Diesis (melodic unit)

The diesis is a small melodic unit of about an augmented comma's size. It is often believed to be of some psychoacoustic significance. In particular, Zhea Erose defines it as, fairly broadly, any interval in the range 31 to 41 cents, or more narrowly 35 to 38 cents; shimmerstep is a synonymous term used by Zhea. When played in the E3-E5 range, those intervals allegedly tend to beat at the speed of typical human singing vibrato. Zhea considers 31edo and 34edo to be special for having an interval in this range:

re: the hyperstep stuff:

Analysis of phonograph recordings of virtuoso string performers (Reger, 1932; Hollinshead, 1932) found rates ranging from 5.6 to 7 Hz (see Table 1). This research concluded that although the extent of the violin vibrato is smaller than for singing, the rates are similar. Cheslock (1931) and Small (1937) analyzed phonograph recordings of performances by Kreisler, Menuhin, Szigeti and others. Vibrato was present in almost all tones, and the mean rate was around 6.3 Hz. Results from the Iowa studies have been largely confirmed in later studies, for example, Fletcher and Sanders (1967) found vibrato rates about 6 Hz, only slightly slower than some of the early reports. Thibeault (1997) studied solo bassists and found rates ranging from 5 to 7 Hz and reported a correlation of vibrato rate with tempo of excerpts, but not with pitch register. Geringer and Allen (2004) studied vibrato characteristics of 40 high school and college violinists and cellists. We analyzed whole notes performed in first position, and we found somewhat slower rates of vibrato, 5.5 Hz.

When we study voices in multiple singing styles and cross culturally we see the average beat rate of vibrato falls between 4.5-6.5 cycles per second. At a C4, the 31edo shimmerstep (1\31) beats at 5.75 times a second which is a clear center of human vibrato rates. Of course the perceived beat rate will change depending on the fundamental but if we take C4 as a nice "center" we see:

at a C4, 261.6 Hz, 29edo seems to beat at ~425 bpm — thus, 29's corrosive step hits at ~7 Hz. 31edo seems to beat at ~345 bpm — thus, 31's shimmerstep hits at ~5.75 Hz 34edo seems to beat at ~275 bpm — thus, 34's shimmerstep hits at ~4.583 Hz slower but still within that normal vibrato range. 41edo seems to beat at ~228 bpm — thus, 41edo's glimmerstep hits at 3.8 Hz which starts to exist outside the boundaries of vibrato typical. For this reason, that is why I tend to work a lot with 29-34 as a general pre-image of notes and why I consider them to be exceptional for overall gestalt and chord work compared to something like 41, 43 or slightly higher etc or 26 or slightly lower. Which is quite interesting because then you start to wrap around on yourself. Those zones to me are less interesting gestalts. — Zhea Erose, https://discord.com/channels/332357996569034752/859884647337033738/1014961523220815892

See also

• Diesis (disambiguation page)