Now as I did last time, let me put in two axes to make the picture a little easier to draw.

和我上次做的一样,画两个纵轴来帮助我们作图

耶鲁公开课 - 博弈论课程节选

Well,if you go back to the formation of musical notation from the ninth through the twelfth centuries we see that very early on these two dimensions of music the two axes of music that we talked about before pitch vertically and duration horizontally, are in place and we have these spots in this grid.

回顾一下从公元九世纪至二十世纪,音乐记谱法的历史形成过程,我们可以看出,音乐的两个维度,就是我们之前提到的音乐的两个轴,纵轴是音高,横轴是时值,在早期已经存在了,我们在这样的网格上用点记录

耶鲁公开课 - 聆听音乐课程节选

On the vertical axis I'll put two vertical axes in, just for the sake of things on the vertical axis I'll put my expected payoffs.

坐标系的纵轴,由于种种原因,我花了两个纵轴,纵轴表示我的预期收益

耶鲁公开课 - 博弈论课程节选

Time. Okay, pitch and time and pitch and duration, excellent, so those are the two dimensions of music and well, indeed we could even call them the axes of music because we tend to think of pitch on a vertical axis.

时间,音高和时间,或者是音高和时值,非常好,它们是音乐的两个维度,其实我们可以称呼它们为音乐的两轴,因为我们趋向于将音高放在竖轴上来考虑

耶鲁公开课 - 聆听音乐课程节选