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#Americans are exhausted by #political #news. #TV ratings and a new AP-#NORC poll show they’re tuning out
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#Americans are exhausted by #political #news. #TV ratings and a new AP-#NORC poll show they’re tuning out
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#Americans are exhausted by #political #news. #TV ratings and a new AP-#NORC poll show they’re tuning out
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#Americans are exhausted by #political #news. #TV ratings and a new AP-#NORC poll show they’re tuning out
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So, my buddy #DJShaxx is hosting a live event this Wednesday -- The Fool’s Last Beg. This event will be the closing party for #WMPG's Spring #Begathon !
Donate and share. WMPG broadcasts shows like #DemocracyNow, #CommunityVoicesForChange, #ReturningTheLand, and much, much more! #CommunityRadio is so important in this age of #CorporateMedia and #Billionaires!
Fool's Last Beg
"On April 1, WMPG’s local music show Local Motives takes over the Portland Media Center for a high-energy, one-night-only celebration: Fool’s Last Beg – the grand finale of Begathon.
"Hosted at the #PortlandMediaCenter on Congress Street, the event brings together live radio, music, and a bit of April Fool’s mischief to mark the final push of WMPG’s week-long listener-powered #fundraising drive.
"The evening will be emceed by Erin Ames of Radio Ya-Ya’s and feature a special live broadcast of Local Motives, WMPG’s beloved showcase of local music. The show will feature a set by Crazy Déjà Vu, known to bring “The New Freakout” vibe that will energize both the studio audience and listeners/viewers tuning in from home.
"Among the highlights of the night is 'Shaxx in the Glass.' #LeftOfTheDial host, DJ Shaxx will spin live from the Portland Media Center’s street-facing window, turning Congress Street into a spontaneous dance floor. Fans can also catch his famously unpredictable Karaoke Weather Report, broadcast live over WMPG’s airwaves.
"Flyer for Fools Last Beg Event“It’s exactly the kind of creative collaboration community media makes possible,” said Nate Eldridge, Executive Director of Portland Media Center. 'When local radio and local television come together, you get something spontaneous, joyful, and uniquely Portland. We’re thrilled to open our studio and our windows to the community for this celebration.'
"After a full week of on-air fundraising, Fool’s Last Beg marks the final opportunity for supporters to join the celebration in person and help push Begathon across the finish line
" 'Begathon is when our listeners remind us just how much WMPG means to them,' said #AnnellaLinton, Development Director at WMPG [and a very cool person!]. 'Fool’s Last Beg is our way of celebrating that relationship, with live music, a little silliness, and the incredible energy that comes from a community that believes in independent, local radio.'
"Come down, celebrate, dance in the street, and help keep Portland’s airwaves vibrant and fiercely local. Dress up (fun and colorful) and be in the live music video shoot for Crazy Déjà Vu."
Source:
https://www.wmpg.org/fools-last-beg-begathon-closing-party-at-pmc/#RadioFreeMaine #CollegeRadio #BuildingCommunity #CommunityVoices #Resistance #MutualAid #MaineEvents #FreeSpeechRadio #FreeSpeech #Begathon
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So, my buddy #DJShaxx is hosting a live event this Wednesday -- The Fool’s Last Beg. This event will be the closing party for #WMPG's Spring #Begathon !
Donate and share. WMPG broadcasts shows like #DemocracyNow, #CommunityVoicesForChange, #ReturningTheLand, and much, much more! #CommunityRadio is so important in this age of #CorporateMedia and #Billionaires!
Fool's Last Beg
"On April 1, WMPG’s local music show Local Motives takes over the Portland Media Center for a high-energy, one-night-only celebration: Fool’s Last Beg – the grand finale of Begathon.
"Hosted at the #PortlandMediaCenter on Congress Street, the event brings together live radio, music, and a bit of April Fool’s mischief to mark the final push of WMPG’s week-long listener-powered #fundraising drive.
"The evening will be emceed by Erin Ames of Radio Ya-Ya’s and feature a special live broadcast of Local Motives, WMPG’s beloved showcase of local music. The show will feature a set by Crazy Déjà Vu, known to bring “The New Freakout” vibe that will energize both the studio audience and listeners/viewers tuning in from home.
"Among the highlights of the night is 'Shaxx in the Glass.' #LeftOfTheDial host, DJ Shaxx will spin live from the Portland Media Center’s street-facing window, turning Congress Street into a spontaneous dance floor. Fans can also catch his famously unpredictable Karaoke Weather Report, broadcast live over WMPG’s airwaves.
"Flyer for Fools Last Beg Event“It’s exactly the kind of creative collaboration community media makes possible,” said Nate Eldridge, Executive Director of Portland Media Center. 'When local radio and local television come together, you get something spontaneous, joyful, and uniquely Portland. We’re thrilled to open our studio and our windows to the community for this celebration.'
"After a full week of on-air fundraising, Fool’s Last Beg marks the final opportunity for supporters to join the celebration in person and help push Begathon across the finish line
" 'Begathon is when our listeners remind us just how much WMPG means to them,' said #AnnellaLinton, Development Director at WMPG [and a very cool person!]. 'Fool’s Last Beg is our way of celebrating that relationship, with live music, a little silliness, and the incredible energy that comes from a community that believes in independent, local radio.'
"Come down, celebrate, dance in the street, and help keep Portland’s airwaves vibrant and fiercely local. Dress up (fun and colorful) and be in the live music video shoot for Crazy Déjà Vu."
Source:
https://www.wmpg.org/fools-last-beg-begathon-closing-party-at-pmc/#RadioFreeMaine #CollegeRadio #BuildingCommunity #CommunityVoices #Resistance #MutualAid #MaineEvents #FreeSpeechRadio #FreeSpeech #Begathon
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So, my buddy #DJShaxx is hosting a live event this Wednesday -- The Fool’s Last Beg. This event will be the closing party for #WMPG's Spring #Begathon !
Donate and share. WMPG broadcasts shows like #DemocracyNow, #CommunityVoicesForChange, #ReturningTheLand, and much, much more! #CommunityRadio is so important in this age of #CorporateMedia and #Billionaires!
Fool's Last Beg
"On April 1, WMPG’s local music show Local Motives takes over the Portland Media Center for a high-energy, one-night-only celebration: Fool’s Last Beg – the grand finale of Begathon.
"Hosted at the #PortlandMediaCenter on Congress Street, the event brings together live radio, music, and a bit of April Fool’s mischief to mark the final push of WMPG’s week-long listener-powered #fundraising drive.
"The evening will be emceed by Erin Ames of Radio Ya-Ya’s and feature a special live broadcast of Local Motives, WMPG’s beloved showcase of local music. The show will feature a set by Crazy Déjà Vu, known to bring “The New Freakout” vibe that will energize both the studio audience and listeners/viewers tuning in from home.
"Among the highlights of the night is 'Shaxx in the Glass.' #LeftOfTheDial host, DJ Shaxx will spin live from the Portland Media Center’s street-facing window, turning Congress Street into a spontaneous dance floor. Fans can also catch his famously unpredictable Karaoke Weather Report, broadcast live over WMPG’s airwaves.
"Flyer for Fools Last Beg Event“It’s exactly the kind of creative collaboration community media makes possible,” said Nate Eldridge, Executive Director of Portland Media Center. 'When local radio and local television come together, you get something spontaneous, joyful, and uniquely Portland. We’re thrilled to open our studio and our windows to the community for this celebration.'
"After a full week of on-air fundraising, Fool’s Last Beg marks the final opportunity for supporters to join the celebration in person and help push Begathon across the finish line
" 'Begathon is when our listeners remind us just how much WMPG means to them,' said #AnnellaLinton, Development Director at WMPG [and a very cool person!]. 'Fool’s Last Beg is our way of celebrating that relationship, with live music, a little silliness, and the incredible energy that comes from a community that believes in independent, local radio.'
"Come down, celebrate, dance in the street, and help keep Portland’s airwaves vibrant and fiercely local. Dress up (fun and colorful) and be in the live music video shoot for Crazy Déjà Vu."
Source:
https://www.wmpg.org/fools-last-beg-begathon-closing-party-at-pmc/#RadioFreeMaine #CollegeRadio #BuildingCommunity #CommunityVoices #Resistance #MutualAid #MaineEvents #FreeSpeechRadio #FreeSpeech #Begathon
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So, my buddy #DJShaxx is hosting a live event this Wednesday -- The Fool’s Last Beg. This event will be the closing party for #WMPG's Spring #Begathon !
Donate and share. WMPG broadcasts shows like #DemocracyNow, #CommunityVoicesForChange, #ReturningTheLand, and much, much more! #CommunityRadio is so important in this age of #CorporateMedia and #Billionaires!
Fool's Last Beg
"On April 1, WMPG’s local music show Local Motives takes over the Portland Media Center for a high-energy, one-night-only celebration: Fool’s Last Beg – the grand finale of Begathon.
"Hosted at the #PortlandMediaCenter on Congress Street, the event brings together live radio, music, and a bit of April Fool’s mischief to mark the final push of WMPG’s week-long listener-powered #fundraising drive.
"The evening will be emceed by Erin Ames of Radio Ya-Ya’s and feature a special live broadcast of Local Motives, WMPG’s beloved showcase of local music. The show will feature a set by Crazy Déjà Vu, known to bring “The New Freakout” vibe that will energize both the studio audience and listeners/viewers tuning in from home.
"Among the highlights of the night is 'Shaxx in the Glass.' #LeftOfTheDial host, DJ Shaxx will spin live from the Portland Media Center’s street-facing window, turning Congress Street into a spontaneous dance floor. Fans can also catch his famously unpredictable Karaoke Weather Report, broadcast live over WMPG’s airwaves.
"Flyer for Fools Last Beg Event“It’s exactly the kind of creative collaboration community media makes possible,” said Nate Eldridge, Executive Director of Portland Media Center. 'When local radio and local television come together, you get something spontaneous, joyful, and uniquely Portland. We’re thrilled to open our studio and our windows to the community for this celebration.'
"After a full week of on-air fundraising, Fool’s Last Beg marks the final opportunity for supporters to join the celebration in person and help push Begathon across the finish line
" 'Begathon is when our listeners remind us just how much WMPG means to them,' said #AnnellaLinton, Development Director at WMPG [and a very cool person!]. 'Fool’s Last Beg is our way of celebrating that relationship, with live music, a little silliness, and the incredible energy that comes from a community that believes in independent, local radio.'
"Come down, celebrate, dance in the street, and help keep Portland’s airwaves vibrant and fiercely local. Dress up (fun and colorful) and be in the live music video shoot for Crazy Déjà Vu."
Source:
https://www.wmpg.org/fools-last-beg-begathon-closing-party-at-pmc/#RadioFreeMaine #CollegeRadio #BuildingCommunity #CommunityVoices #Resistance #MutualAid #MaineEvents #FreeSpeechRadio #FreeSpeech #Begathon
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So, my buddy #DJShaxx is hosting a live event this Wednesday -- The Fool’s Last Beg. This event will be the closing party for #WMPG's Spring #Begathon !
Donate and share. WMPG broadcasts shows like #DemocracyNow, #CommunityVoicesForChange, #ReturningTheLand, and much, much more! #CommunityRadio is so important in this age of #CorporateMedia and #Billionaires!
Fool's Last Beg
"On April 1, WMPG’s local music show Local Motives takes over the Portland Media Center for a high-energy, one-night-only celebration: Fool’s Last Beg – the grand finale of Begathon.
"Hosted at the #PortlandMediaCenter on Congress Street, the event brings together live radio, music, and a bit of April Fool’s mischief to mark the final push of WMPG’s week-long listener-powered #fundraising drive.
"The evening will be emceed by Erin Ames of Radio Ya-Ya’s and feature a special live broadcast of Local Motives, WMPG’s beloved showcase of local music. The show will feature a set by Crazy Déjà Vu, known to bring “The New Freakout” vibe that will energize both the studio audience and listeners/viewers tuning in from home.
"Among the highlights of the night is 'Shaxx in the Glass.' #LeftOfTheDial host, DJ Shaxx will spin live from the Portland Media Center’s street-facing window, turning Congress Street into a spontaneous dance floor. Fans can also catch his famously unpredictable Karaoke Weather Report, broadcast live over WMPG’s airwaves.
"Flyer for Fools Last Beg Event“It’s exactly the kind of creative collaboration community media makes possible,” said Nate Eldridge, Executive Director of Portland Media Center. 'When local radio and local television come together, you get something spontaneous, joyful, and uniquely Portland. We’re thrilled to open our studio and our windows to the community for this celebration.'
"After a full week of on-air fundraising, Fool’s Last Beg marks the final opportunity for supporters to join the celebration in person and help push Begathon across the finish line
" 'Begathon is when our listeners remind us just how much WMPG means to them,' said #AnnellaLinton, Development Director at WMPG [and a very cool person!]. 'Fool’s Last Beg is our way of celebrating that relationship, with live music, a little silliness, and the incredible energy that comes from a community that believes in independent, local radio.'
"Come down, celebrate, dance in the street, and help keep Portland’s airwaves vibrant and fiercely local. Dress up (fun and colorful) and be in the live music video shoot for Crazy Déjà Vu."
Source:
https://www.wmpg.org/fools-last-beg-begathon-closing-party-at-pmc/#RadioFreeMaine #CollegeRadio #BuildingCommunity #CommunityVoices #Resistance #MutualAid #MaineEvents #FreeSpeechRadio #FreeSpeech #Begathon
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🚀 This Week in Fine-tuning & Training: Fastest-Growing Projects — May 04, 2026
This week in the Fine-tuning & Training space, we're seeing a surge in innovative tools that cater to specific needs of AI model training. From fine-tuning large language models (LLMs) with multimodal...
Read full report → https://pullrepo.com/report/this-week-in-fine-tuning-training-fastest-growing-projects-may-04-2026
#AI #OpenSource #GitHub #Tech #Fine-tuningTraining
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🚀 This Week in Fine-tuning & Training: Fastest-Growing Projects — May 04, 2026
This week in the Fine-tuning & Training space, we're seeing a surge in innovative tools that cater to specific needs of AI model training. From fine-tuning large language models (LLMs) with multimodal...
Read full report → https://pullrepo.com/report/this-week-in-fine-tuning-training-fastest-growing-projects-may-04-2026
#AI #OpenSource #GitHub #Tech #Fine-tuningTraining
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🚀 This Week in Fine-tuning & Training: Fastest-Growing Projects — May 04, 2026
This week in the Fine-tuning & Training space, we're seeing a surge in innovative tools that cater to specific needs of AI model training. From fine-tuning large language models (LLMs) with multimodal...
Read full report → https://pullrepo.com/report/this-week-in-fine-tuning-training-fastest-growing-projects-may-04-2026
#AI #OpenSource #GitHub #Tech #Fine-tuningTraining
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🚀 This Week in Fine-tuning & Training: Fastest-Growing Projects — May 03, 2026
This week in the Fine-tuning & Training space, we're seeing a surge in repositories focused on multimodal fine-tuning and efficient training methods. Developers are exploring new ways to optimize thei...
Read full report → https://pullrepo.com/report/this-week-in-fine-tuning-training-fastest-growing-projects-may-03-2026
#AI #OpenSource #GitHub #Tech #Fine-tuningTraining
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🚀 This Week in Fine-tuning & Training: Fastest-Growing Projects — May 03, 2026
This week in the Fine-tuning & Training space, we're seeing a surge in repositories focused on multimodal fine-tuning and efficient training methods. Developers are exploring new ways to optimize thei...
Read full report → https://pullrepo.com/report/this-week-in-fine-tuning-training-fastest-growing-projects-may-03-2026
#AI #OpenSource #GitHub #Tech #Fine-tuningTraining
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🚀 This Week in Fine-tuning & Training: Fastest-Growing Projects — May 03, 2026
This week in the Fine-tuning & Training space, we're seeing a surge in repositories focused on multimodal fine-tuning and efficient training methods. Developers are exploring new ways to optimize thei...
Read full report → https://pullrepo.com/report/this-week-in-fine-tuning-training-fastest-growing-projects-may-03-2026
#AI #OpenSource #GitHub #Tech #Fine-tuningTraining
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🚀 This Week in Fine-tuning & Training: Fastest-Growing Projects — May 02, 2026
This week in the Fine-tuning & Training space, we're seeing a surge of innovative tools that cater to specific needs in AI model training. From fine-tuning multimodal models on Apple Silicon to inject...
Read full report → https://pullrepo.com/report/this-week-in-fine-tuning-training-fastest-growing-projects-may-02-2026-2
#AI #OpenSource #GitHub #Tech #Fine-tuningTraining
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Unique among the senses, the ear expends energy to amplify the stimuli that it detects. New research shows that a segment of mammalian cochlea ex vivo displays features of this active process—amplification, frequency tuning, compressive nonlinearity & generation of distortion products—operating locally & near criticality at a Hopf bifurcation—a unified biophysical principle that underlies auditory processing across species. https://www.pnas.org/doi/10.1073/pnas.2503389122
#PNAS #Hearing #Auditory #Complexsystems -
Tuning my AI in for some much better results for Starsector portraits.
Here's a bunch of the woman portraits.
#AIArt #StableDiffusion #StableDiffusionArt #AIGenerated #Character #CharacterArt #TTRPG #DnD #Pathfinder #Starsector #StarsWithoutNumber #MongooseTraveller
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Ácido y ultrajado: Un desafío de conversión a bajo presupuesto dio como resultado este Bentley Turbo R despojado de su lujo original
#Bentley #BerlinaSedn #Curiosidades #Gasolina #MasDe49 #Tuning #Vdeo #BentleyTurboR #Mercedes600SELAMG #RollsRoyceSilverShadow #TopGear
#espirituRACER #coches #cars -
Ethnic outfits beautifully reflect our heritage while adding a touch of elegance and charm. However, many professionals hesitate to wear ethnic attire to work, believing it may not align with corporate aesthetics. The truth is, ethnic wear can be styled in a way that exudes professionalism, confidence, and elegance, making it a perfect choice for office settings. Read More: https://byshree.com/blogs/news/office-ready-ethnic-wear-styling-tips-for-a-chic-professional-look
#fashion #clothing #shopping #onlineshopping #kurtisale #tops #tunics #kurta #women #kurti -
#AlAhly décroche son 12e titre (dont 6 en 8 ans) de champion d'Afrique ! https://www.lequipe.fr/Football/Actualites/Al-ahly-remporte-encore-la-ligue-des-champions-d-afrique-contre-l-esperance-tunis/1470104
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🧠 New study by Asumbisa, Peyrache & Trenholm (2025): Stereo #olfaction underlies stable #coding of #HeadDirection in blind mice. Inhibiting #odor detection in just one nostril, or removing the spatial difference in airflow, disrupts head direction cell tuning and impairs mice’s spatial orientation → stereo smell is essential for using olfactory cues to form a stable, #allocentric sense of direction.
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Unsloth AI Releases Unsloth Studio: A Local No-Code Interface For High-Performance LLM Fine-Tuning With 70% Less VRAM Usage The transition from a raw dataset to a fine-tuned Large Language Model (L...
#Agentic #AI #AI #Infrastructure #AI #Shorts #Applications #Artificial #Intelligence #Editors #Pick
Origin | Interest | Match -
[Перевод] Генерация BPMN с помощью LLM в диалоговом режиме: эксперименты и выводы
Авторы свежей научной работы попробовали заставить обычные открытые LLM (от 1B до 70B) генерировать валидный BPMN-XML прямо в чате по текстовому описанию процесса. Если вкратце, то без дообучения — полный провал. 80% токенов тратится на XML-мусор, модели сыплются на синтаксисе, забывают ветки и галлюцинируют теги. Работает только на больших моделях и то не очень хорошо. Но вроде просматривается рабочий вариант для генерации BPMN — берем 7–13B модель, дообучаем через LoRA/QLoRA на нормальном датасете, переходим на компактный JSON вместо XML и добавляем Preference Tuning + CoT. Тогда может быть взлетит.
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𝗪𝗜𝗞𝗜𝗣𝗘𝗗𝗜𝗔 𝗣𝗜𝗖𝗧𝗨𝗥𝗘 𝗢𝗙 𝗧𝗛𝗘 𝗗𝗔𝗬
✧ Ibn Khaldun ✧
Ibn Khaldun (1332–1406) was an Arab scholar, historian, philosopher, and sociologist. Born in Tunis into an upper-class Andalusian family of Arab descent, his family's high rank enabled him to study with prominent teachers in Maghreb, where he received a classical Islamic education including the Quran, as well as mathematics, logic, and philosophy...
#BlackDeath #OttomanEmpire #Maghreb #Quran #Wikipedia
https://en.wikipedia.org/wiki/Ibn_Khaldun -
Rabat, Alger et Tunis dans les luttes panafricaines
https://web.brid.gy/r/https://orientxxi.info/Rabat-Alger-et-Tunis-dans-les-luttes-panafricaines
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« Du festival panafricain d’Alger aux Journées cinématographiques de Carthage, en passant par la revue Souffles, se dessine une histoire où le #Maghreb finance des maquis, distribue des passeports et accueille les Black Panthers. »
#HorizonsXXI reçoit #ParaskaTolanSzkilnik, autrice de #MaghrebNoir. Rabat, Alger et Tunis dans les #luttesPanafricaines
https://www.youtube.com/watch?v=mJJ_ESzpm-s
#BlackHistory #panafricanisme #luttesDécoloniales #livres @bookstodon
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Tiny Musical Intervals
Music theorists have studied many fractions of the form
2i 3j 5kthat are close to 1. They’re called 5-limit commas. Especially cherished are those that have fairly small exponents—given how close they are to 1. I discussed a bunch here:
and I explained the tiniest named one, the utterly astounding ‘atom of Kirnberger’, here:
The atom of Kirnberger equals
2161 · 3-84 · 5-12 ≈ 1.0000088728601397Two pitches differing by this ratio sound the same to everyone except certain cleverly designed machines. But remarkably, the atom of Kirnberger shows up rather naturally in music—and it was discovered by a student of Bach! Read my article for details.
All this made me want to systematically explore such tiny intervals. Below is a table of them, where I list the best ones: the ones that are closest to 1 for a given complexity. The first eleven have names, and many of them play important roles in music! But beyond that point, all but one remain unnamed—or at least I don’t know their names. That’s because they’re too small to be audible, and—except for one—not even considered to be of great theoretical importance.
I’ll list these numbers in decimal form and also in cents, where we take the logarithm of the number in base 2 and multiply by 1200. (I dislike this blend of base 2, base 10 and base 12, but it’s traditional in music theory.)
Most importantly, I list the monzo of each numbers. This is the vector of exponents: for example, the monzo of
2i 3j 5kis
[i, j, k]In case you’re wondering, this term was named after the music theorist Joseph Monzo.
Finally, I list the Tenney height of each number. This is a measure of the number’s complexity: the Tenney height of
2i 3j 5kis
∣i∣ log2(2) + ∣j∣ log2(3) + ∣k∣ log2(5)The table below purports to list only 5-limit commas that are close to 1 as possible for a given Tenney height. More precisely, it should list numbers of the form 2i 3j 5k that are > 1 and closer to 1 than any number with smaller Tenney height—except of course for 1 itself.
CentsDecimalNameMonzoTenney height498.041.3333333333just perfect fourth[2, −1, 0]3.6386.311.2500000000just major third[−2, 0, 1]4.3315.641.2000000000just minor third[1, 1, −1]4.9203.911.1250000000major tone[−3, 2, 0]6.2182.401.1111111111minor tone[1, −2, 1]6.5111.731.0666666667diatonic semitone[4, −1, −1]7.970.671.0416666667lesser chromatic semitone[−3, −1, 2]9.221.511.0125000000syntonic comma[−4, 4, −1]12.719.551.0113580247diaschisma[11, −4, −2]22.08.111.0046939300kleisma[−6, −5, 6]27.91.951.0011291504schisma[−15, 8, 1]30.01.381.0007999172unnamed?[38, −2, −15]76.00.861.0004979343unnamed?[1, −27, 18]85.60.571.0003289700unnamed?[−53, 10, 16]106.00.291.0001689086unnamed?[54, −37, 2]117.30.231.0001329015unnamed?[−17, 62, −35]196.50.0471.0000271292unnamed?[−90, −15, 49]227.50.01541.0000088729atom of Kirnberger[161, −84, −12]322.00.01151.0000066317unnamed?[21, 290, −207]961.30.000881.0000005104quark of Baez[−573, 237, 85]1146.0You’ll see there’s a big increase in Tenney height after the schisma. This is very interesting: it suggests that the schisma is the last ‘useful’ interval. It’s useful only in that it’s the ratio of two musically important commas, the syntonic comma and the Pythagorean comma. Life in music would be simpler if these were equal, and in well-tempered tuning systems it’s common to pretend that they are.
All the intervals in this table up to the schisma were discovered by musicians a long time ago, and they all have standard names! After the schisma, interest drops off dramatically.
The atom of Kirnberger has such amazing properties that it was worth naming. The rest, maybe not. But as you can see, I’ve taken the liberty of naming the smallest interval in the table the ‘quark of Baez’. This is much smaller than all that come before. It’s in bad taste to name things after oneself—indeed this is item 25 on the crackpot index—but I hope it’s allowed as a joke.
I also hope that in the future this is considered my smallest mathematical discovery.
Here is the Python code that should generate the above information. If you’re good at programming, please review it and check it! Someone gave me a gift subscription to Claude, and it (more precisely Opus 4.5) created this code. It seems to make sense, and I’ve checked a bunch of the results, but I don’t know Python.
from math import log2 log3 = log2(3) log5 = log2(5) commas = [] max_exp_3 = 1200 max_exp_5 = 250 for a3 in range(-max_exp_3, max_exp_3+1): for a5 in range(-max_exp_5, max_exp_5+1): if a3 == 0 and a5 == 0: continue # Find a2 that minimizes |a2 + a3 * log2(3) + a5 * log2(5)| target = -(a3 * log3 + a5 * log5) a2 = round(target) log2_ratio = a2 + a3 * log3 + a5 * log5 cents = abs(1200 * log2_ratio) if cents > 0.00001: # non-trivial tenney = abs(a2) + abs(a3) * log3 + abs(a5) * log5 commas.append((tenney, cents, a2, a3, a5)) # Find Pareto frontier commas.sort(key=lambda x: x[0]) # sort by Tenney height frontier = [] best_cents = float('inf') for c in commas: if c[1] < best_cents: best_cents = c[1] frontier.append(c) # Print results for tenney, cents, a2, a3, a5 in frontier: log2_ratio = a2 + a3 * log3 + a5 * log5 decimal = 2**log2_ratio if decimal < 1: decimal = 1/decimal a2, a3, a5 = -a2, -a3, -a5 print(f"{cents:.6f} cents | {decimal:.10f} | [{a2}, {a3}, {a5}] | " f"Tenney: {tenney:.1f}")Gene Ward Smith
In studying this subject I discovered that tiny 5-limit intervals were studied by Gene Ward Smith, a mathematician I used to see around on sci.math and the like. I never knew he worked on microtonal music! I am sad to hear that he died from COVID-19 in January 2021.
I may just be redoing a tiny part of his work: if anyone can find details, please let me know. In his memory, I’ll conclude with this article from the Xenharmonic Wiki:
#FindGene Ward Smith (1947–2021) was an American mathematician, music theorist, and composer.
In mathematics, he worked in the areas of Galois theory and Moonshine theory.
In music theory, he introduced wedge products as a way of classifying regular temperaments. In this system, a temperament is specified by means of a wedgie, which may technically be identified as a point on a Grassmannian. He had long drawn attention to the relationship between equal divisions of the octave and the Riemann zeta function.[1][2][3] He early on identified and emphasized free abelian groups of finite rank and their homomorphisms, and it was from that perspective that he contributed to the creation of the regular mapping paradigm.
In the 1970s, Gene experimented with musical compositions using a device with four square-wave voices, whose tuning was very stable and accurate, being controlled by a crystal oscillator. The device in turn was controlled by HP 9800 series desktop computers, initially the HP 9830A, programmed in HP Basic, later the 9845A. Using this, he explored both just intonation with a particular emphasis on groups of transformations, and pajara.
Gene had a basic understanding of the regular mapping paradigm during this period, but it was limited in practice since he was focused on the idea that the next step from meantone should keep some familiar features, and so was interested in tempering out 64/63 in place of 81/80. He knew 7-limit 12 and 22 had tempering out 64/63 and 50/49 in common, and 12 and 27 had tempering out 64/63 and 126/125 in common, and thought these would be logical places to progress to, blending novelty with familiarity. While he never got around to working with augene, he did consider it. For pajara, he found tempering certain JI scales, the 10 and 12 note highschool scales, led to interesting (omnitetrachordal) results, and that there were also closely related symmetric (MOS) scales of size 10 and 12 for pajara; he did some work with these, particularly favoring the pentachordal decatonic scale.
Gene was among the first to consider extending the Tonnetz of Hugo Riemann beyond the 5-limit and hence into higher dimensional lattices. In three dimensions, the hexagonal lattice of 5-limit harmony extends to a lattice of type A3 ~ D3. He is also the first to write music in a number of exotic intonation systems.
Historical interest
• Usenet post from 1990 by Gene Smith on homomorphisms and kernels
• Usenet post from 1995 by Gene Smith on homomorphisms and kernelsSee also
• Microtonal music by Gene Ward Smith
• Hypergenesis58 (a scale described by Gene Ward Smith)References
[1] Rusin, Dave. “Why 12 tones per octave?”
[2] OEIS. Increasingly large peaks of the Riemann zeta function on the critical line: OEIS: A117536.
[3] OEIS. Increasingly large integrals of the Z function between zeros: OEIS: A117538.
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