Fifths Are Everywhere

Staff lines, letter names, and intervals emphasize pitch proximity: diatonic steps and semitone alternations; but fifths occupy an equally important position in the fundamental organization of pitch.

Letter names & intervals

Fifths untangle the messy order of intervals and scales.

Where does the ordering PMMPPMMP come from?

Perfect fifths (or their inverse, perfect fourths) generate all letter names; other intervals can’t do that.

Bbb Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# F##

It is no surprise that intervals can be also ordered by perfect fifths. Doing so reveal the spectrum of qualities. (Since letter names and intervals can be generated using fifths, we can alternatively express intervals as combination of fifths and octave displacements.)

Intervals from middle C; top notes are generated by fifths, then folded into the same octave.

Scales & key signatures

Seven fifths make a diatonic scale. The tone/semitone pattern of TTSTTTS can be more efficiently described as seven fifths, which key signatures imply.

Seven fifths make a diatonic scale.

The circle of fifths show how each shift swaps one note for another, and crucially, why the tonic moves by a fifth. Because the ordering by fifths traces back to scales and letter names themselves.

Intervals & chords in diatonic scales

Perfect and diminished fifths also reveal the hidden structure behind interval and chord qualities in diatonic scales.

Where does the ordering MmmMMmdim come from?

In a diatonic scale, all fifths are perfect except for B to F, a diminished fifth. From the perspective of fifths, this little asymmetry creates the rich variety of intervals and chords in diatonic scales. When intervals in diatonic scales are arranged in generic fifths, the quality changes whenever B transposes to F (arrows below).

Intervals in diatonic scales arranged in fifths.

Chords are different intervals combined. Chords (or any set of notes) in a diatonic scale have as many qualities as there are notes, since each of those B’s have to loop back to F’s at different points. That’s why there’s three types of triads and four types of seventh chords in diatonic scales. Of course, adding accidentals like raised leading tones in minor can further alter these chords.

Chords in diatonic scales arranged in fifths.

TL;DR: Symbolically, abstract pitch concepts emphasizes pitch proximity (steps and semitones); but they are underpinned by a deeper organization based on fifths.

A Pythagorean Postlude

The fifth-based approach above is loosely Pythagorean. Pythagorean tuning uses pure octaves (2:1 frequency, 1:2 string length) and pure fifths (3:2 frequency, 2:3 string length) to generate all notes. I say ‘loosely’ because the pitches above can be mapped to any kind of tuning, and Pythagoreans did other things like worshipping numbers and abstaining from beans. Other tunings imply different kinds of pitch structure. For example, in equal temperament (12TET), F# = Gb, which means that music notation contains redundancies in 12TET. In Pythagorean tuning, the difference between F# and Gb is real (a Pythagorean comma). It doesn’t mean that staff notation and intervals must be tuned in a Pythagorean way, but it best correlates with the methods and structure of Pythagorean tuning.

Midi, Zoom, & Me

Here are some easy, lightweight, plug & play options for sharing music from a MIDI keyboard over Zoom.

MIDI keyboards don’t usually generate sound. You need to plug it into a synthesizer or computer. Here are 4 broad types of options.

For the best chances of success, plug the keyboard in before opening an app. For web apps, use Chrome if possible. In many cases, you also have to select your MIDI keyboard model as the MIDI Input. Audio Output should be the model of your speaker or headphone.

1. Online rooms

EASIEST. With a shared link, people on the other end can listen and even jam from the browser. No zoom is required at all.

My pick: https://musiclab.chromeexperiments.com/Shared-Piano/

Others: https://www.multiplayerpiano.com/

2. Online synths

These web apps generate sound from your MIDI keyboard, but you’d have share it through Zoom.
In Zoom, select share screen, select your browser, and tick shared computer sound.
For sound only, select share screen, go to the advanced tab, select share computer sound only.

My pick: https://dotpiano.com/

Others:https://electrictelepathy.com/web-apps/fluoresynth/
https://onlinesequencer.net/
https://www.caseyrule.com/projects/piano https://virtualpiano.eu/
https://recursivearts.com/virtual-piano/ https://midi.city/
https://synth.playtronica.com/ https://www.webaudiomodules.org/wamsynths/ https://www.gsn-lib.org/apps/cardboardsynth/index.html

Online notation apps like Flat also have in-app keyboards: https://flat.io/help/en/music-notation-software/midistart.html. To play instead of edit, turn off write while playing.

Note: Web apps are not secure; some explicitly broadcast your music. So don’t encode your bank account number as musical notes.

3. Downloadable synths

Mac users rejoice!

GarageBand comes with Macs; it is a basic DAW (Digital Audio Workstation) that can handle MIDI and much more. See https://support.apple.com/kb/PH25066 and https://support.apple.com/kb/PH25039.

There’s still all sorts of piano apps for Windows users, like https://sourceforge.net/projects/freepiano/.

VST

If you don’t like default sound(s) of the apps, there’s a whole wide world of VST instruments. Many are free, some cost you an arm and a leg. You can load VST’s into your DAW, or use a VST host like https://www.tone2.com/nanohost.html or https://www.cantabilesoftware.com/. Here’s some free piano VSTs: https://blog.landr.com/best-free-piano-vsts/. Some, like https://www.native-instruments.com/en/catalog/free/ also provide a standalone app. This is a rabbit hole I’m not diving any further into…

Audio Routing

Last but not least, audio applications often override or bypass normal sound settings, meaning Zoom sometimes doesn’t pick it up the audio at all. (This is why I’m kinda enamored by the web synths.) Test your setup over Zoom with a friend. If it doesn’t work, try the following.

For Mac users, Zoom has a ZoomAudioDevice that your DAW can output to.

If nothing else works, you may have to route your computer sounds (and microphone output) into a virtual input, and then get Zoom to recognize the virtual output as its input. These are super finagly. Here are two popular audio routing apps: https://rogueamoeba.com/loopback/ (Mac), https://www.vb-audio.com/Cable/ (Win).

4. Go Acoustic

Swap your MIDI keyboard for a portable electronic piano (which usually includes MIDI out) or a melodica. Make sure you enable and turn on original sound. https://support.zoom.us/hc/en-us/articles/115003279466-Enabling-option-to-preserve-original-sound

The melodica is young Jacob Collier’s instrument of choice.