What is the Tonality Diamond? (Harry Partch's Theories, Explained) [Harry Partch, Pt. 2/2]

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This was requested by Dustin Troyer, Barun Chanda, Ben Barrett, Lorraine Chamberlain, Clem Billingsly, parsa mostaghim, and Lonchaney Fanch. See all requests at lentovivace.com/classicalnerd....
Sources for this video may be found in my biographical video on Partch, “Harry Partch and his Microtonal Carpentry,” which may be found at • Harry Partch and his M...
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Classical Nerd is a video series covering music history, theoretical concepts, and techniques, hosted by composer, pianist, and music history aficionado Thomas Little.
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[@ClassicalNerd]

*A few notes:* The script for this video was excised from my longer biographical video on Partch-part 1 of this two-part series [ kzbin.info/www/bejne/gYG3c4V8o8hrldk ]. This video is supplementary to that and expands on certain topics, although it was difficult to try to accurately describe the math involved in a KZbin video! Secondly, this is the last video that I filmed at my parents' house in quarantine, so I'm back to my regular bookshelf next video. Finally, I'd like to welcome two new patrons that joined after this video was produced: *Aidan Somsen* and *Forrest Barnum.* Welcome!

[@aanon1342]

@8:55 The undertone series can be generated physically by vibrating a tuning fork against a piece of paper. Adam Neely did a video on it a few years ago.

[@zAvAvAz]

johan sabastian bach 'the well tempered clavier' was a 24 tone per octave system and it is awesome.

[@robbes7rh]

Partch was the real deal. He took his dissatisfaction with equal temperament and used mathematics to recast the basis for melodic scales and harmonic relationships and then designed and constructed instruments that incorporate these new concepts. He composed good music that caught the attention of renowned avant- guard composers and inspired musicians and singers to learn his system and perform his works. I’m amazed by his intellect, spunk, and drive whereby he pushed beyond the heliosphere to conceptualize a new plane of music which is well advanced of the normal but comprehensible, sensual, and aesthetically pleasing. All the while moving across the continent to teach at colleges, apply for grants, work on big projects, move again, and again. He knew everyone in the world of the avant- guard and his ideas and goals largely came to fruition in his lifetime. It’s a shame that all those unique instruments sit silent in storage as his music recedes from its pedestal of the future. He was the personification of the 20th century push into the ultra modern age.

[@alexscott1257]

Harry Partch goes all the way up to 11 😀😀😀

[@wewewewewewewewewe]

just wanted to thank you for these videos and give you some positive energy 💘

[@boazmecham5101]

Thank you SOO much for this video Only video about partch online. Very similar to Ben Johnston's 7-limit String Quartets!👌

[@Berliozboy]

Great primer on this topic. Well explained and not dumbed down. Not easy to do!

[@alexislane3544]

I just watched this whole video and still have no clue how to do my theory homework :( Someone help me!!!

[@RSReffuw]

Man I'm here early. And on a great video to be early on!

[@vincenzollamas]

excellent video

[@lovaaaa2451]

Please do Ben Johnston next !!

[@ClassicalNerd]

Duly noted: lentovivace.com/classicalnerd.html

[@matmaneri5752]

Thank you for this. If you have time, please check out my father's book and Julia Werntz's book as well on the 72 note equal tempered scale based on Ezra Simms' idea.

[@Skansion]

Did Max Meyer's concept of the tonality diamond in his 1929 book "The Musicians Arithmetic" have any influence on Harry Partch's?

[@alsatusmd1A13]

Voicing the diatonic scale as just a tenth also defies 12 tone equal temperament because 1) the near 16/9 minor seventh degree is “out of tune” with a third degree which is supposed to stand for a major 5/4 (or 9/7 or even 14/11) or a minor 6/5 (or 7/6 or even 33/28) and 2) the augmented seventh degree is equivalent to the octave. This is weird because it stays squarely within the first 10 harmonics and the properties of 12 tone equal temperament nevertheless deduce these contradictions by enforcing the seventh of the chord.

[@demoure1680]

a note is note based on the harmonics of another each note has its own harmonics

[@elefo]

Is modulation possible with instruments that don’t have fixed tuning, for example fretless instruments, by reconfiguring the 43 system to the new target tone centre, by ear, theoretically?

[@ClassicalNerd]

Theoretically. You might have to have some of the best ears in human history to do that, but it's possible.

[@felipevaldes9168]

name of instrument in background top left shelf??

[@ClassicalNerd]

That is a really basic zither that I got from my grandmother's basement after she passed.

[@epiphoney]

It's funny. People say they like microtuning because it makes more consonant chords, but not many people use them, besides Jon Catler.

[@EggBenis]

Oh wow

[@Inhibitd]

i hear the 11th harmonic in tb303 ;)

[@DavidA-ps1qr]

Why did he not re-design the ledger lines to accommodate the 43 tone octave? If this was transmitted over 8 octaves on a standard grand piano, the number of notes available would mean that 3 people would be required to play it. If such an instrument had been invented, by Partch, or anyone else for that matter, can you imagine the complexity of what a piano sonata composition could be achieved. Why was this not considered? 6 hands on one keyboard instrument with a 43 tone octave. Vastly interesting upload. Poisonous tomatoes or not! :-)

[@ClassicalNerd]

As far as I understand it, the Chromelodeon is notated the most traditionally of all of Partch's instruments-but, like most of them, he wasn't interested in covering the entire range of a piano with a single instrument; rather, he crafted a set of instruments designed with all the others in mind. Solo piano music was, in many ways, a one-person orchestra for many years, and solo repertoire for a solo one of his instruments would cut against his aesthetic direction of communal music-making. While not in extended just-intonation, and far removed from Partch's rhythmic interests, Ivan Wyschnegradsky's Op. 37 _Arc-en-Ciel_ for six pianos in twelfth-tones approximates some of the sonic possibilities of such a piece.

[@DavidA-ps1qr]

@@ClassicalNerd As always I greatly appreciate your reply and I hope you didn't think my original question outrageously stupid. You can humour me in the future if you like, I wont be offended :-) The roast beef lunch in Simpson's has re--opened, so whenever it's safe to travel to London, the table will be reserved. David A. (Trust me this has to happen)

[@DavidA-ps1qr]

@@ClassicalNerdAs a post script I want to involve you in a small issue I have here in the UK. About a year ago I discovered, by accident, the posts on You Tube of William Blows. He has written 23 symphonies to date only one of which has ever performed (memories of Havergal Brian came instantly to mind). I have been corresponding with him via email and have formed a friendship. I have contacts at the RCM (Royal College of Music in London) and once lockdown is over in the UK am trying to get a student orchestra to perform one his works for him before he dies. He's in his late 70's and still writing, but is so disillusioned with his rejection over the last 40 years. Sadly, the symphonies he publishes on You Tube use "Sibelius" that, in my opinion, do not do them justice, I'd love to hear your views on just one of them. As a failed composer myself and William not having any formal training (similar to another William....Walton) your knowledge of music would be invaluable. Look.... he's not a great composer, but I really want to help this old guy and anything you say would be between you and me. Please don't think this request is anyway related to lunch on me in the finest English Restaurant in London, the horseradish sauce is still waiting!! :-) David A

[@ClassicalNerd]

@@DavidA-ps1qr Alas, as an American, I am effectively quarantined to my home country for the time being. But not to worry; I will be coming to Europe as soon as it's feasible. I will have to check out Blows' music-although my semester has just started, so I'm still trying to figure out my week-to-week schedule!

[@DavidA-ps1qr]

@@ClassicalNerd Thank you so much. My email is [e-mail]

[@mitodrumisra8972]

Woah! How did you found out that he drank tea through washcloth?! Geniunly curious...

[@ClassicalNerd]

My sources are in the description!

[@mitodrumisra8972]

@@ClassicalNerd Understandable....! 😊😊 P.S. - Do you know of - like - any formula for the construction of the tonality diamond?

[@elecoustic123]

I've been an inadvertently doing the same work as Harry for a few years now, and I think that he overlooked a couple of key concepts by trying to be too idealistic and cramming notes into the scale that don't necessarily need to be concrete in the scale. In other words, my theory is that, on piano for example, you could tune an octave to 12 note just intonation, and design a feature that would allow you to modulate specific sets of notes up or down one syntonic comma as needed in order to keep just intonation present in all 12 scales. I think that the scale ought to be more fluid rather than concrete, and you can bring the notes to you as needed rather than have them inherently present in the design of the instrument. I believe that each of the 12 notes can and should be played in multiple pitches depending on the moment, and I think this is the key to perfecting our 12 note system

[@EggBenis]

*drank tea through washcloths*

[@stefan1024]

Not trying to be edgy but I don't think that 11 interval sounded that strange.

[@ClassicalNerd]

Partch's whole point is that it _shouldn't,_ but that it only is perceived that way by Western ears because it lies outside the standard 12-TET.

[@stefan1024]

@@ClassicalNerd Sure, but it had some familiarity to me. Maybe I picked it up from some non-western music or maybe from synth sounds. I mean, after all it is relativiely low in overtone series, right?

[@ClassicalNerd]

@@stefan1024 The relative lowness of it contributes to its relative consonance vis-à-vis the 12-TET tritone-but for Partch, he would have specifically looked at the relative simplicity of its ratio.

[@alsatusmd1A13]

It is just barely a tritone (10^3/3^6*8000/8019) and tritones don’t really sound that strange, at least not the lower 7/5 or 10/7. The strangeness of it is that it defies, or at least seems to defy, a fixed keyboard.

[@demoure1680]

very self indulgent ideas

[@ClassicalNerd]

I don't see how you think that; Partch was basing his ideas on the way that sounds physically work, which had been known and explored since Medieval times.

[@demoure1680]

if you go into a daw and load a track up you can place distortion on said track which increases the volume of all harmonics and overtones to the volume of the fundimental what you get is a change of timbre not equivilent to a sound of a chord made of separte notes so in 2020 we have certain demonstrable informationn that overtones are only related totimbre of audio not harmony of music

[@demoure1680]

please bear with me im typing from my television lol

[@ClassicalNerd]

@@demoure1680 Timbre and harmony are more related than most people realize, which is basically what the Spectralist composers of the mid-to-late 20th century figured out. So yes, you do, indeed, get a change of timbre when you mess with overtones (which is part of the reason that all instruments sound different), but all of the overtones are also precisely consonant with the fundamental. They are their own pitches with their own frequencies and-importantly-their own ratios to the fundamental. Partch analyzed these and turned them into notes in and of themselves. These notes end up being much more consonant than the rougher approximations of those same notes given to us by 12-tone equal temperament.

[@demoure1680]

in the past they did not know overtones and harmonics are only in the category of audio timbre . you cannot build a ratio based system unlless your goal is have 1 note in music which you then change timbre by stacking lookk at the way organs work . electric guitar distorting a note is not creating a chord its only raising volume of overtones a acdc song has no 4 note chords

[@zAvAvAz]

1.49830703021 The reason being is that geometrically mathmatically speaking this number is accurate, just as 1.61826 for 36 edo is exacting geometrically perfect, again the reason being is there are multiple numbers for the physical edges of a shape of a thing, in this case a string in string theory being an outer edge on both sides and a center core. the center core is 1.5 whereas the outer edges of a dimensional string is measured at 1.49830703021. The physical form of this shape creates a vibration an oscillation if you will, that speaks energy forever vibrating by the mere structure of this creation of the word by god. = i am.