A correspondent named Tim Scott has found a typo in the Tableau Comparatif des Intervalles Musicaux, Alain Danielou’s encyclopedic 1958 catalogue of all even marginally significant intervals within an octave. On the right-hand bottom corner of page 48, the interval listed as 569/512 should actually be 567/512, as 3 to the 4th power times 7 is, of course, 567:
And as Tim points out, this is one of the intervals used in The Well-Tuned Piano. All fanatical microtonalists please mark your copies accordingly. That is all.
UPDATE: The day that Amazon extended its reach into the nation’s used-bookstores was one of the greatest days of my life, and has compensated for many of the indignities of living in the 21st century. I first saw Danielou’s Tableau Comparatif des Intervalles Musicaux in La Monte Young’s apartment, and lusted after it mightily. More than a decade later, once the used-bookstores went online, I found it over the web in a little store in Oregon. The nice lady who sent it to me had no earthly idea what it was, but said, “I knew someone was eventually going to know what that was and want it.”
FURTHER UPDATE 2.5.16: In response to this post, over at Disquiet, the ambient/electronica site,
Marc Weidenbaum has posted a series of pieces exploiting the difference between the 567th and 569th harmonics. It seems his internet group, The Disquiet Junto, posts a compositional challenge each week, and everyone has four days to come up with a short piece in response. This is really cool!
I will forgive Danielou for an occasional error. While in India, he took up residence in a deserted palace, undeterred by at least one tiger and one cobra who also enjoyed inhabiting this abode. The snake was fond of lowering itself from the chandelier above the dining room table when guests were around. Alain’s secret to coexisting with the tiger was not to get nervous when it passed by.
KG replies: Cool. I remember you telling me that now.
from Danielou’s “The Way to the Labyrinth: Memories of East and West”
Each year, we would take our trailer and go off on one or two expeditions, accompanied by our two servants, Gulab and Ramprasad, and sometimes even an assistant.
We would stop near rivers and waterfalls, take baths, and wash our clothes. At night, while the heat was slowly subsiding, we would look at the stars and listen to the sounds of the forest. The trailer protected us from tiers, wolves, snakes, and mosquitoes. We often met tigers and leopards; in the morning, we could see their footprints around the trailer. But we strictly observed the law of the forest tribes, which forbids the carrying of any kind of weapon, even a concealed knife, on the grounds that tigers will never attack an unarmed man. When we were in Ramgarh, in the Rajputana, I was calling Raymond to show him a particularly fine sculpture when I suddenly found myself face to face with a tiger, who was just stepping out of the ruined temple. We politely saluted each other, and the tiger continued on his way.
Awesome work on the document above, the Tableau etc. I find it fathomable that such a work could become inspiring if more widely published – where may I find it? Thanks. Kevin
KG replies: Click the blue link.
Thank you again for posting that – especially the info about the coolness of knowing it would come your way – you are a good philosopher of sound. Peace to you always, into the music we soar – soon more for me with keyboards etc. But I hate to have to stack up 12-noted keysets and then wait someday for a new keyboard style with enough notes on it – I’m having to play limited styles until their is one day a huge keybaord style with enough notespaces to even exhibit up to 11-limit sparsely noted…. you know how I mean. I’m cool with sticking to the basics in cycles etc. but I do end up needing more notes than listed on your page even.. but I’m talking about using only the 5-limit tones sometimes and generating pitchspaces by creating cycles up to 3375 or more for combinations in the numerator, or other tones like 625, and cycled further than that or than 729 with the 3s alone, I find it way cool how these notes intersect again into more common notes that are the functional tones we start with. Thanks for posting up this book though, been looking for something like it just within the past weeks, surprise! Peace & thank you.
“All fanatical microtonalists please mark your copies accordingly.”
Fanatical microtonalists may also be interested in this saxophone player – playing 128 notes to the octave:
I’m with you on the Amazon used books – just last month I got a copy of your American Music in the 20th Century that way.