科学与数学en.wikipedia.org
谢泼德音调
Shepard tone
2012 — 2022,它一次次回到首页
黑点是上首页(≥ 50 分)的那次投稿,空心点是没冲上去的投稿,点越大分数越高。
导读
维基百科条目介绍 Shepard tone:一种听觉错觉,由相隔八度的多个音叠加并通过音量包络循环,让人感到音高在无限上升或下降,却始终停留在相近音域。它常被音乐、电影和游戏用来制造持续紧张或无尽循环的效果。
为什么经久不衰:它用一个很简单的心理声学技巧制造出强烈的“无限音阶”错觉,是理解听觉感知、音乐和声音设计的经典入口。
HN 评论精选
Risset rhythm 是节奏版的 Shepard tone,Autechre 有巧妙示例。
概念类似的是 Risset rhythm(文中也简略提到),节奏的速度似乎持续加快或减慢。Autechre 的《Fold4, Wrap5》是个很酷的例子。看懂原理不难,但效果仍然很讨喜:每小节都有一个点,节拍切换成自身的双倍速版本,同时曲子的速度不断降低,使双倍速节奏又过渡回原来的节奏。
smrq查看英文原文
Similar in concept is the Risset rhythm (it's briefly alluded to in the article), where the tempo of the rhythm seems to constantly speed up or slow down. The song "Fold4, Wrap5" by Autechre is a cool example. It's not hard to see how it works, but it's a delightful effect regardless. Each bar has a point at which the beat shifts to a double-time version of itself, while the tempo of the track constantly decreases so that the double-time rhythm transitions back to the original rhythm.
用巴赫低音线类比说明 Shepard tone 的八度循环原理。
有个办法能理解它们如何运作:听巴赫《g小调幻想曲与赋格》BWV 542 中的 Fantasia。约 3:54 有一段著名段落,巴赫开始围绕五度“绕圈”。大致模式是手上和弦的音在“上升”,而脚踏低音在下降。听低音线,它似乎连续三十个音逐级下行;但试着唱任意一个音并连续下行三十音,你可能做不到。若巴赫真在低音里这么做,最后一个音会非常低且松垮。那么低音线如何看似继续逐级下行却仍留在相近音域?答案是一个在一年级乐理课上通常让人极度无聊的两词术语。巴赫正是在音高领域用这个概念达成目的,它类似于频域中产生 Shepard tone 的机制。
jancsika查看英文原文
Here's a way to figure out how they work: Listen to Bach's Fantasia from Fantasia and Fugue in G minor, BWV 542: https://www.youtube.com/watch?v=LWyiiOkhwoc At about 3:54 you'll hear a famous section where Bach starts "circling" around fifths. The general pattern is that the notes of the chords in the hands "rise" while the feet descend. Listen to the bass line. It seems to descend by step for thirty notes in a row. But try singing any note and singing down a scale for thirty notes in a row. You probably can't do it. And if Bach did that in the bassline the final note would be really low and flabby. So how does the bassline seem to continue descending by step while remaining in the same general range? The answer is a two-word phrase that is usually met by profound boredom in first-year music theory classes. But that concept is what Bach uses in the pitch domain here to achieve his aim. And its analogous to what happens in the frequency domain to produce a Shepard tone.
听感并非完美无缝,能察觉重叠音切换的节点。
嗯,对我来说它听起来像一串重叠的下行音。有一个明显的位置,下行音被上方另一个音补充。这大约在 20 秒时首次出现。补充:明显变化似乎非常接近 22 秒。
SideburnsOfDoom查看英文原文
Hm, to me it sounds like a sequence of overlapping falling tones. There's a noticeable point where the falling tone is supplemented by one above it. This first happens about 20s in. edit The noticeable change seems to be very close to 22s.
游戏中的经典应用案例:无限楼梯。
这个效果也被用在《超级马力欧64》的无限楼梯中。
robert-boehnke查看英文原文
This effect was also used for the infinite stairs in Super Mario 64 http://www.youtube.com/watch?feature=player_detailpage&v=70J8SOX5w64#t=30s
历次讨论
同类还值得读
如果月球只有 1 像素:一个极其精确的太阳系模型(2014)
If the moon were only 1 pixel: A tediously accurate solar system model (2014)
一个网页版太阳系模型,以“如果月亮只有 1 像素”的真实比例呈现:你必须一路横向滚动,才能体会行星之间空旷到何等程度。
科学与数学上首页 7 次 · 2014–2025joshworth.com编辑精选沉浸式线性代数(2016)
Immersive Linear Algebra (2016)
《Immersive Linear Algebra》是一本完全免费、开放在线的线性代数“超文本教科书”,其最大特色是大量可交互的图形:读者可以直接拖动、操作图中的向量、矩阵和变换…
科学与数学上首页 5 次 · 2015–2024immersivemath.com编辑精选如何将贝果切成两个相连的半环(2009)
How to Slice a Bagel into Two Linked Halves (2009)
数学家 George Hart 的经典教程,演示如何用一刀把贝果切成两个相互扣住的环,并附上切割步骤与数学原理。
科学与数学上首页 5 次 · 2009–2022georgehart.com“犹太问题”:一组用于歧视的数学题
Jewish problems
一篇 arXiv 论文,整理并讨论苏联时期犹太学生在申请大学数学系时被问到的特殊数学难题:这些题往往有简单解法却极难想到,被用作面试中拒绝犹太考生的手段。
科学与数学上首页 5 次 · 2011–2021arxiv.org你的身体并非为长久而造:人类死亡率数据的一课
Your body wasn’t built to last: a lesson from human mortality rates
文章从人类死亡率随年龄变化的统计规律出发,解释身体并非为长久使用而设计:年轻时死亡风险较低,之后随年龄近似指数上升,像复杂系统在不断累积损伤。
科学与数学上首页 5 次 · 2009–2018gravityandlevity.wordpress.com