Posted on 07/02/2022 8:59:09 PM PDT by nickcarraway
and all the kids in his class called him A square, which pissed him off cause he was more into triangles.
then they would chant B square
finally C you square
or at least that is what I was told once
I tried to follow this distinction beteen notes which are chromatically they same yet differnt but I just couldn’t. it was all greek to me.
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Lack of commas is a grammar crime resulting in a long sentence.
One of his students was the important but often overlooked Treble Clef.
I used a Commodore 64 to tune my musical instruments when I was a kid. I had learned the basics about how one note an octave higher than a second note had twice the frequency. So I calculated the frequency of each note in between to be 1/12th the difference in a logarithmic scale and ruined my sense of pitch. No-one taught me about the comma or any of the finer details of scales.
Imagine the Pythagorean tuning system as a spiral and the 12 tone Equal Tempered tuning as a circle. With the former you can never arrive back at your starting point by stacking consecutive fifths. With the latter each 5th has been flattened a little allowing you to arrive back at your starting point. This great adjustment allowed music to be transposed to all keys and made all keys usable
“I tried to follow this distinction beteen notes which are chromatically they same yet differnt but I just couldn’t. it was all greek to me.”
Pitch is like real numbers. Between 1 and 2, there are an infinite number of numbers, like 1.1 and 1.02976 etc. Between C and C#, there are an infinite number of possible pitches (you hear it when a blues singer goes a little flat on a note and it sounds good or when a guitar player “bends” a note by pushing on a string while it is vibrating).
So the pitches on a piano keyboard are particular spots on that continuous line of possible pitches that have been picked out for common use because of their versatility in different keys.
The term “well-tempered” (Bach’s The Well-Tempered Clavier is probably the most famous use of the term) is a selection of pitches for the notes in a scale so that the same instrument can play compositions in different keys and not sound stupid. Pianos are usually tuned to a well-tempered scale. The intervals between notes in a well-tempered scheme are set just so and they are a little different from note to note. There are a lot of different “well-temperment” schemes and each sounds a little tiny bit different. The Pythagorean temperament discussed in the article is one example.
However, the result of that is that different keys for compositions have a different feel as the interval between the notes changes just a little depending on what key you are in.
Get a pencil and paper, look up the ratios of the overtone series, and it will make sense.
I agree.
Intervals separated by the ratio 81:80 are considered the same note because the 12-note Western chromatic scale does not distinguish Pythagorean intervals from 5-limit intervals in its notation. Other intervals are considered commas because of the enharmonic equivalences of a tuning system. For example, in 53TET, B7♭ and A♯ are both approximated by the same interval although they are a septimal kleisma apart.
“Uh…can ya’ hum it”?——-Glen Campbell.
This thread is useless without pitchers.
People with music degrees can probably understand this much better than me. I’m a musician, I play or sing the note by the pitch apparent to me. I do understand that the math of music does not always agree with the sound of pitches that music comes from. I think the article explains the way around the inexact math of music. I don’t worry about it. When I play the piano I play the notes the tuner gave me and don’t have to think about what it would sound like in a different key. Different keys however do make the same musical piece sound different, that is mostly because of the compromises made with musical math. I play an organ that has a transposer on it. The organ uses a computer to come up with frequencies of each note and can be tuned (programmed) to different pitches. The organ is different than the piano, that is an electronic organ in that the computer recomputes notes based on the frequency of only one octave. Pipe organs on the other hand are individually tuned, each pipe in a pipe organ of perhaps thousands of pipes must be tuned to sound right with the pipes around it. Sounds like a simple task but it isn’t so simple, tuning an organ is a much more complicated task than tuning a piano.
Tuning forks used to be used to tune pianos now a little computer listens to each string and tells you when it is in tune, the better instruments even help you tune the multiple strings of a piano note slightly off of each other to make them blend without beats. Doing this takes care of the same piece played in different keys, for the most part anyway and makes it sound more natural and correct while to some very good ears may make the piano sound out of tune. It can be a real science. I’m glad I just have to play.
BTTT for the Pythagorean comma!
Having said that: I thought I was well-versed in music theory, and I did understand how Pythagoras linked mathematics and music, but I have never heard of this!
As a guitar player and luthier, I see the relationship between the ratios in frequencies and their corresponding position on the fret board. As anyone who plays the guitar would know, twelve frets is twelve semitones which is an octave. The ratio in frequencies between octaves is 1:2; interestingly enough, the twelfth fret is halfway between the nut and bridge. The fretted note at the twelfth fret should sound the same as the harmonic - one octave above the open string; that's how a guitar's intonation is checked.
In 1978 I took music theory as an elective in high school. My teacher was brilliant - played the piano, was a clarinetist in the musician's union who would accompany touring musicians, and spent his retirement building violins. He took a small group of us and taught us to tune pianos. Mind you, in those days, it was done completely by ear, so you had to be able to hear what he heard. You could have used a Conn Strobotuner, but no serious piano tuner would have ever considered using one - it was sacrilegious! We would tune middle C with a tuning fork using sympathetic vibrations. Then, we would tune the A-flat below middle C by playing the middle C, letting it ring, and then play the A-flat and listening for the C harmonic two octaves above middle C - it was in tune when you could hear eight beats a second. Using equal temperament, we tuned the octave between middle C and the C# below it, then we would tune the octaves - as we went up the keyboard, the octaves were slightly sharp, and as went down, the octaves were slightly flat. It's been over forty years and I only did it once, so some of you might know better than I, but it was an experience!
LOL. Celebrate obscurity!
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