To me the Pythagorean one sounds the best. Although, it is not a wolf fifth between the F# and C#, there are no wolf fifths in Pythagorean tuning, there are only diminished sixths and doubly augmented fourths. So you are having that interval be a Gb to C# (a doubly augmented fourth) or F# to Db (a diminished sixth). There are several very interesting layouts to get perfect true intonation (pythagorean) on a keyboard but sadly there is both a lack of will and a lack of awareness in people that it is what it is true and just intonation and is worth the time, effort, and money to seek it out. You need at least 24 notes per octave to be able to play perfectly in tune in any key in Pythagorean just intonaiton, and then have pedals to shift those 24 notes accordingly as one goes up or down the chain of fifths in modulations, but there is no where you can't modulate in that system, and it can be perfectly in tune, even on acoustic instruments. Unfortunately this knowledge is either not known or has been kept from people and instead they are told that five limit (or higher) is just intonaiton and it is impractical so just stick to 12 tet and if that is not enough try 31 tet. It is all very bad. People keep repeating the mantra "Pythagorean major thirds are too high". This is plainly not false. They are not only good and usable but IDEAL. I could not accept this notion at first because of some examples that had been cherry picked or contrived to make Pythagorean tuning look and sound bad, but it is not true. Look on my channel. All the music there (except some in the comparison videos) are all in Pythagorean just, or true intonation. Its all perfectly in tune sounding, ideal (excluding perhaps the one with honey in the thumbnail, that was an experiment with a stretched octave which while interesting is not best. I like now that with computers we can test and hear exact mathmatical conepts with music and tuning, but there is an unhealthy obsession with electronic music and instruments. There must be innovations in acoustic music instruments for playing in tune. But that cannot happen until people start to develope the right concepts behind what is just intonaiton and what is not. If one thinks that 5 limit or higher is ideal, then they will be forever stuck in 12 and 31 tet or worse. This is because the 5/4 is not a major third, but rather merely the fifth harmonic, important in timbre, yes, but not for tuning fundamental pitches to in a musical system of pitch classes. The 5/4 above C is not E, the 5/4 above C is a type of C, not an E, its a timbral note outside the key. A major third above C is derived from a chain of fifths, specifically up four fifths and down two octaves. It is an imperfect consonance, the 81/64, not a perfect consonance as the 5/4 interval would be. The major third is a stable consonance but with some active harmonic beating, that is, the beating frequency is harmonically related to the lower note in the major third, it is not unrelated as is the case with the beating in the 12 tet major third. Not all beating is bad, and less beating does not mean in tune or more in tune. And while there are people who believe this in the world, I am the only one being vocal about it at the moment (to my knowledge). God has music in a way where it can be played in tune, but somewhere along the way man started thinking the major third was the 5/4 which both sounds out of tune in a real musical context, and cannot form a functional system of harmony and melodic pitch classes. People with resources such as yourself would do well to take the knowledge shared here and act accordingly, your music would greatly benefit. Only thing to be mindful of is this: note spellings. If one misspelles notes in Pythagorean tuning, your music will be out of tune. Always consider the tonal FUNCTION of any note or chord in reation to the current tonic chord when speling and tuning notes. As you can hear in the example in your video, this "wolf fifth" sounds bad, it should be spelled and tuned as a perfect fifth either Gb to Db OR F# to C# if the music is calling for a perfect fifth interval. If you are going to have a diminished sixth interval, make sure it is harmonically and melodically justified. This is a more obvious example, but in places in music where the tonic chord is slightly more ambiguous, note spellings can be even more difficult to get right. But the vast majority of time, spelling things according to common practice results in music that is perfectly in tune.
@@RememberGodHolyBible thank you for the correction about the terminology for the Pythagorean fifths. I agree that the Pythagorean third is not too high, but I do think that choice of third depends on musical ideals and goals and context. I personally prefer the just third to the Pythagorean, but having both is even better
@@RememberGodHolyBible I also don't think beating is bad. I also use generally acoustic instruments and there are many ways to play in 5-limit or higher that sounds great. I don't disagree with your points about Pythagorean basis, it is an excellent system that can be developed and continuously expanded. However, there are many ways of developing coherent musical systems based on various limits and interpretations, beating isn't bad, nor is lack of beating, 81/64 is a great third, so is 5/4, so is 400c, it depends entirely on the type of music you want to create
@@noahjordan1066 If one has both the 5/4 and the 81/64 as major thirds, then one cannot claim just intonation. Just intonation implies that every interval has a specific ratio and frequency that is just or right. To have multiple options for major thirds would then be a form of 5 limit rational intonation, for just intonation it really must be one option. The issue as I see it, is that people have confused the diminished fourth with the major third, and then started lusting after a system which not only sounds very out of tune, but is incoherent and unwieldly in the amount of notes needed to have a modulating system of pitches. As a result people have covered themselves in various equal temperaments and other prime number rational intonation scales, none of which are perfect by their own admission, so people bounce from one tuning system to another never being satistifed with any and never fully devoting themselves to one and always seeking that next tuning and nxt scale which "shows promise" only for the process to repeat again. The miccrotonal's darling right now is 31 edo, but no one that I have ever heard of has stated that 31 edo is just intonation. They don't claim meantone is. And they do not know of layouts that can make higher edos practical, and even they are not just, and it is all because people use this term just intonation and do not even know what is just. Some have discovered this, that the term just intonation is meaningless, and to them it is, because they are lost in the weeds because of the 5/4, it is really the main reason all the music in the world is out of tune, because people wish to hold onto the 5/4 as a major third. And I must say, the 5/4 is also not a Pythagorean diminished fourth. Even thoughh the two intervals are less than 2 cents different from one another, there is one very large quality about them makes them quite different to the ear. The diminished fourth is undertonal in nature, and the 5/4 is overtonal, and the ear can hear this quality. And yes, you can in some contexts fool the ear into hearing them as the same, but with testing in real music comparing one with the other, they are different, but neither are a major third. There are many tunings and rational intoantion schemes which can be interesting and beautiful at times in certain pieces. But true intonatoin, Pythagorean just intonatoin, is clean and clear and true to how we naturally hear music and intervals and is profoundly versatile in what it is able to express in terms of musical style. No other tuning has the coherence of true intonation. And it is not only coherent, but it can also be mapped onto fixed pitched instruments like harps and keyboards. This has not happened though because people are lost in the weeds of EDO's and the 5/4. There is so much yet to be discovered in true intonation and much of it has been under our noses, because all standard music notation is notating Pythagorean just intonation, yet we have never heard what is written, let alone all the things which could be written, taking advantage of double, triple quadruple sharps and flats, and taking advantage of enharmonic inequivalence in melody and harmony. There is a piece on my channel called The Last Words of David, I did not write this piece but merely entered it into MuseScore and tuned it. But the composer, being in the world of 12 tet misspelled half of the notes in the song, the entire second half of the piece is misspeleld. So in my version I spelled (and tuned) every note correctly according to common practice. The piece starts in E minor terrritory and ends in G major, in the original score but in my version, the sheet music is on screen, the piece modulate up and up and ends in Fx major, a comma higher than G. And when you understand what the words of the song are about, who said them and what he was speaking of, suddenly the correct spelling makes all the more sense and the music is quite powerful. The music does not sound weird or alien, it sounds perfectly normal, but perfectly in tune as it modulates up and up. 5 limit 7 limit and higher rational intonations cannot be mapped to a keyboard with a meaningful number of notes, in a layout that is functional and intuitive and ergonomic. And with a harp, forget it. But with Pythagorean just intonation you can do it on keyboards and to a large degree on harps as well. The end of lusting after 5 and 7 limit and higher , if one keeps following after that, is merging with machines and AI, everythiing being computerized, or if you stop before then, you have edos which are out of tune from your ideal, or you can only play in 2 or three keys per instrument. The 17 note vicinity that exists for every tonic chord, understanding functional harmony, and testing the boundaries of that. There is so much to be explored that is simply untouched by man because people have all sorts of wrong ideas about tuning, and the most damaging of them all is the notion of 5/4 being a pitch class of its own and also being the major third. I get it, that warm buzz of the major chord with the 5/4 as the third, I get the appeal, I advocated for it for ten years. But it just does not work coherently in music when put to the test, the system is revealed to be incoherent and out of tune compared with true intonation. I have found that letting go of the 5/4 as a pitch class has opened up a whole new world of music to me and one with much profound depth. I find myself frustrated that others are still caught where I was, seeking after the 5/4 or thinking it is at least an option of major third, which keeps one bouncing around in all sorts of tunings that are not solidly coherent.
@@RememberGodHolyBible I suggest you try some acoustic works, I do not agree that Pythagorean intonation sounds better than 5 or 7 limit just intonation. I think extended Pythagorean notation is great, but I personally dont like the sound of a Pythagorean triad. Those who like 5 limit harmony are not lost in the weeds, those who are lost in the weeds are those who claim that there is a best tuning. We each tune to how we hear and how we express. 5 limit harmony is obviously not why the whole world is out of tune, much of the world does not use 5 limit harmony. Please make some acoustic music outline your ideas, because midi compositions played by your computer are really not convincing either. I respect your decision for how you want to tune, but you needn't proselytize to me.
To me the Pythagorean one sounds the best. Although, it is not a wolf fifth between the F# and C#, there are no wolf fifths in Pythagorean tuning, there are only diminished sixths and doubly augmented fourths. So you are having that interval be a Gb to C# (a doubly augmented fourth) or F# to Db (a diminished sixth). There are several very interesting layouts to get perfect true intonation (pythagorean) on a keyboard but sadly there is both a lack of will and a lack of awareness in people that it is what it is true and just intonation and is worth the time, effort, and money to seek it out. You need at least 24 notes per octave to be able to play perfectly in tune in any key in Pythagorean just intonaiton, and then have pedals to shift those 24 notes accordingly as one goes up or down the chain of fifths in modulations, but there is no where you can't modulate in that system, and it can be perfectly in tune, even on acoustic instruments. Unfortunately this knowledge is either not known or has been kept from people and instead they are told that five limit (or higher) is just intonaiton and it is impractical so just stick to 12 tet and if that is not enough try 31 tet. It is all very bad. People keep repeating the mantra "Pythagorean major thirds are too high". This is plainly not false. They are not only good and usable but IDEAL. I could not accept this notion at first because of some examples that had been cherry picked or contrived to make Pythagorean tuning look and sound bad, but it is not true. Look on my channel. All the music there (except some in the comparison videos) are all in Pythagorean just, or true intonation. Its all perfectly in tune sounding, ideal (excluding perhaps the one with honey in the thumbnail, that was an experiment with a stretched octave which while interesting is not best.
I like now that with computers we can test and hear exact mathmatical conepts with music and tuning, but there is an unhealthy obsession with electronic music and instruments. There must be innovations in acoustic music instruments for playing in tune. But that cannot happen until people start to develope the right concepts behind what is just intonaiton and what is not. If one thinks that 5 limit or higher is ideal, then they will be forever stuck in 12 and 31 tet or worse. This is because the 5/4 is not a major third, but rather merely the fifth harmonic, important in timbre, yes, but not for tuning fundamental pitches to in a musical system of pitch classes. The 5/4 above C is not E, the 5/4 above C is a type of C, not an E, its a timbral note outside the key. A major third above C is derived from a chain of fifths, specifically up four fifths and down two octaves. It is an imperfect consonance, the 81/64, not a perfect consonance as the 5/4 interval would be. The major third is a stable consonance but with some active harmonic beating, that is, the beating frequency is harmonically related to the lower note in the major third, it is not unrelated as is the case with the beating in the 12 tet major third. Not all beating is bad, and less beating does not mean in tune or more in tune. And while there are people who believe this in the world, I am the only one being vocal about it at the moment (to my knowledge).
God has music in a way where it can be played in tune, but somewhere along the way man started thinking the major third was the 5/4 which both sounds out of tune in a real musical context, and cannot form a functional system of harmony and melodic pitch classes. People with resources such as yourself would do well to take the knowledge shared here and act accordingly, your music would greatly benefit. Only thing to be mindful of is this: note spellings. If one misspelles notes in Pythagorean tuning, your music will be out of tune. Always consider the tonal FUNCTION of any note or chord in reation to the current tonic chord when speling and tuning notes. As you can hear in the example in your video, this "wolf fifth" sounds bad, it should be spelled and tuned as a perfect fifth either Gb to Db OR F# to C# if the music is calling for a perfect fifth interval. If you are going to have a diminished sixth interval, make sure it is harmonically and melodically justified. This is a more obvious example, but in places in music where the tonic chord is slightly more ambiguous, note spellings can be even more difficult to get right. But the vast majority of time, spelling things according to common practice results in music that is perfectly in tune.
@@RememberGodHolyBible thank you for the correction about the terminology for the Pythagorean fifths. I agree that the Pythagorean third is not too high, but I do think that choice of third depends on musical ideals and goals and context. I personally prefer the just third to the Pythagorean, but having both is even better
@@RememberGodHolyBible I also don't think beating is bad. I also use generally acoustic instruments and there are many ways to play in 5-limit or higher that sounds great.
I don't disagree with your points about Pythagorean basis, it is an excellent system that can be developed and continuously expanded. However, there are many ways of developing coherent musical systems based on various limits and interpretations, beating isn't bad, nor is lack of beating, 81/64 is a great third, so is 5/4, so is 400c, it depends entirely on the type of music you want to create
@@noahjordan1066 If one has both the 5/4 and the 81/64 as major thirds, then one cannot claim just intonation. Just intonation implies that every interval has a specific ratio and frequency that is just or right. To have multiple options for major thirds would then be a form of 5 limit rational intonation, for just intonation it really must be one option.
The issue as I see it, is that people have confused the diminished fourth with the major third, and then started lusting after a system which not only sounds very out of tune, but is incoherent and unwieldly in the amount of notes needed to have a modulating system of pitches. As a result people have covered themselves in various equal temperaments and other prime number rational intonation scales, none of which are perfect by their own admission, so people bounce from one tuning system to another never being satistifed with any and never fully devoting themselves to one and always seeking that next tuning and nxt scale which "shows promise" only for the process to repeat again.
The miccrotonal's darling right now is 31 edo, but no one that I have ever heard of has stated that 31 edo is just intonation. They don't claim meantone is. And they do not know of layouts that can make higher edos practical, and even they are not just, and it is all because people use this term just intonation and do not even know what is just. Some have discovered this, that the term just intonation is meaningless, and to them it is, because they are lost in the weeds because of the 5/4, it is really the main reason all the music in the world is out of tune, because people wish to hold onto the 5/4 as a major third. And I must say, the 5/4 is also not a Pythagorean diminished fourth. Even thoughh the two intervals are less than 2 cents different from one another, there is one very large quality about them makes them quite different to the ear. The diminished fourth is undertonal in nature, and the 5/4 is overtonal, and the ear can hear this quality. And yes, you can in some contexts fool the ear into hearing them as the same, but with testing in real music comparing one with the other, they are different, but neither are a major third.
There are many tunings and rational intoantion schemes which can be interesting and beautiful at times in certain pieces. But true intonatoin, Pythagorean just intonatoin, is clean and clear and true to how we naturally hear music and intervals and is profoundly versatile in what it is able to express in terms of musical style. No other tuning has the coherence of true intonation. And it is not only coherent, but it can also be mapped onto fixed pitched instruments like harps and keyboards. This has not happened though because people are lost in the weeds of EDO's and the 5/4.
There is so much yet to be discovered in true intonation and much of it has been under our noses, because all standard music notation is notating Pythagorean just intonation, yet we have never heard what is written, let alone all the things which could be written, taking advantage of double, triple quadruple sharps and flats, and taking advantage of enharmonic inequivalence in melody and harmony.
There is a piece on my channel called The Last Words of David, I did not write this piece but merely entered it into MuseScore and tuned it. But the composer, being in the world of 12 tet misspelled half of the notes in the song, the entire second half of the piece is misspeleld. So in my version I spelled (and tuned) every note correctly according to common practice. The piece starts in E minor terrritory and ends in G major, in the original score but in my version, the sheet music is on screen, the piece modulate up and up and ends in Fx major, a comma higher than G. And when you understand what the words of the song are about, who said them and what he was speaking of, suddenly the correct spelling makes all the more sense and the music is quite powerful. The music does not sound weird or alien, it sounds perfectly normal, but perfectly in tune as it modulates up and up.
5 limit 7 limit and higher rational intonations cannot be mapped to a keyboard with a meaningful number of notes, in a layout that is functional and intuitive and ergonomic. And with a harp, forget it. But with Pythagorean just intonation you can do it on keyboards and to a large degree on harps as well. The end of lusting after 5 and 7 limit and higher , if one keeps following after that, is merging with machines and AI, everythiing being computerized, or if you stop before then, you have edos which are out of tune from your ideal, or you can only play in 2 or three keys per instrument.
The 17 note vicinity that exists for every tonic chord, understanding functional harmony, and testing the boundaries of that. There is so much to be explored that is simply untouched by man because people have all sorts of wrong ideas about tuning, and the most damaging of them all is the notion of 5/4 being a pitch class of its own and also being the major third. I get it, that warm buzz of the major chord with the 5/4 as the third, I get the appeal, I advocated for it for ten years. But it just does not work coherently in music when put to the test, the system is revealed to be incoherent and out of tune compared with true intonation. I have found that letting go of the 5/4 as a pitch class has opened up a whole new world of music to me and one with much profound depth. I find myself frustrated that others are still caught where I was, seeking after the 5/4 or thinking it is at least an option of major third, which keeps one bouncing around in all sorts of tunings that are not solidly coherent.
@@RememberGodHolyBible just intonation doesn't not exclude the possibility of having various forms of a major third
@@RememberGodHolyBible I suggest you try some acoustic works, I do not agree that Pythagorean intonation sounds better than 5 or 7 limit just intonation.
I think extended Pythagorean notation is great, but I personally dont like the sound of a Pythagorean triad. Those who like 5 limit harmony are not lost in the weeds, those who are lost in the weeds are those who claim that there is a best tuning. We each tune to how we hear and how we express. 5 limit harmony is obviously not why the whole world is out of tune, much of the world does not use 5 limit harmony.
Please make some acoustic music outline your ideas, because midi compositions played by your computer are really not convincing either. I respect your decision for how you want to tune, but you needn't proselytize to me.