- #1
Stephanus
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Dear PF forum,
Do anyone know, why music interval is always
[itex]\sqrt[12]{2}[/itex]?
Do anyone know, why music interval is always
[itex]\sqrt[12]{2}[/itex]?
Hi Mr. Greg Bernhardt,Greg Bernhardt said:Did you read through this wiki?
https://en.wikipedia.org/wiki/Interval_(music)
So this [itex]\sqrt[12]{2}[/itex] predates alphabet, much less Newton G, Avogadro constant, Planck constant, or even Hubble constant.https://en.wikipedia.org/wiki/Diatonic_scale#Prehistory
Prehistory
... There is evidence that the Sumerians and Babylonians used some version of the diatonic scale...
Not as far as I know, and besides 4! = 24. If you look at a piano keyboard, there are twelve keys between successive C keys. A note that is an octave higher (12 halftones) has twice the frequency.Stephanus said:Does 12 has something to do with 4!
4! = 24, Ahh, foolish me of course. Perhaps 12 is the smallest number that have many factor. 2,3,4,6,12.Mark44 said:Not as far as I know, and besides 4! = 24.
Of course Mark44, that goes without saying.Mark44 said:A note that is an octave higher (12 halftones) has twice the frequency.
Stephanus said:Dear PF forum,
Do anyone know, why music interval is always
[itex]\sqrt[12]{2}[/itex]?
atyy said:It's a deliberate error. An ideal perfect fifth should have a frequency ratio of 3/2 = 1.5, but if one uses [itex]\sqrt[12]{2}[/itex] the perfect fifth is 1.498.
The reason is that in Western music, modulation from one key to another...
atyy said:
But this guy can play the quarter tones!
Stephanus said:Thanks Atty for your idea.
But according to this,
http://en.wikipedia.org/wiki/Diatonic_scale#Prehistory
Prehistoric Babylonian and Sumerian also used diatonic scale. So it dates back thousands of years ago.
Stephanus said:But why do re mi fa so la si do?
Why 1 1 ½ 1 1 1 ½? (Of course there many other scale.
Minor scale: 1 ½ 1 1 ½ 1 1
Minor melodic scale: 1 ½ 1 1 1 1 ½ up, 1 1 ½ 1 1 ½ 1, down
Minor harmonic scale: 1 ½ 1 1 ½ 1+½ ½
But why? Why not just 1 1 1 1 1 1?
Although guitars have frets, unlike violins, you can still get intermediate sounds by "bending" the string. You can't do this with piano or harp.Stephanus said:Wow, that's great and odd, too. But only in violin, right. Guitar, Piano, Harp, whistle, flute can't.
Yeah, you rightMark44 said:Although guitars have frets, unlike violins, you can still get intermediate sounds by "bending" the string. You can't do this with piano or harp.
Damn, should have read your answer before I answer to Mark44.thankz said:good electric keyboards have pitch knobs on the side.
atyy said:Here is an example of a non-diatonic scale.
But Arabic music also has the Western major scale.
The word for chess in Russian is Шахматы (transliterates roughly to shakh matiy, "the shah is dead"). The Russian word comes from Persian, which is the origin of the English word "checkmate." (See http://en.wikipedia.org/wiki/Checkmate.)Stephanus said:Chess, originally from India, were introduced to western world by Arabs.
Yes, "Shah" is arabic, I think.Mark44 said:The word for chess in Russian is Шахматы (transliterates roughly to shakh matiy, "the shah is dead"). The Russian word comes from Persian, which is the origin of the English word "checkmate." (See http://en.wikipedia.org/wiki/Checkmate.)
I'm pretty sure "shah" is Persian. Shah Reza Pahlavi was the ruler of Iran before the Revolution in 1979. I'm not aware of any Arab-speaking country whose ruler was a "shah."Stephanus said:Yes, "Shah" is arabic, I think.
Stephanus said:In Indonesian language, "Shah" means King, ruler, leader.
Mat in Indonesian, "mati", is dead.
You're right. I think I'm confusing the word "shah" in my country.Mark44 said:I'm pretty sure "shah" is Persian. Shah Reza Pahlavi was the ruler of Iran before the Revolution in 1979. I'm not aware of any Arab-speaking country whose ruler was a "shah."
Stephanus said:Wow, that woman from the above video, she is great. Can sing in that tone. Must be hard practice.
"Western major scale".
Perhaps we should know that Arabic music predates Western music.
Many knowledge come from Arab World because of the crusade war.
Alchemy, chemistry, astronomy, algebra.
Even our number, except 0 (zero), come from Arab World.
1..9 come from Arab, 0 comes from Hindu.
Chess, originally from India, were introduced to western world by Arabs. (Now chess championship returns to India, Viswanathan Anand)
Stephanus said:They can't communicate, but their "music" interval is most likely ##\sqrt[12]{2}##.
atyy said:But then why 12? It's the simplest, and after that, most musicians are too inaccurate - even great ones - Menuhin was not able to play the quarter tones in the Bartok sonata accurately, so Bartok wrote him an "easier version". However, there historically been attempts to use 41 and 53, as those are the next closest.
http://en.wikipedia.org/wiki/41_equal_temperament
http://en.wikipedia.org/wiki/53_equal_temperament
DrGreg said:The point is that the 12-equal-interval scale (or equal temperament) contains within it good approximations for ratios such as 2:1 (octave), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third). These ratios sound good to the human ear because the notes share some of the same harmonics.
Not really. Music can convey some emotions, maybe, but I don't see how it could be used to convey much more than that.Stephanus said:Speaking of language.
Do you think music is a kind of language?
Twenty six Alphabets + 10 numbers covers 3 octaves in diatonic scale.Mark44 said:Not really. Music can convey some emotions, maybe, but I don't see how it could be used to convey much more than that.
Stephanus said:Continuing your list Dr. Greg
5:3 (perfect sixth, La)
9:5 (perfect sixth, Si)
But 5:3 or 9:5 the divider and modifier distance is not 1, 5:3 is 2, whereas 9:5 is 4
I don't know if this is a good cause for 12 interval
Ahh, you're right Vanadium.Vanadium 50 said:You really should read the article that Greg pointed you to.
There is no perfect sixth. There is a major sixth, and a minor sixth.
Pythagorean said:I think 12 tones (and 24) work so well because of the numerous factors you mentioned (2,3,4,6)
DrGreg said:...2:1 (octave), 3:2 (perfect fifth), 4:3 (perfect fourth), 5:4 (major third), 6:5 (minor third). These ratios sound good to the human ear because the notes share some of the same harmonics.
Music intervals are the distance or relationship between two musical pitches. They are the building blocks of melody and harmony in music.
Understanding music intervals is crucial for musicians because it helps them to accurately perform and interpret music. It also allows for improvisation and composing new music.
Music intervals are measured in half steps, which is the distance between two adjacent keys on a piano. They can also be measured in whole steps, which is equivalent to two half steps.
A major interval is a wider distance between two pitches, while a minor interval is a narrower distance. Generally, major intervals sound more uplifting and happy, while minor intervals sound more melancholic and sad.
No, each music interval has a distinct sound and feeling. For example, a perfect fifth interval has a very harmonious and stable sound, while a tritone interval has a very dissonant and tense sound.