Hmmm. The reason for going up in pitch is not to make it sound brighter. Else you could just go up half a note. The reason is,that when tuning a string with lower tension, when you strike it, it will start with high pitch and end with low pitch, cause the tension significantly changes by striking it. This is the characteristic honky tonk tone. If you make it with a little more tension, the increased tension doesnt matter so much anymore. Thus less honky tonk effect. Modern materials can withstand more tension than older pianos, as older pianos where made out of wood. Modern ones have a steel core. Thats why we now can increase the pitch while maintaining the thickness of a string.
The problem with 12 Pythagorean fifths not coming out the same as 7 octaves is just this: a Pythagorean fifth is a pitch ratio of 3/2, and (3/2)^12 is not equal to 2^7. (3/2)^12 is approximately 129.746338, while 2^7 is exactly 128. The failure to be equal is by about 1.364%, easily heard by typical human hearing. It seems clear that the 7 octaves must be maintained, so it is the fifth that has to be tweaked.
Yes! It is however not clear that the octave has to be preserved. This is only clear for instruments like a piano, that have a wide range. Also it is clear, if you want to play together with other instruments,which might play at other octaves. However if you stick to one or two octaves Pythagorean tuning might sound bether especially together with a singer, that might automatically stick more to pythagorean than to Well tempered. So yes in most cases this is clear, but not all of them.
I've got idea how I found this video or what you were talking about but thankyou because I will now study this topic. Just changed my guitar tuning to 432 and will tinker and investigate other frequencies. Very interesting.
Octave to octave, in just tuning, is off by +24 cents. Hence the slightly sharper sound of each ascended (higher) octave, 8ov. This sharperness also becomes more pronounced from octave to sequentially higher octaves, e.g., 16ov, 24ov, etc. Also note, moving from octave to lower octave will produce a slight flatness, this is because the +24 cents is "pushing" the octave to lower octave tone "down." To overcome this you subtract 2 cents from the tuning of one chromatic tone to the next, this will establish tempered tuning from octave to octave. The reason this happens is because we think of an octave as a circle, but it is actually a spiral from octave to octave. The "extra" 24 cents occurs because of the additional "height" of sound, not just the "distance", from one octave to the next in a spiral. I hope this is understandable and illuminating. If not, there is a video called "music theory is witchcraft" that has some visuals to help understand this concept.
9:25 its well explained. Very well explained. There is a ton of music theory. We know exactly how sound works, and how ears work. The only thing that is subjective is, how much dissonance is accepted by a human. This is the only discrepancy here. However this has more to do about being used to something/a personal opinion, than a mystery of the universe.
@@pr44pr44 No thats just human brain. Comes from genetics and experiences. It may not be easy to predict, but it is not a mystery. If you listen to a lot of atonal music, and know the music theory behind it,you might start liking it more and more.
Hitting those weird sounding intervals reminded me of some Terry Riley stuff :) like The Harp Of New Albion, good good stuff, but idk if that's your thing. Or Lou Harrisson piano concerto with javanese gamelan. When i first heard those weird tuned instruments i felt like i had been missing out for a while 😅
He said they have been raising the tunings throughout the past decade. No. They raised the tuning 125 years ago to 440hz and it has not been raised since
Somewhere around the 3 minute mark you say that the C note isn't the same (as the double up) after going through the circle of fifths. I thought that well tempered all notes are imperfect intervals. Is that what you were trying to get at?
It's not mysterious. It's how the math works out. You keep saying you're not quite clear about things. Why not learn about it. It has nothing to do with a mystery in the cosmos.
This well-produced video is a very digestible introduction to the subject: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-nK2jYk37Rlg.htmlsi=TADckD8NOpoSIL9d
@@Paul-talk As you correctly noted, an octave of a given tone is double that tone's frequency. The interval between the octave and the starting tone can thus be expressed as the ratio 2:1. Now, a perfect fifth can be expressed as the ratio 3:2 between the fifth and the starting tone. We simply need to check if the number we get by multiplying by this 3:2 ratio 12 times is identical to the number we get by multiplying by 2:1 (or simply by 2) a certain number of times. What we'll find is that the number we get from (3:2)^12 is around ~129.74633... The closest we can get by just multiplying by 2 seven times is 128 (2^7). The small discrepancy between the two numbers amounts to about the fourth of a regular piano semitone. It is called the Pythagorean comma. Western alphabetic notation is designed to keep track of the perfect fifths and it implies the derivation of all notes from perfect fifths, so it can help us see what's going on here. Bear in mind that the alphabetic notation starts at A and stops at G, looping around afterwards (ABCDEFGABCDEFG...). Say we start from the note C and go twelve fifths up. Since the fifth of a note, as the name itself implies, always needs to be the fifth letter from said note (counting the note itself), the fifth of C will be C-D-E-F-G. If we do this twelve times, this is the sequence of notes we get: C G D A E B F# C# G# D# A# E# B# Instead of closing the circle back at C, we've arrived at a new note: B#. In the modern piano tuning, these would be represented by the same key and sound the same, but this is because the fifths of the piano are tuned slightly narrow of perfect, so that the circle closes. A pure octave of C can never be reached using actual perfect fifths, because no power of 3 (the number which we use to get fifths) equals any power of 2 (octaves).
@@Paul-talkI sometimes have nightmares about being surrounded by guitars facing me and being constantly plucked and tightened over and over until they burst violently. It’s hucking forrible.
Well it could be harder to play because the strings are tighter. The same happens if you choose hard tension strings as opposed to lower tension ones, but tune them the same at 440. You won't be able to fret them as easily. It hurts more. You can't bend notes as easily. I admit the tone can sound nicer, but that depends on all sorts of other things, the particular guitar, the age of the strings, their natural tension, your plucking/strumming technique, etc. In some circumstances, it can sound dull, and you can also get more unwanted rattles on the frets. And this idea that they've been constantly ramping up the tuning over several decades to compete, and it's going to continue until it's a screech, is just plain wrong. No-one is planning to increase it. It's a universal standard. There's a pseudo-scientific woo-woo fad at the moment about a special Earth-resonant tuning. Like Gurdieff, it's garbage. :)
