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Delightful DAC Week :~)


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Hi Ric, it must have been some 25 years ago since I bought (and still have) a pair of EVS stepped attenuators from you. I'm personally too chicken to void a warranty on a Yggy but some of those tweaks are super easy to do. I'll bookmark your Yggy mod link for future reference. Thanks for posting.

2 Ch stereo

Auralic Aries>Wireworld AES>Kitsune Holo Spring DAC L3>Van Den Hul-The Second balance cable>Sonic Euphoria (fully balance autoformer)>Van Den Hul-The Second balance cable>D-Sonic M3-1200S-A (Anaview AMS1000-2600)>Synergistic Tesla Accelerator cable>Ohm 3000 speakers plus Omni Harmonizer super tweeter

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Please pardon the below shameless product design mugging; I promise that it will clear up closed form math questions. Incorporated in the Yggy and also in the new multibit Gungnir - The Schiit Footlong Mega Combo Burrito Digital Filter:

 

 

It is a digital filter/sample rate converter designed to convert all audio to 352.8 or 396KHz sample rates so that it may drive our DACs. You get it uniquely from us; it is our filter. It took five people many years to design and perfect at the dawn of digital playback, way back in the early eighties. It keeps all original samples; those samples contain frequency and phase information which can be optimized not only in the time domain but in the frequency domain. We do precisely this; the mechanic is we add 7 new optimized samples between the original ones.

 

 

All digital filters multiply the original audio signal by a series of coefficients which are calculated by a digital filter generator. Over the years, before Theta Digital was born (my original company), we developed this filter design/generator. The common digital filter method is a Parks-McClellan algorithm, which has been used in all of the older oversampling chipsets, and persists to this day as the input filter in most ds DACs. Why? I assume it is because it is royalty-free, and the algorithm is widely available as are digital filter software design packages to aid in a cookbook aproach to the design. Now Parks McClellan an open form math solution, which means that the coefficient calculation is a series of approximations which always get halfway there. This of course, means it never completely solves. The worse news is that all original sample are lost, replaced by 8 new approximated ones. Further, the Parks McClellan optimization is based on the frequency domain only – flat frequency response, with the time (read spatial) domain ignored.

 

 

Our filter is based upon closed form math – the coefficients are not approximations, the equations solve; the matrices invert and the math is done. The filter also optimizes the time domain.

 

 

This is the reason that on good recordings (with good playback system as well) through Yggy (and now Gungnir multibit) you can hear the hall, its dimensions, and the exact position of anyone coughing or farting in the room, the motions and locations of instruments being hoisted in preparation of being played, etc. etc. Details such as sheet music pages being turned are not muddled because of clear differential spatial cues. This comes exclusively from our filter. A friend of mine, Jonathan Horwich, sells master tapes in ½ track form – at least 15 IPS, and 30 (I believe) as well. On those analog masters, you can also hear the entire environment before the music starts – what is amazing there is that even if on accounts for hearing “down into” the analog noise, the S/N indicates a 14 bit performance at best for those tapes. 14 bit or not – those tapes, totally scratch my itch. If you want that, we got that and more for your digital pleasure.

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Please explain how 18,000 taps plays into this filter and is 18,000 taps available to both Yggy and multibit Gumby?

2 Ch stereo

Auralic Aries>Wireworld AES>Kitsune Holo Spring DAC L3>Van Den Hul-The Second balance cable>Sonic Euphoria (fully balance autoformer)>Van Den Hul-The Second balance cable>D-Sonic M3-1200S-A (Anaview AMS1000-2600)>Synergistic Tesla Accelerator cable>Ohm 3000 speakers plus Omni Harmonizer super tweeter

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Just to let all know, that I am Co-Founder of Schiit Audio, the designer of all Schiit Digital products and therefore quite partisan.

 

Designer of the first (Theta) and second (Schiit) DACs I owned and thus responsible for 25 years or more of my listening pleasure - thanks.

 

I am not sure it's possible to answer all my questions about the filter, just due to the level of my curiosity. If it gets tiresome, I'm sure you'll have no problem not answering. :)

 

The problem other filters have with frequency and time domain being conjugate variables, so as one is optimized the other is "pessimized" - this isn't a universal problem brought on by real world conditions not meeting the Sampling Theorem's requirements, and doesn't apply to your filter? So it doesn't ring, neither does it alias? Or it does?

One never knows, do one? - Fats Waller

The fairest thing we can experience is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science. - Einstein

Computer, Audirvana -> optical Ethernet to Fitlet3 -> Fibbr Alpha Optical USB -> iFi NEO iDSD DAC -> Apollon Audio 1ET400A Mini (Purifi based) -> Vandersteen 3A Signature.

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Baldr, is there a reason for not offering a USB Gen 3 as an upgrade for the multibit Gumby?

2 Ch stereo

Auralic Aries>Wireworld AES>Kitsune Holo Spring DAC L3>Van Den Hul-The Second balance cable>Sonic Euphoria (fully balance autoformer)>Van Den Hul-The Second balance cable>D-Sonic M3-1200S-A (Anaview AMS1000-2600)>Synergistic Tesla Accelerator cable>Ohm 3000 speakers plus Omni Harmonizer super tweeter

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Baldr is gone for now, but this quote "...those samples contain frequency and phase information which can be optimized not only in the time domain but in the frequency domain", sure sounds a lot like what Meridian MQA Master Quality Quality Authentication process is also trying to do.

2 Ch stereo

Auralic Aries>Wireworld AES>Kitsune Holo Spring DAC L3>Van Den Hul-The Second balance cable>Sonic Euphoria (fully balance autoformer)>Van Den Hul-The Second balance cable>D-Sonic M3-1200S-A (Anaview AMS1000-2600)>Synergistic Tesla Accelerator cable>Ohm 3000 speakers plus Omni Harmonizer super tweeter

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Please pardon the below shameless product design mugging; I promise that it will clear up closed form math questions. Incorporated in the Yggy and also in the new multibit Gungnir - The Schiit Footlong Mega Combo Burrito Digital Filter:

 

 

It is a digital filter/sample rate converter designed to convert all audio to 352.8 or 396KHz sample rates so that it may drive our DACs. You get it uniquely from us; it is our filter. It took five people many years to design and perfect at the dawn of digital playback, way back in the early eighties. It keeps all original samples; those samples contain frequency and phase information which can be optimized not only in the time domain but in the frequency domain. We do precisely this; the mechanic is we add 7 new optimized samples between the original ones.

 

 

All digital filters multiply the original audio signal by a series of coefficients which are calculated by a digital filter generator. Over the years, before Theta Digital was born (my original company), we developed this filter design/generator. The common digital filter method is a Parks-McClellan algorithm, which has been used in all of the older oversampling chipsets, and persists to this day as the input filter in most ds DACs. Why? I assume it is because it is royalty-free, and the algorithm is widely available as are digital filter software design packages to aid in a cookbook aproach to the design. Now Parks McClellan an open form math solution, which means that the coefficient calculation is a series of approximations which always get halfway there. This of course, means it never completely solves. The worse news is that all original sample are lost, replaced by 8 new approximated ones. Further, the Parks McClellan optimization is based on the frequency domain only – flat frequency response, with the time (read spatial) domain ignored.

 

 

Our filter is based upon closed form math – the coefficients are not approximations, the equations solve; the matrices invert and the math is done. The filter also optimizes the time domain.

 

 

This is the reason that on good recordings (with good playback system as well) through Yggy (and now Gungnir multibit) you can hear the hall, its dimensions, and the exact position of anyone coughing or farting in the room, the motions and locations of instruments being hoisted in preparation of being played, etc. etc. Details such as sheet music pages being turned are not muddled because of clear differential spatial cues. This comes exclusively from our filter. A friend of mine, Jonathan Horwich, sells master tapes in ½ track form – at least 15 IPS, and 30 (I believe) as well. On those analog masters, you can also hear the entire environment before the music starts – what is amazing there is that even if on accounts for hearing “down into” the analog noise, the S/N indicates a 14 bit performance at best for those tapes. 14 bit or not – those tapes, totally scratch my itch. If you want that, we got that and more for your digital pleasure.

 

Enjoyed a Theta Gen V for years, ran it into mono tube amps with Rick S's (also on this thread) stepped attenuators...lots of good, swinging music!

 

Disappointed to see that the Schit Audio big boy DAC is lacking a variable analog out...these days, all music sources are digital, no channel switching needed, so a preamp is a waste of space, resources, circuitry...for many.

 

Theta team figured this out/saw the future decades ago with its Pre units. Many still had vinyl, tapes, FM tuners back then and a DAC with a Pre was one preamp circuit too many so solution was "before its time", which is now.

 

You guys thinking of a real 2015 product for digital music only folks?

 

I for one will never buy another preamp...flogged off a $7+K two chassis 8 x NOS Siemens E88CC one when I switched to the stepped attenuators with the Gen V...which had strong output, as you might remember, and sounded more like real music sans preamp.

Tone with Soul

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First met Mike back in the good old days a couple of time he stopped by Chestnut Hill Audio in Philly. It is nice to see he hasn't changed much! I had his DS Pro Basic which I upgraded to mark III status (when the red light was replaced with the cobalt blue one) for years in my system; I still have it it is just not in the system. When I got into computer based audio I grabbed the Gungnir based on my experience with him and Theta. I found it to be an excellent upgrade from my Basic. Until a friend got the Yggy I was a happy camper but the Yggy sounded sensational. I just could not get the price point past the finance committee. 25 years of marriage only gets me so far! So, when I saw the Gumby come down the pike, I got one. The best $500 (plus shipping!) I have ever spent in this hobby. I can't believe the detail the Gumby is retrieving from CD rips. The hall spaciousness on live recordings is superb. I am hearing most if not all what I have heard in about 8 hours of listening to the Yggy. We will be doing a Yggy/Gumby shootout in my friend's system in a week or two hopefully to see how much separates these two. I bet it isn't all that much.

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JoeWhip, we've been leading the same life. :) Also a customer of Jack's, chatted with Mike by phone in the early days, started with the Pro Basic and upgraded it, went to Bifrost....

One never knows, do one? - Fats Waller

The fairest thing we can experience is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science. - Einstein

Computer, Audirvana -> optical Ethernet to Fitlet3 -> Fibbr Alpha Optical USB -> iFi NEO iDSD DAC -> Apollon Audio 1ET400A Mini (Purifi based) -> Vandersteen 3A Signature.

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I used to work in Center City Philadelphia at the time and used to stop in a chat with Jack once a week and listen to some tunes and what he had new that had come in which is how I met Mike. I ended up staying all afternoon and into the evening that day. I have remained friends with Jack ever since even with all his travels. He was a member of our area audio group until he moved to Florida to be closer to his son. Jack is one of the nicest people I have met in this hobby.

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It is a digital filter/sample rate converter designed to convert all audio to 352.8 or 396KHz sample rates so that it may drive our DACs. You get it uniquely from us; it is our filter. It took five people many years to design and perfect at the dawn of digital playback, way back in the early eighties. It keeps all original samples; those samples contain frequency and phase information which can be optimized not only in the time domain but in the frequency domain. We do precisely this; the mechanic is we add 7 new optimized samples between the original ones.

 

Hmm. You'd think this would actually be easier to do mathematically -- that is, keep the original samples and just interpolate between them for the extra samples. So it is puzzling why "everybody" doesn't just do it that way. But I am undoubtedly vastly underestimating the difficulty of doing so...

 

The other thing to address is that the Yggy, being a true ladder DAC, is advertised as only being able to express at most 21 bits of depth. I know the traditional defense for that is "you can't hear the lost bits anyways above the noise floor", but that is kind of a lame defense IMHO; it's exactly the argument that opponents of HiRes audio throw at it in the first place. I wonder if the best PDM DACs are equally unable to express the equivalent of that bit depth. If not, then the deficiency is shared, but if so, then that could be a point against the Yggy.

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So for decades nobody else has thought of publishing or even implementing a sample-preserving/phase-shift-minimizing upsampling algorithm for PCM? Again, seems hard to believe. Is there nobody out there with the necessary knowledge willing to examine these claims critically?

 

Acc'd to Schiit, they invested years of man hours by some high level minds into the filter. So doesn't seem hard to believe at all that they were the first to do it.

To do such a thing your approach would have to be that it is absolutely the best way to get good results. I'd wager that there are a lot of audio people (most?) who differ in approach and see no reason to make such a large, time consuming investment in writing such a filter.

Main listening (small home office):

Main setup: Surge protector +>Isol-8 Mini sub Axis Power Strip/Isolation>QuietPC Low Noise Server>Roon (Audiolense DRC)>Stack Audio Link II>Kii Control>Kii Three (on their own electric circuit) >GIK Room Treatments.

Secondary Path: Server with Audiolense RC>RPi4 or analog>Cayin iDAC6 MKII (tube mode) (XLR)>Kii Three .

Bedroom: SBTouch to Cambridge Soundworks Desktop Setup.
Living Room/Kitchen: Ropieee (RPi3b+ with touchscreen) + Schiit Modi3E to a pair of Morel Hogtalare. 

All absolute statements about audio are false :)

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Hmm. You'd think this would actually be easier to do mathematically -- that is, keep the original samples and just interpolate between them for the extra samples. So it is puzzling why "everybody" doesn't just do it that way. But I am undoubtedly vastly underestimating the difficulty of doing so...

 

The other thing to address is that the Yggy, being a true ladder DAC, is advertised as only being able to express at most 21 bits of depth. I know the traditional defense for that is "you can't hear the lost bits anyways above the noise floor", but that is kind of a lame defense IMHO; it's exactly the argument that opponents of HiRes audio throw at it in the first place. I wonder if the best PDM DACs are equally unable to express the equivalent of that bit depth. If not, then the deficiency is shared, but if so, then that could be a point against the Yggy.

 

Regarding "mathematically easier" - intuitions based on simple arithmetic do not translate well to a world of Fourier transforms, matrices and such.

 

Regarding bit depth - no, it's really not a problem. It's explained in an FAQ at the Schiit website, and has been discussed here in other threads.

One never knows, do one? - Fats Waller

The fairest thing we can experience is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science. - Einstein

Computer, Audirvana -> optical Ethernet to Fitlet3 -> Fibbr Alpha Optical USB -> iFi NEO iDSD DAC -> Apollon Audio 1ET400A Mini (Purifi based) -> Vandersteen 3A Signature.

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So for decades nobody else has thought of publishing or even implementing a sample-preserving/phase-shift-minimizing upsampling algorithm for PCM? Again, seems hard to believe. Is there nobody out there with the necessary knowledge willing to examine these claims critically?

 

Folks have, which is why I'm curious to find out more about the Schiit filter. Miska I believe has mentioned he has done filters that keep the original samples, but likes them less well than others he provides with his software.

 

The other thing I see people say Oh Wow about regarding the filter is the 15,000 taps. First, this is actually not necessarily a high number. iZotope SRC bundled with A+ can be adjusted to use a couple million taps if desired. Second, higher is not necessarily better. Taps can be thought of as the number of times the filter touches or adjusts the signal, and therefore more taps = steeper cut = more ringing, ordinarily.

 

What I'd love to know is whether this filter is claimed to solve the conjugate variable problem.

One never knows, do one? - Fats Waller

The fairest thing we can experience is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science. - Einstein

Computer, Audirvana -> optical Ethernet to Fitlet3 -> Fibbr Alpha Optical USB -> iFi NEO iDSD DAC -> Apollon Audio 1ET400A Mini (Purifi based) -> Vandersteen 3A Signature.

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This is the reason that on good recordings (with good playback system as well) through Yggy (and now Gungnir multibit) you can hear the hall, its dimensions, and the exact position of anyone coughing or farting in the room, the motions and locations of instruments being hoisted in preparation of being played, etc. etc. Details such as sheet music pages being turned are not muddled because of clear differential spatial cues. This comes exclusively from our filter. A friend of mine, Jonathan Horwich, sells master tapes in ½ track form – at least 15 IPS, and 30 (I believe) as well. On those analog masters, you can also hear the entire environment before the music starts – what is amazing there is that even if on accounts for hearing “down into” the analog noise

 

Thoroughly interesting info on the filter construction as well as the retrieval of low-level details. The first time you hear them on your system it is quite stunning and you're incredulous at first.

 

This reminds me of some of the low-level details I heard when first trying BugHead on WAV - people shifting, chairs sliding, etc...

 

These are the kinds of detail that are lost if the system is even slightly noisy.

Dedicated Line DSD/DXD | Audirvana+ | iFi iDSD Nano | SET Tube Amp | Totem Mites

Surround: VLC | M-Audio FastTrack Pro | Mac Opt | Panasonic SA-HE100 | Logitech Z623

DIY: SET Tube Amp | Low-Noise Linear Regulated Power Supply | USB, Power, Speaker Cables | Speaker Stands | Acoustic Panels

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Regarding bit depth - no, it's really not a problem. It's explained in an FAQ at the Schiit website, and has been discussed here in other threads.

 

The FAQ claims that the ENOB ("effective number of bits", learned a new acronym today) for "32-bit DACs" is 19.5, yet here there is a claim it's actually 22.5 on the ESS Sabre:

 

Schiit Yggdrasil Impressions thread - Page 53

 

Assuming that poster's method of deriving it from the datasheet SNR is accurate.

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My time is limited, trying to get my Schiit together for RMAF, but I cannot resist some quick comments to several of the above posts. Lots of taps permit a much higher slope in the transition band performance, a higher frequency response before the transition band begins (in our case .98 of nyquist), and much more attenuation in the stopband. The filter indeed rings, as all finite impulse response filters do., and it does indeed alias at 700 and something Khz, which is easy to filter in the analog domain without screwing up the sound. There is nothing faith-based about this filter, nor any exemptions from sampling theory. A frequency and time domain optimized filter is NOT mutually exclusive. The key word is optimized; not perfected. The filter has been tested by a non-partisan user here:

 

 

yggdrasil technical measurements

 

 

Those users with good time domain response speakers are well equipped to hear spatial cues should be impressed if imaging is a priority for them. Such cues are far more difficult to hear on headphone systems, but should be audible with the best phones.

 

 

All Schiit specs are very conservative; I have been doing this a very long time since I built and sold the very first D/A converter back in the 1980's. I have built not just for myself but for many other companies dozens of designs, from multibits at the beginning to ds designs and now back to multibits again. (They sound waaaaaaaaay better!) It took several years to reapply all of my original audio technology to modern industrial/defense/medical D/A converters; at Schiit, I am now migrating the technology downwards into all of our upgradable DACs. If you do not believe me, or think I am some carnival barker with a straw hat and a cane selling nebulous sound as euphones or something, then just do not buy my stuff. There is plenty of other stuff out there. One of my favorite sayings is that God could appear to me and tell me how to build the perfect DAC and there are those out there who would accuse me of false claims or numinous science.

 

 

Schiit audio really is a populist audio company. We want to offer the best value products. It therefore has limited products in its line; simplifying the line makes us more efficient. We try to pack in as much as possible at every price point. Understand, we make DACs from $100 to $2300. Generally, our products are compared to products selling for much more. We do not offer multi-colors or D/A converters with volume controls built-in. The Yggy has high enough output to be used with an external attenuator. So get one if that is what you want. We cannot please everyone.

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Mike, I'm glad you didn't resist. What you wrote is exactly what I was looking for. It all looks really good, and I look forward to hearing you and meeting Yggy at RMAF. :)

One never knows, do one? - Fats Waller

The fairest thing we can experience is the mysterious. It is the fundamental emotion which stands at the cradle of true art and true science. - Einstein

Computer, Audirvana -> optical Ethernet to Fitlet3 -> Fibbr Alpha Optical USB -> iFi NEO iDSD DAC -> Apollon Audio 1ET400A Mini (Purifi based) -> Vandersteen 3A Signature.

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My time is limited, trying to get my Schiit together for RMAF, but I cannot resist some quick comments to several of the above posts. Lots of taps permit a much higher slope in the transition band performance, a higher frequency response before the transition band begins (in our case .98 of nyquist), and much more attenuation in the stopband. The filter indeed rings, as all finite impulse response filters do., and it does indeed alias at 700 and something Khz, which is easy to filter in the analog domain without screwing up the sound. There is nothing faith-based about this filter, nor any exemptions from sampling theory. A frequency and time domain optimized filter is NOT mutually exclusive. The key word is optimized; not perfected. The filter has been tested by a non-partisan user here:

 

 

yggdrasil technical measurements

 

 

Those users with good time domain response speakers are well equipped to hear spatial cues should be impressed if imaging is a priority for them. Such cues are far more difficult to hear on headphone systems, but should be audible with the best phones.

 

 

All Schiit specs are very conservative; I have been doing this a very long time since I built and sold the very first D/A converter back in the 1980's. I have built not just for myself but for many other companies dozens of designs, from multibits at the beginning to ds designs and now back to multibits again. (They sound waaaaaaaaay better!) It took several years to reapply all of my original audio technology to modern industrial/defense/medical D/A converters; at Schiit, I am now migrating the technology downwards into all of our upgradable DACs. If you do not believe me, or think I am some carnival barker with a straw hat and a cane selling nebulous sound as euphones or something, then just do not buy my stuff. There is plenty of other stuff out there. One of my favorite sayings is that God could appear to me and tell me how to build the perfect DAC and there are those out there who would accuse me of false claims or numinous science.

 

 

Schiit audio really is a populist audio company. We want to offer the best value products. It therefore has limited products in its line; simplifying the line makes us more efficient. We try to pack in as much as possible at every price point. Understand, we make DACs from $100 to $2300. Generally, our products are compared to products selling for much more. We do not offer multi-colors or D/A converters with volume controls built-in. The Yggy has high enough output to be used with an external attenuator. So get one if that is what you want. We cannot please everyone.

 

Mike , I will be the first to admit I was skeptical of the multibit claim until I upgraded my D/S Gungnir to Multibit . I was simply speechless when I heard the transformation and that was cold immediately out of the box .

 

I was so impressed I bought a Yggdrasil immediately and look forward to hearing it .

 

I am no longer a skeptic regarding

multibit dacs.

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My time is limited, trying to get my Schiit together for RMAF, but I cannot resist some quick comments to several of the above posts. Lots of taps permit a much higher slope in the transition band performance, a higher frequency response before the transition band begins (in our case .98 of nyquist), and much more attenuation in the stopband. The filter indeed rings, as all finite impulse response filters do., and it does indeed alias at 700 and something Khz, which is easy to filter in the analog domain without screwing up the sound. There is nothing faith-based about this filter, nor any exemptions from sampling theory. A frequency and time domain optimized filter is NOT mutually exclusive. The key word is optimized; not perfected. The filter has been tested by a non-partisan user here:

 

 

yggdrasil technical measurements

 

 

Those users with good time domain response speakers are well equipped to hear spatial cues should be impressed if imaging is a priority for them. Such cues are far more difficult to hear on headphone systems, but should be audible with the best phones.

 

 

All Schiit specs are very conservative; I have been doing this a very long time since I built and sold the very first D/A converter back in the 1980's. I have built not just for myself but for many other companies dozens of designs, from multibits at the beginning to ds designs and now back to multibits again. (They sound waaaaaaaaay better!) It took several years to reapply all of my original audio technology to modern industrial/defense/medical D/A converters; at Schiit, I am now migrating the technology downwards into all of our upgradable DACs. If you do not believe me, or think I am some carnival barker with a straw hat and a cane selling nebulous sound as euphones or something, then just do not buy my stuff. There is plenty of other stuff out there. One of my favorite sayings is that God could appear to me and tell me how to build the perfect DAC and there are those out there who would accuse me of false claims or numinous science.

 

 

Schiit audio really is a populist audio company. We want to offer the best value products. It therefore has limited products in its line; simplifying the line makes us more efficient. We try to pack in as much as possible at every price point. Understand, we make DACs from $100 to $2300. Generally, our products are compared to products selling for much more. We do not offer multi-colors or D/A converters with volume controls built-in. The Yggy has high enough output to be used with an external attenuator. So get one if that is what you want. We cannot please everyone.

 

C'mon Mike. Don't be modest. It's well known

in Norse circles what happened that smokey

night in Asgard back-stage at God and the

Sacred Schiits concert......not to mention there

is a 15 day trial period, albeit 5% restock +

ship. Now let's get dem back orders out.....

ha ha............

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Regarding the Yggy, the beginning of the video in this link has some very interesting comments from Bob Katz and Tyll:

 

Big Sound 2015: Biting the Bullet with Bob Katz | InnerFidelity

Speaker Room: Lumin U1X | Lampizator Pacific 2 | Viva Linea | Constellation Inspiration Stereo 1.0 | FinkTeam Kim | dual Rythmik E15HP subs  

Office Headphone System: Lumin U1X | Lampizator Golden Gate 3 | Viva Egoista | Abyss AB1266 Phi TC 

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