Just how accurate is ‘in tune’?

Short answer: within 5.9 Hz of your target frequency.

The long answer, though, is a little more involved…

According to Jake Mandell, at 500 Hz, a normal person can reliably differentiate two tones 6 Hz apart. For harpists, this little tidbit of information is potentially revolutionary. It means that …

if I tune my harp string incorrectly by 5.9 Hz, or less, the average person won’t be hear that it’s out of tune. 

This may sound unimportant, but…  

I spend around 13 hours a year tuning my harp!

It takes me 3 minutes, around 250 times a year. If I can shorten my time by one minute every time I tune my harp, and still achieve a sound acceptable to most humans, I’ll save 4 hours of my life every year… and I’d gladly watch a few films rather than tune my harp, thank you very much!! 🙂

Quick caveat: 500 Hz is around the B natural above middle C. Does the normal person’s sensitivity to pitch change according to the register of the two tones; e.g. if we pluck 2 of the high strings on the harp, or 2 the lowest strings? Probably. Also, perhaps a normal person’s sensitivity to pitch changes according to whether two notes are sounded simultaneously OR one after the other. I’ve emailed an expert asking these questions and am currently waiting on their answer. But while I’m waiting, for a fun experiment, let’s presume that the average person’s differentiation of two tones is >6Hz at all registers of the harp, and for tones plucked simultaneously and consecutively. So…

For the average person to hear something as ‘in tune’ we have to make sure that the interval between 2 imprecisely-tuned strings is less than 6 Hz. 

That’s easy, right? I’ll just tune each string within 5.9 Hz of its correct pitch! Bingo!

But … we hear strings in relation to one another. If one string is 5.9 Hz sharp, and the next string played is 5.9 Hz flat, the interval between both pitches will be bigger than normal by 11.8 Hz, and therefore the average listener will hear the interval as ‘wrong’.

So my second idea is: let’s make sure that each string is tuned to within 2.95 Hz of its intended correct pitch. Now, if one string is 2.95 Hz sharp, and the one played after it is 2.95 Hz flat, the difference will be 5.9 Hz, which is less than 6 Hz, and therefore (in theory!) our listener will think it sounds beautiful, even though in theory it’s out of tune!!!

Next step: the unit of measurement we’ve been using so far is “Hertz”. However, the majority of harp tuners use a unit of measurement called ‘cents’. So we have to translate the 2.95 Hz into cents. 

I did this in an Excel file, which I include below; the column marked ‘2.95 Hz in cents’ is the hypothetical margin of error for a harpist so that they sound in tune… even when, precisely speaking, they’re not!! I’m a bit sceptical, myself… according to these calculations, the lowest C on my harp can be 77 cents out of tune and the average human won’t notice. I have more faith in humanity – I think they’ll notice the harp sounds a bit dodgy. Help me out here…  try tuning your harp with my crazy experiment and tell me how it goes!

Note: Hertz are logarithmic (they multiply from one tone to the next), cents are linear. So the margin of error for each string is different. 

LEVER HARP 8VENote2.95 Hz in cents
LEVER HARP 8VE 5C 276
LEVER HARP 8VE 5C # 2 /D b 272
LEVER HARP 8VE 5D 268
LEVER HARP 8VE 5D # 2 /E b 264
LEVER HARP 8VE 5E 260
LEVER HARP 8VE 4F 257
LEVER HARP 8VE 4F # 2 /G b 254
LEVER HARP 8VE 4G 251
LEVER HARP 8VE 4G # 2 /A b 248
LEVER HARP 8VE 4A 245
LEVER HARP 8VE 4A # 2 /B b 243
LEVER HARP 8VE 4B 240
LEVER HARP 8VE 4C 338
LEVER HARP 8VE 4C # 3 /D b 336
LEVER HARP 8VE 4D 334
LEVER HARP 8VE 4D # 3 /E b 332
LEVER HARP 8VE 4E 330
LEVER HARP 8VE 3F 328
LEVER HARP 8VE 3F # 3 /G b 327
LEVER HARP 8VE 3G 325
LEVER HARP 8VE 3G # 3 /A b 324
LEVER HARP 8VE 3A 323
LEVER HARP 8VE 3A # 3 /B b 321
LEVER HARP 8VE 3B 320
middle CC 419
LEVER HARP 8VE 3C # 4 /D b 418
LEVER HARP 8VE 3D 417
LEVER HARP 8VE 3D # 4 /E b 416
LEVER HARP 8VE 3E 415
LEVER HARP 8VE 2F 414
LEVER HARP 8VE 2F # 4 /G b 413
LEVER HARP 8VE 2G 413
LEVER HARP 8VE 2G # 4 /A b 412
LEVER HARP 8VE 2A 411
LEVER HARP 8VE 2A # 4 /B b 411
LEVER HARP 8VE 2B 410
LEVER HARP 8VE 2C 59
LEVER HARP 8VE 2C # 5 /D b 59
LEVER HARP 8VE 2D 58
LEVER HARP 8VE 2D # 5 /E b 58
LEVER HARP 8VE 2E 58
LEVER HARP 8VE 1F 57
LEVER HARP 8VE 1F # 5 /G b 57
LEVER HARP 8VE 1G 56
LEVER HARP 8VE 1G # 5 /A b 56
LEVER HARP 8VE 1A 56
LEVER HARP 8VE 1A # 5 /B b 55
LEVER HARP 8VE 1B 55
LEVER HARP 8VE 1C 65
LEVER HARP 8VE 1C # 6 /D b 64
LEVER HARP 8VE 1D 64
LEVER HARP 8VE 1D # 6 /E b 64
LEVER HARP 8VE 1E 64
LEVER HARP 8VE 0F 64
LEVER HARP 8VE 0F # 6 /G b 63
LEVER HARP 8VE 0G 63
LEVER HARP 8VE 0G # 6 /A b 63
LEVER HARP 8VE 0A 63
LEVER HARP 8VE 0A # 6 /B b 62

Lost your keys?!

Let’s set the scene: one of my fave songs starts in F# minor, flirts with F# mixolydian, and then starts the chorus firmly in F# dorian. I’m currently sifting through 16 songs like this to figure out which to put on the album, plus experimenting with harp accompaniment. My head is MELTED! Fortunately a few years back I made this quick-reference table for a workshop on trad accompaniment. I hope to goodness I get this done ASAP, and here’s hoping the table might help you too some day!

ÚNA’S TABLE OF TONAL CENTRES

 MAJORMIXOLYDIANDORIANMINOR
B♭, E♭, A♭, D♭, G♭,C♭, F♭C flat majorG flat mixD flat dorianA flat minor
B♭, E♭, A♭, D♭, G♭,C♭G flat majorD flat mixA flat dorianE flat minor
B♭, E♭, A♭, D♭, G♭D flat majorA flat mixE flat dorianB flat minor
B♭, E♭, A♭, D♭ A flat majorE flat mixB flat dorianF minor
B♭, E♭, A♭E flat majorB flat mixF dorianC minor
B♭, E♭B flat majorF mixC dorianG minor
BF majorC mixG dorianD minor
NO # OR C majorG mixD dorianA minor
F# G majorD mixA dorianE minor
F# C# D majorA mixE dorianB minor
F# C# G# A majorE mixB dorianF# minor
F# C# G# D#E majorB mixF# dorianC# minor
F# C# G# D# A# B majorF# mixC# dorianG# minor
F# C# G# D# A# E#F# majorC# mixG# dorianD# minor
F# C# G# D# A# E# B#C# majorG# mixD# dorianA# minor

How to survive a harmonic analysis assignment – if you’re not a classical musician

I’m from a traditional music background. For my undergraduate music degree it was required that I do a western art music analysis course – PANIC!!! These are a few things that helped me hack that skill-set, and pass!

  • Go to all the lectures. You’re starting on the back foot, so you can’t afford to miss any.
  • Read the assignment very carefully. Ask the lecturer for a sample answer if they don’t give one.
  • You’ll probably be asked to analyse a piece from the canon of western art music, e.g. a string quartet by Shostakovich, or a Bach chorale. If your lecturer hasn’t recommended a particular recording, go to Youtube / Spotify / the library and find a recording from an authoritative source, that you enjoy listening to. Listen to the presribed music on repeat in the background.
  • Read all of the assigned readings / literature available on the assigned work. (Make note of the title, author and publisher of everything you’ve read for your bibliography.) Highlight any text that seems relevant to your assignment, and keep it all in one Word doc. You can refer to this later if you need to write a commentary / essay.
… If the notes on your score are tiny and low-contrast, you’ll save yourself a lot of grief by creating your own score in Finale / Sibelius.
  • If you struggle with sight-reading, you may find it helpful to create your own score. But don’t worry – I don’t propose that you transcribe every individual note into your computer! A lot of the canon of western art music is public domain, and has already been transcribed by enthusiasts. So…
  1. Go to www.musescore.com , and search for your assigned work (If you don’t find the piece on www.musescore.com , search the internet at large for <title of your piece> and <.xml> or <.mxl> )
  2. When you find a version, spot-check a few chords in the new version against the original score, to ensure it’s accurate (I haven’t come across an inaccurate transcription yet)
  3. On MuseScore, click ‘Download’, select ‘MusicXML’, download the .xml file
  4. Open your music notation software, and import the MusicXML file (In Finale: go to File menu, click ‘Import’, click ‘MusicXML…’, select the relevant file in your downloads folder, click ‘open’)

… and ta-DA … you should now have your own score in front of you, which you can edit to help you learn!

  • You’ll need to look up bars, and then reference bars, as quickly and clearly as possible. I suggest that before you start your assignment, you put a measure number on every single bar. If you’re old-skool then handwrite it on your printed score. If you’re a techie, use your music notation software to add it (In Finale 25, click to ‘Measure’, select all, click on ‘Measure’ menu, then click ‘Show Measure Numbers’.)
  • If you’re analysing a piece with viola clef and reading this slows you down… how about using tech to change the viola staff to the bass clef? (In Finale 25, select the ‘Clef’ tool, double-click bar 1 of the viola staff, the ‘change clef’ window will pop up, select bass clef, then click ‘OK’)
  • More than likely, the learning objective of your assignment is the skill of chord diagnosis, and the concepts of harmonic analysis. Because I wasn’t a fast sight-reader during my undergrad, diagnosing each chord was painfully slow, and I had less time to work on understanding broader harmonic concepts. So I encourage students to work at their music literacy, but seperately to their analysis assignments. How about putting your piece into AlphaNotes font, which has the letter name of the note in its notehead? (In Finale, select all, then click on the Plugins menu, select ‘Note, Beam and Rest Editing’ and select ‘AlphaNotes’). Your chord diagnosis will now be exponentially faster.
Úna’s sneaky hacks: notes in AlphaNotes font, and viola staff in bass clef
(sssh, don’t tell anyone 🙂 )
  • There are loads of different schools of musical analysis; Schenkerian, etc. . However, they nearly all require analysing chords, cadences and tonality.
  • If you’re diagnosing a chord, but are uncertain about your results, try checking your diagnosis against the free online tool, the Chord Identifier. Input up to 6 notes, and this amazing gadget gives you a list of what chords these notes could comprise. In my experience the Chord Identifier gives many results, but is not exhaustive; I use it as a brainstorming tool, rather than an ultimate authority.
Chord Identifier inputting system
  • If you’re diagnosing a chord, and are unsure what it is, then I say – totally ignore the notes. Get the recording, close your eyes and LISTEN. At the relevant point, ask yourself… what note is most prominent? What feels like ‘doh’? Does it sound major / minor / diminished / augmented? Where does it want to go? These questions may bring you some clarity.
  • This is a decent index of various cadences, with audio examples. Again, if uncertain about the nature of a cadence, you could close your eyes while listening and asking yourself a few questions: How does it feel? What feels like home? Where does the melody want to go?
  • Is the melody modulating or not? Answer: if a melody has a chromatic note, THEN a cadence (even an unfinished cadence!), the melody has modulated. But … if a melody has a chromatic note, and no cadence following, it’s an inflection.

Agus sin é!! I hope these tips save you some grief, and help you actually enjoy the beautiful music of Bach / Shostakovich / Beethoven!

Úna