Temperaments - What you need to know

[@virginiaorganbuilder]

For more than three decades I have been building and tuning organs in many different temperaments, and I feel like I understand the concept pretty well. I have never seen a better presentation of the subject than this wonderful video, which I will share over and over. Thank you for everything you do!

[@m-hayek1985]

Christopher Bono why is B# not equivalent to C?

[@virginiaorganbuilder]

@@m-hayek1985 Well...for the same reason that C# is not equivalent to Db and so on. A friend of mine once said that he believes that temperaments are proof that God has a sense of humor.

[@m-hayek1985]

Christopher Bono I actually did not know that C# is not equivalent to Db. So if I understand correctly, calling B# a C is like calling 0.99999 a 1?

[@virginiaorganbuilder]

@@m-hayek1985 Welcome to the wonderful world of temperaments! Actually B# and C are considerably farther apart than 0.00001. This is a truly fascinating field, and worth learning about. There are many excellent videos about temperaments (and keep in mind that only keyboard and fretted instruments like guitars that need to be tempered, since their pitches are fixed), such as the one above! Here is a dramatic display of the differences between sub-semitones: kzbin.info/www/bejne/bXjLcqiQfZujntU Down the rabbit hole we go!

[@victotronics]

@@m-hayek1985 B# according to the circle of fifths has the same frequency as C times (3/2) to the power 12. That is almost the same, but not quite, as going up 7 octaves, which gives you the original frequency times 2 to the power 7.

[@PaganVegas]

I'm a Piano Tuner & Technician. This is by far the best basic explanation of Temperament that I've seen. I learn so much on your channel! It might be helpful to note that to "temper" a tuning is the same word that we use when we speak of "tempered steel" - which is bent, folded, and hammered until it is the appropriate strength and quality. Pretty much the same with keyboard tunings.

[@The-George]

Indeed. In Dutch temperen means to make something less expressive or pronounced or.....to adjust something.

[@olly8453]

This is by far the best presentation of temperament I've ever seen -- well done!

[@fredhoupt4078]

agreed. Superb and easy to follow, though very complex. These guys are the best.

[@cardinalflower6959]

@@fredhoupt4078 And they're funny, too!

[@baizzang1]

One of the best videos since my KZbin experience for the past 15 years.

[@derycktrahair8108]

Beautifully explained. That's why in the 'Blues' we sit on a b3 & b7 . Not "out of tune", it creates the tension required in the style. We HEAR it. Now we know why. Thanks.

[@bifeldman]

Best discussion on this topic ever. In my house we call equal temperament twelfth comma.

[@weissrw1]

Thank you for giving the audio examples so we could hear the differences. Very helpful!!!!

[@RizalBudiLeksono]

17:00 The concept of dark side (remote keys in the cycle of fifth) and bright side (neighbouring notes in the cycle of fifth) using th picture of outer sky and the earth is briliant

[@seekind_the_artist]

Looks to me like two paintings of Hieronymus Bosch combined. :)

[@thomashughes4859]

Your visual for the "comma" is now well-temper ... er ... -understood. Now, I am going to geek out over the maths involved in this "comma", which I imagine will take me to the world of logs, powers, and Calculus! Thank you, Elam!!!

[@samuelbeltrami5647]

Man i'm italian, and your Italian pronunciation is perfect

[@francescoborghini7669]

Molto bene, nonostante non conosca l'inglese, pure correndo dietro ai sottotitoli, ho finalmente capito cosa si intenda per "giro delle quinte"!... È molto ben detto poi che una tendenza al sistema equabile ha sempre accompagnato i metodi di accordatura dal seicento al settecento!!...Questo dovrebbe essere spiegato anche chi si picca di suonare Mozart e compagni in mesotonico!! Grazie! E ancora complimenti!

[@cesarmayoli8457]

Im a piano Tuner and Im very thakfully for my teacher for know this perfect tunning since my first tunning, its a great video, thank you very much

[@adrianocastaldini]

The Motion Graphics effects are stunning! A pedagogical gem. Brilliant guys!

[@amelia1507]

This is honestly the best video I've ever watched. Thank you for making a concept that I was finding unbelievably difficult to understand so simple. I can't thank you enough.

[@DavidBennettPiano]

This is a brilliant video that answered at least twenty-seven questions I had about tuning and temperament! Keep it up 🙏🙏🙏

[@WilliamFord972]

Look up the book “How Equal Temperament Ruined Harmony” by Ross Duffin. He’s a professor at my alma mater.

[@danielwalbridge1406]

0

[@AlainNaigeon]

I imagine your 28th question might have been "why some temperaments are called meantone ? Does it mean (ha ha) that not all tones are equal in some temperaments ?" Yes indeed, you may find some 9/8 tones and 10/9 tones sometimes (the product is equal to 5/4 = pure third). Meantones are a whole family in which tones are all equal (thus taking a "mean" value). He could have said a few words about that IMHO, because the name "meantone" doesn't come from nowhere !

[@MANUEL7560]

1y

[@Williamegert]

I've been playing guitar for about 20 years, and started playing the keyboard about 5 years ago. I had a bad habit of tuning my guitar over a chord. I would, for example, strum a G chord and then, with my right hand, reach over and tune the pegs. My musical friend, however, would always tune the strings to each other, not to a chord. It didn't take me long to realize that this is best: everything sounds ever so slightly out of tune as opposed to one key being in tune and the others being unplayable. Now, before I play, I make sure to make the open strings sound agreeable together, and this makes all they keys sound acceptable.

[@MarkHoemmen]

William Egert It’s interesting to me that if I tune a guitar in lute tuning (the G string in F#) by ear, I have a harder time making some of the chords sound in tune - that third-fret A either sounds bad with the D string, or the second-fret E on the D string sounds bad with the B string.

[@Williamegert]

@@MarkHoemmen That is interesting. That is a tuning I have yet to try!

[@zfm1097]

I understand the rationale behind meantone temperaments to be, that it's more important to preserve the purity of 3rds than P5ths because there is more audible beating (because the notes are closer together), especially because organs were the main reference for what's ideal, i.e. sustainable chords. I believe 1/6th comma meantone was settled on by the mid C18th (in Germany) as the best compromise for all instruments except the keyboard(?) but there's no obvious audible difference between 1/4 comma & 1/6 comma 3rds. It's notable that 1/6 comma meantone corresponds to a 55 point equal division of the octave. There was no mention of double-fretted string instruments or split-key keyboards for meantone tunings. For 12 key keyboards, irregular temperaments were supposedly quicker to tune than equal temperament because some of the 5ths were pure, so there was no need to count beats for those. Irregular temperaments also provide 'key characteristics' that were exploited by composers. Perhaps the introduction of cast iron framed pianos (and so increased string tension) made equal temperament more practical and the tone of later pianos compensated for the indiscrepancy ...especially since inharmonic overtones are part of what gives the piano its slightly bell-like tone due to high string tension stretching harmonics. I mean, don't piano tuners compare the 2nd partial to the octave above because it is noticeably stretched? The slightly inharmonic partials and rich tone of a modern piano might make equal temperament less obvious than it was on the harpsichord or fortepiano.

[@eenayeah]

I've been a singer my whole life, been a classical guitarist half my life, and a classical pianist less than a quarter of my life, and I had NEVER even heard of the WORD temperament. This is such a weird concept to me how deep in my musical journey I discovered this. I only learned about it after looking at the instruction manual of my digital piano last night and seeing it gave the option to change ”temperament”. Hence I simply had to know what the heck it was! Thank you for this great video!

[@ZiadKreidy]

Superb video, clear and educational. I watched it with my students at the Versailles Conservatory when I gave them a course on the history of tuning.

[@zeytoonak]

An astonishing effort. A labour of love merged with the highly scientific perception to musicology. looking impatiently to hear more. Thank

[@gringochucha]

Excellent video. Rarely have I seen this subject approached with such clarity.

[@gliuto]

This must be one of the finest channels in the yt galaxy. Thank you so much for all this!

[@hucbald37]

Please be sure: it is!

[@marycavender7136]

I heard it said that if you really want to understand something then you must go to the origins of the subject matter. I like how through you tell about this. The simplicity of a deeper more sophisticated subject. I have a keen ear to discern questions you reveled right away! I had to learn about the harmonic series in brass techniques class back in music school. This goes further and is better detailed to help one appreciate this history much more so! I think you've opened a channel to challenge the dormancy of my fascination of the physics of pitch and harmony! Excellently done!🎼🎶🎵🎭🤗🤔🧩👍❤️❗

[@kathyjohnson2043]

Thanks for the refresher (all in once place!). I bought a harpsichord yesterday and was just going to go tune it and was wondering what system I was going to use!!!! True story!

[@BassAdvisor]

Finally I found an easy and clear explanation of the Pythagorean comma and the equal temperament. A million thanks!

[@patrickfinley5087]

As a teacher of AP music theory for many years, this video is a priceless addition to curriculum. Bravo. Love your other videos as well.

[@brianbuch1]

You're right about tuning for the specific piece. I'm sure that was done all the time. I have a 17th c-style virginal, with only one course of strings. It's very easy (like a minute) to reset an interval or two to match the piece.

[@VaughanMcAlley]

Froberger wrote ricercares in F# minor and C# minor in the 1650s. Looking briefly at the score of the F# minor ricercare, you could probably get away with retuning 3 D#s, 2 A#s and 2 E#s. Froberger was being experimental, but was he interested in exotic keys for their own sake, or was he thinking of temperaments that could modulate better?

[@John081590]

This is a clear explanation of temperaments! Thanks!

[@vinwey]

this is an incredible video. The quality is so so so good

[@Mosil0]

Would be interesting ot hear some pieces that exploit "bitter" keys for expressive purposes.

[@YavorArseniev]

John Moraitis has a couple of fantastic videos on that very topic!

[@The_SOB_II]

Agreed

[@martinh1277]

Bach, Capriccio über die Abreise des geliebten Bruders, BWV 992. You need a harpsichord in meantone. Then you can hear the friends weeping, the wolf, and later you can hear the galloping of a horse. See Couperin, the pieces in an extreme key, and compare the titles.

[@peterwelsh1932]

First piece that pops to mind: "Farewell" Symphony ( Haydn No. 45 / F♯ minor

[@mobtek]

@@martinh1277 thank you :)

[@AlexandraZernerRocks]

I keep watching these videos over and over again not only because they're are oustandingly good, but also because I am obsessively interested in the topic and it's always good to review some details. I personally love the 1/6 comma temperaments, especially Silbermann and I wish I could find a way to tune my guitars into it. Thank you for making all these videos! It's enormously fulfilling to watch them!

[@Retro6502]

Love your videos, but this is a pet peeve of mine with music theory videos I see all the time: when comparing sounds and intervals people play one, then talk a bit, then play the other. It's so much harder to compare them and hear the difference with discussion in between and not hearing them back to back. It seems like everyone makes their videos this way, so you're definitely not alone in this. It would just be much easier to hear the difference if there was no break between playing notes / intervals being compared.

[@gonzoengineering4894]

RE: foot note 9, if you go justst one step beyond the 31 pitch gamut, you arrive at a nearly perfectly tuned 5th. I believe it was Vincentino who noticed and tried to exploit this, but I do tend to get my 16th century Italian theorists mixed up at 3:30 am

[@csabrendeki]

I love your subtle jokes, guys! I'm laughing so hard at them! And all that embedded in a very informative and intelligently presented subject. Keep up the great work!

[@the_eternal_student]

The real value in these videos is that they can reveal the need for preserving the knowledge of the oldest masterpieces we have complete knowlegde for to avoid the injury to progress caused by the lack of continuity in the histories of European musics.

[@Doeff8]

These videos are so clear, so informative, well structured and funny!

[@broadsworddannyboy5057]

Interesting- l am a professional piano tuner time served in Germany and l learnt about all of this over 30 yrs ago - as you said this is only a very short summary of the tuning temperaments used. I enjoyed your video

[@felipexis010]

Thank you, you saved me from a presentation I have next week. Good work

[@paulogazola]

I'm fortunate for having a digital piano (Casio PX-560) with a temperament feature. It's very interesting adjusting the temperament to a particular music (like using the Werckmeister in Beethoven sonatas, adjusted specifically to the sonata tone). It sounds so nice that returning to the equal temperament feels wrong and blurred. It's a problem without solution.

[@RickGraham]

This channel is awesome.

[@Oron354]

OMG Rick😯😯

[@distortion1222]

Its so good mate

[@j.p.westwater2334]

Wow. I've been looking into different temperaments and intonations and having trouble sorting through all the information out there. This video is by far the best I've found, and I feel like I understand temperaments much more clearly with the outstanding visuals and apothegmatic presentation. Fantastic stuff

[@victotronics]

You'll have to check out their videos about pure tuning and comma drift and all that goodness.

[@nilsfrederking62]

Thanks for the excellent video! "without tuning machines it is in fact very hard to tune 12 fifth that are each smaller than pure by exactly a 12th of a comma". Actually that is the way we tune our harp and I would say if you have enough experience it sounds better than when tuned with a tuning machine. But of course it depends on what you call exact ;-) The trick is that you need to know the degree of how "spicy" the fifth is, but once you have the "feeling for that" it is not that difficult, plus you have the possibility to countercheck in-between with enharmonic pitches, but then the mechanic of the harp has to be very accurate to not mislead you. And as the mechanic over Time becomes less accurate, we need to get our pedal harps serviced from time to time.

[@waynedombrowski7568]

Thank you for bringing much clarity to a complex subject! Fascinating! This subject is still being dealt with today,with so many musicians from different cultures collaborating.

[@yuvalne]

W... Was that a 17th-century licc? 10:32

[@AntonNidhoggr]

The Noble Licc as we call it O_-

[@YavorArseniev]

Ah, the good old licke!

[@AndrewGordonBellPerc]

The technical term is the Cantus Liccus

[@felixmarques]

I HADN'T NOTICED.

[@santotiago80]

I'M IN SHOCK

[@meantoneorgan]

This is a very nicely made video explaining the need for temperament, together with animation and audio, which makes it easy to understand to a wide audience. Students of music should take note that the historical overview is outdated - and very much incorrect from the beginning of European music up until the 16th century and maybe also beyond. There was a difference between scholastic theory and musical practice, which scholars of the 20th century did not recognize, as well as many sources on practical temperament not properly interpreted (or not interpreted at all). Pythagorean mathematics of music (including Pythagorean temperament, or "tuning", however you wish to call it) was a scholastic exercise which university students had to learn in order to get an advanced degree. However, it did not describe practice. There is only evidence it was used by one person, on a clavichord in the 15th century, mostly likely a conscious attempt to learn about classical (quadrivium) theory. Many organetto players are using Pythagorean temperament today, which is certainly interesting for those who are looking for new sounds, but they have probably re-invented something which was not used for the purpose. Practical temperaments (i.e. non-Pythagorean) were being used on organs probably from the beginning of the flourishing of the organ, and demonstrably by the 1200s. At the Orgelpark in Amsterdam, the 15th century style Dutch replica organ has been tuned approximately in one of the old temperaments of the medieval and Renaissance eras. In this era, as well as for some organs in later eras, the tempering needed to achieve "sweet" thirds was concentrated on a small number of heavily tempered fifths usually only used in minor, leaving others purer favoring major keys. A sample of one of these older styled temperaments can be heard here: kzbin.info/www/bejne/fIDNdnd9gahjpJY.

[@ricktownend9144]

Really fascinating, and the musical examples you pick illustrate your points brilliantly. There's an interesting run-down of how folk musicians approach/use this at the Fiddle Channel - 'the use of non tempered notes or scales in traditional music' (traditional musicians probably work in a way more similar to the original 'early' musicians than do classical musician of today - and since the conservatoire style of musical education took over). Other musics - e.g. Turkish - use different notes (from the equal-temperament scale), which create special 'atmosphere' - after all, we musicians are just trying, with the resources we have (voices, bits of wood/metal/gut/plastic/carbon-fibre, musical experience) to communicate a special feeling (happy/sad/exciting/impressive/magic etc.) to our audience/selves/co-musicians.

[@attilakovacs5803]

Enjoyable, clear, well understandable presentation! Thanks!

[@BlakleyBassoon]

THANK YOU for one of the best explanations of temperament that I have come across I will surely share this with my students.

[@zeralita0]

that coffee sip at the end was so worth it. gonna get some coffee now, and think about temperaments. gracias!!

[@donaldgoodell7675]

Mozart told his English pupil in Vienna Thomas Atwood (on a page from his student notebook K. 505a dated 5 August 1785) that ‘NB stringed & Wind instruments (along with the human voice) do not always have to adhere to equal or well-temperaments and make distinctions between A-flat & G-sharp for example; this nowadays is only needful with klaviers (i.e. keyboard instruments such as harpsichords, organs or fortepianos) whose intervals must always be equal to 1/12 of any Octave...’ It would have been very helpful for us moderns if Atwood wrote down M.’s exact words (which in August 1785 had started out in Italian for his lessons with Attwood and later moved into broken English which often included crude jokes (‘you are an Ass’) M. would write all over Attwood’s initial attempts at the harmonic exercises that M. set for his homework-6 day’s a week at 3:00 sharp !

[@p07a]

Is this possibly the first time the channel ever mentioned Bach?!!! I’ve been here since forever and I’m sure this is first, haha.

[@martineslava8642]

Potasmic I believed he has been mentioned at least several times. I remember they mentioned he used keyboard tablature sometimes when he ran out of room on scores. That video was from a while ago now, I believe.

[@p07a]

Martin Eslava ah i remember that being mentioned too! So it seems I’m wrong, he was mentioned before

[@p07a]

Martin Eslava 14:49 in this Video kzbin.info/www/bejne/pJ2UnmqYhNR8bas

[@stevecreswell9962]

Bach who?

[@DaveMiller2]

I'm not a musician, but I have been studying some aspects of music theory, such as intervals, temperaments, and tunings. This is by far the best and most in depth explanation I have come across. I learned quite a bit here. It seems to me that the tuning or temperament used in various points in history is related to or reflective of the kind of music being played at that time. Tuning or temperament changes when music changes.

[@meantoneorgan]

There was less evolution in actuality than the video suggests (the sources of scholarship he used were a little outdated)

[@Itemtotem]

Exceptional video. Clear speech, enough information but not too much. Succinct and yet very descriptive. Wunderbar!

[@edwardblair4096]

In your diagram of Pythagorean Tuning, it might be clearer if you also included a point for D# (like you did for C/B# with the equal temperament diagram). Then it would be obvious that the G# to E-flat is the "wrong" interval.

[@BFDT-4]

This is incredibly good! I have heard this in performances, but never learned the "guts" of it! THANKS!

[@carlstenger5893]

Absolutely fascinating (and quite informative)! Thanks so much. I wish my college courses (40 years ago) had explored this topic more than they did. Clearly, I'm going to have to spend more time reading about this topic. Thanks so very much!

[@chaenattapol2872]

Fry dm Free Pm

[@aimilios439]

There were advanced enough mathematics at the time (at least from the Era of Enlightment) to know and approximate accurately enough the twelvth root of two, and with use of a monochord find the exact pitches (for a human ear) of equal temperament. Great video, thanks!

[@weijiafang1298]

Approximations to equal temperaments (in the sense that all fifths are slightly out of tune) was known as early as Aristarchus (in Greece) and He Chengtian (in China). Mathematical description, however, came much later. When Zhu Zaiyu developed the theory in 1584 (although nearly nobody noticed his works), he had to divide the work into three steps to find a suitable geometric interpretation: squaring a rectangle 1 by 2 to find “the rate for tritone” (square root of 2), then squaring another to find “the rate for minor third” (fourth root), and finally cubing a cuboid to find “the rate for semitone” (12th root).

[@Mona_Hilaly]

Thank you for this very interesting and clear episode as always :) I would like to add that when you say at 4'58 "no temperament or tuning has "survived" from older times", it may be interesting to precise that this is applicable only to western classical music : a diversity of ways of tuning and temperaments still exists in many classical and popular musical traditions worldwide, including Europe. (In France we have acces to some recordings of traditionnal folk music from the 70/80 where the musicians used scales composed of microtonal intervals that can sound very harsh for our mordern ears :'))

[@kennethbolt959]

oopooooooo

[@StephenBaggaley]

Elam, a great episode as always. Thanks to you and Johannes.

[@kiteguitar]

Very nice video Elam! To clarify for others, there are two different commas here. When the video talks about meantone, e.g. quarter comma meantone, it's talking about the syntonic comma 81/80. But when it talks about well temperaments, e.g. one-sixth comma for Valotti, that's the pythagorean comma (3^12)/(2^19). The pythagorean comma is explained at 2:41. The syntonic comma is the difference between the pythagorean and pure thirds, shown at 6:38.

[@EarlyMusicSources]

Thank you! We wrote about it in footnotes, you can have a look.

[@electric7487]

An neat little fact I've noticed recently is that 11 Pythagorean commas is almost exactly equal to 12 syntonic commas. The difference between these, (524288/531441)^11 * (81/80)^12, is known as Kirnberger's Atom, an error of only 0.01536 cents or 1 in 112703.

[@oneirdaathnaram1376]

You guys are just great! You put that much effort into details - it's just a pleasure to watch this video, and listen to it. Many thanks for sharing this huge work for free. It's an art, explaining difficult things simply. I just couldn't happen not to understand!

[@thibaultl1570]

Great video, thanks a lot! I would suggest additional ideas (maybe you already treat them in other videos, I'm still discovering them!): 1) giving more sample with organ 2) explaining the incredible discovery of polyphony with perfect chords that leads to perfect harmonic superposition with very simple mathematics (starting with 5th+4th=8ve 3/2*4/3=2 that leads to Pythagorian tuning/medieval polyphony and continuing with 3rdM+3rdm=5th and 3rdm+3rdM=5th that lead to pure intonation and renaissance music and more...) 3) speaking about the meantone 1/3 and the unbelievable harpsichord with 19 notes per 8ve that can play any tonalities with that temperament 4) speaking about combination tone and their importance in tuning, temperaments (and in music!)

[@thibaultl1570]

Here is an example of the harpsichord I mentioned in 3): www.christopherstembridge.org/cromatico.htm

[@JesusRiveraPercusion]

This is pure education guys, great video!

[@Melimelum]

This is amazing. Thanks a lot! Cheers from Argentina.

[@dthomson8619]

Thank you so much! My first thought was "finally! I have found the right place to learn the missing part of my music education." I did click "like" and I did click "Subscribe." I will also share your channel with others.

[@ChristianJarhult]

Again, another extremely interesting, well-made episode. I don't regret my patreonship!

[@marcbongers4676]

Thank you so much for this excellent explanative video!

[@TheMidnightMusician]

Certainly one of the best videos explaining temperaments, helped a lot!

[@十蘭コメント]

講義を、ありがとうございます。とても、勉強に、なります。

[@normanspurgeon5324]

Great video- amazing, valuable subject. Tone and pitch are inextricably wed, in my modest musical world. Thanks

[@HenJack-vl5cb]

This is a treasure! Thank you!

[@joeowens6180]

At last, an explanation of this complicated matter that I finally can understand! Exceptionally well done visuals and narration. Thanks!

[@darb.musica]

Excellent explanation of the temperaments. Thank you!

[@nomansland5113]

Awesome, clear, entertaining presentation. Like for equality, for the 12-tone equal temperament, the imperfect, yet optimal tuning

[@rossharmonics]

The problem when explaining non-tempered systems is freeing the learner's mind of assumptions from the historically developed musical theory. Prior to being trained in cultural musical systems, certain concepts do not exist. The statement often made and made here is that the circle of fifths is presented as something assumed as necessary and the nature of pure musical sound is the problem. A limitless number of musical systems based on pure sound can be created. The question is: how do you build any musical system from scratch out of the pure sounds so that they work well and are very compelling? That is what I have devoted my life to.

[@JazzGuitarScrapbook]

Guys - I'm really surprised you don't mention this re: lutes and viols... They don't have to use Equal Temperament. You can move the frets, not only moving them up and down but also to lie diagonally! They are only gut (or nylon these days) tied on. In practice you can easily sweeten up a lute to play in G, for instance. Not sure if that would have been CLOSE enough to play with keys, but I remember picking up my guitar after a week of lute and being shocked at how rank Equal Temperament sounded to me.

[@EarlyMusicSources]

Intersring point! Do you know a source describing this?

[@adrianciuca2547]

@@EarlyMusicSources Many gambists play today with diagonal or doubled frets when necessary. Unfortunately I have no patience for digging about that, but an interesting survey of some historical sources on lute intonation can be found here scholarworks.iu.edu/dspace/bitstream/handle/2022/18424/Wead%2C%20Adam%20%28DM%20EMI%29.pdf?sequence=1&isAllowed=y

[@RolandHutchinson]

@@adrianciuca2547 The practice of split double frets on viols basically has no historical support. Tastini on lutes do have some historical support, but there's nothing similar for viols. The standard historical treatment is Mark Lindley's book "Lute, Viols, and Temperament". The DMus paper you linked to (which cites Lindley) looks quite good, too -- thanks for sharing.

[@meantoneorgan]

Historically there were two ways of tuning fretted string instruments, one very unequal, and one equal. That was attested to by Bottrigari in the late 1500s, describing the practice of his day. What he said is confirmed by physical instruments, not only fretted strung ones, but also flutes and keyboards.

[@alext8828]

This is exactly what I've been looking for. I hope I didn't put the kibosh on it by saying that. Great graphics!

[@98olober]

Thank you for this! I'm currently writing my bachelor's essay about meantone temperament so this video came fittingly :-) Edit: btw. my essay subject was very much inspired by your last video about temperaments

[@ZapataCarratala]

This is probabably one of the most valuable video in unvaluable channel!

[@MrBanzoid]

Great video, thank you. When I'm playing guitar, I generally need to nudge the tuning a little bit depending on which key I'm playing in, to make the tuning "nicer".

[@Lucius_Chiaraviglio]

I would like to point out that while 12 equal divisions of the octave results in thirds that are impure relative to the ideal ratio 5/4, they are highly pure relative to the ratio 63/50 (a bit rough, but serviceable), while the minor thirds are impure relative to the ideal ratio 6/5, but within a couple of cents of 25/21 and 19/16. This is presumably a large part of what enables 12 note equal temperament to work so well (in addition to the fifths being not quite even a couple of cents flat of 3/2). Likewise, 7/4 gets tempered to 16/9, so that it sounds decent despite being even further off from the ideal ratio than both types of thirds. Likewise, the Pythagorean major third, despite being considerably sharp of the ideal of 5/4, falls exactly on the just ratio of 81/64, and the Pythagorean minor third, despite being considerably flat of the ideal of 6/5, falls exactly on the just ratio of 32/27. If you go to the Microtonal Guitar channel videos comparing tunings, the non-ideal ratios do not sound bad so much as simply lacking the resonance (presumably from sympathetic string vibration) that is produced when using an guitar fretted for the ideal ratios.

[@ros8737]

Oh! I love this subject and these sounds. thanks for explaining it so well within the time of my short attention span.

[@gemmamerinserra4988]

Crystal clear. I love this channel!

[@hetedeleambacht6608]

enlightening as always!

[@kuroimusic]

Best explaination on KZbin. Thanks and great work.

[@webbophone3377]

Fantastic vid!

[@MrJonahWhaler]

Thank you! Beautiful job as usually! Keep it up! I understand it is not your profile but it would be great to extend this kind of topics into modern aspects too... I am convinced that moden modality (like in modern fusion-jazz or in minimalists music) is all about equal temperament developed to an extent... like all the tensions and distinctions are gone and they start looking for other means of expression beyond pitch-related. It is very interesting process

[@camtaylormusic]

Fantastic video so far, just a little note, which may already have been corrected by somebody - the "wolf" or diminished sixth in Pythagorean[12], when compared to a pure 2:3 fifth, is smaller/narrower, rather than "excessively large" as the video states, although the meantone[12] wolf or diminished sixth is certainly "excessively large".

[@EarlyMusicSources]

Indeed we mixed it with the Meantone wolf! thanks for noticing. We added a note about it.

[@RolandHutchinson]

You beat me to it. Well spotted!

[@artofmusic303]

The excellent visuals really help the understanding of this complicated topic.

[@stephenhetzel8437]

Thank you for this video.... bu far the best of it's kind. I use Thomas Young 1/6 comma on my church organ.

[@radiognome1971]

By buying a spinet to complement my transistor organ, I really stepped into a journey.... Thanks for this guidance.

[@alexrichardson6461]

All my life, I have wondered about this. Thank you so much

[@Yuki_Manu]

This is a very clear and interesting video to complement my knowledge that I learned through studying musicology at university!! I enjoy it a lot, thank you so much from Japan

[@mtsanri]

The visualizations are the best I've seen on this subject! Great video.

[@eytonshalom]

מה שלא הוגן הוא שאני צריך לעבוד לפרנסתי ... אני מוזיקאי חובב ואוהב את הערוץ שלך .... הייתי מקשיב שעות אם הייתי יכול. אני מודה, בהיותי גם דובר עברית חובב, אני נהנה מאוד מהגרסה הספציפית שלך לאנגלית עם מבטא עברי. שלום

[@otv88]

Thanks so much. This is extremely well done and incredibly helpful. I’m reading Harmonic Experience by W.A. Mathieu and your video just brings many aspects together. Excellent work.

[@Hamstray]

one should also mention the wider adoption of instruments such as the piano which are more forgiving to the ear when it comes to equal temperament as opposed to the harpsichord.

[@Zxymr]

It's also a really interesting observation that 12 is a very suitable number for the number of tones in an equal temperament, for a couple of reasons: - There are some "magic numbers" for the number of tones that approximate the harmonic series (overtone + undertone) especially well, when errors are weighed more heavily for simpler pitch ratios. 12, 24, 31, 41 & 53 are some examples. - You can make a logical argument that when there are more keys in a scale, the more complex it is to compose or play in that scale. As a result, 12-tone equal temperament is the simplest scale to manage whilst being a very good approximation of the harmonic series. Makes me wonder if the number 12 was used because Renaissance musicians knew of its accuracy, or because it was a "whole" number for Christianity in Western history. Perhaps both.

[@subjectline]

It's also convenient number for much older reasons - the Babylonian base 60 on which our divisions of time are based leads naturally to a 12-based system providing many different options for easily-found equal divisions. I use it a lot when I improvise knitting patterns. If they thought of music as decorated time, and thereby related to astronomy and cosmology, then perhaps 12 is just the most obvious choice.

[@hucbald37]

Thank you so much for this wonderful video; I'm sure also my students will love it!

[@spencer.eccles]

ALL temperaments are Beautiful