Another great publication, containing all or almost all of acoustics (with a chapter dedicated to Musical Scales and temperaments), but for whose understanding a certain mastery of mathematics is still required, is: "Appunti di Acustica Musicale" by Andrea Frova, professor of Physics and lecturer of Musical Acoustics at La Sapienza, Rome.
The notes are extracted from the Book, by the same author, "Fisica nella Musica", Bologna, 1999, for Zanichelli types, ISBN 9788808090126.
This approach is however expensive (the book costs 70 Euro) and, if you don't like mathematics, burdensome.
A treatment of more than good quality - accessible to anyone, even without excessive mathematical mastery - is present in the English Edition of Wikipedia, starting from the Links:
The mathematics that made me suffer so much over the years but that has always fascinated me!!
I have never dealt with acoustics in my studies and, if I am not mistaken, it requires mathematics that I did not study well (Fourier series, Laplace transforms); anyway, I will evaluate carefully, very gladly accepting good advice. thank you and compliments on your contributions
ascending and progressive major thirds and sixths. The progression in the central section of the thirds F3-A3, A3-C#4, C#4-F4, F4-A4, with approximately 5-7-9-11 beats per second respectively. You can start already from the thirds. They are heard better. And then, perhaps, verify fourths and fifths.
Thanks a lot Paolo! Always available!
Does the rule always hold that the inversion of an ascending interval is descending with the same number of beats?
If so, can ascending major thirds be further checked with their inversion, specifically with the minor sixth which should be descending?
Yes, but almost never declining for the same number of beats. The situation is complex. For having said in a video "..for the same number of beats..." I had the other experts on me.
G
Gennarino
Reply 25 by Gennarino
It is absolutely true, if you try to be effective and reach everyone a little bit, you must simplify. (Later, over time, precision can be progressively increased).
I don't think it is therefore right for experts to suffer, as the teacher's effort is to plant a seed, not to show that they have ready-made plants; otherwise, teaching becomes impossible.
Since you are talking about pitch vibrato, allow me a question:
My father, who as you know had a splendid voice and tenor studies, taught me that there are two types of vibrato in singing: throat vibrato, produced by the uvula, and normal vibrato, produced by the movement of the diaphragm. According to classical definitions, vibrato is the variation in pitch (frequency) of a sound, while tremolo is the variation in amplitude (average sound pressure) of the same, and I believe no singer can achieve the first without the second. When you speak of a singer's pitch vibrato, what are you referring to? Let us know!
I fully agree that steadiness can be unpleasant, even though it was through one of your tips that I met musicians of the caliber of Arvo Pärt!
Besides, I think many of us like—at times—to gaze for a long time at the calm sea from the beach or to watch the very slow rising of the sun.
And let us vibrate then with the "Song in Memory of Benjamin Britten" by Arvo Pärt
More properly, it is amplitude vibrato!!! Right!!!!! But singers call it pitch vibrato. Singers often use phrases and improper expressions dictated by tradition. For example, they use the term "diaphragmatic breathing"..... when one should know that the diaphragm is a muscle that descends (as the lungs expand downwards), but does not rise. Through the contraction of the abdominals and, finally, the intercostals, the singer achieves "breath pressure". The violinist, however, simulates amplitude vibrato with pitch vibrato. Thank you for giving me the opportunity to clarify..... I hope I have been more "precise"..... and then ...on with the singers!!!!!!
Yes, but almost never flat for the same number of beats. The situation is complex. For having said in a video "..for the same number of beats..." I had the other experts on me. <THEY are right!!!!! The inversion of a flat fifth does not have the same number of beats. The fourth becomes beating for almost double. We also have to deal with the overall disharmony of the instrument or with the disharmony "in some areas" of it. I ask for forgiveness ..I stated it this way because I was giving generic notions and did not want to go into specific and complex detail. Anyway, what governs it is the progression of major thirds (progressive increase in beat speed). The ear enjoys them very much. In reality, they are sisters to the pitch vibrato that is generated (I say generated and not created!!) by the singer during vocal emission. That vibrato that the violinist seeks on a single note. "Fixity" is unpleasant. ...you decide!!! (Watch out for GENNARINO... who has already opened the cabinet of formulas.....(POOR ME!!!!!!))
Perfect Paolo! One thing is not yet clear to me (I don't want to stress you too much... a little bit of knowledge every now and then!! 🙄 :rolleyes: ):
while tuning by fourths and fifths one performs a real cycle that allows you to tune the entire octave, with thirds I don't think this is possible, so after having tuned the four thirds how do you proceed? I believe the number of beats in the thirds indicated by you is not an absolute rule but depends on the disharmony ....true?
Could it be that after creating the compartment I find myself with the last interval not quite pleasant and forced to start over by modifying the beat speed of the thirds! Correct me!
Of course. It is not that easy. Anyway, tuning by thirds is safer and more professional. Fifths suffer more from disharmony. And it is harder to listen to the speed of their beats. The progressive speed of the thirds must be respected. You should find your way. Check the fifths, fourths, and sixths.
In fact, I am tuning an old piano belonging to a friend, which had practically not been tuned for more than 20 years.
It was practically a tone flat. I am trying to bring it back little by little and after the second tuning it seems to be stabilizing, so I'm doing a favor for a friend and one for myself 😛 :P 😛 ; he doesn't know he is my guinea pig 😉
In fact, at first I couldn't hear the thirds, but now they are so clear to me... 😮 and I must say it is truly moving to hear a piano that had once unrecognizable notes because it was so out of tune, start to live again. Of course, we are talking about an almost sufficient tuning, but I am happy!!
I performed the tuning with software based on the frequency of each note, but I would like to learn how to hit the mark by ear because, in my opinion, it is the only way to have a tuned piano.
Am I asking too much?
Ps) I greatly appreciated Paolo's video, to whom all my respect goes for his availability in creating technical tutorials, and to all the participants in these very useful discussions.
Ciao Gianni
B
BackSpace
Member
Reply 31 by BackSpace
Posts
181
lorenzo wrote:
In fact, I am tuning an old piano belonging to a friend, which had practically not been tuned for more than 20 years.
It was practically a tone flat. I am trying to bring it back little by little and after the second tuning it seems to be stabilizing, so I do a favor to a friend and one to myself.
But in this case, wouldn't it be better to do the first tuning 1/2 tone higher and then, after the soundboard has settled, do a retuning?
If you are a Musician and have studied irregular groupings, you can set the metronome to 60 and think or pronounce groups of five, seven, or nine notes in one second... good exercise, right? You will begin to familiarize yourself with the beats of the FA-LA third, the LA-DO third, and so on......it is just a practical expedient, and I ask forgiveness from colleagues who invoke precise values. Learning to hear thirds saves us from the disharmony of fifths and fourths that sometimes lead us astray. In short, major thirds and sixths are, as we know, the test of a good division of beats in the central octave and more.
Dear Paolo, Even if it's a year later, I wanted to pick up the discussion to understand each other better.. I tried for the third from the F of the third octave as you wrote, after tuning the central A and bringing it down an octave, but I didn't understand if I should hear the beats by opening the F with the A or by closing it.. excuse the stupidity of the question, but I can't quite find my bearings and it's a continuous process of correcting one note rather than another because a sixth sounds good but a fourth doesn't etc.. I have entered a vicious circle! =D rather, + than a circle, it seems to me like a Dantean infernal circle =D but it excites me to enter it, and it is truly difficult to reach an acceptable result for the ear, so my dear Virgil, if you could indicate the right path or even a small path, I would be humbly grateful.. =D
Perhaps it is easier to listen to it than to "explain it." One risks entering into a minute, "goody-two-shoes" disquisition. I have read many books that teach tuning, but to be honest, I learned through a lot of practice. The fact is that we must deal, as many know, with inharmonicity. This "nasty beast" alters the level of partial sounds. Well, we also have digital tuners (even a common Tunelab) that take this into account. I, respectfully, approach these with great caution, on tiptoe. Sometimes it has happened that some friends compared one of my tunings with the "system." I must say it doesn't hold up. I believe that our ear continues to be unsurpassed in the measurement and evaluation of related frequencies. It evaluates errors, compensates for them, accepts them, and regarding even temperament—as we know well—it knows which ones to accept and which ones to reject. An ear that tunes destines its tuning to another ear. It is not certain that the first is more refined and/or expert than the second. It is a challenge. However, it is not certain that a Tunelab can satisfy the most demanding person. Sometimes even timbre or intonation can be deceptive. Rust on the strings, load on the soundboard, etc., can significantly affect the evaluation and therefore favor certain compensations that do not correspond to measurements. This is my idea expressed intuitively. What do you think?
Sorry I didn't respond anymore.. of course I would like to hear and play a piano first tuned by ear and then retuned with an electronic tuner to deeply understand the differences.. in the end I had it tuned by the tuner (who used a Yamaha electronic tuner) refining by ear and then limiting myself to correcting a few out-of-place notes and a few things slightly out of unison, but when he started tuning it he told me that the only tuned note was A at 440 =D I would say, a good disastrous start =D with time..
Most electronic tuners, in my opinion, do not measure inharmonicity very well. I have just finished preparing a Steinway B intended for a piano sound library. According to many pianists, it turned out excellent, especially and above all due to the accurate work of Simone Renzi, who handled the sound recording and editing. I started working with Tunelab... but some things weren't right. I had to correct very noticeable things by ear. It is not presumption. I couldn't find some frequencies in the mid, low-mid, and even in the cantabile range to be correct.
I take the liberty of pointing one thing out. Electronic tuners measure inharmonicity very well! The problem of inaccuracy during the tuning phase has implications that have more to do with psychoacoustic science than mathematical science. The measurement of inharmonicity is carried out by performing a Fourier transform of the signal heard from the microphone. The software then compares the actual measured harmonics with the theoretical ones, which are exact multiples of the fundamental. In this context, inharmonicity represents precisely the frequency deviation of the real harmonic from the theoretical one. A non-linear fit, performed by finding the curve resulting from the interpolation of all these points (one per harmonic), then determines the inharmonicity coefficient. It must also be said, however, that measuring inharmonicity on sections of the keyboard (one note every octave) might be mathematically insufficient, because inharmonicity does not increase/decrease constantly across the keyboard... Every note has its own inharmonicity coefficient, and this is felt in the beat counting where it becomes significant. The tuner's dissatisfaction when using this tool, besides what has been said, also lies in the fact that the frequency deviation curve is subjective (varies from individual to individual) in the low and high ranges; specifically, the ear tends to drop on high frequencies (which is why it becomes necessary to pull up the treble and super-treble sections), and tends to rise on low frequencies (which is why the tuner tends to pull down the bass section).
