term for what you call the "width" or "thickness" or "diameter" of the string is its gauge. Take your guitar to a qualified guitar technician or luthier, or at least to your local music store, and have ...


10

I would say yes, and yes. You've explained the problem pretty clearly, and explained its consequence. Choirs frequently find that they sing everything internally, consistently in-tune throughout a piece, but then at the end of the piece, they discover that they are no longer in tune with the reference pitches upon which they started the piece. The frame of ...


9

Schoenberg is talking about the difference between just intonation (which he refers to as "natural semi-tones") and 12-tone equal temperament (which he refers to as "tempered" semi-tones). This is a complicated subject. You can find several long posts about this subject on this site, or you can find a lot of references elsewhere on the Internet. The gist of ...


8

I wish to elaborate on @Tim's answer, which is correct. Actually, it was easier to discern the "color" before the modern system of 12-tone equal temperament for piano tuning. In Chopin's time and before, pianos and other keyboard instruments were tuned to one of many different systems of temperament, some of which sounded quite different in certain keys, ...


8

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 ...


7

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. ...


6

It shouldn't damage anything. However, it will make the strings slightly closer together and it may cause additional wear at the point the string goes over the saddle, since you are now causing a slight sideways angle. If you go through a few sets of strings and aren't breaking an unreasonable amount of strings because of it, you should be fine. A tiny ...


6

An article by Joe Monzo at http://tonalsoft.com/enc/s/savart.aspx defines the savart as 1/300 of an octave. A savart is calculated as the 300th root of 2, or 2(1/300), with a ratio of approximately 1:1.002313162. It is an irrational number. A savart has an interval size of approximately 4 cents. savart = 1000log10(f2/f1) cents = 1200log2(f2/f1)


6

If it's an exceedingly low-quality product, it could just be that the fretboard is badly designed enough that the notes are just not in the right place, but realistically, all guitars exhibit tuning issues with fretted notes. Equal temperament is a compromise to begin with, and the guitar itself even more so. Assuming it's not actually a manufacturing ...


6

Yes string length does affect intonation and so does a proper set up with regard to neck, bridge, string guage, and action. Before going into any Bigsby enhancements lets review the key differences between a Gibson Tune-o-matic bridge vs. a Wraparound bridge. The Tune-o-matic allows for fine tuning the intonation, while the standard Wraparound has fixed ...


5

Probably before temperate tuning, where each note is the same distance from the next, it would have been possible to discern - maybe because an instrument could sound in tune in one key, but not in a different key ! Please look at Wheat's answer for enlightenment on tuning. Someone who has absolute ('perfect') pitch will be able to tell, because they ...


5

Now that you've explained that your tuning is G-D-D-F-G#-B, I understand why you have problems with intonation, and problems with some strings being too high over the nut or bridge. From your earlier comment, do you mean to say that your local guitar store selected six individual strings for you based on those pitches in your tuning? Or did they sell you a ...


4

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 ...


4

Get the heaviest gauge strings that you can handle, don't worry about the material properties of the strings. The string tension itself is the primary variable affecting unintentional bending. Obviously, using heavier gauge strings results in higher tension (for a given tuning) Note that longer scale length (e.g. 25.5") will also have higher string tension ...


4

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 440 Hz, the tuning is as follows: E 660Hz A 440Hz D 293.33Hz G 195.56Hz If you tune by ear from A, your ...


4

First of all, Pythagorean (PT), Just Intonation (JT) and Equal Temperament (ET) are different (families of) tunings. Therefore, note frequencies will be different in each case. You can find frequency charts for them on Wikipedia. For any tuning, you need a reference frequency. Currently, 440 Hz for A above middle C is the most widely used standard. But ...


4

For a classical orchestra the priority is, to be in tune with your voice group e. g. first violins. A voice group consists of same instruments, so no problem, they play as you've been teached. The instruments with discrete tuning are only a few (piano, celesta, marimbaphone, xylophone, organ come to my mind) and these are unlikely to have prominent sustained ...


3

You are working with a violin. It has four strings tuned in perfect fifths. Intonation on a violin, which has no frets, is something that you produce with your fingers, not with an electronic measuring device like your tuner. You can produce any kind of intonation or temperament on a violin that you can train your ears and fingers to recognize. You are not ...


3

Another factor is the frets on the guitar. Tall "jumbo" frets have more clearance between the top surface of the fret and the fingerboard. If you press down hard when you fret the string, the pitch might be pulled sharp. Tall frets have been popular on guitars for the last thirty years or so; "vintage" electric guitars tended to have small frets that are not ...


3

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 ...


3

I have come across an even more astonishing system for producing pure intervals on a guitar. A Turkish guitarist, Tolgahan Çoğulu, has patented a system for building a guitar that has channels under each string position that allows the quick installation or removal of any number of tiny partial frets, each one string-space wide, which can be adjusted up or ...


3

A relatively new company in Sweden, True Temperament, retrofits electric, acoustic and classical guitars with new necks or fingerboards with heavily modified fret positions that are designed to improve intonation. If I understand their intent, their "Thidell" design is for playing with something closer to pure intervals, but chiefly in the most common ...


3

Here is a table that I have adapted from one in Wikipedia that illustrates how just intonation differs from 12-tone equal temperament. In modern instrument tuning, an octave is divided into 1200 cents. There are 100 cents in an equal-tempered half-step, and all half-steps are equal in their distance apart. However, in just intonation, not all half-steps ...


3

Okay, I've been working a while with many different fields of music... I certainly wouldn't say that vocals are my specialty; however, rather than doing what every other answer suggests (having you use a program that "trains" your intonation to become more in tune), I think it'd be a lot more effective and genuine if you were to just simply work on the ...


3

Assuming A = 440 Hz, the octave starting on Middle C has the frequencies (in Hz): C♭ = 244.1687412149232 C = 260.74074074074076 (B♯3 = 264.298095703125) D♭ = 274.6898338667886 C♯ = 278.4375 D = 293.3333333333333 E♭ = 309.02606310013715 D♯ = 313.2421875 F♭ = 325.5583216198976 E = 330.0 F = 347.65432098765433 E♯ = 352.3974609375 G♭ = 366.2531118223848 F♯ = ...



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