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18

There are physical and psychoacoustics reasons behind it. A vibrating string held by its two extremities can only vibrate at certain frequencies (cycles per second, expressed in Hertz, i.e. 1/second), which relates to the characteristics of the string (e.g. its weight per unit of length, its flexibility) and how it is used (e.g. the vibrating length — which ...


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, ...


7

We first need to categorize each interval, assign it a "consonance amount". That's the first problem we find. In the case of the fourth, for example, some consider it perfect consonance, and others consider it a dissonance, depending context (and who you ask). For simplicity, let's define ours based on Wikipedia's: 1: Perfect consonances: unison, octave, ...


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

My answer is no, it isn't really possible to use a fingering technique to play an A440 recorder at A415. No professional would even try; they would instead, as Wheat noted, have a real A415 instrument or, if extremely confident and well rehearsed, transpose on-the-fly down a half-step. One can indeed bend most notes up or down quite a bit using half-holes, ...


5

If you are planning to play with piano in future, I would definitely use equal temperament. To be honest, to learn to play in tune with the widest range of other musicians, equal temperament would be most useful too. And initially, as a beginner, you are unlikely to notice the difference much, so this would be another reason to choose equal temperament. ...


5

This blog post compares the three forms of the minor seventh (with sound samples). His conclusion is that the harmonic seventh (7/4) is used as a blue note, but that it is too stable for use in a dominant seventh chord. The extra dissonance of 16/9 gives it the need to resolve that is lacking in 7/4.


5

FWIW, late organ builder and writer Stephen Bicknell, in this introductory description of temperaments mentions tuning a continuo organ to quarter-comma meantone for a performance of Monteverdi by the Taverner Choir & Consort.


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

"Are there other examples of common practice period manuscripts, or other documents that provide some indications on how to tune the instrument?" I think you're mostly looking for examples of scores/manuscripts, but as far as "other documents" go, there are certainly period treatises that describe various temperaments. One such example is "Lettre touchant ...


5

ALL notes in a JI system are a series of ratios in relation to the tonic. So what path you choose to get to any particular note is important in determining what its tuning is going to be. This means in JI a modulation is possible, but will bear little resemblance to a modulation in a tempered tuning system. The consonance of a secondary dominant is ...


4

For your specific points: 1) For most/all* instruments, the amplitude of the partials decreases as the partial number (i.e. frequency goes up). Thus, for almost all musical sounds there is "more of" the (first) octave and the fifth and less of the higher harmonics. So adding a second sound whose fundamental is at one of the lower harmonics reinforces ...


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 ...


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

I recommend equal temperament, in particular with Suszki: When you learn to play in more and more keys it will be easier because they will sound and "feel" more similar to the keys you are playing in as a beginner. If you use just temperament you will get overly attached to Keys like G, D, and A major because the violin will be more resonant due to ...


3

For a number of years I was publicity, marketing and business manager for a Baroque chamber orchestra in Atlanta, Georgia, United States of America. I have put the question of temperament and tuning for Monteverdi's Orfeo to several friends who perform with that group. If I hear back from them, I will post their answers here. I fear that I may have confused ...


3

The technical term for this practice in pianos is called stretch tuning. Read the Wikipedia article here.


3

I do not play recorder, or harpsichord, but I have friends who do, as I'm a fan of Baroque music. Let me tell you what I do know. A=440 and A=415 are exactly one half-step or 100 cents apart (relative to 12-tone equal temperament). I don't have a definitive answer, but the problem is that neither the recorder nor the harpsichord are (typically) tuned in ...


1

The standard tuning is tuning A to a reference, and tuning perfect fifths from there. That's what you need for double stops, and it's pretty standard when playing with others to avoid empty strings in slow playing, also because long notes are usually played with vibrato (actually, you can even play an empty string "with vibrato" by doing the vibrato on a ...


1

Octaves on a piano are not tuned pure. Because of inharmonicity, the higher partials of a single piano string are slightly sharper than theory would predict. Ideal harmonic series above 100Hz: 100 200 300 400 etc Actual harmonic series above 100Hz (approximation): 100 200.05 300.2 400.6 The higher the partial; the sharper the pitch. Shorter piano ...


1

You cannot tell which configuration of sharps or flats are in a given key that is being played, when the modern equal temperament is used. The spacing between all the 12 semitones is identical, and so keys do not have their own color (beyond whatever color is imparted to them by their absolute tuning). When we modulate from, say, C to C#, the frequencies of ...


1

For your further exploration: Wendy Carlos has an album called "Beauty in the Beast" with some pretty exotic temperaments realized with interesting synth timbers. She has a site at wendycarlos.com. http://www.wendycarlos.com/resources/pitch.html http://www.pandora.com/wendy-carlos/beauty-in-beast (tracks 2 and 4 are good) Harry Partch composed for some ...


1

http://www.TallKite.com/alt-tuner.html Alt-tuner is a midi effect for your DAW, very powerful. You can sweep the whole spectrum of meantone (1/3 comma, 2/7 comma, 1/4 comma, 1/5 comma, 1/11 comma = 12-ET, 0 comma = pythagorean) and you can even do this with a foot pedal as you are playing, via midi learn. It also does well-temperament, any kind. It does ...



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