Corda Jazz: Measurements

Audio, Tech
by Mike Clements

I own this headphone amp and use it every day at work. It has great sound quality with some unique features. I previously reviewed it and compared with other amps here.

Earlier this year I loaned this amp to Amir to measure for Audio Science Review, here. Amir does a great service to the audiophile community, I’ve met him in person and he’s a good guy with industry experience and a knowledgeable audiophile. However, we are all human with different opinions, and even objective measurements can be misleading.

Take SNR (signal:noise ratio) and SINAD (Signal over Noise and Distortion) for example. These are typically measured at a device’s full scale output, as this usually gives the highest number. But with headphone amps, we don’t listen at full volume. Their max output level is around 2-4 Vrms, sometimes more. This is far too loud for average listening levels; it would be painful or cause hearing damage. We typically listen with average levels around 70 or 80 dB SPL, which, perceptually, most people would describe as medium-loud. Most headphones reach this level with a voltage around 50 mV.

For example, consider the Matrix Audio Element, which Amir recently reviewed. It is one of the best DACs he’s ever measured, with a SINAD of 120 dB. However, its 50 mV SINAD is only 81 dB.

For comparison, The Corda Jazz measured about 87 dB SINAD at full output, and 90 dB at 50 mV output.

This illustrates an important point. We start with 2 devices. One has a SINAD of only 87 dB, which seems low. The other has a SINAD of 120 dB, which is the best he’s ever measured. Objective measurements tell us one is better! However, that is highly misleading because when you measure the output at levels we actually use, the exact opposite happens. The Jazz is actually 9 dB better than the Matrix. That’s a 65% drop in noise & distortion, which is a significant, audible improvement.

In short, the max SINAD measurement is correct, but misleading because it describes conditions that nobody actually uses when listening. The 50 mV SINAD is a better measurement because it represents actual listening conditions. But virtually nobody measures this; Amir (much to his credit) is the only person I know of who does this. Furthermore, the large variance between these two belies their similarity: as in the above example, the devices measuring the highest peak SINAD often do not measure the highest 50 mV SINAD, which proves how important it is to understand the measurements we make and their relevance to what we hear.

Enough said about this. Next I’ll talk about how the way an amp is designed affects this. If you don’t care about engineering details just skip to the conclusion.

Lesson learned: an amplifier’s SNR or SINAD can be quite different at 50 mV than it is at full output. How does this happen? The conventional amplifier has its internal gain-feedback loop set to whatever fixed gain ratio produces the desired maximum output, and the volume control is a potentiometer (variable resistor) that attenuates this. This “fixed gain with attenuation” means the noise level is relatively constant (based on the gain ratio, which is fixed), so as you turn the volume down, you reduce the SNR and SINAD at the same time.

This is easily seen with the Matrix. Full output is 3.9 V, so 50 mV is 38 dB quieter. And its 81 dB 50 mV SINAD is 39 dB less than 120 dB. What a coincidence: turn the volume down by 38 dB and SINAD drops by 39 dB! They have a virtually perfect 1:1 relationship. Not a coincidence; that’s by design.

So what’s happening with the Jazz? Its SINAD actually gets better at lower volumes. The Jazz is designed differently from typical amps. It does not use fixed gain with separate attenuation, but instead it uses variable gain to set the attenuation you need, obviating any need for separate attenuation.

The Jazz volume control changes the resistors in its internal gain-feedback loop. At low volumes, it has less gain and more negative feedback (wider bandwidth, lower noise and distortion). As you turn up the volume, you are increasing the gain (reducing negative feedback). [Incidentally, this means it must be inverting, for its gain-feedback loop to have less than unity gain. But its final fixed-gain stage is also inverting, so overall it does not invert.] Finally, this volume control is not a potentiometer; there is no potentiometer in the signal path.

This means the Jazz produces its best sound quality at the low to medium levels we actually use for listening. It also means the Jazz has perfect channel balance at every volume setting. Another observation from Amir’s measurements is that the Jazz is not current limited. It puts out 10x more power into 30 ohms, than 300 ohms.

Conclusion

Amir didn’t like the Jazz in his review, mainly because of its limited output power. One of the limitations of the Jazz’s unique volume control is that the resistors in the gain-feedback loop can only handle limited voltages. If you turn up the volume too high, it produces huge amounts of audible distortion due to input stage voltage clipping. The Jazz maximum output level before the onset of this clipping & distortion is about 3.7 V. That equates to 116 dB SPL with Sennheiser HD-580 and 120 dB on Audeze LCD-2. This is more than loud enough for me. Anyone listening this loud risks damaging his hearing. In fact, with the LCD-2 headphones I use the Jazz in low gain mode which is 16 dB quieter than this.

In summary, the Jazz is an amp that Amir’s measurements show has perfectly flat frequency response, perfect channel balance at all volume settings, less than 1 ohm output impedance (not current limited), and SINAD among the best he’s ever measured, at actual listening levels (50 mV). Yet he doesn’t recommend this amp because of its limited output voltage. At the same time, he does recommend amps like the Matrix, which have higher output power, but inferior measurements at the levels we actually listen. Amir is correct that exceeding an amp’s power limits creates audible distortion, thus is the most likely way listeners will hear distortion from an amp. However, if the limits are high enough (as with the Jazz), we won’t exceed them.

Put differently: it makes no sense to sacrifice sound quality at the moderate volume levels we actually use, in order to gain more power that we can’t use without damaging our hearing.

Classical Music Streaming: Primephonic & Idagio

Audio, Tech
by Mike Clements

The Problem

Streaming classical music has 2 basic problems.

Note: I use the term “classical” in the most general sense, from ancient (pre-renaissance) to modern, including early music, baroque, classical, romantic, etc.

Fast forward 3 years and I'm now using Qobuz. I've added Qobuz to some of the comments below.

Metadata

ID3 has become the standard metadata for music, defining fields like title, artist, album, etc. This has an impedance mismatch with classical music. For example, if the Chicago Symphony is playing the Brahms violin concerto with conductor Reiner and soloist Heifetz, who is the artist? Brahms, Chicago Symphony, Reiner or Heifetz? What is the title? Violin Concerto in D Major, Opus 77, Chicago Symphony Live, or some nickname? If you search for this piece on streaming services like Spotify, Tidal, or Amazon, you will find all of the above, each individual recording having different metadata. Exacerbating this problem is the fact that every piece from every composer typically has tens if not hundreds of different recorded performances by different artists. This inconsistency makes it frustrating to find classical music.

Sound Quality

The sonic quality of the recording presents another problem. Most popular music is recorded with terrible sound quality: massive dynamic compression with clipping, and extreme amounts of EQ and other processing. They’re engineered to sound as loud as possible for radio, streaming and listening in noisy environments with crappy earbuds. This makes it easier for streaming, since the recording was already squashed to death by the studio during production, sound quality doesn’t matter because there’s nothing to preserve. However, sound quality matters with classical music. These recordings are made to a higher standard, having minimal studio processing, preserving dynamics and detail that lossy compression would destroy. This is important to reveal subtle variations in artistry, such as how a pianist voices chords, to a cello player’s bowing technique, to a flute player’s tone colors. This makes it harder to stream classical music.

So while there is plenty of classical music on standard streaming services, finding the piece you want, and the available recordings, is frustrating if not impossible. And when you finally do find it, listening to it through the streaming service’s lossy compression can be more disappointing than satisfying.

Thus it comes as no surprise that streaming accounts for only about 25% of classical music consumption, compared to 64% for the rest of the market.

The Solution

Even though classical makes up only about 3% of music sales, companies have formed to solve these problems. The 2 most popular are Idagio and Primephonic, and they address both of the above problems. I did not explore Naxos, because my experience owning about 100 of their CD recordings is that their sound quality (with a few notable exceptions) is second rate, and they only stream their own content, making great performances of the past inaccessible.

These classical music streaming services define and populate their own metadata customized for classical music, and they stream at lossless CD quality. This transforms the classical music streaming experience and has the potential to fundamentally change how music lovers experience classical music.

If that last statement sounds over the top, let me explain. With hundreds of composers, each writing hundreds of works, each having hundreds of recordings by different artists, each bringing something new to the artistic expression of the work, there is more classical music than any normal person can listen to in one lifetime. Of course, not all performances, nor all recordings, are equal. So music lovers have relied on reviewers to help sort through all of this. But reviewers and listeners are all people with different opinions. The work or recording a listener is interested in might not have been reviewed. When it has, a listener might find to his consternation that he disagrees with the reviewer. And many other works that a listener doesn’t even know about might be worth consideration. For decades, classical music listeners have relied on reviewers as gatekeepers and guides.

Streaming upends all of this by reducing to zero the marginal cost of the next recording you listen to. Browse the full catalog, using the classical music customized metadata to find works and performances in your area of interest. Take a chance on new works, recordings or artists, that the cost of individual CDs or downloads might have prevented you from listening to. Listen to everything and decide for yourself; the only constraint is your time. And, listen anywhere you are: home, work, in the car or wherever.

Furthermore, these streaming services cost less than a subscription to a classical music magazine like Grammophon or Fanfare. More on costs below.

Review

Idagio is a German company that’s about 4 years old. They are based in Berlin and their service became available in the USA about a year ago (September 2018).

Primephonic is a newcomer; their service started about a year ago (August 2018).

Both companies are staffed by a mix of musicians, musical scholars, agents and software engineers. They believe in what they’re doing and have the domain expertise to do it right.

I found many reviews of Idagio and Primephonic, but most were pretty shallow, as if the reviewers didn’t actually use the services in-depth on different devices and situations to discover their strengths & weaknesses. Since both services provide a 2-week free trial, I did this myself during a period where I did some business travel so I got their full experience from home, work, and traveling. Here is what I learned.

Getting Started

Both services offer a 14-day free trial. Primephonic is the quickest and easiest, since they don’t require a credit card. Just sign up with your email and it’s ready to go. Idagio requires a credit card to sign up for the trial, but they don’t bill anything to it until the 14th day.

Both services also let you sign up with a Facebook or Google account instead of using your email. I don’t do social media and prefer not to link online accounts, so I did not use this option.

Catalog

Their catalogs are roughly the same total size, and similar: both services had about 75% of the pieces I searched for, from early (pre-renaissance) music to modern. Where they differ, Primephonic has better coverage of early music, and less well known works and artists. Idagio has better coverage of baroque to modern classical music. For example, Idagio didn’t have some Piffaro (only 3 albums versus 6) and Joel Frederiksen early music albums that Primephonic had. Primephonic didn’t have Levin’s Mozart Requiem performance with the Violins du Roy, but Idagio did.

Some notable works were missing from both catalogs. Neither had anything from Jacqueline DuPre, nor did either have the Hillier Ensemble’s Age of Cathedrals (this is just one of several albums I have that was not in the catalogs of either service).

Addendum: Qobuz’s catalog is also fairly complete: with very few exceptions, everything I could find on Idagio or Primephonic is on Qobuz.

Metadata and Search

They both have metadata customized for classical music. You can search by any keyword, from composer to work to group, to album. And the search results are cross-referenced, so if you find a work, for example, you can click on it to see all other works from that composer, or all albums having that work.

I found their metadata doesn’t have much information about the album. For example if I search for “Liszt Transcendental Etudes”, they both show a list of albums. If I click on one, say Berezovsky (available in both), it shows me a picture of the album cover and says, “1996 Teldec Classics”. But there is no catalog number or other recording info, not to mention liner notes.

Both Idagio & Primephonic have the album booklets in PDF format for many albums (but not all). Primephonic has them more often than Idagio, and Primephonic makes them available in the mobile app as well as the browser, in contrast to Idagio which makes them available only in the browser. Coverage is gradually increasing with both services.

Primephonic’s search may not be quite as robust as Idagio. I searched for the Brahms Piano Quintet Op 34 in both. Idagio showed several recordings of it. It did not appear in Primephonic at all, as if they didn’t have this popular work in their catalog. When I mentioned this to Primephonic support, they sent me a link to the piece and said they would update their search. So they do indeed have it, but it wasn’t coming back in search results. But it did come back the next day, so they are listening to customers and actively improving their platform.

Addendum: Qobuz metadata is terrible. It’s not specific to classical music, but the same as other pop-oriented services like Spotify.

Music Discover-Ability

Despite this Primephonic glitch, in the Android app, their search is better than Idago’s. This is best explained by example. Suppose you want to find recordings of Liszt’s Transcendental Etudes.

In Primephonic: search for Liszt, tap him in results, and it shows a list of popular works. Tap Show All, but this list is too long to bother scrolling through, and you’re not sure whether it will appear under E for Etudes or T for Transcendental. The app has a Sort By box, enabling you to sort by Opus number, then you scroll to 139. Tap this, and it shows you 83 recordings which you can sort by popularity, A-Z, Z-A, newest, oldest, longest or shortest.

In Idagio: search for Liszt, tap him in results, and it shows 3 tabs: Works, Recordings, Albums. The Works tab has no way to sort or sub-search, it’s unclear how it’s sorted, and the list is too long to scroll, so that’s not helpful. The Recordings tab can sort by Date, Most Popular, or Recently Added, none of which help you find the Transcendental Etudes, so that’s not helpful. The Albums tab can sort by year or alphabetically, so this is not helpful either.

In short: Idagios’s Android app lacks sub-search or sort, making it more difficult to find the pieces you’re looking for. It’s easier to find things in the Primephonic app.

However, Idagio’s web browser does better than their app. Here, when you tap Liszt, Works can be grouped by Keyboard, Secular, Chamber, etc. This makes it easier to find stuff, but sort is still only by popularity or alphabet, so it’s still not as good as Primephonic.

Addendum: Qobuz scores low marks in this area, due to their metadata.

Applications / Players

Both services are fully functional in a web browser, and in Android and iOS apps that are free to install (not including the subscription price) from the standard app stores. By fully functional I mean you can search the catalog and play music. I ran both services on my Browser (Chrome & Firefox on Ubuntu 16 and 18), phone (Galaxy Note 4 SM-N910T running LineageOS 16 / Android 9) and my tablet (Galaxy Tab S SM-T700 running LineageOS 14 / Android 7).

Primephonic audio had brief gaps or glitches every 10 seconds or so when playing from Firefox on my laptop (which makes listening impossible), but this didn’t happen from Chrome on the same laptop, nor did it happen in Firefox on my desktop. So this problem was probably Firefox, not Primephonic. Audio from both apps was seamless on my phone & tablet.

UPDATE: these audio glitches turned out to be caused by Pulseaudio. Idagio streams at lossless CD quality which Pulseaudio handled just fine. Primephonic streams at higher than CD quality which was causing buffer under-runs in Pulseaudio. I reconfigured Pulseaudio to increase audio buffering and this made Primephonic glitch-free at all audio rates up to 192-24.

Idagio is more reliable with faster, smoother performance in both the browser and the Android app. Primephonic occasionally hung (both the app, and the web page) and had to be restarted or reloaded, which Idagio never did. Also, Primephonic had a bug in which the app’s streaming quality settings don’t appear to be saved, but revert to the defaults every time I saw them, even after I changed them.

UPDATE: as of June 2020, Primephonic has fixed these bugs in their app.

The Primephonic app supports both portrait & landscape mode, which makes it easier to use on my tablet. This is a nice little touch compared to Idagio’s app, which is always in portrait mode, even on the tablet.

Both apps enable you to download tracks or entire albums to your device so you can play them back anytime, even when disconnected. This was great on a cross-country flight. However, neither app supports external SD cards, so whatever you download consumes internal storage. When downloading, Idagio’s app creates an Android notification with a progress bar, and it also indicates in your music library the pending download status. Primephonic’s download is more of a black box – it doesn’t have a notification and you’re never sure exactly when it’s downloading, or when it might finish. But it does mark which tracks or albums in your library are downloaded, when complete.

UPDATE: as of June 2020, Primephonic app downloads give status notifications like Idagio.

Both apps stream smoothly and seamlessly, whether live streaming or playing pre-downloaded content, listening on headphones plugged into the device, or over bluetooth in my car. And my car’s audio next/previous track controls also worked when playing music from the apps on my phone.

Addendum: Qobuz is excellent here. They have their own player clients for popular platforms (iOS, Android, Windows, Mac) but they also are the only music streaming service that fully supports standard browsers in full audio quality – all the others compress or resample music streamed to a browser. Qobuz also has an open API, so for example USB Audio Player Pro plays Qobuz natively bit-perfect, so if you have an Android device it becomes an ideal source to feed into your DAC.

Sound Quality

Both support CD quality streaming as FLAC, which uses lossless compression. Listening to them on my audio system, the sound quality of both services was as good (or bad) as the recordings themselves on CD. To test this, I configured each service to stream in CD quality, then found CDs in my collection in each service, and streamed it with the CD playing, and quick switching back and forth I found them indistinguishable. My audio system is quite transparent and I can distinguish 320 kbps MP3 from CDs in blind listening tests, so this test suggests that each service is streaming the audio stream as-is, without processing it.

Primephonic streams at higher than CD quality for titles that support it. Primephonic’s highest audio quality setting uses MPEG4-SLS which streams the lossless raw recording when network bandwidth supports it, and falls back to AAC lossy compression when it doesn’t. As of June 2020, roughly half the content I listen to on Primephonic streams at higher than CD quality. I’ve seen sample rates of 44.1k, 48k, 88.2k, 96k, 176.4k and 192k, so it appears that Primephonic is streaming whatever raw bits the record companies provide, without resampling or converting them.

Both services also support lower quality (lossy compression) streaming to reduce data usage, which is useful for phones. These still offer good sound quality (192-320 kbps) that exceeds most other music streaming services.

Primephonic has settings for different rates on mobile versus Wifi data, which is useful and distinguishes it from Idagio, which just has a single quality setting.

Primephonic has gapless playback, but Idagio does not. Frequently, classical tracks or movements blend right into each other without any break in the music. Without gapless playback, the audio system inserts a break. This could be an important consideration for some listeners.

Qobuz is excellent here. They stream exactly what the studios or music rights owners give them, bit perfect. No resampling, lossy compression, or other processing.

Data Consumption

I mentioned that both apps can stream audio at true CD quality, yet they also provide lossy compression to save mobile data. This is especially useful because when listening on your phone, you’re often in a situation where reference quality audio isn’t needed: in the car or other noisy environment, using BlueTooth audio or earbuds plugged into your phone. Even some of the best IEMs and earbuds don’t have the same reference audio quality as full size headphones or listening rooms. So CD quality streaming only wastes mobile data when you can’t hear the difference.

I measured the actual data usage by each app when streaming audio over my mobile connection.

Before getting into the differences, here is approximate expected data usage per hour at a few standard music streaming rates:

  • 128 kbps = 1 MB / minute, 60 MB / hour
  • 320 kbps = 2.4 MB / minute, 144 MB / hour
  • CD (44 k / 16 b uncompressed)  = 1,411 kbps = 10.5 MB / minute, 640 MB / hour
  • CD FLAC (lossless compression) = 6 MB / minute, 400 MB / hour
  • 192-24 (the highest audio rate you’ll likely use)= 9,216 kbps = 69 MB / minute, 4.14 GB / hour

Primephonic

Offers 4 quality settings: Normal (128 kbps), High (256 kbps), Superior (320 kbps), Full (lossless up to 192-24). Also, allows different settings on WiFi versus mobile, which is quite useful.

However, when streaming music in the mobile app, Primephonic consumed about 200 MB per hour regardless of the setting. That is higher than 320 kbps. This is a bug in their Android app that makes it essentially unusable for streaming over mobile.

Update: As of June 2020, Primephonic has fixed this bug.

Idagio

Offers 3 quality settings: Normal (AAC 192 kbps), High (MP3 320 kbps), Lossless (FLAC of 1411 kbps). This is a single global setting whether on WiFi or mobile. It also offers a quality setting for downloads: Normal (750 Kb per minute, about 128 kbps), High (2.5 Mb per minute, about 320 kbps), or Lossless (up to 10 Mb per minute, but about 2/3 of that due to lossless compression).

When streaming music, Idagio consumed about 80 MB per hour at Normal and 200 MB per hour at High.

Customer Support

I emailed support for both services with various bug reports & suggestions. Both responded to all my emails, and not robotically but from an actual human who understood my message and gave a courteous, intelligent response. Primephonic was a bit faster, responding in less than 24 hours even on weekends. Idagio took a couple of days to respond, which is still quite good.

Addendum: Qobuz has great support. Every time I’ve emailed them I get a reply within 24 hours from a real human who understands the issue and is helpful.

Cost

Their cost is similar but not the same. Idagio is simple with a single service tier: $10 / month. No discount for buying a year up front, so it’s $120 / year.

Primephonic has tiered service depending on the streaming audio quality. It costs $10 / month for up to 320kbps lossy, and $15 / month for CD quality or higher. Primephonic has discounts for buying a year up front, which costs $100 and $150 respectively.

So, Primephonic can be the same price or more expensive than Idagio, depending on whether you want full CD quality streaming

Addendum: Qobuz used to be very expensive, but they lowered their prices a couple of years ago. They cost $11.90 / month all-in including taxes, or $143 / year.

Artist Reimbursement

Both services reimburse performers differently from other streaming services, in a way that is better suited to classical music, where track lengths vary tremendously. Reimbursing by track play starts just doesn’t make sense. Instead, they reimburse performers based on the time individual subscribers spend listening to specific tracks. In short, reimbursement is based on time spent, not starts.

Conclusion

To say that I’ve enjoyed these trials would be an understatement. It’s wonderful to have such a huge library of classical music at my disposal to listen wherever I want, at home, at work, in my car, or while traveling. Also, each service has curated lists of music in different areas of interest, which can be a useful exploration guide.

I like early music so I lean toward Primephonic due to their slightly better coverage, gapless playback, and their slightly better music search & discover-ability. However, the fact that their Android app always consumes 200 MB / hour when streaming is a show-stopper. And they’re more expensive, at least for full CD quality, and their app is a little more buggy.

I’m definitely going to subscribe to one of these services, but I still haven’t decided which one. They’re quite similar, each has its minor differences, pro & con, and neither is clearly better. I hope this detailed review has helped you decide whether you want a service like this and which might be best for you.

Addendum: after Apple acquired Primephonic, they only streamed to Apple devices, so I switched to Qobuz. The metadata is crappy for classical music, but I am enjoying the excellent sound quality and wide range of genres beyond just classical.

Miro Quartet at Orcas Island

Flying, Music
by Mike Clements

Michelle and I flew in for the Orcas Island Chamber Music Festival this year and caught the Miro Quartet playing with Aloysia & Jon on Tue Aug 13. Our last-minute decision afforded stage seating, stage right behind the musicians. We really liked this. The experience and sound is different and quite wonderful, reminding me of my own weekly chamber music rehearsals years ago.

Miro opened with the Mozart quartet K 458 The Hunt. Their sound struck me like a velvet hammer: big, round, smooth, rich and fat yet detailed. A huge grin spread across my face and the back of my neck tingled. I especially noticed their dynamics, micro and macro, and their tight timing playing off each other handing the lead back & forth every few bars like a great jazz ensemble, yet with all the musical refinement that Mozart demands. The menuette bounced and the adagio soared, breaking tradition as they came in that order. The allegro set it on fire and summed it up.

Kevin Puts entered the stage and introduced his piece, Arcana for solo cello and string quartet. He described how watching the sun rise over a volcano on Maui inspired him to write this impressionistic piece. Julian Schwarz (son of Gerard Schwarz, prior conductor for Seattle Symphony, who was also visiting the OICMF this year) and Aloysia Friedmann joined Miro to play the lead cello and supporting violin, respectively.

The guest musicians left the stage and Miro played Schubert’s Death and the Maiden. More specifically, the andante which is an absolute classic of the chamber music repertoire and structured as a theme and variations. It ranges widely from lyricism to flaming virtuosity giving each musician a showcase and the Miro quartet just nailed it. The piece had a few moments in the lyrical sections when Ching (lead violin) sounded just slightly off in timing or intonation, but it could have been my own ears.  That’s part of the character and expressive joy of live music performance: every piece is unique rather than perfect in the robotically sterile way that recordings sometimes can be, and this enhances the experience. A robust standing ovation delayed the intermission.

Upon returning, Jon Kimura-Parker was scheduled to play a Clara Schumann piece, but instead played Schubert Impromptu Op. 90 # 3, one of my favorites of the solo piano repertoire. He played with a depth, delicacy and refined power that perfectly suits this piece. The performance reminded me of Radu Lupu’s style, but Jon made it his own. For me, this piece was the highlight of the concert in terms of emotional intimacy.

Last yet certainly not least, Miro joined Kimura-Parker on stage to perform the famous Brahms piano quintet in F minor Op. 34. A few years ago when Michelle and I last attended an OICMF concert they also played this piece, so I knew we were in for a treat. We were not disappointed. We were sitting just behind Kimura-Parker so close we could have reached out and touched him. I was reading his tattered and heavily annotated (in different colors!) sheet music as he played and his daughter turned pages for him. We could hear and feel the power and wonderful woody resonance of the Steinway Model D in the FFF sections. The strings were no less in the game as they brought the piece to its fiery and satisfying conclusion.

Headwinds & Tailwinds

Flying
by Mike Clements

It seems obvious that head and tail winds are equally likely. That is, assuming the direction of the wind and your flight are both random, head and tail winds should be equally likely. But it’s wrong.

Of course, even if head and tail winds were equally likely, you would spend more time flying in headwinds, simply because they slow you down. But that’s not the reason I’m talking about here.

The reason is simple. When the wind is 90* to your direction of flight, you have to turn toward it slightly to maintain your desired direction of flight, so it slows you down. Visualize the entire 360* circle that the angle of the wind can have relative to your direction of flight. If wind at exactly 90* slows you down, then more than half of the range of the circle slows you down. A wind from the side must be slightly behind you in order for the loss of speed turning toward it, to be countered by the gain in speed it adds pushing you along. In other words, when the wind is from the side, it must be slightly behind you to break even.

Of course, the same applies to boats. But not cars, because you don’t need to steer into a crosswind when driving (well you do, but it requires so much less correction as to be insignificant).

Spins!

Flying
by Mike Clements

Spins can be a contentious topic among some pilots because not all airplanes are approved for intentional spins, the maneuver is no longer required for private pilot certification (though it is for becoming a CFI), and the reason the FAA removed the spin requirement was because spin training was causing more deaths than than the training was preventing.

However, I believe spins still make valuable flight training, when approached from a careful perspective. Entering & recovering from spins is quite simple, not requiring the kind of stick and rudder finesse of other maneuvers like chandelles. But spins do something that those maneuvers don’t: they familiarize the pilot with aggressive airplane behavior under unusual attitudes, and reinforce a methodical response rather than panicked reaction.

Review: what is a spin? It’s when an aircraft is stalled, and one wing is more stalled than the other. You can’t spin unless you first stall, and for a stall to become a spin, the angle of attack must be different on each wing. That means your flight must be uncoordinated. Conversely, if you maintain coordination you will never spin, even if you stall the airplane while banked in a turn. Spins are sometimes confused with a tight spiral dive, especially in airplanes like the 172 that are spin resistant. That is, the pilot attempts to spin the airplane, but he fails to overcome the airplane’s spin resistance and the stall becomes a tight spiral. Videos like this are common on youtube (“Hey, watch this spin!” … That’s not a spin, it’s only a spiral dive. Looks like you don’t really know what a spin is.).

Before spinning an airplane, here are some regs to consider:

  • Aerobatic flight: FAR 91.303
    • Away from congested areas, assembly of people, airways, controlled airspace
    • Above 1500′ AGL
    • At least 3 miles visibility
  • Parachutes: FAR 91.307
    • Required when you have passengers (non crewmembers) on board and…
    • Intentionally banking > 60*, pitching > 30*
    • Exception for maneuvers required for certification, including spins, when given by a CFI
    • For more detail, see PS at the bottom of this page.
  • Airplane limitations: the POH
    • Airplane must be approved for intentional spins
    • The POH may specify W&B necessary for spins: follow it
    • The POH may specify spin recovery different from the standard PARE: know it

Further thoughts on parachutes. It doesn’t help you if you can’t get out of the airplane. And it’s pretty darn hard to get out of an airplane in flight. Even at slow airspeeds there’s so much air pressure on the doors it’s hard to open them enough to depart the airplane (especially if said airplane is not in straight & level flight, but spinning or otherwise flailing around the sky). That’s why skydiving airplanes have a door entirely removed, or a special door designed to open in flight. Also, a chute doesn’t help you if you don’t know how to use it. Woe betides you if the first time you ever have to use a chute for real, is a bona fide emergency. So if you’re doing aerobatics and wearing a chute, believing you’re both legal and safe, you may be deluding yourself. Ensure you have a way to depart the aircraft while in flight, and do a few jumps to familiarize yourself with the chute.

Here’s how I interpret this flying my 1980 C-172 Superhawk.

  • Spins are approved only in utility class, which means GW < 2100# and CG < 40.5″.
    • With 180# solo pilot, fuel must be 35 gals or less (full fuel is 40 gals).
    • With 2 people up front, any amount of fuel can be used so long as total weight < 2100#. With full fuel, that’s up to 380# in front seats.
  • Empty back seat, baggage, tail; clean airplane with no FOD.
    • Last thing you want is loose items flying around the cabin, possibly obstructing the controls or lodging in the tail cone, moving the CG rearward.
  • If you’re doing spins solo or with a CFI, you don’t need parachutes (and they wouldn’t be much help in a 172, unless you removed a door before flight). If you have a passenger, you do need them.
  • Altitude: at least 6,000 AGL for spins up to 2-turns (higher for more).
  • Spin entry: Cessna 172 L and later models don’t like to spin and will only spiral unless the spin is entered with an aggressive stall. So:
    • Start with a partial power-on stall, so you have a higher nose angle and a crisp breaking stall.
    • Just as the stall breaks (not before), briskly pull the yoke all the way back and stomp full rudder in the direction you want to spin.
      • NOTE: it will spin L easier than R due to engine torque, but you can spin it in either direction.
    • If the airplane goes into a spiral instead of a spin, immediately release the pro-spin inputs, level the wings, climb back to altitude and try again.
      • NOTE: how to tell if you’re in a spin, or just a tight spiral?
      • A spin is a low-G maneuver: the airplane is mostly unloaded and you don’t feel much G force (even though you’re spinning around). If you feel significant Gs, you’re probably in a spiral not a spin.
      • In a spin, the stall horn squeals loud and hard constantly. If the stall horn is silent, or is just barely squealing, you’re probably in a spiral not a spin.
      • In a spin, the airplane rotates quickly: it literally spins. If the airplane is “flying” around in tight circles, you’re in a spiral not a spin.
    • While spinning, hold these pro-spin control inputs at full maximum.
  • Spin recovery: Cessna 172s follow the standard PARE (power, aileron, rudder, elevator) recovery. They are spin-resistant and will recover instantly as soon as you reduce pressure on pro-spin controls. However, best practice is to firmly apply proper anti-spin controls:
    • Throttle to idle (pull all the way back)
    • Ailerons neutral
    • Briskly stomp and hold full opposite rudder
      • If you’re not sure which way you’re spinning, look through the windshield at how the Earth is rotating:
        • If CW, stomp R rudder (you’re spinning to the L)
        • If CCW, stomp L rudder (you’re spinning to the R)
    • Just after the rudder hits the opposite stop, briskly push the yoke forward
    • Hold these anti-spin inputs until rotation stops
      • NOTE: as soon as rotation stops, the spin becomes a steep dive. You must take the next step quickly to avoid over-speeding or over-stressing the airframe.
    • Neutralize rudder and smoothly pull out of the dive
      • If you pull too hard, you may exceed airframe G limits
      • If you pull too gently, you may exceed airframe Vno speed

PS: The regulations may allow more than just a CFI as an exception to parachutes rule. This postscript develops this topic.

FAR 91.307 requires parachutes for aerobatic flight only when there are non-crewmembers on board. Specifically:  no pilot of a civil aircraft carrying any person (other than a crewmember) may execute any intentional maneuver that exceeds…

Here’s how 14 CFR 1.1 defines a crewmember: Crewmember means a person assigned to perform duty in an aircraft during flight time.

Note that 14 CFR 1.1 does not specify what that duty must be. And FAR 91.307 does not say “required crewmember”. By this definition, a crewmember is anyone the PIC (pilot in command) says is a crewmember. As PIC, I can say to the right front seat passenger, “Please look out the window and tell me when you see other airplanes.” If she agrees, she’s been assigned a duty during flight making her a crewmember.

Having done this, we can legally do spins and other aerobatic maneuvers without wearing parachutes because everyone on board the airplane (other than the pilot)  is a crewmember, which complies with the exception in FAR 91.307.

Now, whether this is a good idea, or whether you want to test this interpretation with the FAA, is an entirely different question. This is a convoluted interpretation of the regulations and I mention it only for academic interest – it’s useful to chase down the regs and read what they actually say! The intent of FAR 91.307 seems clear: the FAA doesn’t care if you want to risk your own life – as a private pilot you’ve earned the right to make your own risk decisions. But when your decisions involve the safety of other people, the FAA sets minimum standards to a higher bar.

SRAM Bike Brake Stiff Lever

Exercise
by Mike Clements

Update: 1 year later

The levers got slow again. Not as stiff as before, just slow to return. On disassembly, the problem wasn’t the pistons, but the seals, which had swelled. Maybe because I put a drop of oil on them when I reassembled them, and oil can have seal swelling additives.

Anyway, all I needed was new seals. But new seals alone are not available, as far as I can tell. You have to buy an entire brake lever rebuild kit! However, I did find replacement pistons that come with new seals, and the pistons are machined aluminum, and they only cost $5-$10 each. Better than OEM quality, and perfect fit.

—

The brake levers on my MTB have been gradually getting stiffer to operate, more friction in the brake pull with a weaker return upon release. I bought this bike in late 2014 and have bled the brakes and replaced the pads. The lever stiffness has been gradually increasing. On my most recent ride on Tiger Mtn, the brakes were dragging pretty hard because the levers wouldn’t return. This was an incredible PITA on the steep uphills, and risks overheating the brake pads & rotors.

At Tiger summit, one of the other riders mentioned this was a known problem with SRAM hydraulic brake levers. When I got home I checked it out and found that was indeed true. Some people had returned their levers to have SRAM replace under warranty. But they said it was a PITA and took a long time because SRAM support dragged their heels not wanting to admit there was a problem. So I figured it was worth at least trying to fix it myself.

There are several YouTube videos about this. Here is one I found useful: https://www.youtube.com/watch?v=Ex882BIH-Fo

Here’s a summary of the problem and fix. Each brake lever has a small master cylinder inside, a piston with rubber seals. The piston is made of plastic and the cylinder is metal. Inside the master cylinder there is also a spring that pushes back against the piston to help it return to the neutral position. When the entire assembly gets warm/hot, the piston expands more than the cylinder, scuffing against the inside of the cylinder, increasing friction and getting stuck. It gets stuck so hard that the spring can’t push it back.

The solution is to remove the master cylinder piston and use fine (600#) emery paper to scrub off edge material (gently, smoothly, evenly), making it slightly smaller in diameter. To do this you must remove the brake lever from the hose, drain the brake fluid from the lever, disassemble the lever, remove the piston and its rubber seals, sand it down until it freely slides back & forth in the cylinder, clean everything up, reassemble it, then re-bleed the brakes. The procedure is tedious manipulating some tiny parts, and requires an experienced touch sanding down the pistons. But it doesn’t require any special tools, just the usual stuff: torx wrenches, brake bleed syringes, fresh DOT 4 or 5.1 fluid, etc.

The procedure was successful; my brakes are like new again. This took me almost all day, but I hadn’t done it before. I could do it again in less than half a day.

The problem is definitely not about the piston’s rubber seals. I removed those before sanding it, and the piston was super-tight in the cylinder even with the rubber seals removed and the cylinder cleaned. I sanded the piston until it was loose in the cylinder, easily sliding back & forth from gravity just tilting the assembly up and down.

The piston’s rubber seals are tight and one-directionally facing. Remove with care, ensuring you don’t scratch or score them, and ensure they’re facing the right direction when you reinstall. Before reassembling, make sure everything is scrupulously clean. You don’t want sanding dust from the piston or other crud inside your brakes!

I can’t figure out how or why this problem took 4-5 years to manifest. The piston was not deformed in any obviously visible way. Why didn’t this happen during the first year of ownership?

Magnepan/Dipole Speaker Setup

Audio
by Mike Clements

Having owned Magnepan 3.6/R for 20 years and set them up in 3 very different listening rooms, I’ve learned a few things. I want to capture the important things here.

Overview

Definitions:

  • Front wall: in front of the listener, behind the speakers.
  • Rear wall: behind the listener, in front of the speakers.
  • SBIR: speaker boundary interference response
    • The total response at the listener position includes sound reflected from the front and side walls near the speaker.
    • This response depends on the distance and angle of the speaker to these walls, and the treatment of those walls.
  • LBIR: listener boundary interference response
    • The total response at the listener position includes sound reflected from the rear and side walls near the listener.
    • This response depends on the distance and angle of the listener to these walls, and the treatment of those walls.
  • Speed of sound: 1130 f/s at sea level and 70*. Slower when cold, faster when warm.

All speakers are sensitive to room setup, but planars are dipoles which are more sensitive than conventional speakers. This is both a blessing and a curse. The blessing: if something isn’t right you can often fix it with simple rearrangement. The curse: for ideal sound, the speakers are going to be further into the room away from the walls.

SBIR

All speakers (even forward-firing cones) propagate both forward and back. But a dipole’s back wave has inverted amplitude.

Note: inverted amplitude is is often called or 180* out of phase, which is misleading. 180* out of phase means a shift, while inverted means a flip. Music has many frequencies superimposed so one wonders, 180* out of phase at what frequency? It is more precise to call it an amplitude inversion. More on this here.

Example 1: consider a speaker parallel to the front wall, 3′ away, which is 1/4 wavelength of 94 Hz. The back wave hits the front wall, reflects and as it passes the speaker it has traveled 1/2 wavelength, so it is 180* out of phase with the direct (non-reflected) wave from the speaker. This attenuates 94 Hz. But if the speaker is a dipole, it does the opposite (boosts) because the back wave started out with inverted amplitude, so shifting it 180* out of phase brings it back in-phase.

Conclusion: due to SBIR, dipoles boost the 1/4 wavelength frequency.

Example 2: consider what that same speaker does at 188 Hz (twice the frequency, half the wavelength). Now the 3′ distance is 1/2 wavelength, so the distance traveled is a full wavelength. A conventional speaker will boost this frequency because it’s in phase. A dipole will cut this frequency.

Conclusion: due to SBIR, dipoles cut the 1/2 wavelength frequency.

Direct vs. Reflected

Dipoles (electrostatic or planar magnetic) have a flatter impedance vs. frequency curve, without the strong Q resonances that conventional speakers have. This makes them a near-resistive load which is easy for amps to drive and gives them flatter phase response and group delay. I believe this contributes to their big, open, transparent sound relative to conventional speakers which can sound thick and muddy in comparison.

With all speakers, the sound you hear is a mix of direct and reflected. With dipoles this mix has relatively more reflected, less direct. This can make them sound big and phasey in underdamped rooms. With dipoles your room typically needs more damping than it does with conventional speakers.

One way to tackle this is to damp the walls to reduce reflection. How much damping you need and where to put it depends on the room size, shape, materials, and your personal preference. Too much damping and the dipole will sound thick & muddy like a conventional speaker.

Some dipoles (like Magnepans) have a rise in bass response that is supposed to be attenuated by the back wave reflected from the front wall. Because of this, they need to be the right distance from the front wall, and you don’t want to damp that wall too much.

Conclusion: in small to medium sized rooms, you will need to damp the wall behind dipoles to some extent, but not entirely. This damping must be effective down into bass frequencies, so it can’t just be acoustic foam; it must be tube traps, bass traps, etc.

LBIR

This topic doesn’t at first appear to be unique to dipoles, but it turns out to have an important difference. Consider a listener 3′ in front of the rear wall. Sound from the speakers reflects from the rear wall and comes forward, having traveled 6′ when it reaches the listener again. At 94 Hz, this is half a wavelength, so it attenuates that frequency. At 188 Hz this is a full wavelength, so it boosts that frequency.

What’s different about dipoles: the LBIR and SBIR distances, when equal, negate each other’s effects. With conventional speakers, they exaggerate each other. That is: if the speakers are 3′ from the front wall and the listener is 3′ from the back wall, the reflected waves don’t affect frequency response; SBIR cuts the same frequencies that LBIR boost. Conventional speakers give a double-sized cuts and boosts at the same frequencies.

Conclusion: when setting up dipoles in a small to medium sized rooms, try to make the LBIR and SBIR distances roughly equal. Put differently: the distance from the listener to the back wall should be the same as the distance from the speakers to the front wall.

Planar Speakers

Audio
by Mike Clements

More specifically, why I like planar magnetic speakers (and headphones!).

Sound quality: this one is subjective, yet important. When set up properly, planars sound more natural, open, and transparent than conventional speakers. They’re perfect for acoustic music across all genres from small to large ensemble classical, jazz, vocals, etc. Solo piano, vocals and chamber music are particularly good on planars. Their midrange is uncolored, having incredibly high resolution, yet without the artificial detail of boosted upper mids/treble, and without adding the glare or edginess of conventional dynamic drivers — unless that edginess is in the recording itself! With the 3.6/R I frequently hear subtle musical details or tone/balance shifts that I never hear even on the best headphones. Music is mostly midrange, and that is what planars do best. And the treble is simply astounding. No speaker on Earth matches the high frequency extension and linearity of those huge ribbon tweeters. The transition from the mid panel to treble ribbon is seamless, preserving the timbre and harmonic structure of acoustic instruments and voices. And that bass… clean, tight, with a seamless linear transition from the mids.

Low distortion: Measuring total distortion in Room EQ Wizard, my  Magnepan 3.6/R measure about -60 dB (0.1%) in the treble, -50 dB (0.3%) in the midrange, and -40 dB (1%) in the bass (at 60 Hz). That’s lower than most conventional speakers, even lower than most headphones. And it is an uncorrected figure, including the distortion in the microphones, amplifier, and DAC; the actual distortion from the speakers alone is even lower. The Audeze LCD-2 headphones (planar magnetic) measure < 1% total distortion throughout the entire frequency spectrum, even to sub-bass frequencies. No conventional headphone matches that, not even the Sennheiser HD-800.

Why is planar distortion so low? I can think of 2 reasons. First, each Mag 3.6 panel spans the area of about six 12″ woofers, and its ribbon tweeter is 5′ long. Such physically large drivers take only very small movement/excursion to produce a given sound level. And the distortion that a driver produces is related to its excursion. Second, the drivers don’t have as strong Q resonances as conventional drivers do, both mechanical and electrical.

Linear phase: The 3.6/R have a relatively flat impedance curve: 4.2 ohms in the bass, to 3.3 ohms in the treble. They don’t have the big impedance vs. frequency swings that conventional speakers have. This promotes linear phase and flat group delay.  The 3.6/R measure group delay of a flat zero through most of the frequency range, and only exceeds 10ms in the bass (below 80 Hz).

Easy load: Because planars have relatively flat impedance vs. frequency, they are primarily resistive loads that are easy for amplifiers to drive, despite their lowish impedance.

Drawbacks

Planars are dipoles, so they radiate equal energy front and rear, and the rear energy has inverted phase. This makes them more sensitive to room setup than conventional speakers. This can be a blessing or a curse, depending on your situation.

Planars tend to be inefficient, so they require more power for the same listening level. However, their dispersion is line-source (rather than a point-source), so the volume does not drop with distance as quickly as with conventional speakers.

Planars have limited maximum loudness. In a medium-large listening room, the bass distortion of my 3.6/R begins to rise at 95-100 dB SPL (and requires 400+ watts per speaker to attain). This is plenty loud enough for me, but it’s not for those who listen at ear-shattering levels.

Planars are difficult to measure because near-field, you can’t “hear” all the drivers from a single microphone position. And far-field, what you measure is as much the room as it is the speakers.

Planar drivers are side by side (the panel and the ribbon tweeter). They can’t be aligned vertically like conventional speakers, so the midrange to treble timing and impulse response depends on the angle between the speakers & listener. More specifically, the speakers should be angled so the panels are about 2″ closer to the listener than the ribbon tweeters.

Planars usually require a big room, and sound best when placed well into the room away from the walls. This leads to a low wife-approval-factor, and requires a dedicated audio room.

While planars have taut, low distortion bass, they usually don’t reproduce the lowest octave. The larger ones, like the 3.6/R, are good down to about 30 Hz, and 25 Hz is clearly audible though attenuated, which is fine for most music. But if you want that room-shaking 20 Hz rumble for movies with explosions and such, you’ll need a subwoofer.

Meier Audio “FF” Frequency Adaptive Feedback

Audio
by Mike Clements

Meier Audio has a feature in their amps called “FF” or Frequency Adaptive Feedback. Jan Meier describes it here. His article is detailed yet long. I wrote this article to complement it to help in understanding.

Musical Hearing

When it comes to human perception of sound and music, all frequencies are not created equal. The ear is most sensitive to frequencies from around 600 to 3000 Hz. And, most music (at least voices and acoustic music) is concentrated in this range.

Consequently, this is the most critical range for reducing distortion. You probably cannot hear 1% (-40 dB) distortion at 60 Hz, but you can hear it at 2000 Hz.

Analogy: Dolby B and RIAA equalization

Readers with a few grey hairs remember cassette tapes and Dolby B noise reduction from the 1970s and 80s. Dolby B was brilliant in its simplicity. Tape hiss has a wide frequency spectrum but it’s most noticeable in the treble (this is where our hearing is most sensitive). If you cut the treble during playback, it reduces hiss but it also dulls the music. So when recording, boost the treble. Then during playback, cut the treble by the same amount you boosted it. You get the same hiss reduction without any reduction in treble, because you’re only cutting exactly what you boosted earlier. The music has flat frequency response and sounds cleaner with higher S/N ratio.

The RIAA curve does the same thing for LPs. The pre-emphasis equalization curve cuts the bass relative to the treble before cutting the record groove. This reduces the groove and needle excursion needed to handle low frequencies, reducing distortion and noise. On playback, the phono head amp applies the opposite de-emphasis equalization curve, restoring flat frequency response.

The main drawback to this is that boosting the treble when recording limits the dynamic range. You can only boost it so far, before it reaches peak levels and overloads. Boosting the treble may require you to reduce the overall recording level. Alternately, reducing the bass lowers the SNR of the bass. Yet it improves the SNR of the treble, and this is a desirable tradeoff since that is where our hearing is much more sensitive to it.

Amplifier Feedback

Solid state amplifiers have a negative feedback loop that reduces distortion, increases bandwidth, and increases stability. Contrary to what we may read in some audiophile circles, negative feedback is A GOOD THING.

What exactly is negative feedback? An opamp’s native or open loop response, gain-bandwidth curve or transfer function, is not linear in both frequency and amplitude. So a portion of its output signal is inverted and fed back into the input, which offsets these non-linearities.

Furthermore, an opamp’s open loop response drops with frequency, around 20 dB per decade or 6 dB per octave. This means negative feedback has much stronger low frequencies than high frequencies. We can quantify this. Human hearing from roughly 20 Hz to 20 kHz spans a frequency range of 1000:1, or about 3 decades. So negative feedback is roughly 60 dB stronger at 20 Hz, than at 20 kHz.

More on negative feedback here.

This means most of the benefits of negative feedback are focused in the low frequencies. Higher frequencies have progressively less negative feedback. But perceptually, we want the opposite! Distortion & noise are much easier to hear in the high frequencies. So applying a pre-emphasis curve to the signal, similar to what RIAA does for vinyl, can be beneficial in the gain-feedback loop.

Frequency, Energy and Amplitude

Most of the amplitude in a musical signal is in the low frequencies. The midrange and treble, where our hearing is most sensitive, is just a smaller ripple riding on the much bigger bass wave. Reducing the amount of bass shrinks the entire signal, without any loss of amplitude or resolution in the midrange and treble. This keeps the signal away from the near-full-scale amplitude swings where devices get less linear.

This is particularly true of DACs – they get less linear for near-full-scale signals. Reducing the amount of bass before D to A conversion, then boosting it back afterward, can reduce distortion by keeping the DAC operating in its most linear region.

Frequency Adaptive Feedback

Combine these 4 ideas and you have Meier Audio’s FF. Start with the musical signal.

  • Step 1: pre-emphasis: boost the critical frequency range (midrange-treble)
    • Alternately, attenuate frequencies outside this range. This can be a better approach since attenuation means no chance of clipping.
    • This is the first thing you do when the signal enters the amp.
  • Step 2: pass this emphasized signal through the amp’s gain-feedback loop
    • Or through the DAC for D to A conversion
    • This weights negative feedback effects toward the critical frequency range
    • This reduces the signal from near full scale to the DAC’s more linear region
  • Step 3: de-emphasis: attenuate the critical frequency range
    • Do the reverse of what you did in step 1.
    • This is the last thing you do before the signal leaves the amp.

In summary, FF has 2 potential benefits:

  • Compensate for negative feedback’s bass-heavy content, giving relatively more correction at midrange/treble frequencies
  • Reduce signal level to stay below peak levels having higher distortion, without reducing midrange/treble resolution

FF can be particularly effective for modern recordings which use heavy dynamic range compression with peak levels near full scale, or even have intersample overs or clipping.

Incidentally, the Redbook CD specification has something called “emphasis”, which is similar to FF. It boosts high frequencies (from 1 khz to 20 kHz). CD players are expected to attenuate those frequencies on playback. This is akin to Dolby B for digital audio.

Counterarguments

Here we’ll play some devil’s advocate.

If distortion is already below audibility, then FF is a solution looking for a problem – what is the point? In fact, the cure could be worse than the disease! FF requires filters on the input and output to shape the frequency response. These filters cause their own distortions (such as phase shift from analog filters or minimum phase digital filters). The overall effect is a trade-off between the benefits of FF and the drawbacks of having this extra signal processing.

Most opamps have far more gain than we need, so we must use a lot of negative feedback. So much, that the bandwidth is several times wider than audio, 100 kHz or more. Thus, even high frequencies have enough negative feedback to reduce distortion below audible levels, even if they have less feedback than low frequencies.

FF actually increases distortion outside the critical frequency range! With FF you will have higher distortion at lower frequencies (because FF attenuates them in the feedback loop). But you’ll have lower distortion in the midrange and treble. FF shapes distortion to match the sensitivity of our hearing: less distortion where our hearing is most sensitive, at the cost of higher distortion at low frequencies where we can’t hear it.

Fractional Octaves

Audio, Math
by Mike Clements

I’ve been working with parametric EQ settings lately; here’s a quick cheat sheet.

Overview

We perceive the frequencies of sounds logarithmically. Each doubling of frequency is an octave. Thus, the difference between 40 and 80 Hz sounds the same as the difference between 4000 and 8000 Hz. Even though the latter difference is 10 times greater, it sounds the same to us. This gives a range of audible frequencies between 9 to 10 octaves, which is much wider than the range of frequencies of light that we can see.

Ratios

Two frequencies 1 octave apart have a frequency ratio of 2:1; one has twice the frequency of the other. A half octave is halfway between them on a logarithmic scale. That is, some ratio R such that f1 * R * R = f2. Since f2 = 2 * f1, R is the square root of 2, or about 1.414. Sanity check: 40 * 1.414 = 56.6, and 56.6 * 1.414 = 80. Thus 56.6 Hz is a half-octave above 40, and a half-octave below 80. Even though 60 Hz is the arithmetic half-way point between 40 and 80 Hz, to our ears 56.6 sounds like the half-way point between them.

More generally, the ratio for the fractional octave 1/N, is 2^(1/N). Above, N=2 so the half-octave ratio is 1.414. If N=3 we have 1/3 octave ratio which is 2^(1/3) = 1.260. Here is a sequence taken to 4 significant figures:

  • 1 octave = 2.000
  • 3/4 octave = 1.682
  • 1/2 octave = 1.414
  • 1/3 octave = 1.260
  • 1/4 octave = 1.189
  • 1/5 octave = 1.149
  • 1/6 octave = 1.122
  • 1/7 octave = 1.104
  • 1/8 octave = 1.091
  • 1/9 octave = 1.080
  • 1/10 octave = 1.072
  • 1/11 octave = 1.065
  • 1/12 octave = 1.059

The last is special because in western music there are 12 notes in an octave. With equal temperament tuning, every note has equally spaced frequency ratios. Thus the frequency ratio between any 2 notes is the 12th root of 2, which is 1.059:1. Every note is about 5.9% higher in frequency than the prior note.

Bandwidth with Q

Another way to express the frequency range or bandwidth of a parametric filter is Q. Narrow filters have big Q values, wide filters have small Q values. A filter 2 octaves wide (1 octave on each side of the center frequency) has Q = 2/3 = 0.667.

For a total bandwidth of N octaves (N/2 on each side of center frequency), the formula is:

Q = sqrt(2^N) / (2^N - 1)

Here are some example values. You can check them by plugging into the formula.

  • N=2, Q=0.667
  • N=1.5, Q=0.920
  • N=1, Q=1.414
  • N=2/3, Q=2.145
  • N=1/2, Q=2.871

Note that these N octave fractions are total width, which is twice the above table which shows octave on each side of the center frequency.

Gotchas

Whatever tool you’re using for this, make sure you know whether it expects total bandwidth around the center frequency, or bandwidth on each side. And make sure you know whether it expects frequency ranges as raw ratios, fractions of an octave, or Q.

For example, consider a center frequency of 1,000 Hz with Q=0.92. The total bandwidth is 1.5 octaves, which is 3/4 octave on each side of the center frequency. The frequency ratio will be 1.682:1 on each side, or 2.83:1 total. Thus, this filter will affect frequencies between 1000 / 1.682 = 595 Hz and 1000 * 1.682 = 1,682 Hz. The total range is 595 to 1682 Hz which has a ratio of 2.83:1.

Real-World Correction

The above formula comes straight from any textbook. But these Q factors may give wider ranges than expected, due to an assumption it makes. This assumption is that the range of the filter is where the peak amplitude (at its center) drops to half its value. So the filter is still taking effect at these edges. If you want the filter to taper to zero at the edges, you need to use a bigger Q value to get a narrower filter. Roughly speaking, this means multiply the Q value by 2.0.

For example consider a filter that is -4 dB at 3,000 Hz, 3/4 octave wide on each side. That is a ratio of 1.682:1, so this filter tapers to zero at 3,000 / 1.682 = 1,784 and 3,000 * 1.682 = 5,045 Hz. Total width is 1.5 octaves (5,045 / 1,784 = 2.83 = 2^1.5). The above formula says this is Q=0.92. But that will be a wider filter. It will reduce to half (roughly +2 dB) at 1,784 and 5,045 Hz. If you want it to taper to zero at these edged then use Q = 0.92 * 2.0 = 1.84.

Note: this is an approximate / rough guide.

Example

Suppose you are analyzing frequency response and see a peak between frequencies f1 and f2. You want to apply a parametric EQ at the center point that tapers to zero by f1 and f2.

First, find the logarithmic midpoint. Compute the ratio f2 / f1 and take its square root to get R. Multiple f1 by R, or divide f2 by R and you’ll have the logarithmic midpoint.

For example if f1 is 600 Hz and f2 is 1700 Hz, the ratio is 2.83:1, so R = sqrt(2.83) = 1.683. Double check our work: 600 * 1.683 = 1010 and 1010 * 1.683 = 1699. Close enough.

So 1,010 Hz is the logarithmic midpoint between 600 and 1700 Hz. We center our frequency here and we want it to taper to zero by 600, and 1700. That range is a ratio of 1.683 on each side, which in the above list is 3/4 octave, or Q=0.920. Multiply Q by 2.0 to get Q=1.84 since you want this filter to have no effect (taper to zero) at these 2 endpoint frequencies. So now we know the center frequency and width of our parametric EQ.