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Pꝛaiſe God!

Pꝛaiſe the Loꝛd God. I am glad thou didſt enioy it.

another thing to take into account is the halving/double sequences of the frequencies of our notes in relation to accidentals/beating frequencies and combination tones, 320 is a few octaves above 5, 256 above 2, 384 above 3, 448 above 7, so on and so forth, our brainwaves/states of consciousness are influenced by these and exhibit certain characteristics or shifts when entrained to them via external stimulation over long periods, to fully and comprehensively make use of all the properties of sound and psycho-acoustic phenomena, from ultra low frequencies to tones to harmonious intervals to the distribution of frequencies across the broader hearing spectrum, I believe is key to unlocking the full objective truth and meaning of the music

@@pauwel9380 The problem with higher limit tunings above 3 is that 1, fundamentally they are illogical systems, and 2, they inevitably sound out of tune. Yes, in certain situations you as the composer can trick the ear and hide certain intervals, and coax the ear into hearing something as in tune, but it will always be at the expense of the holistic listening experience. Where the listeners mind is both relaxed completely and aware intently, accounting for the notes and harmonies in the moment as well as the notes and chords that came before and anticipating what may come next. Using higher limit tunings makes one only listen or primarily listen in the moment, and not over time. Music is something that happens both over time and in the moment. but because the melodic intervals are so out of tune in 5 and 7 limit and higher, the ear and brain start to only listen in the present moment, to the buzz of the chords, and all sense of melodic and interval awareness is lost. In terms of just adjusting by ear on the fly, this also is not right. Yes it can be done, and is done, but it is not ideal, it is the result of a compensation for errors, adjusting so the entire piece does not become more and more entropic. There were two groups in the past the harmonists and the canonists, the harmonists, had this approach you speak of, go by ear, it is emotional, nothing is exact, go by feel, they did not think notes had specific pitches to rigidly adhere to. The canonists said that pitches were specific frequencies, that and A was an A, an E was an E in a given piece, for example, always the same pitches per given name. Cb was a different note than B, which was a different note than Ax. For a harmonist Cb, Ax, and B are really essentially the same thing, the same note, that are written or spelled differently for the coherence of the score, but not 3 distinct exact pitches. The harmonist view won out in the world currently, and has lead to nilism and post modernism, and an anything goes mentality, expanding outside the realm of music. Not saying music is the sole cause of that, but definitely a major contributing factor. In 5 and 7 limit tunings and higher, one always has compromises to make, and if you go into it deeply enough & your listening has not been compromised into only listening in the present moment, you will eventually find 5 and 7 limit tuning to be unuseful in music. I say this as someone who worked exclusively in 5 and 7 limit tuning for nearly 10 years. In True Intonation, no compromise is ever needed. Notes are exact frequencies which you other hit exactly or not, and there is clarity in both harmony and melodic intervals. But in order to hear 3 limit as in tune, one must decondition their ears from 5 limit and 7 limit philosophy which if you are into tuning theory, you will have no doubt undergone this conditioning at some point. This conditioning of only listening vertically, as opposed to vertically and horizontally at once. For me I had to focus on more on horizontal listening at first, or my ear would go right back to vertical only. Even in Barbershop music if you probe the experts of that field deep enough you can eventually get them to reluctantly admit that 7 limit intonation is not a coherent system, it needs compromise and trickery of the ear, and hiding of melodic lines to be somewhat presentable. Because all they are looking for is presentability and a ringing chord, not a functional system of tuning. For a major chord on C, hearing the C, E and G, as a 1st degree, 3rd degree, and 5th degree of the scale sounding at once be present in your awareness and let the combined sound speak for itself, as opposed to looking for a 4:5:6 timbral sound. C is 3 to the 0th power, E is 3 to the 4th power, and G is 3 to the 1st power. All pitch classes as powers of 3, and powers of 2 for all octaves of those pitch classes. Growing up singing in choir, whenever I had to sing the 3rd of a major chord, I never knew EXACTLY where I was aiming for, the piano was off, and no tuning theory taught. With 5 limit and higher you need a LOT of theory to avoid pitch drifting unintentionally and weird intervals that sound out of tune and are melodically incoherent and harmonically fused and obfuscated. In 3 limit, True Intonation, you just sing what is written on the page as is.

Thank you for the comment. Yes, with common tones the pitch does drift, and in this piece it does so multiple times just in this tag. I definitely understand people's preferences can be conditioned in to hearing various things as in tune or out of tune. I once heard 5 limit tuning as in tune for a decade, now it almost always sounds out of tune to me. This happened when I changed how I was listening. For years I had conditioned myself to hear 5 limit as in tune, even 7 limit, but I was only listening to intonation vertically, never horizontally. Once I started listening horizontally also, the whole way I heard music changed, and the problems with 5 limit and 7 limit that you find on paper, with keyboard designs that don't work, and insufficient ways to notate them as sheet music, became audible to me. The sound became not only confused, that is, everything was fused together, and muddy with little distinction between lines, but the melodies within chords sounded out of tune, like they never fully got up to pitch, or making up for not getting up to pitch on the previous notes, and singing a wider interval than it should be. Yes, someone else had mentioned tuning the melody to 3 limit or equal temperament and adjusting the rest of the notes. But before this someone said that isn't right, it should be the root of each chord that remains Pythagorean or equal tempered. I obviously chose the later, as I was less familiar with this method of tuning. But in terms of making the melody equal tempered, I did not want to do that because I wanted to test alleged just intonation against alleged just intonation, I did not want to involve any cheating compromises of tempered notes. I wanted to see and test if 7 limit is a viable functional system of tuning, or if at best it is an aural trick, that some people prefer in certain or all styles, but one that involves mandatorily tricking and or distracting the ear, so as not to sound out of tune. Keeping the roots Pythagorean allowed for the 7 limit to remain purely harmonic, and as I always say 12 tone equal temperament is just approximating Pythagorean tuning. Now if I did tune the melody to Pythagorean and adjusted the other notes accordingly it would create other problems or recreate ones you heard in the above example that I tried to fix. For example, in the measure that I made 5 limit dominant seventh chords, if I had made the C natural in the lead part the 7/4 of the D7 and also pitched down the F major down just before it so as to keep it smooth, then at the end of the measure the lead goes from a C to a D. If that C and D are Pythagorean, a 9/8, than the bass part will have to leap from a reciprocal septimal D (the root of the last D7 in that measure) to a Pythagorean G note to be a perfect fifth with the lead's D note. That interval of reciprocal septimal D\, a 8/7, to a Pythagorean G, would sound quite jarring and out of tune. That 8/7 I believe is almost 23 or 25 cents sharp of the Pythagorean D, and there would be quite the jarring effect with that leap in the bass. Also in the third to last measure, the part that I said sounded very bad before I made the dotted half note E into a tie to pitch it up, it would again have the same problem of the tenor line there sounding terribly flat. This is because in that part, the worst offending interval was between the 5/3 A note to the 7/4 Bb of the C7 chord which follows (which in this scenario would be a C+7 chord in Johnston notation). And even though the A minor chord would still be an A+ minor chord as you hear in the video, the C7 would also now be up a syntonic comma to accommodate. Even if it would work out where it wasn't a C+7 there or an A+ minor, the relationship between those chords would always remain the same with the tuning scheme of keeping the lead part Pythagorean. I think a lot of quartets cheat frankly, knowingly or unknowingly, they compromise intervals to make up for things drifting or sounding even more out of tune. There may be a perfect way to tune 7 limit as just intonation, but I certainly do not know it. But I think this video shows pretty conclusively that the system of 7 limit tuning is not functional, it is at best a trick. A careful tricking of the ear to hear it as in tune, distracting your ear with better sounding lines, to cover up the terribly out of tune lines, all for the sake of that sweet ring people are looking for. At this point though, most that sing barbershop or listen to it frequently I would imagine are already in a place where there ear only checks for vertical intonation. It is understandable because that is what is seen as important in that genre. But in terms of a coherent musical system that is harmonic, only 3-limit works and sound in tune, clear, with distinct lines, and locking harmonies, not 5 limit, not 7, not any other higher limit, the higher the limit the worse it tends to be. If it was not for the traditional bias that has developed around barbershop, and the unfortunate untruths spoken about 3-limit having out of tune thirds, I do believe people would unanimously prefer the 3 limit and would even feel comfortable calling it true intonation.

Just one correction to my first reply to you. I realized I was assuming that that measure of 5 limit dominant 5 chords would be changed to 7 limit ones. If I did not make them 7 limit, the problem I described above would not happen. But the lead melody line in the next measure would not sound as I have often heard it performed. The lead seems to go into the 7 dimension of the F of the G7/D chord in that measure. But if the lead remains Pythagorean on that F note, the D in the bass will have to be an 8/7 to the C in the following measure, so in the bass voice you would have a reciprocal septimal D moving to a Db- in the next chord. Now maybe that may be passible in context, but that interval between reciprocal septimal D to Db- is pretty wide, and the harmony set up of V to bII to I7, (thinking of this section in isolation in C), that V is not is a 3/2 relation ship to the C, it is much sharper. And while you may be able to trick the listener by having them only focus on the in tune Pythagorean melody while the bass sings a rather off interval and the ring makes one forget the sound of the out of tune V chord on G7/D in relation to the C7 chord on the down beat of the next measure, it could be at least passible to listeners. But to me that would not prove it a functional tuning, but only lend it self to the notion of 7 limit is a thing used as a spectacle, one that requires you trick the listener so they do not perceive it as out of tune. I may go back and retune the melody in Pythagorean and see what happens when I do. I may then isolate the voices to see if each line also is coherent when solo. It may be a good follow up video, to really examine the notion of 7 limit and it's functionality or the lack thereof.

The term "just intonation" means many things to many people. What you are probably meaning as just intonation is 5 limit tuning. Which can be heard in this video, the second and third iterations. Traditionally barbershop music often employs 7 limit tuning as well, which can be heard in the 4th example. Technically all of the examples after the first are just intonation because the frequencies are all in whole number ratios to the fundamental, in this case, the Eb. Contrary to what the world teaches though, 5 limit tuning is not the true just intonation, nor 7 limit, I would say that it is what the world calls Pythagorean tuning. The world falsely claims Pythagorean tuning to be out of tune and only suited for melodies but not chords, this could not be more false. As you can hear in the last example in this video, it sounds quite nice, and in my opinion, it is the only one that actually sound rightly in tune. That is why I call it true intonation. The reason there are 2 different 5 limit tuning examples is because in 5 limit there are sometimes options for tuning certain notes. In this case the Db in the bass could be tuned to the Pythagorean 16/9 or the 5 limit 9/5, since every limit composes all of the notes of the previous limit tuning. So in certain circumstances I could see some 5 limit proponents objecting to me choosing one over the other, so I included both options in this video. For the 7 limit just intonation example. The only note that is different from the 5 limit ones is again with the Db, now both of them being tuned to a 7/4 ratio to the Eb, it's 7th harmonic. All the other notes in the 7 limit are the same as the 5 limit examples. With the True intonation/Pythagorean/3-limit example, the last one in the video, all of the notes are different from the previous 3 examples, except for the Eb, Ab, and Bb. The G, F, Cb, Gb ... all the others are unique. The Pythagorean Db in the last example can also be heard in the third example in the bass part like I said before. I and currently only very few others have come to the conclusion after years of study in intonation and tuning, that extended Pythagorean tuning is the True Intonation. The reason I say extended Pythagorean is because it is not limited to only 12 notes per octave, it goes as far out as is needed to tune properly. It is the ONLY just intonation that is reflected in our music notation system. A system of 7 notes that are modified up and down by sharps and flats. All other so called just intonations must invent myriad accidentals to notate properly, none of which are practical and legible on the page.

Good points about the pentatonic in 3 limit Pythagorean, but not in 5 limit, at least not without a wolf fifth. i think the hexatonic scale is indeed ambiguous whether F or C is the tonic. But the reason that the tonic more strongly moves to C with 7 notes is because of where the tritone lies in the scale in relation to the chord of C, if you are in C major. That F to B tension resolves by limmas in contrary motion to the root and major third of the C major chord. So there is a strong tension which steps by limma in contrary (balanced) motion to C and E, the 2 most important notes in a C major chord. I definitely would consider the 9/8 to be a harmony in many contexts, and a non chord tone in others. Much of the way we perceive consonance and dissonance is largely determined by rhythm and where changes in chords and melodies occur in a musical phrase. Even with notes from F to B in an unbroken chain of six fifths, F can still be heard as a stable tonic. All of the 7 diatonic modes can be heard as a stable tonic if you know how to put certain chord changes at certain places and with certain rhythms. Wherever the tritone is in relation to the tonic chord must be observed and handled accordingly. but even Locrian can be satisfactorily stabilized and heard as the tonic chord. I think Major is as prominent as it is because the tritone can be easily resolved to the tonic chord root and third by limmas in contrary motion. no other mode has this. I think minor was attributed to Aeolian because the i iv and v chords are all naturally minor as a mirror to the I IV and V major chords in Ionian. And to create that same tritone resolution we see in major resolving by contrarily moving limmas, the G is raised to a G#, moving that tension from F to B, to D and G#. Plus the major 2nd and b6 lend itself as generally easier to stabilize, One thing I did not mention in this video, is that in 5 limit, the brain has to track motion of pitch classes in 2 different dimensions and combinations of those dimensions. A voice can move in the 3 limit direction or in the 5 limit dimension and in different proportions of those. This makes the voices much more difficult to track and process. If all pitch classes are powers of 3, then suddenly it is much more straight forward. Then voices either move in the sharp direction or the flat, and there are no combinations of dimensions in different proportions, all pitch classes are in one dimension, with only octaves existing as another dimension. So would you say that a C69 chord voiced C E G A D sounds bad or out of tune to you? Considering you say that the 9/8 does not sound harmonic? I mean by it's definition is not the 9/8 a literal harmonic and thus a harmony? What do you hear as a better major second? And btw you can even hear my wife laughing at me in the background in this very video. I am teaching her, but having to go slow. I have been at this a long time and I have never really had the opportunity to teach it before, especially to someone who is starting music from the very beginning.

Sorry I couldn't follow your explanation of why C becomes tonic (starting at F) from 7 notes onward. Something about limmas in contrary motion (?). I don't know if anyone has ever tackled this subject convincingly but I haven't done much research either. My reason for suspecting the involvement of 4:5:6 triads is that 7 is the first number of notes where 3:2 steps and 4:5:6 triads produce a scale of the same form. The next such number is 10 which corresponds to the combination of both major and minor scales in the same key. After that the next is 12. 10 is of interest because David had a harp of 10 strings. Octaves can be played on the "harmonic" on harps, so it is quite possible to play 2 octaves of a key in both major and minor on a 10 string harp. Also, the tonnex diagram for this fits on a Star of David ✡️ with major triads pointing upwards and minor downward. I'm not sure I really think he had one carved on his harp to remind him how to tune it!

@@RememberGodHolyBible another observation that has just come to me is that there are no (approximate) triads (major or minor, if minor should be significant) until the 5th tone has been added by Pythagorean progression in 5ths e.g. starting with C, G, D, A there is no triad until E is added: both major and minor triads contain the E.

Ugh, you tube deleted my response. To put it shortly. Yes, I just discovered the same thing, it is pretty neat. I would not think the hexagram would be on David's harp considering it's ties in witchcraft and it's absence from the Scriptures apart maybe from the star of Rempham, the idol. I know what you mean with the tonnetz, but the tonnetz implies a 5 limit not 3 limit tuning. A 10 note major minor scale is neat, but if that was on a harp you could only play the high octave or the low octave, not both at once. I wonder if there is a compelling 9 note scale that repeats the octave on the tenth note. For a 10 note scale the Phrygian mixolydian scale may be interesting as well. On C: C, Db, D, Eb, E, F, G, Ab, A, Bb, (C) 10 is a strange and interesting number I have been thinking a lot about recently. Our system of counting is base 10 and God's system of numbers is centered on base ten. Base 12 and 6 are fascinating, but it is not what God ordained in scripture, neither in chapter in verse numbers, nor in the text itself. I do eagerly await the day to play the instrument of heaven and sing. To see and hear, and understand the tuning they employ.

ref

Yes, I and many others have thought of a twelve note color scheme. The problem is color contrast while tiny on the page AND also the fact that there are more than 12 notes. If you used one color for Bb, what about A#? The whole music system is based off of 7 and alterations of the 7. This may seem unintuitive, but as someone who has tried out many alternatives for over 10 years, I can say confidently there is good reason for it. Having the 7 colors be the 7 colors of the rainbow allows the note letter names to be sequential. Most people know ROYGBIV and the order. It follows the intensity of light particles. There is something innate there in the sequence tying in with nature and it allows the brain to pick it up quicker. With all that being said. Since coming across a teacher who independently discovered the same things about 3 and 5 limit JI, I at the moment do not use this system of notation anymore. I conceived of this notation for 5 limit JI, it is why I sought out a new notation system to begin with. Because in 5 limit you have multiple versions of every note that you have in 3 limit. You for example have Eb-, Eb, and Eb+, then D#-, D#, D#+, etc, all different pitches. Finding a clear and intuitive way to notate these differences is why I invented the system you see in this video. And it does work quite well. But for 3 limit it is a bit redundant for professional musicians, and it cannot be written as small as standard music notation. It would possibly be really good for children, but the more I learn, maybe not, standard in 3 limit may be even better. not sure 100% about that part. However since learning from this teacher, who has been working with 3 and 5 limit longer than I have, I have come to realize that standard music notation not only works for 3 limit just intonation but was built on it and is really ideal in almost every way. nothing needing fixing. I only thought it needed fixing because i was so caught up in 5 limit for a decade. 5 limit, I get the appeal, I really do, I was a major advocate for 10 years for it. but it is not good. The appeal is the resonant buzzing of the major and minor thirds. But melodically it is not in tune, and it is not how our brain really hears intervals in music. 5 limit is also plagued with commas and wolf intervals, even within the 7 note diatonic scale. 3 limit is the true intonation, even for major and minor triads. The whole reason I shunned 3 limit for so long is because I believed the lie that people seem to repeat endlessly is that the Pythagorean major third at 81/64 is "too sharp" and is "out of tune". This is not true, even in chords 3 limit triads are the way. What I didn't understand is that musical intervals cannot be judged in a vacuum , but rather within the context of a piece of music and timbre must be looked at as well. Different timbres can decieve how in tune something is especially if you are only listening vertically (harmonically) and horizontally (melodically). I would hear the buzzing of the 5/4 major third from 5 limit and think is must be the true way because of the buzzing, it was mesmerizing to me compared to 12 tet. But I did not realize that that 5/4 ratio is not for tuning notes of a scale to, but is there in the overtone series to give timbral distinction to individual pitches. The higher overtones as well, not for note tuning, but for timbre of an individual pitch's harmonic profile. You can see if you look closely in the video, some of the notes have a little thin bracket on the right or left side of the note head, this is for the alternate 5 limit versions of certain notes, like i said i made this thinking of 5 limit, but when I put it into the Musescore the Lord would only let me adjust it to 3 and not 5 limit. Now when I listen to 5 limit music, it sounds out of tune to me, because i am not hearing only vertically as I was before, but also horizontally, melodically. And even in chords I hear the major third as in tune at 81/64 and out of tune at 5/4. MANY MANY people have made this same error. Nearly all famous musicians and youtubers that talk of just intonation make this same error. They say 5 limit is the way which is incorrect. One other major advantage of 3 limit, is the ability to create a functional, fun, playable, and reasonably sized acoustic keyboard instrument. I have 53 notes per octave in 3 limit in pure harmony and a near perfect "circle" of fifths. But in 5 limit I had over 160 notes per octave and because of various factors, there are very few ways to arrange them on a keyboard that works for the hands, and no design was ideal. And it did not loop as accurately or cleanly as it does in 3 limit. You can even retune electronic keyboards to a 12 tone 3 limit scale and play a lot of music with it. I def recommend playing and learning and exploring music in 3 limit true intonation.