Pitagoras Pitch

I briefly mentioned "Pythagorean intervals"（pitagoras pitch） in the previous Yuzunote. I would like to look into this theme a little further.

Pythagorean intervals(pitagoras pitch) are tuned by taking perfect fifths ascending and descending based on "la". Melodies sound beautiful by this tuning. The sharp notes sound a touch higher and the flat notes sound a touch lower. There is also a tone (like Ces) which is better to take as low as minus 20, almost reaching the next halftone. （this scale of saying min20 means ,if you devide half tone in 20 ）In practice, we tune with these notes on open strings, which are, in the case of the violin, G, D, E, A. And of course you have to take a consequences that you play a harmonie like major 3rd ,then you have to adjust on that matter ,not on Pitagoras pitch

Just intonation is another tuning system in which the scale is constituted by tones which belong to the natural harmonics series only, and harmonies sound beautiful. The key is how to take the third note.

Equal temperament is the way to tune keyboard instruments as a compromise of the above methods in order to overcome a problem, which is that with the above methods, music may sound good in one key but not in another. As it is called "the same note with different names", ces becomes h and fes becomes e. The great Bach produced 48 superb preludes and fugues for equal temperament, which has existed since the baroque period and is the tuning system for the piano today. However, I have heard a different interpretation, that the original "tempere" means adjusting the temperature of a room, or soothing, so "temperament" is a mistranslation. I think this sounds persuasive, too.

I also feel that there are pianists who are good at intervals and those who are not, when I perform with them. Why does this happen? Why do some sound harmonious and some donﾕt, when they hit the same keys? This is due to characteristics of tones and the balance among strong and weak sounds. Good harmony is created with a third tone that is a bit weak.

The intervals are different in a subtle way in each case, such as playing solo without piano, playing with piano, playing chamber music with string instruments only, and playing with an orchestra. Recently I have heard that the guitar is tuned with perfect 4th and major 3rd, which makes it difficult to play with other instruments like the violin. Perfect 4th and major 3rd is exactly what I use when I teach the scale of major 3rd harmony.

I often talk about "tuning to bass notes". The ways to take the pitch of a note to bass notes are different depending on whether a melody is ascending or descending. When a melody is descending, if one plays a semitone strangely higher, the melody does not sound smooth.

There could be infinite observations.
Which method can one judge as correct? What are comfortable intervals?
For the time being, as I stated above, Pythagorean intervals are good for melodies, just intonation is good for harmonies, and equal temperament is for playing with piano. In marginal cases, which to use when is ultimately up to individual taste and preference.

When one says "technique", it implies an element of "being capable of taking perfect intervals". That is because it is an easily recognizable barometer that a player is no good when he or she plays out of tune. However, not playing out of tune is not necessarily playing at the right intervals.

I am always concerned with intervals. A conclusion I have reached after various searches is that good intervals mean the music flows fluently. When one plays music in a detailed and subtle manner, music appears all the more natural as if no particular technique is applied. It might be similar to the fact that smooth animation is only possible by so many detailed pieces of pictures. When I think that way I feel relaxed. I myself can be music itself.
"Music" comes out naturally.