18. Why G# and Ab are Not the Same Note

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This video explores historical and mathematical reasons why black notes have two names - a sharp and a flat. Historically, these were actually two separate notes with two distinct frequencies. It was only with the introduction equal temperament tuning that the black notes were united into one.

[@Petfal]

On my guitar, the fourth fret on the first string sounds exactly like the fourth fret on the first string... I can't tell if it's sharp or flat...

[@Talurdevendrakumar]

You are amazing👌

[@RememberGodHolyBible]

Pythagorean is consistent, it is the only consistent tuning that is actually perfect intonation. It doesn't loop at 12 though. It does however loop at 53 in a similar way as it almost does at 12 with 7 octaves but closer. 53 pure 3/2 fifths are almost exactly 31 octaves. The result is that the two ends of the chain of 53 fifths are less than 4 cents flat of a perfect fifth. If D was your 1/1, the center, than Ebbbb and Cxx would be almost exactly a perfect fifth apart. So close almost no one could tell. If you make a chain of 60 or 77 fifths, it gives extra room around the cross over point at 53, so if you wanted to modulate out that far you could and remain completely pure, but if you wanted to loop and cross over at 53 you could to with only 3.86 cents off I believe. If somehow you could get to 665 fifths, that loop of pure fifths is for all intents and purposes perfect, as the offset at the 666th fifth that would go back to your 1/1 an octave higher is less than 8 hundredths of a cent off perfect, completely inaudible. Maybe somehow a keyboard could be created for that, But with 53 to 77 is definitely manageable today with out technology to create an acoustic piano and organ in Pythagorean tuning.

[@Veepee92]

What does it mean that "Pythagorean tuning is consistent"? It's certainly not _concordant_ in any way, since all harmonies in Pythagorean tuning, generally considered, are extremely complex and have a high degree of entropy, making _everything_ but Sus2 and Sus4-type chords dissonant and really ugly compared to basically anything. The meantone temperament adjusting Pythagorean thirds was invented for a really good reason. 53-edo _does_ have its fair share of supporters, but it's because it is a really close approximation of 5-limit just intonation, which - ironically - is one of the furthest things to Pythagorean tuning one can think about.

[@RememberGodHolyBible]

@@Veepee92 Meantone tuning is out of tune. This hath been demonſtrated quite well by Marcel de Velde on his channel. And in MuſeScoꝛe 4 on my own. Moſt people only tell myths and lies about Pythagoꝛean tuning citing the high whole number ratios. What they miſſe is that ALL pitch claſſes are powers of 3. So when thou heareſt 81/64, the iuſt maioꝛ third, thy bꝛain counteth not 81 againſt 64, it heareth 3 to the fourth power ouer 2 to the fifth power. Becauſe all pitches are powers of 3 and then the octaues are the powers of 2, the bꝛain can, and doth, track very well the ratio relationſhips between the notes. Eſpecially out to 17 notes per tonic choꝛd's vicinity. Foꝛ example the vicinity of notes vnderſtood by the bꝛain in C maioꝛ is: Gb - Db - Ab - Eb - Bb - F - C - G -D -A - E - B - F# - C# - G# - D# - A# 7 natural, 5 flats, 5 ſharps. In C maioꝛ, if notes come in that are beyond theſe, ſuch as B# oꝛ Fb, it implieth to the eare that a modulation hath occurred. Oꝛ it is likely an indication that one is miſſpelling a note. The bꝛain heareth muſicke and it's notes deriued from a chain of fifths. Meantone euen doth this, but detuneth the fifths to make the maioꝛ third into the 5th harmonic, which it is not. The 5/4 is moꝛe akin muſically to the diminiſhed fourth, 8 fifths down the chain of fifths, rather than the maioꝛ third: four 5ths vp the chain. This miſconception about what a maioꝛ third is, hath cauſed almoſt all pꝛoblems in tuning. A maioꝛ third is four fifths vp and two octaues down. The 5th harmonic is not related muſically. See, it is alſo impoꝛtant to know what a "key" is. A key is defined as 7 notes deriued from an vnbꝛoken chain of 6 perfect fifths. When thoſe fifths are tuned pure at a 3/2 ratio, the muſicke is perfectly in tune as it ſhould be (as long as one ſpelleth notes and choꝛds coꝛrectly). Meantone and its confuſion about the maioꝛ third hath one detuning the moſt fundamental harmonic, ſaue the octaue. This is all to make the maioꝛ third into ſomething it is not. When one heareth the 5/4 it is not in the chain of vnbꝛoken fifths, it is outſide in another dimenſion, the "5th dimension". This is why it ſoundeth out of tune in real muſicke. In 5 limit tuning one muſt track pꝛopoꝛtionally varying combinations of 2's 3's and 5's that are not at all conſiſtent. This cannot be tracked by the bꝛain, one cannot reliably pꝛedict the tuning of any chꝛomatic oꝛ diatonic interual; things are always ſhifting around by vnfoꝛſeen commas. This is not how the bꝛain heareth and tracketh muſicke. One may ſay, that the 81/64 beateth. And I would ſay, yes it doth in certain timbres, vſually faker electronic timbres, but ſometimes in acouſticke as ones as well. This is another very difficult thing foꝛ moſt to graſp. But whether a note beateth oꝛ not ſaith nothing of whether ſomething is in tune oꝛ not. And in the context of this interual , the 81/64, the rate of the beating is harmonic in nature, it being an octaue reduced note of the 17th harmonic. If the beating ſoundeth rough, one hath an iſſue of bad timbꝛe and not an iſſue of bad intonation. Vnleſſe one hath been trained to hate Pythagoꝛean tuning and loue the 5/4 as the maioꝛd third, people will tend to pꝛefer the 81/64 in the context of real muſicke, euen in choꝛds. I and others haue polled people about this, muſicians and non muſicians alike pꝛefer Pythagoꝛean tuning. Only thoſe who haue gotten into microtonality and been taught that the 5/4 is better, actually conſciouſly pꝛefer it IN CONTEXT of real muſicke. In context is key. Out of context, the beating of the 81/64 may ſound woꝛſe than the 5/4 as a mere ſound. But in muſicke only the 81/64 ſoundeth perfectly in tune and the 5/4 ſoundeth like it is quite flat and that the third neuer got vp to pitch. When I ſaid Pythagoꝛean is conſiſtent, I mean that there is 1 tuning foꝛ a maioꝛ ſecond. There is 1 tuning foꝛ a diatonic ſemitone. There is 1 tuning foꝛ a chꝛomatic ſemitone. There is 1 tuning foꝛ euery interual thou findeſt in ſheet muſicke, and onely 1. This cannot be ſaide foꝛ the other tunings. Euen 12 tet hath a diminiſhed third and a maioꝛ ſecond being the ſame ſounding interual. In Pythagoꝛean, euery interual is conſiſtent & vnique & harmonic. In 5 limit tuning oꝛ 7, there are many ways to tune euery interual becauſe of the commas that come vp in thoſe methods of tuning. Meantone tuning maketh the 5ths impure, like I ſaide aboue becauſe of a miſplaced appreciation foꝛ the 5/4. But the maioꝛ third was alwaies conſidered an "imperfect conſonance". A title that deſcribeth the 81/64 perfectly, conſonant, ſtable, but not perfect as the fifth, fourth, and octaue. The 5/4 is moꝛe like a "perfect" interual, but onely out of context of real muſicke becauſe as I ſaide it occureth not in a chain of fifths. If one actually putteth theſe tunings to the teſt as I and ſome others haue, with realiſtic timbres, onely then will one truely vnderſtand theſe things. When thou tuneſt octaues and fifths as 2/1 and 3/2 and make ſure to ſpell notes pꝛoperly accoꝛding to their harmonic function, the bꝛain can and doth hear all as perfectly in tune, euen in choꝛds. Thou canſt hear many examples on my channel. Euerything is in Pythagoꝛean tuning except when noted otherwiſe. I call Pythagoꝛean tuning "True Intonation" interchangeably becauſe I am not a fan of Pythagoꝛas and he did not inuent this tuning, ſo iuſt know that, they are the ſame tuning. There is a lot moꝛe I could ſay but this is a lot alreadie foꝛ one comment.

[@batner]

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[@dirkbertels3872]

The title is a little misleading since you're proving your statement using non-equal-temperament tuning. Your vid on 'key moods' on the other hand describes keys having different moods a 'myth' using exactly the opposite argument, i.e. equal-temperament tuning. It's just confusing to the music novice. Music theory today is an odd blend of the old and the new. It is still based on the 12 notes derived from the circle of fifths. But in modern times the notes have been adjusted (equally tempered) to make it sound more consistent in all keys. I would have emphasised the fact that c sharp and d flat are not the same in theory (using Pythagorean tuning). But that in reality both notes sound exactly the same.

[@Veepee92]

The circle of fifth itself is a tempering solution: to close the circle you have to temper out 531441/524288, which is about a quarter of a semitone by itself. However, it is spread over all the notes equally, making it functionally disappear entirely. Most microtonal equal divisions of the octave that support meantone temperaments don't close that circle of the Pythagorean comma, giving you a circle of fifths, for example, at 19 notes.

[@johncruz7895]

They look the same and they sound the same. They may belong to different chords, but they are the same note!

[@BeauTylerMakesMusic]

Respectfully, that’s not what “note means”. They are the same pitch, but not the same note. The narrator is correct. Notes rely on context. Pitch does not.

[@johncruz7895]

@@BeauTylerMakesMusic Musical note = a notation representing the pitch and duration of a musical sound.

[@debrucey]

No they aren't

[@chielvooijs2689]

They really only sound the same in equal tempered tuning. As a horn player, I sometimes flatten/sharpen certain notes to make them sound better. So no, they aren't necessarily even the same pitch

[@johncruz7895]

@@chielvooijs2689 As with the guitar, you can bend the string to get a different tone/sound. Not the piano - same note same sound, although you can get different effects playing it softly or loudly. I always wanted to play the horn, so I'm a bit jealous of horn players.

[@batner]

First thoughts: Humans are not frequency analyzers. We don't have 24bit/96khz sampler and FFT with spectrum window in our heads. So if we take a pythagorean octave ratio with A=440hz, 220hz, 880hz. The idea of the octave, to me, is that "its the same note in a higher or lower register". It is somehow natural and instinctive for me and others to sing an octave higher or lower than others while thinking "yep we are singing the same tune". But how accurate does it have to be for humans to hear "an octave"? Will 218hz still be "an octave" from A=440hz or will some people yell "its flat!!"? People are more or less sensitive to physical phenomena including smell, color and probably sound frequency, so there must be an individual difference and probability in perception of "the octave". I don't like Pythagoreans, like any other religious extremists. Not everything in the world is a ratio between whole numbers. Yes, I'm a heretic.

[@FernieCanto]

"We don't have 24bit/96khz sampler and FFT with spectrum window in our heads." That's true: we have *two* frequency analysers. They''re called the cochleae. We have a fully analogical FFT system in our inner ears, and that's really how the human brain perceives and understands pitches. Read about it, it's fascinating. The extremely weird part is that, when it comes to explaining consonance vs. dissonance, and how Western harmony works, people will ramble on and on about the harmonic series, about the "inherent beauty" of "simple ratios" like 3/2 and 5/4, and how the diatonic scale is a direct product of the harmonic series, which means Western music is scientifically perfect. But then, when we're discussing the inherent inconsistencies of the Western system, then the whole discourse is turned upside down! Suddenly the ratios don't matter anymore, 'cause "we're not frequency analysers"! How come? Well, the cold hard fact is that the things this video is talking about are so true and relevant that *MANY* books about this were written throughout the Renaissance. The supposed "irrelevance" of such small ratios is debunked simply by hearing examples of comma pumps in just intonation (Early Music Sources has a a whole video about that). Hell, there's a whole book out there called "How Equal Temperament Is Killing Music" or something like that, and the argument is that the "dissonances" within equal temperament are terrible for harmony. Also, this has nothing to do with Pythagoreans at all! This has nothing to do with their cultism. This has to do with simple human perception. Pythagoreans were gone for centuries when this discussion on enharmonic notes and the Pythagorean comma became important in the West.