Meantone Temperament and Other Historical Tuning Systems, Part 1

[@robbes7rh]

I love the excerpts from Rossi's Toccata Settima you played on the Harpsichord. Quite adventuresome for early 17th century, but sounds so wonderful in meantone temperament. It's a rare treat to hear pure major thirds on a keyboard instrument.

[@paperbranchesmystic]

excellent job! My dad frequently plays on an meantone organ and it sounds like heaven

[@jackhayter276]

Many thanks. Well explained and fascinating to me as a pedal steel player. A pedal steel guitar is basically a 10 string unfretted (slide) guitar with pedals and levers that enable the slurring of, (and within) chords. You can imagine the shrill arguments and head scratching over how to temper the tuning. Even though we can temper on the fly through miniscule movements of the slide bar, the pedals and knee levers are largely fixed interval for mechanical reasons. What frequently happens is that the instrument gets tuned pure thirds so sounds great in the "cowboy keys", but when people try to take the instrument into other more chromatic genres it sounds odd. So we all come up with different tuning sweetening schemes . It's one of the factors that has largely kept pedal steel sadly almost locked in a country music ghetto even though it's an incredibly versatile instrument.

[@louzander]

Pedal steel is absolutely one of the most beautiful instruments. Who are some musicians that are pushing the steel into new areas, or using different temperaments than the pure thirds you mentioned? I'd love to find more pedal steel musicians to listen to!

[@darbyms94]

Fascinating stuff, makes me feel a bit sad to be trapped in equal temperament though. loved the piece at the end and way you played it, crazy indeed!

[@nitairiello1534]

Great explanation Alice! Keep it up, KZbin needs more informative early music videos!

[@harpsichord]

Thank you so much! And I agree--KZbin definitely needs more early music videos!

[@BestMusicToolsOfficial]

This really made my head explode! 🤯 Great video!

[@lincethomas2365]

loved that you played the pieces and showed us how it sounds rather than just an explanation. Great vid !

[@gerardquinn4513]

A wonderful lady. So well explained. Something quite complicated made easy to understand. Well done. I love your style and examples from real music. Looking forward to another video.

[@FranBarajasMusic]

VERY interesting! Thank you so much for this video! You discovered me the Toccata by Rossi and was extremely intense and surprising!

[@dieterpeszat]

Very frequently occurring questions about the tuning of instruments are explained very quickly in their own way. Thanks.

[@RockStarOscarStern634]

Those Instruments have been retuned later on down the road when people wanted to use Equal temperament

[@RockStarOscarStern634]

Alot of Organs aren't in their Original tuning anymore, they were retuned to Equal temperament when the music that has many key changes was being written.

[@aaronfast]

This is fabulous. Thank you. I have had such a long-standing interest in tuning, but it is hard to find such concise, clear information in one place. I really appreciate all the time you put in, and particularly loved your explanation and performance of the Rossi piece at the end...after decades of music, I am rediscovering a new joy in hearing sounds that were until now unexplored. Hearing the piece stretching in and out of relative harmonic coherence as it journeys away from the key center was a novel experience for my "equal tempered" brain...it feels a bit like a doppler effect, where the harmonic fabric stretches and contracts as we get further away from, and then closer to "home"... If you hadn't set it up beforehand with your lucid explanation, I wouldn't have been able to experience it. Thank you so much.

[@granite_planet]

Wow, doppler effect isn't actually a bad analogy at all :D

[@microtonalguitar]

Great channel!

[@harpsichord]

Thank you so much!

[@electric7487]

6:34 Technically, the most extreme meantone tuning is 1/2-comma meantone, equivalent to 33 equal temperament with the 33C val. This one is very much an oddball. Slightly less extreme is 1/3-comma meantone, equivalent to 19 equal temperament. Minor thirds are close to perfect at 0.2 cents sharp, while the perfect fifths are 7.2 cents flat and major thirds are 7.4 cents flat. Then you have 1/4-comma meantone, which for all practical purposes is equivalent to 31 equal temperament. Major thirds are close to perfect at only 0.8 cents sharp, while the perfect fifths are 5.2 cents flat and minor thirds 6 cents flat. (This is personally my favourite tuning system that isn't 12-tone or 24-tone equal temperament.) To "tame the wolf" if one is limited to 12 pitches per octave, one very nice option is 1/5-comma meantone, equivalent to 43 equal temperament. Major sevenths are close to perfect at 0.1 cents sharper than 15:8, perfect fifths are 4.3 cents flat, major thirds are 4.4 cents sharp, and minor thirds are 8.7 cents flat.

[@dr.danielkester9313]

I'm very impressed with your teaching

[@harpsichord]

The subject of historical temperaments and tuning systems is super complex and often confusing, so let me know any and all questions you have about meantone and other temperaments and I’ll try to clarify things!

[@Anonymous-df8it]

Has anyone used key modulations in meantone to build up tension? I feel like quote unquote 'unusable keys' would actually have a purpose there!

[@nmerdon]

you explained this soo well thank u

[@harpsichord]

Thank you so much! I'm so glad you thought so!!

[@robertd3564]

Thanks for your encyclopedic treatment of this difficult topic. I will have to listen to this several more times to absorb it all. Well done.

[@chadthomson4596]

This is mindblowing.

[@nickukiah810]

Wonderful. Thank you. The Rossi was crazy!

[@harpsichord]

Thanks! I love the Rossi (and pretty much all early Italian Baroque music)!

[@popnocturne7909]

You can't beat this explanation.

[@sarahsterankaflute]

Fantastic video! Exceptional explanations and love your visual displays. Thank you so much for making this!

[@harpsichord]

Thank you so much for your kind words! I'm so glad you found it interesting and informative!

[@pedacodesuino]

Just found your channel by chance. Amazing work, thanks for that! Cheers from Brazil.

[@vapourmile]

Very good. Clear, lucid and well-developed.

[@enzocypriani5055]

This was exactly the video i needed

[@jim4489]

legitimately fantastic video, thanks so much :)

[@harpsichord]

Thank you so much! I’m glad you liked it!

[@davegallagher4498]

Very clear explanation to a topic that can be a bit challenging. And a great demonstration too

[@nervousharpist]

Thank you Alice, I commented on your 1/4 comma meantone video about how I messed up my pedal harp with the wrong tuner settings, because I thought I was tuning in equal temperament but I wasnt and couldnt figure out why it sounded weird haha

[@MichaelBakrnchev1989]

Excellent resource - thank you!

[@electric7487]

8:34 When you cycle through all natural, sharp, and flat notes, you get 35 notes, but with four notes that overlap with each other. Since log₂(5) is irrational, no non-zero amount of 5:4 thirds or meantone fifths will ever close exactly at a whole number of octaves. Quarter-comma meantone separates A𝄪 from C𝄫, B𝄪 from D𝄫, D𝄪 from F𝄫, and E𝄪 from G𝄫 by 6 cents to close the loop. Nowadays, we use 31-tone equal temperament which has a major third 0.8 cents sharper than 5:4, and it closes the loop by making the aformentioned pairs of double sharps and double flats enharmonically equivalent to each other.

[@alexanderteachernyc]

Thank you for making a complex topic understandable and fun.

[@harpsichord]

Thank you so much! I'm so glad you liked the video!

[@grahamhall2662]

Absolutely fascinating. Loved your choice of piece as an example.

[@toptrump1499]

Awesome awesome video. Thanks!

[@josephbrantley625]

Super informative! Thank you!

[@RockStarOscarStern634]

Those Organs that used to be at 466 have been tuned down to 415 (around 1793) when they went under a major rebuild.

[@classicalguitargirl]

Thanks so much . You are wonderful

[@RockStarOscarStern634]

5:28 Octaves are an exception though

[@danjonesguitarist]

That was a really great video. Super-interesting. I have all sorts of issues with my guitar (fretted of course) trying to find solutions.

[@GrimLordofOregon]

I really enjoy your channel and the information you are making public. Quick question for 1/4 comma Meantone. Is the synthetic comma split evenly between all the 5ths or do some 5ths get more of the comma and others less?

[@harpsichord]

Thank you so much for your kind words about my channel and for your question! In quarter-comma meantone, the syntonic comma is split evenly between all the fifths, except for the one wolf fifth--usually G#-Eb--that's actually a diminished sixth. So, in other words, about 5.5 cents comes out of each of these 11 fifths: C-G-D-A-E-B-F#-C#-G# and C-F-Bb-Eb, and then you're left with a super wide G#-Eb (or you could place the wolf interval somewhere else, such as between C#-Ab if you were playing something in f minor, for example, and needed an Ab). I hope that's clear and please let me know if you have any more questions! Thanks for watching!

[@AnonymousBN]

Awesome! Thanks for making this video

[@harpsichord]

Thank you! I'm so glad you found it helpful!

[@carolusmagnus7116]

Very cool!

[@MikeDGuitar]

I'm a few minutes in, and I find this great so far! Did mean-tone temperament limit the key signatures of keyboard instruments; that is, were said instruments limited to two flats and three sharps from the Renaissance to the early Baroque era?

[@mosankoba]

"It's totally unusable.... in any key." nice. :)

[@harpsichord]

😁

[@Anonymous-df8it]

@@harpsichord Is it though? It could be used to build up tension, right?

[@cl9826]

​@@Anonymous-df8itit usually just makes me laugh which is the opposite of tension though

[@kwixotic]

Do you know about the modern temperament devised by Owen Jorgensen in which the white keys are equally tempered and the same is then true for the black keys? Has a fair number of microtonal intervals and makes use of 12th intervals in a composition he wrote.

[@margueritepan9647]

Are there any books that explore piano tuning systems such as the meantone temperament? Great video by the way!

[@jowen85]

Hi, I would like to play Mozart period music in a temperament but i'm undecided which would be best. 1/4 comma may be too early, so I was thinking of maybe a Well Temperament or a 1/6 comma, or even a Young. Finding the Hz for the tunings is almost impossible. Do you have any ideas on which temperament may be most suited and where I can find either the maths to calculate, or the Hz required to tune. Thanks.

[@electric7487]

Here are the equally-tempered equivalents of five of the most important historical tunings: Pythagorean tuning = 53 EDO 1/3-Comma meantone = 19 EDO 1/4-Comma meantone = 31 EDO 1/5-Comma meantone = 43 EDO 1/6-Comma meantone = 55 EDO EDO = Equal Divisions of the Octave

[@Violedegambe]

Is that true that in meantone temperaments, the tone is equal but the semi-tone is divided between a major diatonic semi tone and a minor chromatic semi tone (which means Mi-Fa in solmisation is bigger than a chromatic semitone). Thanks for your help and knowledge!

[@ClaudiMeneghin]

Very neat, thank you :)

[@harpsichord]

Thank you so much! I’m glad you liked it!

[@longshot789]

Fantastic

[@harpsichord]

Thank you so much!

[@Lucius_Chiaraviglio]

I just noticed that while the score of the Rossi piece has a standard 5 line treble staff, it has a bass staff of well over 5 lines (specifically 8), with 2 clef symbols in it. . . . And I was just wondering a bit earlier if any music score composition software would support staves having more than 5 lines . . . .

[@sugardaddy4714]

Cool. Clearest explanation I've heard yet. Wikipedia pages on the subject are too science-y and confusing...

[@ryanranocchini]

Are there electronic keyboards that will recalibrate the intervals according to the key you are playing in as you instruct it to to change the tone? Not sure if I am using the right words here ...

[@granite_planet]

There are software (VST) instruments that allow you to adjust the temperament. And there are some programs that re-tune your MIDI input on the fly to a specific temperament, like Mutabor, which allows you to play pretty much any software instrument in any tuning. The MIDI standard itself contains an extension to specify the tuning called MTS, and there are a few software and hardware instruments that support that.

[@YoVariable]

One notable electronic keyboard that you should check out is the Lumatone, a 280-key isomorphic keyboard. An important aspect of it is that it allows you to play in historical and microtonal tunings. A good practical advantage is that it retains the familiarity of equal temperament, allowing you to freely transpose and switch keys. However, 12-tone equal temperament, also called 12-EDO for equal divisions of the octave, which is discussed in this video, is not the only equal temperament. Some other equal temperaments or EDOs that the Lumatone supports are 31-EDO, a great approximation of 1/4-comma meantone temperament and 19-EDO, an approximation of 1/3-comma meantone temperament.

[@YoVariable]

Here are some examples of exploring 31-EDO (1/4-comma meantone approximation) on the Lumatone: kzbin.info/www/bejne/sInShpJtqNCNZ6M kzbin.info/www/bejne/eKSQfmh9jbKJeJo

The thing with these temperaments is that, at least for me, it's impossible to consciously identify it. I cannot say just by listening to it: "oh, you're playing Bach in Vallotti temperament, how barbaric!" But when someone plays Bach in, say Jägermeister III (Haugsand 3.5, not necessarily an authentic temperament), I just think "wow, it sounds so nice, what a nice instrument you have!", without being conscious of what is actually going on. Some music simply sounds dull in some temperaments, and shines in others, for a mysterious reason (well, not really, if you think about it, but so difficult to perceive just by listening to it).

[@granite_planet]

A bit like how humans can tell apart thousands of faces without necessarily being able to tell the difference between each of them. Few people can look at faces like "This person's nose is two millimeters longer than John's, and eyes are the same distance apart as Anna - that means I'm looking at Fred". Just like few people can listen to music and extract the temperament just by analyzing narrow and wide intervals.

[@martinh1277]

Jägermeister is a famous herbal liquor. Andreas Werckmeister wrote a book with 5 tunings. Werckmeister III is sometimes used. If you have Jägermeister III, tuning does not matter any more. :-)

[@dbadagna]

Could you please add the link to the Rossi organ recording to the video description above?

[@johnlaw7017]

Really interesting, thanks a lot! But I have the feeling - might be because I'm so conditioned to hearing music in ET - that that chromatic ending to the Toccata, with the wonderful imitation in the parts (brilliantly played!), would sound better in ET, like on a piano. ET has so many advantages, one of them being the super smooth gliding chromatically between different key centres.

[@RockStarOscarStern634]

4:46 OK so Equal Temperment is the only temperment with Enharmonics.

[@electric7487]

There are other equal temperaments with enharmonics, but they are very weird and obscure. Alice, however, is still entirely correct in the regard that 12-tone equal temperament and some of its derivatives are the only tunings where C♯ = D♭, D♯ = E♭, F♯ = G♭, G♯ = A♭, A♯ = B♭, B♯ = C, C♭ = B, E♯ = F, and F♭ = E. For example, ⅓-Comma meantone (19 notes per octave) has two particularly interesting ones: B♯ = C♭ and E♯ = F♭. All the other sharps and flats, however, are distininguished. Instead of D♯ = E♭, you have D♯ = E𝄫 and E♭ = D𝄪 and so on. B = C𝄫, C = B𝄪, E = F𝄫, and F = E𝄪. In ¼-comma meantone (31 notes per octave), they get even crazier. A half sharp = B𝄫, D half flat = C𝄪, C♭ = B half sharp, B♯ = C half flat, etc. Only at the far end of the circle of fifths do you actually get some ones that are familiar: D𝄪 = F𝄫, A𝄪 = C𝄫, E𝄪 = G𝄫, and B𝄪 = D𝄫.

[@cannadineboxill-harris2983]

Hello Alice, why couldn't you Try Remaking A Daddy Grand Piano by putting on 88 Tuning Forks like what you did on an Upright Piano, Please do the Same Thing on a Daddy Grand Piano For Most of us KZbinrs, It will be a much Better Idea For us so we can Try and See and Hear Pianos with 88 Tuning Forks inside Thank You.

[@jaredhoeft2832]

Couldn't the wolf fifth be used for specific effect? In the context of modern music written specifically to use the, uh, unique sound of the wolf fifth?

[@martinh1277]

Joung Bach did so. Capriccio über die Abreise des geliebten Bruders. It only works in meantone. You can hear the friends weeping and a galloping horse.

[@liberty1795]

This short video explained things clearly that I've been grappling with for years. Thank you!

[@harpsichord]

I'm so glad you found my video helpful! Thank you for your comment!

[@adammikulasek]

Hello, really interesting, however it is awful that KZbin do not find any video about historical temperaments on electronic keyboard. My Tyros 5 knows Pythagorean, meantone, Workmeister, Kirchberger and two temperament presets called Pure major and Pure minor. Its also possible tune the scale manually in cents, much much simple than tuning real harpsichord and other acoustic keyboard instruments. :-) My plan is to create such video but my English is not good. :-) Have nice time and I wish you good luck. Zahir

[@journeymancellist9247]

So far quite nice, but would prefer less preliminary blather. PSyoundidnt explain “cents.” Really enjoyed this. Watched it all and will again.

[@robertporch5218]

Just one point E-G# 3rd is about 7 beats wide and Ab-C is about 8.5 beats in ET. You said they are exactly the same, beats wise, no but I understand your drift as in 'equal '. Maj 3rds steadily increase in speed as we increase in pitch.

[@nidurnevets]

My question is what temperament do string players typically play in? If I compare my own intonation on the violin to a tuner I don't seem to be playing in equal temperament, as those tuners operate in that temperament. Thank you

[@martinh1277]

Pythagorean. But if the tones come fast enough, they will lift the lower tone of a semi tone, so that it sounds as if it was in tune. This can be the half of a semitone. They do it and don't know it. If they play sonatas with a piano, they tune the G-String a bit higher. Some take the first chord of the 6 partitas with a high b-flat and have a long pure 6th. Viola players in an orchestra use "antemperiert". The semitone is slightly greater.

[@martinh1277]

Play (Downbow, legato) d (short), c (short), b (short), c (short) and b (upbow, long). I expect you to play the second b to high. Reason is, you have taken the first b. This is high. Intonation on a Violin depends on the circumstances. You can not explain circumstances to a tuner. Viola player prefer a balanced stringing. A- D- and G- strings should have the same strength of overtones. This is just ideal, not reality. C- string should sound like a typical C- String. The audience hear a clean intonation, if all the tones in a melody have the same sound. If one tone in the middle sounds brighter, it will be looked upon as higher. For the audience, to a certain degree, sound can be the same as intonation. This is the reason, why violinists prefer a shift up and later a shift down, rather to play a melody in the same position. Now explain it to your tuner.

[@rickjensen2717]

The reason we get 'commas' is because an octilave cannot be split into 12 equal pitches and be pure. You can try 19 and that sounds a lot purer but you will need lots of (split) keys on any instrument.

[@roberthubbard5696]

Where is the Part 2 of this Temperament discussion. I count 33 videos and am a subscriber but I don't see it.

[@harpsichord]

@@roberthubbard5696 Thanks for your comment! Here’s a link to Part 2: kzbin.info/www/bejne/aWGcmIGKlJxlhMUsi=3OMmqGXr6Bc51JhW

[@roberthubbard5696]

Oops, I found it but am disappointed that it was so short compared to the thorough Part 1. It would be nice to know what you think of the possible unique temperament in the decoration for WTC2.

[@RockStarOscarStern634]

Our modern Day Fretted Instruments such as that Wood Violins 7 String Fretted Viper are in Equal Temperament which appears to be most appropriate for modern performances. The thing w/ Equal temperament is that it's outta tune, so all the Chromatic Fretted Instruments that are in equal temperament (every note where the needle is in the Center of that Chromatic Tuner) are actually compromised so that they're equally outta tune on each note. Lots of Fretted Instruments from the old days like Gambas & Lutes have movable frets tied on (you can even tie Movable frets on a Fretless instrument so that you give the notes more clarity) around the neck & moving them really helps.

[@ajames283]

Impure 3rd sounds like an augmented triad 😮

[@dougmiles7124]

It would appear a number of composers of the Renaissance and Baroque eras deliberately used unusable intervals.

[@jaycoover]

Pianos are stretch tuned, so not exactly equal temperament. If pianos were tuned to ET, there would be no need for human piano tuners who have highly trained ears and experience. Equal temperament doesn't really actually exist except on computers and synthesizers.

[@cubicinfinity2]

Excellent video. Offensive slightly.

[@RockStarOscarStern634]

There's the True Temperment Guitar.

[@RockStarOscarStern634]

Alice M. Chuaqui Baldwin, harpsichordist I have this bright Yellow Book called 24 Italian Songs & Arias Complete which all have Realized Continuo done by Parisotti since it's all Continuo Arias, which as a Singer & Multi-Instrumentalist find them fantastic.

[@RockStarOscarStern634]

I've used that w/ my Reed Organ after repairing it.

[@markcerisano4268]

Just one clarification. In ET, the M3's increase speed as you go up, so you might say they are not equal. F3A3 = 6.9bps but F4A4 = 13.8 bps.

[@Anonymous-df8it]

How can you tune your thirds to increase it's speed?

[@markcerisano4268]

@@Anonymous-df8it just look up any aural tuning instructions. It’s how we do it.

[@matthiaswilhelm9813]

Bach the old Undertaker💀of good Tunings😪😂🗿Others Tuning Tables much Vetter for my ears.good Regards.

[@erikolsen1333]

🎉🎉😂😂🎉

[@DG-ss1gc]

It’s like I always say. If it’s not baroque … don’t fix it.

[@RockStarOscarStern634]

The thing w/ all the Fretted Instruments in Equal Temperment is that they're compromised so that they're equally outta tune.

[@AspartameBoy]

As bad